docs/Notebook S11. PartMC Simulations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center>  Notebook S11. Coagulation Theory and PartMC Simulations </center> \n",
    "\n",
    "<b> Notebook Version 2: This notebook has been updated to reflect changes made to the package <i> DifferentialMobilityAnalyzers.jl </i> to work with the Julia v1 series (tested with Julia 1.1.0). To read the original supplement published with the paper please switch to v1.0.0 of the package <i> DifferentialMobilityAnalyzers.jl </i> and/or download the virtual machine on zenodo.org which contains a complete installation that works with Julia 0.6.4 </b> \n",
    "\n",
    "\n",
    "This notebook presents an overview over coagulation theory. It is shown how to predict the coagulated distribution using Size Distribution Arithmetic (Notebook S3). The approach is compared to model predictions with the Particle-resolved Monte Carlo code for atmospheric aerosol simulation [(PartMC)](http://lagrange.mechse.illinois.edu/partmc/). The notebook is a supplement to the manuscript <br>\n",
    "\n",
    "Petters, M. D. (2018) <i> A language to simplify computation of differential mobility analyzer response functions</i>, Aerosol Science & Technology. <br>\n",
    "\n",
    "__ Note that exectuting this Notebook requires that PartMC is installed. The Julia/PartMC interface has only been tested on a linux install. __\n",
    "\n",
    "### Problem description\n",
    "Two aerosol populations with identities \"1\" and \"2\" are introduced into in a chamber. Each population has unique and defined chemical composition, charge state (0, ±1, or ±2) and size distribution (𝕟₁ and 𝕟₂). Chemical composition and charge state are identical for particles within a population. There are no wall losses in the chamber. What is the size distribution of dimers comprising one \"1\" and one \"2\" particle (denoted 𝕟₁₂) after elapsed time $t$ due to coagulation?\n",
    "\n",
    "<img src=\"Figures/nbs11_f01.png\" width=\"800\" align = \"middle\">\n",
    "<b> Figure 1. </b> Schematic of problem setup. The two populations, each generated by a differential mobility analyzer, enter a chamber where they are allowed to coagulate. After time $t$ (1,2) coagulated particles emerge. This sheet demonstrates how to model that distribution. <br>\n",
    "\n",
    "\n",
    "### Coagulation Theory\n",
    "\n",
    "For monodisperse particles the rate of coagulation is <br>\n",
    "\n",
    "<center> $\\frac{dN}{dt} = \\beta_{i,j}N_iN_j$ </center>\n",
    "\n",
    "where $N_i$ and $N_j$ are number concentrations and $\\beta_{i,j}$ is the coagulation kernel. For submicron particles, Brownian motion dominates the collision rate between particles of size $i$ and $j$ and is given by (Jacobson, 2005, Eq. 15.33)\n",
    "\n",
    "<center> $\\beta_{i,j}^B = \\frac{4\\pi\\left(r_i + r_j\\right)\\left(D_{i} + D_{j}\\right)}{\\frac{r_i + r_j}{r_i + r_j + \\sqrt{\\delta_i^2 + \\delta_j^2}} + \\frac{4\\left(D_{i} + D_{j}\\right)}{\\sqrt{v_{p,i}^2 + v_{p,j}^2}\\left(r_i + r_j\\right) } }$ </center> \n",
    "\n",
    "where, $\\beta_{i,j}^B$ denotes the Brownian coagulation kernel, $r_i$ and $r_j$ are the radii, $D_i$ and $D_j$ are the diffusion coefficient, and $v_i$ and $v_j$ are thermal velocities of particles $i$ and $j$ in air. The parameters $\\delta_i$ and $\\delta_j$ are the mean distances from the center of a sphere reached by particles leaving the sphere’s surface and traveling a distance of particle mean free path. Using the following relationships, the coagulation rate can be readily computed.\n",
    "<center> $\\delta_i = \\frac{\\left(2r_i + \\lambda_{p,i} \\right)^3 - \\left(4r_i^2 + \\lambda_{p,i}^2\\right)^{3/2}}{6r_i\\lambda_{p,i}} - 2r_i$ <br>\n",
    "$\\lambda_{p,i} = \\frac{8D_i}{\\pi v_i}$<br>\n",
    "$v_i = \\sqrt{\\frac{8k_bT}{\\pi M_i}}$<br>\n",
    "$M_i = \\frac{4}{3}\\pi r_i^3 \\rho_i$<br></center>\n",
    "$D_i$ is defined in Notebook S1, and $\\rho_i$ is the density and particle sphericity is assumed. The Brownian coagulation rate depends thus on the diameters $D_i$, $D_j$, densities $\\rho_i$, $\\rho_j$ as well as pressure and temperature for the free molecular regime corrections. <br>\n",
    "\n",
    "Coagulation rates are enhanced or suppressed if particles carry the charges of the same or opposite polarity, respectively. The effect is described by Zebel (1958)\n",
    "\n",
    "<center> $\\beta_{i,j}^{z(k_i,k_j)} = \\beta_{i,j}^B \\frac{\\frac{a}{r_i + r_j}}{exp\\left(\\frac{a}{r_i + r_j}\\right)-1 + G_0 \\frac{a}{rij} \\exp{\\frac{a}{r_i + r_j}}}$ </center>\n",
    "<center> $a = k_i k_j\\frac{e^2}{k_bT}$ </center>\n",
    "<center> $G_0 = 4\\frac{D_i + D_j}{r_i + r_j} \\sqrt{\\frac{M_i M_j}{(M_i + M_j) 3k_b T}}$ </center>\n",
    "where, $k_i$, $k_j$ are the charges and $\\beta_b$ is Boltzmann's constant, and $e$ is the elementary charge ($e = \\sqrt{1.43996\\; MeV\\; fm}$). The Zebel-corrected Brownian coagulation rate ($\\beta_{i,j}^{z(k_i,k_j)}$) depends on the diameters $D_i$, $D_j$, densities $\\rho_i$, $\\rho_j$, charges $k_i$, $k_j$, as well as pressure and temperature for the free molecular regime corrections. Note that for either $k_i = 0$ or $k_j = 0$ the regular Brownian coagulation rate is retained, i.e. $\\beta_{i,j}^{z(k_i,k_j)} = \\beta_{i,j}^B$  <br>\n",
    "\n",
    "The above functions are implemented in file coagulationrates.jl. The rate is obtained through the function call\n",
    "\n",
    "```julia\n",
    "    β12 = β12(Dp_i, Dp_j, k_i, k_j;ρi = 1000.0, ρj = 1000.0, p = 1e5, T = 293.0)\n",
    "```\n",
    "The truncated call \n",
    "```julia\n",
    "    β12 = β12(Dp_i, Dp_j, k_i, k_j)\n",
    "```\n",
    "assumes that ρi = 1000 kg m⁻³, ρj = 1000 kg m⁻³, p = 1e5 Pa, T = 293 K. Coagulation rates between particles of the same diameter (i.e. Dp_i = Dp_j) and enhancement factors based on charge state as a function of diameter are shown in Figure 2 below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "    <script class='js-collapse-script'>\n",
       "        var curMatch =\n",
       "            window.location.href\n",
       "            .match(/(.*?)\\/notebooks\\/.*\\.ipynb/);\n",
       "\n",
       "        curMatch = curMatch ||\n",
       "            window.location.href\n",
       "            .match(/(.*?)\\/apps\\/.*\\.ipynb/);\n",
       "\n",
       "        if ( curMatch ) {\n",
       "            $('head').append('<base href=\"' + curMatch[1] + '/\">');\n",
       "        }\n",
       "    </script>\n"
      ],
      "text/plain": [
       "HTML{String}(\"    <script class='js-collapse-script'>\\n        var curMatch =\\n            window.location.href\\n            .match(/(.*?)\\\\/notebooks\\\\/.*\\\\.ipynb/);\\n\\n        curMatch = curMatch ||\\n            window.location.href\\n            .match(/(.*?)\\\\/apps\\\\/.*\\\\.ipynb/);\\n\\n        if ( curMatch ) {\\n            \\$('head').append('<base href=\\\"' + curMatch[1] + '/\\\">');\\n        }\\n    </script>\\n\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<script class='js-collapse-script' src='/assetserver/2b173c803613f398a23fcc9b3acf1ad072d0a466-assets/webio/dist/bundle.js'></script>"
      ],
      "text/plain": [
       "HTML{String}(\"<script class='js-collapse-script' src='/assetserver/2b173c803613f398a23fcc9b3acf1ad072d0a466-assets/webio/dist/bundle.js'></script>\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<script class='js-collapse-script' src='/assetserver/2b173c803613f398a23fcc9b3acf1ad072d0a466-assets/providers/ijulia_setup.js'></script>"
      ],
      "text/plain": [
       "HTML{String}(\"<script class='js-collapse-script' src='/assetserver/2b173c803613f398a23fcc9b3acf1ad072d0a466-assets/providers/ijulia_setup.js'></script>\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "  <script class='js-collapse-script'>\n",
       "    $('.js-collapse-script').parent('.output_subarea').css('padding', '0');\n",
       "  </script>\n"
      ],
      "text/plain": [
       "HTML{String}(\"  <script class='js-collapse-script'>\\n    \\$('.js-collapse-script').parent('.output_subarea').css('padding', '0');\\n  </script>\\n\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Plots, Plots.PlotMeasures, DifferentialMobilityAnalyzers, Printf, Random, LinearAlgebra\n",
    "plotlyjs();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "k₁=0, k₂=0",
         "line": {
          "color": "rgba(0, 0, 0, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 2
         },
         "mode": "lines",
         "name": "k₁=0, k₂=0",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10,
          10.47615752789664,
          10.974987654930569,
          11.497569953977356,
          12.04503540258781,
          12.61856883066021,
          13.219411484660288,
          13.848863713938718,
          14.508287784959402,
          15.19911082952933,
          15.92282793341094,
          16.68100537200059,
          17.47528400007683,
          18.307382802953697,
          19.179102616724887,
          20.09233002565046,
          21.04904144512022,
          22.051307399030453,
          23.10129700083158,
          24.201282647943835,
          25.353644939701113,
          26.56087782946684,
          27.82559402207126,
          29.150530628251758,
          30.53855508833412,
          31.992671377973846,
          33.51602650938841,
          35.111917342151344,
          36.78379771828634,
          38.53528593710527,
          40.37017258596558,
          42.29242874389499,
          44.30621457583878,
          46.41588833612782,
          48.62601580065353,
          50.94138014816375,
          53.366992312063125,
          55.90810182512222,
          58.57020818056662,
          61.359072734131765,
          64.28073117284319,
          67.34150657750816,
          70.54802310718645,
          73.90722033525775,
          77.42636826811277,
          81.11308307896873,
          84.97534359086438,
          89.02150854450392,
          93.260334688322,
          97.70099572992247,
          102.35310218990269,
          107.22672220103232,
          112.33240329780266,
          117.68119524349991,
          123.28467394420659,
          129.15496650148827,
          135.30477745798075,
          141.7474162926805,
          148.49682622544665,
          155.56761439304722,
          162.97508346206436,
          170.7352647470692,
          178.8649529057435,
          187.3817422860383,
          196.30406500402725,
          205.65123083486515,
          215.44346900318823,
          225.70197196339217,
          236.44894126454074,
          247.70763559917086,
          259.50242113997376,
          271.858824273294,
          284.8035868435799,
          298.3647240283341,
          312.5715849688235,
          327.4549162877732,
          343.04692863149194,
          359.38136638046257,
          376.49358067924715,
          394.4206059437656,
          413.20124001153346,
          432.87612810830615,
          453.4878508128582,
          475.08101621027936,
          497.7023564332114,
          521.4008287999684,
          546.2277217684338,
          572.236765935022,
          599.4842503189409,
          628.0291441834247,
          657.9332246575682,
          689.2612104349695,
          722.0809018385471,
          756.463327554629,
          792.4828983539169,
          830.2175681319752,
          869.7490026177835,
          911.1627561154886,
          954.5484566618346,
          1000
         ],
         "xaxis": "x1",
         "y": [
          1.9121396626604057,
          1.9491878449186737,
          1.985948160115937,
          2.022270454595213,
          2.0579898675783013,
          2.0929272365285603,
          2.1268899746765397,
          2.159673486179367,
          2.191063168698472,
          2.2208370294240294,
          2.2487689088702925,
          2.2746322683043045,
          2.2982044538673243,
          2.3192713069154465,
          2.3376319503810317,
          2.353103549973142,
          2.3655258313905843,
          2.37476513386043,
          2.380717797806253,
          2.38331271953335,
          2.382512955361635,
          2.3783163165488563,
          2.3707549583654344,
          2.3598940253767897,
          2.3458294647479683,
          2.328685156185836,
          2.3086095289546535,
          2.285771843238918,
          2.2603583066792874,
          2.2325681800326853,
          2.2026100020197066,
          2.1706980359315873,
          2.1370490124626516,
          2.1018792168252456,
          2.0654019450449645,
          2.0278253352552844,
          1.9893505650449368,
          1.9501703952508453,
          1.910468033548143,
          1.870416287141245,
          1.8301769721495176,
          1.7899005472918061,
          1.7497259406734762,
          1.7097805404352204,
          1.6701803224038427,
          1.6310300904511301,
          1.5924238078536512,
          1.5544450004492358,
          1.5171672147437183,
          1.4806545163043647,
          1.4449620157737237,
          1.4101364116514876,
          1.3762165406306714,
          1.3432339277498284,
          1.3112133299468924,
          1.2801732677848052,
          1.250126541174819,
          1.2210807258601797,
          1.1930386482492887,
          1.1659988369114862,
          1.139955949677209,
          1.1149011758244327,
          1.0908226132914076,
          1.0677056212376166,
          1.0455331485868227,
          1.024286039433701,
          1.003943316384211,
          0.9844824430349371,
          0.965879566883489,
          0.9481097440048155,
          0.9311471468327727,
          0.9149652563557934,
          0.8995370399754499,
          0.8848351161908509,
          0.8708319071648357,
          0.857499780103913,
          0.8448111782478547,
          0.8327387421208448,
          0.8212554215495499,
          0.8103345788088442,
          0.7999500831186117,
          0.7900763965900017,
          0.7806886516116048,
          0.7717627195799894,
          0.7632752708189563,
          0.7552038255011989,
          0.7475267953868819,
          0.7402235162274796,
          0.7332742707494432,
          0.7266603022288447,
          0.720363818791236,
          0.7143679887156669,
          0.7086569271797091,
          0.703215675046749,
          0.6980301704565579,
          0.6930872141271408,
          0.6883744293993342,
          0.6838802181480271,
          0.6795937137377636,
          0.6755047322117365
         ],
         "yaxis": "y1",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "k₁=+1, k₂=-1",
         "line": {
          "color": "rgba(204, 0, 0, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "k₁=+1, k₂=-1",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10,
          10.47615752789664,
          10.974987654930569,
          11.497569953977356,
          12.04503540258781,
          12.61856883066021,
          13.219411484660288,
          13.848863713938718,
          14.508287784959402,
          15.19911082952933,
          15.92282793341094,
          16.68100537200059,
          17.47528400007683,
          18.307382802953697,
          19.179102616724887,
          20.09233002565046,
          21.04904144512022,
          22.051307399030453,
          23.10129700083158,
          24.201282647943835,
          25.353644939701113,
          26.56087782946684,
          27.82559402207126,
          29.150530628251758,
          30.53855508833412,
          31.992671377973846,
          33.51602650938841,
          35.111917342151344,
          36.78379771828634,
          38.53528593710527,
          40.37017258596558,
          42.29242874389499,
          44.30621457583878,
          46.41588833612782,
          48.62601580065353,
          50.94138014816375,
          53.366992312063125,
          55.90810182512222,
          58.57020818056662,
          61.359072734131765,
          64.28073117284319,
          67.34150657750816,
          70.54802310718645,
          73.90722033525775,
          77.42636826811277,
          81.11308307896873,
          84.97534359086438,
          89.02150854450392,
          93.260334688322,
          97.70099572992247,
          102.35310218990269,
          107.22672220103232,
          112.33240329780266,
          117.68119524349991,
          123.28467394420659,
          129.15496650148827,
          135.30477745798075,
          141.7474162926805,
          148.49682622544665,
          155.56761439304722,
          162.97508346206436,
          170.7352647470692,
          178.8649529057435,
          187.3817422860383,
          196.30406500402725,
          205.65123083486515,
          215.44346900318823,
          225.70197196339217,
          236.44894126454074,
          247.70763559917086,
          259.50242113997376,
          271.858824273294,
          284.8035868435799,
          298.3647240283341,
          312.5715849688235,
          327.4549162877732,
          343.04692863149194,
          359.38136638046257,
          376.49358067924715,
          394.4206059437656,
          413.20124001153346,
          432.87612810830615,
          453.4878508128582,
          475.08101621027936,
          497.7023564332114,
          521.4008287999684,
          546.2277217684338,
          572.236765935022,
          599.4842503189409,
          628.0291441834247,
          657.9332246575682,
          689.2612104349695,
          722.0809018385471,
          756.463327554629,
          792.4828983539169,
          830.2175681319752,
          869.7490026177835,
          911.1627561154886,
          954.5484566618346,
          1000
         ],
         "xaxis": "x1",
         "y": [
          9.767449717370534,
          9.356549638633334,
          8.954352436191535,
          8.563070020938447,
          8.184617524523679,
          7.820550397268465,
          7.4720337677698145,
          7.139840671019205,
          6.824373501915959,
          6.525702102512579,
          6.24361200224459,
          5.9776571512912335,
          5.727212670701753,
          5.491524410181466,
          5.269753269652519,
          5.061013205849931,
          4.8644025795323795,
          4.67902901468873,
          4.504028272674501,
          4.338577832578956,
          4.181905953062452,
          4.033297002643271,
          3.892093809668002,
          3.757697717979272,
          3.6295669524009755,
          3.5072138086862092,
          3.390201092072557,
          3.278138141849235,
          3.170676699800606,
          3.0675068103566923,
          2.96835288104419,
          2.87296998377405,
          2.781140440244903,
          2.6926707073212865,
          2.607388559314278,
          2.5251405521124077,
          2.4457897475239254,
          2.3692136735446288,
          2.295302496295236,
          2.2239573810454476,
          2.1550890222646575,
          2.088616325440239,
          2.024465226105201,
          1.962567633894355,
          1.9028604913974116,
          1.8452849390768535,
          1.7897855786007408,
          1.7363098276697784,
          1.6848073598705473,
          1.6352296233417523,
          1.5875294321692246,
          1.5416606244892361,
          1.4975777813263904,
          1.455236000257329,
          1.4145907180973691,
          1.375597576967159,
          1.3382123283145686,
          1.3023907697414752,
          1.2680887098090279,
          1.2352619563591158,
          1.203866324282554,
          1.1738576590746055,
          1.1451918729344612,
          1.1178249905763948,
          1.091713202317598,
          1.0668129223832463,
          1.0430808507167093,
          1.0204740368973906,
          0.9989499450472759,
          0.9784665188472939,
          0.9589822459862961,
          0.9404562215279131,
          0.9228482098060299,
          0.9061187045495541,
          0.89022898699473,
          0.875141181771559,
          0.860818310354489,
          0.8472243418503687,
          0.8343242408643157,
          0.8220840121413888,
          0.8104707416346842,
          0.7994526336042482,
          0.7889990433114864,
          0.7790805048460097,
          0.7696687536109235,
          0.760736743002592,
          0.7522586548548651,
          0.7442099032779304,
          0.7365671316085919,
          0.729308202300808,
          0.7224121797196921,
          0.7158593059549875,
          0.7096309699337481,
          0.7037096702806764,
          0.6980789725380079,
          0.6927234615075271,
          0.6876286896050171,
          0.6827811222152179,
          0.6781680810958624,
          0.6737776868986636
         ],
         "yaxis": "y1",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "k₁=+2, k₂=-2",
         "line": {
          "color": "rgba(255, 140, 0, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "k₁=+2, k₂=-2",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10,
          10.47615752789664,
          10.974987654930569,
          11.497569953977356,
          12.04503540258781,
          12.61856883066021,
          13.219411484660288,
          13.848863713938718,
          14.508287784959402,
          15.19911082952933,
          15.92282793341094,
          16.68100537200059,
          17.47528400007683,
          18.307382802953697,
          19.179102616724887,
          20.09233002565046,
          21.04904144512022,
          22.051307399030453,
          23.10129700083158,
          24.201282647943835,
          25.353644939701113,
          26.56087782946684,
          27.82559402207126,
          29.150530628251758,
          30.53855508833412,
          31.992671377973846,
          33.51602650938841,
          35.111917342151344,
          36.78379771828634,
          38.53528593710527,
          40.37017258596558,
          42.29242874389499,
          44.30621457583878,
          46.41588833612782,
          48.62601580065353,
          50.94138014816375,
          53.366992312063125,
          55.90810182512222,
          58.57020818056662,
          61.359072734131765,
          64.28073117284319,
          67.34150657750816,
          70.54802310718645,
          73.90722033525775,
          77.42636826811277,
          81.11308307896873,
          84.97534359086438,
          89.02150854450392,
          93.260334688322,
          97.70099572992247,
          102.35310218990269,
          107.22672220103232,
          112.33240329780266,
          117.68119524349991,
          123.28467394420659,
          129.15496650148827,
          135.30477745798075,
          141.7474162926805,
          148.49682622544665,
          155.56761439304722,
          162.97508346206436,
          170.7352647470692,
          178.8649529057435,
          187.3817422860383,
          196.30406500402725,
          205.65123083486515,
          215.44346900318823,
          225.70197196339217,
          236.44894126454074,
          247.70763559917086,
          259.50242113997376,
          271.858824273294,
          284.8035868435799,
          298.3647240283341,
          312.5715849688235,
          327.4549162877732,
          343.04692863149194,
          359.38136638046257,
          376.49358067924715,
          394.4206059437656,
          413.20124001153346,
          432.87612810830615,
          453.4878508128582,
          475.08101621027936,
          497.7023564332114,
          521.4008287999684,
          546.2277217684338,
          572.236765935022,
          599.4842503189409,
          628.0291441834247,
          657.9332246575682,
          689.2612104349695,
          722.0809018385471,
          756.463327554629,
          792.4828983539169,
          830.2175681319752,
          869.7490026177835,
          911.1627561154886,
          954.5484566618346,
          1000
         ],
         "xaxis": "x1",
         "y": [
          43.62062669914001,
          42.44474741906402,
          41.279660774217994,
          40.12410599377127,
          38.976893085060205,
          37.83692537398197,
          36.70322376974133,
          35.5749519826285,
          34.451441709534976,
          33.33221663687234,
          32.217014025457566,
          31.105802660548292,
          29.998796082489804,
          28.896460250864447,
          27.7995151097263,
          26.708929869955355,
          25.62591215591884,
          24.551891429723437,
          23.488497274032632,
          22.437533173208344,
          21.400946398150733,
          20.380794511643526,
          19.37920892138947,
          18.39835587117676,
          17.440395317108937,
          16.50743830050717,
          15.601503685570984,
          14.724475432273872,
          13.878061857415117,
          13.063758528447465,
          12.282816476661168,
          11.536217275406813,
          10.824656205881352,
          10.148534261634468,
          9.507959183050446,
          8.902755136993456,
          8.332480135210526,
          7.796449874506271,
          7.293766416762419,
          6.823350017937435,
          6.383972450920104,
          5.97429032040069,
          5.592877103093533,
          5.238252926370413,
          4.9089113890247935,
          4.603343002880297,
          4.320055075032353,
          4.05758804753868,
          3.814528461075687,
          3.5895188133092875,
          3.381264646672799,
          3.188539230835685,
          3.0101862098341305,
          2.845120569727652,
          2.6923282559965287,
          2.550864735860466,
          2.419852763290111,
          2.2984795666455766,
          2.185993642634677,
          2.0817013069143036,
          1.9849631218581687,
          1.895190296057197,
          1.8118411279835185,
          1.7344175477227963,
          1.6624617954386993,
          1.5955532628987068,
          1.5333055145687648,
          1.4753634970946208,
          1.4214009400766598,
          1.3711179465949102,
          1.3242387686757644,
          1.2805097605723867,
          1.2396975011579845,
          1.2015870757381912,
          1.1659805070400329,
          1.132695324920394,
          1.1015632643697084,
          1.0724290815974193,
          1.0451494783225337,
          1.0195921248144428,
          0.9956347727068752,
          0.9731644491197985,
          0.952076724155245,
          0.9322750443735098,
          0.9136701253995856,
          0.8961793973521603,
          0.8797264973263801,
          0.8642408036956706,
          0.8496570075252942,
          0.8359147169089255,
          0.8229580905463586,
          0.8107354973722932,
          0.7991991995164534,
          0.7883050563202372,
          0.7780122475459439,
          0.7682830142865638,
          0.7590824164092126,
          0.7503781056391637,
          0.7421401136094703,
          0.7343406543619849
         ],
         "yaxis": "y1",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "k₁=+1, k₂=+1",
         "line": {
          "color": "rgba(204, 0, 0, 1.000)",
          "dash": "dashdot",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "k₁=+1, k₂=+1",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10,
          10.47615752789664,
          10.974987654930569,
          11.497569953977356,
          12.04503540258781,
          12.61856883066021,
          13.219411484660288,
          13.848863713938718,
          14.508287784959402,
          15.19911082952933,
          15.92282793341094,
          16.68100537200059,
          17.47528400007683,
          18.307382802953697,
          19.179102616724887,
          20.09233002565046,
          21.04904144512022,
          22.051307399030453,
          23.10129700083158,
          24.201282647943835,
          25.353644939701113,
          26.56087782946684,
          27.82559402207126,
          29.150530628251758,
          30.53855508833412,
          31.992671377973846,
          33.51602650938841,
          35.111917342151344,
          36.78379771828634,
          38.53528593710527,
          40.37017258596558,
          42.29242874389499,
          44.30621457583878,
          46.41588833612782,
          48.62601580065353,
          50.94138014816375,
          53.366992312063125,
          55.90810182512222,
          58.57020818056662,
          61.359072734131765,
          64.28073117284319,
          67.34150657750816,
          70.54802310718645,
          73.90722033525775,
          77.42636826811277,
          81.11308307896873,
          84.97534359086438,
          89.02150854450392,
          93.260334688322,
          97.70099572992247,
          102.35310218990269,
          107.22672220103232,
          112.33240329780266,
          117.68119524349991,
          123.28467394420659,
          129.15496650148827,
          135.30477745798075,
          141.7474162926805,
          148.49682622544665,
          155.56761439304722,
          162.97508346206436,
          170.7352647470692,
          178.8649529057435,
          187.3817422860383,
          196.30406500402725,
          205.65123083486515,
          215.44346900318823,
          225.70197196339217,
          236.44894126454074,
          247.70763559917086,
          259.50242113997376,
          271.858824273294,
          284.8035868435799,
          298.3647240283341,
          312.5715849688235,
          327.4549162877732,
          343.04692863149194,
          359.38136638046257,
          376.49358067924715,
          394.4206059437656,
          413.20124001153346,
          432.87612810830615,
          453.4878508128582,
          475.08101621027936,
          497.7023564332114,
          521.4008287999684,
          546.2277217684338,
          572.236765935022,
          599.4842503189409,
          628.0291441834247,
          657.9332246575682,
          689.2612104349695,
          722.0809018385471,
          756.463327554629,
          792.4828983539169,
          830.2175681319752,
          869.7490026177835,
          911.1627561154886,
          954.5484566618346,
          1000
         ],
         "xaxis": "x1",
         "y": [
          0.0009853034808527648,
          0.0013892197098174504,
          0.0019339527126573772,
          0.0026594173986609123,
          0.0036138599717754714,
          0.004854740059336672,
          0.006449470711738081,
          0.008475938240960103,
          0.011022716378125701,
          0.014188886114843967,
          0.018083375424226538,
          0.02282374325025418,
          0.028534350722446252,
          0.035343889848054436,
          0.04338227541043947,
          0.05277694786087526,
          0.06364868095482938,
          0.07610703413950937,
          0.09024563201124604,
          0.10613748712663947,
          0.12383060403593994,
          0.14334410847333223,
          0.16466513438303612,
          0.187746672689061,
          0.21250654092361201,
          0.2388275750687135,
          0.26655907854822714,
          0.2955194933637651,
          0.32550019033621286,
          0.35627021450930035,
          0.3875817724884991,
          0.41917621419649037,
          0.4507902441861562,
          0.4821620976907815,
          0.5130374329445134,
          0.5431747216156922,
          0.5723499601341812,
          0.6003605723690117,
          0.6270284244942753,
          0.6522019221966717,
          0.6757572054313665,
          0.6975984943157093,
          0.7176576699400052,
          0.7358931952207918,
          0.7522884935483771,
          0.7668499076261243,
          0.7796043587337864,
          0.7905968190833872,
          0.7998876984619515,
          0.8075502323998159,
          0.8136679439398389,
          0.8183322357718242,
          0.8216401548595121,
          0.8236923583100496,
          0.8245912974871537,
          0.8244396274345884,
          0.8233388405941328,
          0.8213881175005865,
          0.8186833824686024,
          0.8153165490600817,
          0.8113749381225338,
          0.806940850200809,
          0.8020912739395292,
          0.7968977125212788,
          0.7914261110595824,
          0.7857368690436294,
          0.7798849232960217,
          0.773919888361246,
          0.7678862427181466,
          0.7618235506488946,
          0.7557667109612917,
          0.7497462250235251,
          0.7437884777153325,
          0.7379160259189491,
          0.7321478900661301,
          0.7264998450272169,
          0.7209847072822543,
          0.7156126158616848,
          0.710391304996965,
          0.7053263667915998,
          0.7004215025236792,
          0.6956787614349919,
          0.6910987660617296,
          0.686680923329888,
          0.6824236207857279,
          0.6783244074680834,
          0.6743801590629649,
          0.6705872271187758,
          0.6669415722469435,
          0.6634388813902533,
          0.6600746694098708,
          0.6568443654204149,
          0.6537433844852688,
          0.6507671854672575,
          0.6479113160038702,
          0.6451714457347888,
          0.6425433890430027,
          0.6400231186723601,
          0.6376067716469882,
          0.6352906489372996
         ],
         "yaxis": "y1",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "k₁=+2, k₂=+2",
         "line": {
          "color": "rgba(255, 140, 0, 1.000)",
          "dash": "dashdot",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "k₁=+2, k₂=+2",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10,
          10.47615752789664,
          10.974987654930569,
          11.497569953977356,
          12.04503540258781,
          12.61856883066021,
          13.219411484660288,
          13.848863713938718,
          14.508287784959402,
          15.19911082952933,
          15.92282793341094,
          16.68100537200059,
          17.47528400007683,
          18.307382802953697,
          19.179102616724887,
          20.09233002565046,
          21.04904144512022,
          22.051307399030453,
          23.10129700083158,
          24.201282647943835,
          25.353644939701113,
          26.56087782946684,
          27.82559402207126,
          29.150530628251758,
          30.53855508833412,
          31.992671377973846,
          33.51602650938841,
          35.111917342151344,
          36.78379771828634,
          38.53528593710527,
          40.37017258596558,
          42.29242874389499,
          44.30621457583878,
          46.41588833612782,
          48.62601580065353,
          50.94138014816375,
          53.366992312063125,
          55.90810182512222,
          58.57020818056662,
          61.359072734131765,
          64.28073117284319,
          67.34150657750816,
          70.54802310718645,
          73.90722033525775,
          77.42636826811277,
          81.11308307896873,
          84.97534359086438,
          89.02150854450392,
          93.260334688322,
          97.70099572992247,
          102.35310218990269,
          107.22672220103232,
          112.33240329780266,
          117.68119524349991,
          123.28467394420659,
          129.15496650148827,
          135.30477745798075,
          141.7474162926805,
          148.49682622544665,
          155.56761439304722,
          162.97508346206436,
          170.7352647470692,
          178.8649529057435,
          187.3817422860383,
          196.30406500402725,
          205.65123083486515,
          215.44346900318823,
          225.70197196339217,
          236.44894126454074,
          247.70763559917086,
          259.50242113997376,
          271.858824273294,
          284.8035868435799,
          298.3647240283341,
          312.5715849688235,
          327.4549162877732,
          343.04692863149194,
          359.38136638046257,
          376.49358067924715,
          394.4206059437656,
          413.20124001153346,
          432.87612810830615,
          453.4878508128582,
          475.08101621027936,
          497.7023564332114,
          521.4008287999684,
          546.2277217684338,
          572.236765935022,
          599.4842503189409,
          628.0291441834247,
          657.9332246575682,
          689.2612104349695,
          722.0809018385471,
          756.463327554629,
          792.4828983539169,
          830.2175681319752,
          869.7490026177835,
          911.1627561154886,
          954.5484566618346,
          1000
         ],
         "xaxis": "x1",
         "y": [
          3.7320430516170877e-11,
          1.1479479567424754e-10,
          3.3661875713724136e-10,
          9.42965217768398e-10,
          2.528428051060051e-09,
          6.501551551229604e-09,
          1.6060844027658085e-08,
          3.818031982082131e-08,
          8.748403680761172e-08,
          1.9350825200101364e-07,
          4.1379184284417227e-07,
          8.565943555100091e-07,
          1.718893292913131e-06,
          3.34768667175676e-06,
          6.3354637773740895e-06,
          1.1663814890277394e-05,
          2.091216837794628e-05,
          3.655102026482616e-05,
          6.234002797193617e-05,
          0.0001038501208234396,
          0.00016912445177897143,
          0.00026948480761211874,
          0.0004204775227041014,
          0.0006429359828960112,
          0.0009641160629733554,
          0.0014188376527407788,
          0.0020505418997692694,
          0.0029121527382164327,
          0.004066615996549829,
          0.005586983383403834,
          0.007555915185632419,
          0.010064497029774064,
          0.013210303644548336,
          0.01709469540797455,
          0.021819398489954164,
          0.027482491173128495,
          0.03417398995980733,
          0.041971290558483,
          0.050934761871402445,
          0.061103808077856134,
          0.07249370001493302,
          0.08509343143036292,
          0.0988647819374035,
          0.11374267446497625,
          0.12963681159133775,
          0.14643447465036197,
          0.1640042835107608,
          0.18220065253733903,
          0.20086864473291813,
          0.21984892241774048,
          0.23898251605120305,
          0.2581151769722583,
          0.2771011373121281,
          0.2958061632207313,
          0.3141098488176916,
          0.3319071525252987,
          0.3491092212138139,
          0.36564357934991704,
          0.38145378015345877,
          0.3964986248670027,
          0.4107510565546185,
          0.42419682858038876,
          0.43683303724579275,
          0.448666594912399,
          0.45971270586599705,
          0.46999339336006396,
          0.47953611350607167,
          0.48837248043021125,
          0.49653711761026087,
          0.5040666425736592,
          0.5109987860832303,
          0.517371642387484,
          0.5232230438576972,
          0.5285900511530844,
          0.5335085487361494,
          0.538012934909991,
          0.5421358954011245,
          0.545908249725294,
          0.5493588600369848,
          0.5525145927871808,
          0.5554003242313355,
          0.5580389815915843,
          0.5604516124497645,
          0.5626574757085958,
          0.5646741481940158,
          0.5665176416756026,
          0.5682025257516725,
          0.5697420526819305,
          0.57114828085507,
          0.5724321941534837,
          0.5736038150235332,
          0.5746723095782617,
          0.5756460835474968,
          0.5765328683463821,
          0.5773397969515324,
          0.5780734696500398,
          0.5787400100534545,
          0.5793451120416212,
          0.5798940785145446,
          0.5803918529815373
         ],
         "yaxis": "y1",
         "zmax": 0.1,
         "zmin": -0.1
        }
       ],
       "layout": {
        "annotations": [],
        "height": 288,
        "legend": {
         "bgcolor": "rgba(255, 255, 255, 1.000)",
         "bordercolor": "rgba(0, 0, 0, 1.000)",
         "font": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 14
         },
         "tracegroupgap": 0,
         "x": 1,
         "y": 1
        },
        "margin": {
         "b": 20,
         "l": 0,
         "r": 0,
         "t": 20
        },
        "paper_bgcolor": "rgba(255, 255, 255, 1.000)",
        "plot_bgcolor": "rgba(255, 255, 255, 1.000)",
        "showlegend": true,
        "width": 432,
        "xaxis": {
         "anchor": "y1",
         "domain": [
          0.2623456790123456,
          0.9908865558471858
         ],
         "gridcolor": "rgba(0, 0, 0, 0.100)",
         "gridwidth": 0.5,
         "linecolor": "rgba(0, 0, 0, 1.000)",
         "mirror": false,
         "range": [
          0.94,
          3.06
         ],
         "showgrid": true,
         "showline": true,
         "showticklabels": true,
         "tickangle": 0,
         "tickcolor": "rgb(0, 0, 0)",
         "tickfont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "tickmode": "array",
         "ticks": "inside",
         "ticktext": [
          "10^1.0",
          "10^1.5",
          "10^2.0",
          "10^2.5",
          "10^3.0"
         ],
         "tickvals": [
          10,
          31.622776601683793,
          100,
          316.22776601683796,
          1000
         ],
         "title": "Diameter (nm)",
         "titlefont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "type": "log",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1.000)"
        },
        "yaxis": {
         "anchor": "x1",
         "domain": [
          0.1294109069699621,
          0.9863298337707787
         ],
         "gridcolor": "rgba(0, 0, 0, 0.100)",
         "gridwidth": 0.5,
         "linecolor": "rgba(0, 0, 0, 1.000)",
         "mirror": false,
         "range": [
          -3,
          2
         ],
         "showgrid": true,
         "showline": true,
         "showticklabels": true,
         "tickangle": 0,
         "tickcolor": "rgb(0, 0, 0)",
         "tickfont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "tickmode": "array",
         "ticks": "inside",
         "ticktext": [
          "10^-3",
          "10^-2",
          "10^-1",
          "10^0",
          "10^1",
          "10^2"
         ],
         "tickvals": [
          0.001,
          0.01,
          0.1,
          1,
          10,
          100
         ],
         "title": "Rate × 10⁻¹⁵ (m⁻³ s⁻¹)",
         "titlefont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "type": "log",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1.000)"
        }
       }
      },
      "image/svg+xml": [
       "<svg class=\"main-svg\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"432\" height=\"288\" viewBox=\"0 0 432 288\"><rect x=\"0\" y=\"0\" width=\"432\" height=\"288\" style=\"fill: rgb(255, 255, 255); fill-opacity: 1;\"/><defs id=\"defs-3b7e40\"><g class=\"clips\"><clipPath id=\"clip3b7e40xyplot\" class=\"plotclip\"><rect width=\"222.20496743462624\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip3b7e40x\"><rect x=\"80.01543209876542\" y=\"0\" width=\"222.20496743462624\" height=\"288\"/></clipPath><clipPath class=\"axesclip\" id=\"clip3b7e40y\"><rect x=\"0\" y=\"23.390201224846894\" width=\"432\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip3b7e40xy\"><rect x=\"80.01543209876542\" y=\"23.390201224846894\" width=\"222.20496743462624\" height=\"212.51589384660252\"/></clipPath></g><g class=\"gradients\"/></defs><g class=\"bglayer\"/><g class=\"layer-below\"><g class=\"imagelayer\"/><g class=\"shapelayer\"/></g><g class=\"cartesianlayer\"><g class=\"subplot xy\"><g class=\"layer-subplot\"><g class=\"shapelayer\"/><g class=\"imagelayer\"/></g><g class=\"gridlayer\"><g class=\"x\"><path class=\"xgrid crisp\" transform=\"translate(86.30543209876542,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(117.85543209876542,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(159.56543209876543,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(191.1154320987654,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(222.66543209876542,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(264.37543209876543,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(295.93543209876543,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/></g><g class=\"y\"><path class=\"ygrid crisp\" transform=\"translate(0,193.40020122484688)\" d=\"M80.01543209876542,0h222.20496743462624\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,150.9002012248469)\" d=\"M80.01543209876542,0h222.20496743462624\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,108.4002012248469)\" d=\"M80.01543209876542,0h222.20496743462624\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,65.89020122484689)\" d=\"M80.01543209876542,0h222.20496743462624\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/></g></g><g class=\"zerolinelayer\"/><path class=\"xlines-below\"/><path class=\"ylines-below\"/><g class=\"overlines-below\"/><g class=\"xaxislayer-below\"/><g class=\"yaxislayer-below\"/><g class=\"overaxes-below\"/><g class=\"plot\" transform=\"translate(80.01543209876542, 23.390201224846894)\" clip-path=\"url('#clip3b7e40xyplot')\"><g class=\"scatterlayer mlayer\"><g class=\"trace scatter tracef7c3da\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M6.29,73.04L29.58,69.84L31.7,69.65L48.64,68.98L50.76,69.01L67.69,70.18L69.81,70.43L90.99,73.85L93.1,74.26L158.75,86.96L160.86,87.26L186.27,90.19L188.39,90.38L215.92,92.25\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 2px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace8e42bd\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M6.29,42.94L52.87,59.92L54.99,60.57L95.22,71.99L97.34,72.56L135.45,82.05L137.57,82.5L162.98,87.15L165.1,87.47L192.62,90.65L194.74,90.83L215.92,92.29\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(204, 0, 0); stroke-opacity: 1; stroke-width: 1px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace0b191c\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M6.29,15.31L29.58,21.56L31.7,22.22L48.64,28.46L50.76,29.36L67.69,37.57L69.81,38.71L122.75,67.72L124.87,68.69L141.81,75.62L143.92,76.38L160.86,81.62L162.98,82.17L182.04,86.3L184.15,86.67L207.45,89.87L209.56,90.09L215.92,90.71\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(255, 140, 0); stroke-opacity: 1; stroke-width: 1px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace81b3fe\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M6.29,212.79L16.88,183.35L18.99,178.11L29.58,154.78L31.7,150.66L40.17,135.85L42.29,132.55L50.76,120.86L52.87,118.3L61.34,109.41L63.46,107.51L71.93,101.06L74.05,99.71L82.52,95.31L84.63,94.42L95.22,91.13L97.34,90.67L110.04,88.95L112.16,88.81L129.1,88.7L131.22,88.78L160.86,90.62L162.98,90.76L211.68,93.24L213.8,93.31L215.92,93.38\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(204, 0, 0); stroke-opacity: 1; stroke-width: 1px; opacity: 1; stroke-dasharray: 9px, 3px, 3px, 3px;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace7f455f\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M6.29,528.23L29.58,342.88L31.7,330.03L46.52,254.32L48.64,245.32L57.11,213.19L59.23,206.06L67.69,180.76L69.81,175.19L78.28,155.61L80.4,151.35L88.87,136.6L90.99,133.45L99.46,122.72L101.57,120.47L110.04,112.97L112.16,111.43L120.63,106.38L122.75,105.36L133.34,101.43L135.45,100.84L148.16,98.24L150.28,97.93L167.21,96.31L169.33,96.18L198.98,95.23L201.09,95.2L215.92,95.05\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(255, 140, 0); stroke-opacity: 1; stroke-width: 1px; opacity: 1; stroke-dasharray: 9px, 3px, 3px, 3px;\"/></g><g class=\"points\"/><g class=\"text\"/></g></g></g><g class=\"overplot\"/><path class=\"xlines-above crisp\" d=\"M79.01543209876542,236.4060950714494H302.2203995333916\" style=\"fill: none; stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 1;\"/><path class=\"ylines-above crisp\" d=\"M79.51543209876542,23.390201224846894V235.9060950714494\" style=\"fill: none; stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 1;\"/><g class=\"overlines-above\"/><g class=\"xaxislayer-above\"><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(86.30543209876542,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(117.85543209876542,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(159.56543209876543,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(191.1154320987654,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(222.66543209876542,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(264.37543209876543,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(295.93543209876543,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(86.30543209876542,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">10</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(117.85543209876542,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">2</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(159.56543209876543,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">5</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(191.1154320987654,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">100</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(222.66543209876542,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">2</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(264.37543209876543,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">5</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(295.93543209876543,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">1000</text></g></g><g class=\"yaxislayer-above\"><path class=\"ytick ticks crisp\" d=\"M80.01543209876542,0h5\" transform=\"translate(0,193.40020122484688)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M80.01543209876542,0h5\" transform=\"translate(0,150.9002012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M80.01543209876542,0h5\" transform=\"translate(0,108.4002012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M80.01543209876542,0h5\" transform=\"translate(0,65.89020122484689)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"ytick\"><text text-anchor=\"end\" x=\"75.61543209876541\" y=\"5.949999999999999\" transform=\"translate(0,235.9102012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">0.001</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"75.61543209876541\" y=\"5.949999999999999\" transform=\"translate(0,193.40020122484688)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">0.01</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"75.61543209876541\" y=\"5.949999999999999\" transform=\"translate(0,150.9002012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">0.1</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"75.61543209876541\" y=\"5.949999999999999\" transform=\"translate(0,108.4002012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">1</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"75.61543209876541\" y=\"5.949999999999999\" transform=\"translate(0,65.89020122484689)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">10</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"75.61543209876541\" y=\"5.949999999999999\" transform=\"translate(0,23.390201224846894)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">100</text></g></g><g class=\"overaxes-above\"/></g></g><g class=\"polarlayer\"/><g class=\"ternarylayer\"/><g class=\"geolayer\"/><g class=\"pielayer\"/><g class=\"sunburstlayer\"/><g class=\"glimages\"/><defs id=\"topdefs-3b7e40\"><g class=\"clips\"/><clipPath id=\"legend3b7e40\"><rect width=\"127\" height=\"116\" x=\"0\" y=\"0\"/></clipPath></defs><g class=\"layer-above\"><g class=\"imagelayer\"/><g class=\"shapelayer\"/></g><g class=\"infolayer\"><g class=\"legend\" pointer-events=\"all\" transform=\"translate(305, 20)\"><rect class=\"bg\" shape-rendering=\"crispEdges\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; fill: rgb(255, 255, 255); fill-opacity: 1; stroke-width: 0px;\" width=\"127\" height=\"116\" x=\"0\" y=\"0\"/><g class=\"scrollbox\" transform=\"translate(0, 0)\" clip-path=\"url('#legend3b7e40')\"><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 15.6)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">k₁=0, k₂=0</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 2px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"167\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 36.8)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">k₁=+1, k₂=-1</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(204, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"167\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 58)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">k₁=+2, k₂=-2</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(255, 140, 0); stroke-opacity: 1; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"167\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 79.19999999999999)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">k₁=+1, k₂=+1</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(204, 0, 0); stroke-opacity: 1; stroke-dasharray: 9px, 3px, 3px, 3px; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"167\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 100.39999999999999)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">k₁=+2, k₂=+2</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(255, 140, 0); stroke-opacity: 1; stroke-dasharray: 9px, 3px, 3px, 3px; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"167\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g></g><rect class=\"scrollbar\" rx=\"20\" ry=\"3\" width=\"0\" height=\"0\" style=\"fill: rgb(128, 139, 164); fill-opacity: 1;\" x=\"0\" y=\"0\"/></g><g class=\"g-gtitle\"/><g class=\"g-xtitle\" transform=\"translate(0,-13.906095071449386)\"><text class=\"xtitle\" x=\"191.11791581607855\" y=\"296.9060950714494\" text-anchor=\"middle\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); opacity: 1; font-weight: normal; white-space: pre;\">Diameter (nm)</text></g><g class=\"g-ytitle\"><text class=\"ytitle\" transform=\"rotate(-90,36.015432098765416,129.64814814814815)\" x=\"36.015432098765416\" y=\"129.64814814814815\" text-anchor=\"middle\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); opacity: 1; font-weight: normal; white-space: pre;\">Rate × 10⁻¹⁵ (m⁻³ s⁻¹)</text></g></g></svg>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure(\"Nimbus Sans L\", 2, 3, 2, 8)\n",
    "Dp = exp10.(range(log10(10e-9), stop=log10(1000e-9), length=100))\n",
    "βᵢⱼ = map(Dp->β12(Dp, Dp, 0, 0), Dp)  # no charge\n",
    "βᵢⱼᶻ⁽¹⁻¹⁾ = map(Dp->β12(Dp, Dp, 1, -1), Dp)  # +1 -1 charge\n",
    "βᵢⱼᶻ⁽²⁻²⁾ = map(Dp->β12(Dp, Dp, 2, -2), Dp)  # +2 -2 charge\n",
    "βᵢⱼᶻ⁽¹⁺¹⁾ = map(Dp->β12(Dp, Dp, 1, 1), Dp)   # +1 +1 charge\n",
    "βᵢⱼᶻ⁽²⁺²⁾ = map(Dp->β12(Dp, Dp, 2, 2), Dp)   # +2 +2 charge\n",
    "plot(Dp*1e9, βᵢⱼ*1e15, xaxis = :log10, xlabel = \"Diameter (nm)\", yaxis = :log10, ylim = (1e-3, 100),\n",
    "    ylabel = \"Rate × 10⁻¹⁵ (m⁻³ s⁻¹)\", label = \"k₁=0, k₂=0\", left_margin = 30px, color = :black, lw = 2)\n",
    "plot!(Dp*1e9, βᵢⱼᶻ⁽¹⁻¹⁾*1e15, label = \"k₁=+1, k₂=-1\", color = RGBA(0.8,0,0,1))\n",
    "plot!(Dp*1e9, βᵢⱼᶻ⁽²⁻²⁾*1e15, label = \"k₁=+2, k₂=-2\", color = :darkorange)\n",
    "plot!(Dp*1e9, βᵢⱼᶻ⁽¹⁺¹⁾*1e15, label = \"k₁=+1, k₂=+1\", color = RGBA(0.8,0,0,1), ls = :dashdot)\n",
    "plot!(Dp*1e9, βᵢⱼᶻ⁽²⁺²⁾*1e15, label = \"k₁=+2, k₂=+2\", color = :darkorange, ls = :dashdot, fmt = :svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Figure 2.</b> Zebel-corrected Brownian coagulatation rates between particles of the same diameter. Coagulation between oppositely charged particle is enhanced while coagulation between particles of equal polarity is suppressed. The effect of particle charge is strongest in the free molecular regime. Suppression of coagulation due to repelling charges is stronger than enhancement due to attraction. This is because the enhancement is proportional to $k_i k_j\\frac{e^2}{k_bT(r_i + r_j)}$ while the supressenion is proportional to $\\exp\\left(k_i k_j\\frac{e^2}{k_bT(r_i + r_j)}\\right)$ (Zebel, 1957).\n",
    "\n",
    "### Application to Distributions\n",
    "\n",
    "Recall the original problem definition: two aerosol populations with identities \"1\" and \"2\" are introduced into in a chamber. Each population has unique and defined chemical composition, charge state (0, ±1, or ±2) and size distribution (𝕟₁ and 𝕟₂). Chemical composition and charge state are identical for particles within a population. There are no wall losses in the chamber. What is the size distribution of dimers comprising one \"1\" and one \"2\" particle (denoted 𝕟₁₂) after elapsed time $t$ due to coagulation? And further recall\n",
    "\n",
    "<center> $\\frac{dN}{dt} = \\beta_{i,j}N_iN_j$ </center>\n",
    "\n",
    "The general solution to this problem requires a coagulation model. However, assuming that the rate of dimer formation is small enough that number concentrations $N_1$ and $N_2$ are constant, assuming that $\\beta_{i,j}$ is constant over the spread the size distribution, one might intuit the following solution to the stated problem in terms of the size distribution arithmetic formalism developed in Notebook S3\n",
    "\n",
    "```julia\n",
    "𝕟₁₂ = f⋅((β₁₂ᶻ*t)*(𝕟₁*𝕟₂))\n",
    "```\n",
    "where $t$ is time elapsed, β₁₂ᶻ is the Zebel-corrected Brownian coagulatation rate $f = \\frac{\\sqrt[3]{D_m^3 + D_m^3}}{D_m} = \\sqrt[3]{2}$, $D_m$ is the mode diameter of the distribution, $⋅$ is the operator that shifts the distribution along the diameter axis, $*$ is the operator that scales the concentration of a distribution, $.*$ is the square of two size distributions. The factor $f$ accounts for the increase in sphere equivalent volume of the formed dimers.\n",
    "\n",
    "Although intuitive, it is neither immediately obvious that the above is correct, nor how the above could be formally proved. To do so, the Particle-resolved Monte Carlo code for atmospheric aerosol simulation (PartMC) is used (Riemer et al., 2009). The model is run in a similar manner than the chamber simulations described by Tian (2017).\n",
    "\n",
    "### PartMC Model\n",
    "The PartMC model conceptualizes the population as a discrete number of individual particles. The model assumes that coagulation evens are stochastic following a Poisson distribution. The assumed coagulation rate is also calculated using Eq. (15.33) in Jacobson (2005). \n",
    "\n",
    "PartMC is free software available under the GNU General Public License v2 (http://lagrange.mechse.illinois.edu/partmc/). Version 2.4.0 was used. In a first test, the model is initialzed with two lognormal size distributions that have equal mode diameter and geometric standard deviation, but different number concentrations. The composition of the two distributions is assumed to be of different composition, although density and molecular weight of the two types are identical. The model is initialized with 10⁶ particles and the simulation proceeds for 60s. The model tracks the number of original particles from each source that formed each aerosol particle (n_orig_part), the constituent masses of each aerosol particle (aero_particle_mass), and the number concentration associated with each particle (aero_num_conc). From these fields the number size distribution of dimers comprising one \"1\" and one \"2\" particle is reconstructed as a function of time. The PartMC predicted 𝕟₁₂ is then compared to the prediction from the simple semi-analytical programatic solution conjectured above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "push!(LOAD_PATH, \"PartMC/\")    # RunPartMC is a module that is located in the PartMC folder\n",
    "using RunPartMC, Interpolations, LsqFit, ProgressMeter, DataFrames, Printf, Random, Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Module RunPartMC is a wrapper to initialize PartMC solutions and process the netCDF output produced by the model. Model runs are initialized as follows\n",
    "```julia\n",
    "ics = InitialConditionLogNormal(N1, N2, Dm, σg)\n",
    "```\n",
    "where N1, N2 are number concentrations N1 and N2, Dm is the mode diameter, and σg is the geometric standard deviation of a lognormal distribution. The simulation is executed via\n",
    "```julia\n",
    "x = runSimulation(ics,i,\"logn\"; verbose = true, repeat = 1)\n",
    "```\n",
    "The wrapper creates a copy of the PartMC input files hosted in directory PartMC/ and creates a copy in directory \"logn$i\" (i = 1 -> logn1/). Underlying parameters of the simulation can be changed in the relevant input files to PartMC. Verbose pipes the PartMC output to julia. Repeat sets the number of repeats of the Monte-Carlo simulation. Note that PartMC must be installed on the computer and executable from the shell (i.e. the executable should be in the /usr/bin or /usr/local/bin). PartMC or its dependencies are not provided by this package. Detailed documentation of PartMC and inputs/outputs is provided on the model source website (http://lagrange.mechse.illinois.edu/partmc/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1     0s  997678       0       0        0         0       0     0s     0s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    10s  997039    2987       0        0         0       0    21s   103s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    20s  996425    2964       0        0         0       0    21s    43s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    30s  995753    3044       0        0         0       0    22s    22s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    40s  995140    3048       0        0         0       0    23s    11s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    50s  994511    2968       0        0         0       0    24s     5s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    60s  993869    2979       0        0         0       0    25s     0s\n"
     ]
    }
   ],
   "source": [
    "cd(\"PartMC\")  # Descend into directory PartMC\n",
    "Random.seed!(20)     # Pick a random seed \n",
    "ics = InitialConditionLogNormal(1e11, 1.5e11, 100.0, 1.1)    # Set initial conditions\n",
    "x = runSimulation(ics,1,\"logn\"; verbose = true, repeat = 1)  # Run simulations\n",
    "cd(\"..\")      # Come back "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable x is a complex data-type that contains the output from the model simulation. See comment in the code below for description. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>Input</th><th>PartMC</th></tr><tr><th></th><th>Float64</th><th>String</th></tr></thead><tbody><p>2 rows × 2 columns</p><tr><th>1</th><td>1.0e11</td><td>1.0E+11</td></tr><tr><th>2</th><td>1.5e11</td><td>1.5E+11</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& Input & PartMC\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & String\\\\\n",
       "\t\\hline\n",
       "\t1 & 1.0e11 & 1.0E+11 \\\\\n",
       "\t2 & 1.5e11 & 1.5E+11 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "2×2 DataFrame\n",
       "│ Row │ Input   │ PartMC  │\n",
       "│     │ \u001b[90mFloat64\u001b[39m │ \u001b[90mString\u001b[39m  │\n",
       "├─────┼─────────┼─────────┤\n",
       "│ 1   │ 1.0e11  │ 1.0E+11 │\n",
       "│ 2   │ 1.5e11  │ 1.5E+11 │"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "𝕟0 = lognormal([[0, 100, 1.1]]; d1 = 10.0, d2 = 1000.0, bins = 256);  # empty size distribution\n",
    "r = 1                    # repeat number\n",
    "Dm  = ics.Dm             # recover Dm from initial condition\n",
    "N₁  = ics.Nt1            # recover N₁ from initial condition\n",
    "N₂  = ics.Nt2            # recover N₂ from initial condition\n",
    "t   = x[r].r[end,end].t  # end time of simulation. \n",
    "\n",
    "# Hack: The constructed D grid from PartMC causes an error. Adding an empty size distributio\n",
    "#       fixes the diameter grid by interpolating it onto the regular lognormal grid\n",
    "𝕟₁  = (𝕟0 + x[r].s1)            # reconstructed size distribution for 𝕟₁ from model output \n",
    "𝕟₂  = (𝕟0 + x[r].s2)            # reconstructed size distribution for 𝕟₂ from model output \n",
    "𝕟₁₂ = (𝕟0 + x[r].r[end,1].sc12) # reconstructed dimer size distribution 𝕟₁₂ from model output \n",
    "\n",
    "DataFrame(Input = [N₁,N₂], PartMC = [@sprintf(\"%.1E\", sum(𝕟₁.N)), @sprintf(\"%.1E\", sum(𝕟₂.N))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Table 1. </b> Comparison of assumed input number concentration and reconstructed output number concentration from PartMC simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>PartMC</th><th>Analytical</th></tr><tr><th></th><th>String</th><th>String</th></tr></thead><tbody><p>1 rows × 2 columns</p><tr><th>1</th><td>1.075E+09</td><td>1.097E+09</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& PartMC & Analytical\\\\\n",
       "\t\\hline\n",
       "\t& String & String\\\\\n",
       "\t\\hline\n",
       "\t1 & 1.075E+09 & 1.097E+09 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "1×2 DataFrame\n",
       "│ Row │ PartMC    │ Analytical │\n",
       "│     │ \u001b[90mString\u001b[39m    │ \u001b[90mString\u001b[39m     │\n",
       "├─────┼───────────┼────────────┤\n",
       "│ 1   │ 1.075E+09 │ 1.097E+09  │"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "β₁₂ = β12(Dm*1e-9, Dm*1e-9, 0,0)         # Zebel-Brownian coagulation rate for no charge\n",
    "β₁₂ᶻ⁽¹⁻¹⁾ = β12(Dm*1e-9, Dm*1e-9, 1,-1)  # +1 -1 charge\n",
    "β₁₂ᶻ⁽²⁻²⁾ = β12(Dm*1e-9, Dm*1e-9, 2,-2)  # +1 -1 charge\n",
    "f   = 2.0^(1.0/3.0)                      # diameter shift for dimers particles\n",
    "\n",
    "𝕟ₚᵇ = f⋅((β₁₂*t)*(𝕟₁*𝕟₂))              # Semi-analytical estimate using Browninan Kernel\n",
    "𝕟ₚᶻ¹ = f⋅((β₁₂ᶻ⁽¹⁻¹⁾*t)*(𝕟₁*𝕟₂))       # Estimated enhancement for +1/-1 charged case\n",
    "𝕟ₚᶻ² = f⋅((β₁₂ᶻ⁽²⁻²⁾*t)*(𝕟₁*𝕟₂))       # Estimated enhancement for +2/-2 charged caseprintln()\n",
    "\n",
    "DataFrame(PartMC = [@sprintf(\"%.3E\",sum(𝕟₁₂.N))], Analytical = [@sprintf(\"%.3E\",sum(𝕟ₚᵇ.N))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Table 2. </b> Comparison of assumed PartMC inferred number concentration and number concentration obtained from f$⋅$((β₁₂$*$t)$*$(𝕟₁$.*$𝕟₂))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "𝕟₁ = 𝓛𝓝 (N₁,Dₘ,σ)",
         "line": {
          "color": "rgba(0, 0, 0, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "𝕟₁ = 𝓛𝓝 (N₁,Dₘ,σ)",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.090350448414474,
          10.273507681793024,
          10.273507681793024,
          10.459989534302535,
          10.459989534302535,
          10.649856353504289,
          10.649856353504289,
          10.84316958237171,
          10.84316958237171,
          11.039991779173976,
          11.039991779173976,
          11.240386637720556,
          11.240386637720556,
          11.44441900797323,
          11.44441900797323,
          11.652154917032231,
          11.652154917032231,
          11.863661590503344,
          11.863661590503344,
          12.079007474252842,
          12.079007474252842,
          12.298262256557319,
          12.298262256557319,
          12.521496890655566,
          12.521496890655566,
          12.748783617709826,
          12.748783617709826,
          12.98019599018381,
          12.98019599018381,
          13.215808895645086,
          13.215808895645086,
          13.455698580999508,
          13.455698580999508,
          13.699942677165545,
          13.699942677165545,
          13.948620224196498,
          13.948620224196498,
          14.201811696858716,
          14.201811696858716,
          14.459599030674116,
          14.459599030674116,
          14.722065648435406,
          14.722065648435406,
          14.989296487202608,
          14.989296487202608,
          15.261378025789629,
          15.261378025789629,
          15.538398312749738,
          15.538398312749738,
          15.820446994869037,
          15.820446994869037,
          16.10761534617715,
          16.10761534617715,
          16.39999629748447,
          16.39999629748447,
          16.69768446645562,
          16.69768446645562,
          17.00077618822873,
          17.00077618822873,
          17.309369546590553,
          17.309369546590553,
          17.623564405717435,
          17.623564405717435,
          17.94346244249247,
          17.94346244249247,
          18.269167179409244,
          18.269167179409244,
          18.600784018072822,
          18.600784018072822,
          18.938420273308882,
          18.938420273308882,
          19.282185207891956,
          19.282185207891956,
          19.632190067904055,
          19.632190067904055,
          19.988548118735103,
          19.988548118735103,
          20.35137468173687,
          20.35137468173687,
          20.72078717154221,
          20.72078717154221,
          21.096905134061714,
          21.096905134061714,
          21.479850285170084,
          21.479850285170084,
          21.869746550094703,
          21.869746550094703,
          22.266720103519187,
          22.266720103519187,
          22.67089941041491,
          22.67089941041491,
          23.08241526761366,
          23.08241526761366,
          23.501400846134892,
          23.501400846134892,
          23.927991734281377,
          23.927991734281377,
          24.36232598151701,
          24.36232598151701,
          24.804544143141136,
          24.804544143141136,
          25.25478932577379,
          25.25478932577379,
          25.713207233666548,
          25.713207233666548,
          26.179946215854002,
          26.179946215854002,
          26.65515731416115,
          26.65515731416115,
          27.138994312082165,
          27.138994312082165,
          27.6316137845464,
          27.6316137845464,
          28.133175148587764,
          28.133175148587764,
          28.6438407149338,
          28.6438407149338,
          29.163775740531204,
          29.163775740531204,
          29.693148482024785,
          29.693148482024785,
          30.232130250207152,
          30.232130250207152,
          30.78089546545674,
          30.78089546545674,
          31.339621714182158,
          31.339621714182158,
          31.90848980629108,
          31.90848980629108,
          32.48768383370232,
          32.48768383370232,
          33.07739122991996,
          33.07739122991996,
          33.6778028306889,
          33.6778028306889,
          34.289112935751355,
          34.289112935751355,
          34.911519371724424,
          34.911519371724424,
          35.54522355611888,
          35.54522355611888,
          36.19043056252011,
          36.19043056252011,
          36.847349186952165,
          36.847349186952165,
          37.51619201544639,
          37.51619201544639,
          38.19717549283665,
          38.19717549283665,
          38.89051999280318,
          38.89051999280318,
          39.59644988918792,
          39.59644988918792,
          40.31519362860439,
          40.31519362860439,
          41.04698380436544,
          41.04698380436544,
          41.792057231753,
          41.792057231753,
          42.55065502465411,
          42.55065502465411,
          43.323022673587985,
          43.323022673587985,
          44.10941012514944,
          44.10941012514944,
          44.910071862894306,
          44.910071862894306,
          45.72526698969311,
          45.72526698969311,
          46.55525931157958,
          46.55525931157958,
          47.400317423121166,
          47.400317423121166,
          48.26071479433915,
          48.26071479433915,
          49.13672985920654,
          49.13672985920654,
          50.02864610575234,
          50.02864610575234,
          50.93675216780135,
          50.93675216780135,
          51.861341918379274,
          51.861341918379274,
          52.80271456481317,
          52.80271456481317,
          53.76117474555825,
          53.76117474555825,
          54.73703262878217,
          54.73703262878217,
          55.73060401273886,
          55.73060401273886,
          56.74221042796429,
          56.74221042796429,
          57.77217924132721,
          57.77217924132721,
          58.8208437619687,
          58.8208437619687,
          59.888543349164614,
          59.888543349164614,
          60.975623522145916,
          60.975623522145916,
          62.08243607191253,
          62.08243607191253,
          63.20933917507671,
          63.20933917507671,
          64.35669750977287,
          64.35669750977287,
          65.52488237367147,
          65.52488237367147,
          66.71427180413495,
          66.71427180413495,
          67.92525070055476,
          67.92525070055476,
          69.15821094890896,
          69.15821094890896,
          70.41355154858087,
          70.41355154858087,
          71.69167874147956,
          71.69167874147956,
          72.9930061435042,
          72.9930061435042,
          74.31795487839462,
          74.31795487839462,
          75.66695371401163,
          75.66695371401163,
          77.04043920109092,
          77.04043920109092,
          78.43885581451562,
          78.43885581451562,
          79.8626560971533,
          79.8626560971533,
          81.31230080630368,
          81.31230080630368,
          82.78825906280481,
          82.78825906280481,
          84.29100850284559,
          84.29100850284559,
          85.82103543253415,
          85.82103543253415,
          87.37883498527172,
          87.37883498527172,
          88.9649112819833,
          88.9649112819833,
          90.5797775942566,
          90.5797775942566,
          92.22395651044235,
          92.22395651044235,
          93.8979801047696,
          93.8979801047696,
          95.60239010953076,
          95.60239010953076,
          97.33773809039202,
          97.33773809039202,
          99.10458562488608,
          99.10458562488608,
          100.90350448414475,
          100.90350448414475,
          102.73507681793026,
          102.73507681793026,
          104.59989534302535,
          104.59989534302535,
          106.4985635350429,
          106.4985635350429,
          108.4316958237171,
          108.4316958237171,
          110.39991779173975,
          110.39991779173975,
          112.40386637720557,
          112.40386637720557,
          114.44419007973231,
          114.44419007973231,
          116.5215491703223,
          116.5215491703223,
          118.63661590503344,
          118.63661590503344,
          120.79007474252845,
          120.79007474252845,
          122.98262256557321,
          122.98262256557321,
          125.21496890655568,
          125.21496890655568,
          127.48783617709826,
          127.48783617709826,
          129.8019599018381,
          129.8019599018381,
          132.15808895645085,
          132.15808895645085,
          134.55698580999507,
          134.55698580999507,
          136.99942677165546,
          136.99942677165546,
          139.48620224196497,
          139.48620224196497,
          142.01811696858715,
          142.01811696858715,
          144.59599030674116,
          144.59599030674116,
          147.22065648435404,
          147.22065648435404,
          149.89296487202606,
          149.89296487202606,
          152.6137802578963,
          152.6137802578963,
          155.38398312749737,
          155.38398312749737,
          158.20446994869036,
          158.20446994869036,
          161.07615346177147,
          161.07615346177147,
          163.9999629748447,
          163.9999629748447,
          166.9768446645562,
          166.9768446645562,
          170.0077618822873,
          170.0077618822873,
          173.0936954659055,
          173.0936954659055,
          176.23564405717434,
          176.23564405717434,
          179.43462442492472,
          179.43462442492472,
          182.69167179409243,
          182.69167179409243,
          186.00784018072818,
          186.00784018072818,
          189.3842027330888,
          189.3842027330888,
          192.8218520789196,
          192.8218520789196,
          196.32190067904054,
          196.32190067904054,
          199.88548118735102,
          199.88548118735102,
          203.51374681736868,
          203.51374681736868,
          207.2078717154221,
          207.2078717154221,
          210.96905134061717,
          210.96905134061717,
          214.79850285170085,
          214.79850285170085,
          218.69746550094703,
          218.69746550094703,
          222.66720103519188,
          222.66720103519188,
          226.70899410414913,
          226.70899410414913,
          230.82415267613658,
          230.82415267613658,
          235.01400846134894,
          235.01400846134894,
          239.27991734281375,
          239.27991734281375,
          243.6232598151701,
          243.6232598151701,
          248.04544143141135,
          248.04544143141135,
          252.5478932577379,
          252.5478932577379,
          257.13207233666543,
          257.13207233666543,
          261.79946215854,
          261.79946215854,
          266.5515731416115,
          266.5515731416115,
          271.3899431208216,
          271.3899431208216,
          276.31613784546397,
          276.31613784546397,
          281.33175148587765,
          281.33175148587765,
          286.438407149338,
          286.438407149338,
          291.637757405312,
          291.637757405312,
          296.9314848202479,
          296.9314848202479,
          302.32130250207155,
          302.32130250207155,
          307.8089546545674,
          307.8089546545674,
          313.3962171418216,
          313.3962171418216,
          319.08489806291084,
          319.08489806291084,
          324.8768383370232,
          324.8768383370232,
          330.7739122991996,
          330.7739122991996,
          336.7780283068889,
          336.7780283068889,
          342.89112935751353,
          342.89112935751353,
          349.1151937172442,
          349.1151937172442,
          355.4522355611888,
          355.4522355611888,
          361.9043056252011,
          361.9043056252011,
          368.4734918695216,
          368.4734918695216,
          375.16192015446387,
          375.16192015446387,
          381.97175492836647,
          381.97175492836647,
          388.9051999280318,
          388.9051999280318,
          395.96449889187926,
          395.96449889187926,
          403.15193628604396,
          403.15193628604396,
          410.4698380436544,
          410.4698380436544,
          417.92057231753,
          417.92057231753,
          425.5065502465411,
          425.5065502465411,
          433.23022673587985,
          433.23022673587985,
          441.09410125149435,
          441.09410125149435,
          449.100718628943,
          449.100718628943,
          457.2526698969311,
          457.2526698969311,
          465.55259311579584,
          465.55259311579584,
          474.0031742312117,
          474.0031742312117,
          482.6071479433915,
          482.6071479433915,
          491.36729859206537,
          491.36729859206537,
          500.2864610575233,
          500.2864610575233,
          509.36752167801353,
          509.36752167801353,
          518.6134191837928,
          518.6134191837928,
          528.0271456481318,
          528.0271456481318,
          537.6117474555825,
          537.6117474555825,
          547.3703262878216,
          547.3703262878216,
          557.3060401273885,
          557.3060401273885,
          567.4221042796428,
          567.4221042796428,
          577.7217924132722,
          577.7217924132722,
          588.2084376196871,
          588.2084376196871,
          598.8854334916462,
          598.8854334916462,
          609.7562352214592,
          609.7562352214592,
          620.8243607191254,
          620.8243607191254,
          632.093391750767,
          632.093391750767,
          643.5669750977287,
          643.5669750977287,
          655.2488237367147,
          655.2488237367147,
          667.1427180413494,
          667.1427180413494,
          679.2525070055476,
          679.2525070055476,
          691.5821094890896,
          691.5821094890896,
          704.1355154858088,
          704.1355154858088,
          716.9167874147956,
          716.9167874147956,
          729.9300614350419,
          729.9300614350419,
          743.1795487839462,
          743.1795487839462,
          756.6695371401163,
          756.6695371401163,
          770.4043920109092,
          770.4043920109092,
          784.3885581451563,
          784.3885581451563,
          798.626560971533,
          798.626560971533,
          813.1230080630369,
          813.1230080630369,
          827.8825906280481,
          827.8825906280481,
          842.9100850284559,
          842.9100850284559,
          858.2103543253414,
          858.2103543253414,
          873.7883498527173,
          873.7883498527173,
          889.649112819833,
          889.649112819833,
          905.797775942566,
          905.797775942566,
          922.2395651044235,
          922.2395651044235,
          938.9798010476961,
          938.9798010476961,
          956.0239010953076,
          956.0239010953076,
          973.3773809039202,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x1",
         "y": [
          9.46810013300733e-125,
          1.118864971142895e-122,
          1.118864971142895e-122,
          1.363302303709405e-120,
          1.363302303709405e-120,
          6.763368967718927e-119,
          6.763368967718927e-119,
          6.921642113440284e-117,
          6.921642113440284e-117,
          7.490161991817119e-115,
          7.490161991817119e-115,
          3.4914078111390584e-113,
          3.4914078111390584e-113,
          3.109184027556042e-111,
          3.109184027556042e-111,
          2.9883087630538943e-109,
          2.9883087630538943e-109,
          1.3033674066253193e-107,
          1.3033674066253193e-107,
          1.0141223954540685e-105,
          1.0141223954540685e-105,
          8.657647309437534e-104,
          8.657647309437534e-104,
          3.520471800253454e-102,
          3.520471800253454e-102,
          2.4018274462999074e-100,
          2.4018274462999074e-100,
          1.8214592571433225e-98,
          1.8214592571433225e-98,
          6.883368905350908e-97,
          6.883368905350908e-97,
          4.1304896160103184e-95,
          4.1304896160103184e-95,
          2.782846223431059e-93,
          2.782846223431059e-93,
          9.746171372690099e-92,
          9.746171372690099e-92,
          5.1578697857150745e-90,
          5.1578697857150745e-90,
          3.087551390201621e-88,
          3.087551390201621e-88,
          9.99634572620211e-87,
          9.99634572620211e-87,
          4.676803386597052e-85,
          4.676803386597052e-85,
          2.487708675460908e-83,
          2.487708675460908e-83,
          7.42922965696115e-82,
          7.42922965696115e-82,
          3.0792044423065615e-80,
          3.0792044423065615e-80,
          1.4556277298315473e-78,
          1.4556277298315473e-78,
          4.001714360189491e-77,
          4.001714360189491e-77,
          1.4721069496157113e-75,
          1.4721069496157113e-75,
          6.185456537901593e-74,
          6.185456537901593e-74,
          1.5625683585062754e-72,
          1.5625683585062754e-72,
          5.110370115974353e-71,
          5.110370115974353e-71,
          1.9088378260232217e-69,
          1.9088378260232217e-69,
          4.423867536309373e-68,
          4.423867536309373e-68,
          1.2881848819564272e-66,
          1.2881848819564272e-66,
          4.27806477793269e-65,
          4.27806477793269e-65,
          9.082498835588321e-64,
          9.082498835588321e-64,
          2.3578575070179084e-62,
          2.3578575070179084e-62,
          6.963249672294262e-61,
          6.963249672294262e-61,
          1.3524172173683435e-59,
          1.3524172173683435e-59,
          3.1337983791499518e-58,
          3.1337983791499518e-58,
          8.231294024757341e-57,
          8.231294024757341e-57,
          1.4607410621586074e-55,
          1.4607410621586074e-55,
          3.0244002397218106e-54,
          3.0244002397218106e-54,
          7.066771609999281e-53,
          7.066771609999281e-53,
          1.1445696132031421e-51,
          1.1445696132031421e-51,
          2.1194477717334809e-50,
          2.1194477717334809e-50,
          4.406320112009501e-49,
          4.406320112009501e-49,
          6.506714522178695e-48,
          6.506714522178695e-48,
          1.0785043108457884e-46,
          1.0785043108457884e-46,
          1.995438421156521e-45,
          1.995438421156521e-45,
          2.683932451619709e-44,
          2.683932451619709e-44,
          3.985081112294821e-43,
          3.985081112294821e-43,
          6.5631622777763e-42,
          6.5631622777763e-42,
          8.033550971697025e-41,
          8.033550971697025e-41,
          1.069224467106965e-39,
          1.069224467106965e-39,
          1.5678542484224666e-38,
          1.5678542484224666e-38,
          1.7450268938517384e-37,
          1.7450268938517384e-37,
          2.0831344450435357e-36,
          2.0831344450435357e-36,
          2.7203271308599854e-35,
          2.7203271308599854e-35,
          2.7509629557618237e-34,
          2.7509629557618237e-34,
          2.947016424180495e-33,
          2.947016424180495e-33,
          3.4281877799755936e-32,
          3.4281877799755936e-32,
          3.1476191606086345e-31,
          3.1476191606086345e-31,
          3.0273644710590498e-30,
          3.0273644710590498e-30,
          3.1379148957991224e-29,
          3.1379148957991224e-29,
          2.6140796929146927e-28,
          2.6140796929146927e-28,
          2.2582067502413968e-27,
          2.2582067502413968e-27,
          2.0861993376576747e-26,
          2.0861993376576747e-26,
          1.5758573848904716e-25,
          1.5758573848904716e-25,
          1.2231489500464135e-24,
          1.2231489500464135e-24,
          1.0074266682860554e-23,
          1.0074266682860554e-23,
          6.895992024618724e-23,
          6.895992024618724e-23,
          4.810733793676508e-22,
          4.810733793676508e-22,
          3.533612313151644e-21,
          3.533612313151644e-21,
          2.1906696786115542e-20,
          2.1906696786115542e-20,
          1.3739127860402545e-19,
          1.3739127860402545e-19,
          9.002785093704714e-19,
          9.002785093704714e-19,
          5.052127661241261e-18,
          5.052127661241261e-18,
          2.849195359943896e-17,
          2.849195359943896e-17,
          1.6660651616020206e-16,
          1.6660651616020206e-16,
          8.45871750646986e-16,
          8.45871750646986e-16,
          4.2904188860307456e-15,
          4.2904188860307456e-15,
          2.2395906875965263e-14,
          2.2395906875965263e-14,
          1.0282097024322746e-13,
          1.0282097024322746e-13,
          4.691271295169864e-13,
          4.691271295169864e-13,
          2.1868107325213744e-12,
          2.1868107325213744e-12,
          9.0744186391138e-12,
          9.0744186391138e-12,
          3.724719324296586e-11,
          3.724719324296586e-11,
          1.5510427002566308e-10,
          1.5510427002566308e-10,
          5.814705235980484e-10,
          5.814705235980484e-10,
          2.1473717348711747e-09,
          2.1473717348711747e-09,
          7.991168479665367e-09,
          7.991168479665367e-09,
          2.705323354169442e-08,
          2.705323354169442e-08,
          8.989382438232592e-08,
          8.989382438232592e-08,
          2.9907118050803023e-07,
          2.9907118050803023e-07,
          9.139092854791069e-07,
          9.139092854791069e-07,
          2.7324952253275947e-06,
          2.7324952253275947e-06,
          8.130554229340444e-06,
          8.130554229340444e-06,
          2.241756225038273e-05,
          2.241756225038273e-05,
          6.03105895249467e-05,
          6.03105895249467e-05,
          0.000160564816591912,
          0.000160564816591912,
          0.0003992851830055348,
          0.0003992851830055348,
          0.000966561929535367,
          0.000966561929535367,
          0.0023033948141853444,
          0.0023033948141853444,
          0.005164102804948146,
          0.005164102804948146,
          0.011247725916358534,
          0.011247725916358534,
          0.024003634530457153,
          0.024003634530457153,
          0.048498698350334796,
          0.048498698350334796,
          0.09503755917777496,
          0.09503755917777496,
          0.1817100113783823,
          0.1817100113783823,
          0.330746135935819,
          0.330746135935819,
          0.5830656846151003,
          0.5830656846151003,
          0.9992548603205159,
          0.9992548603205159,
          1.637926159811997,
          1.637926159811997,
          2.5973294015005415,
          2.5973294015005415,
          3.991823233515128,
          3.991823233515128,
          5.890246522595441,
          5.890246522595441,
          8.400769958454076,
          8.400769958454076,
          11.584191185919952,
          11.584191185919952,
          15.382129396012955,
          15.382129396012955,
          19.728237157097524,
          19.728237157097524,
          24.420861435117214,
          24.420861435117214,
          29.170710125549853,
          29.170710125549853,
          33.637879107291646,
          33.637879107291646,
          37.398850055780336,
          37.398850055780336,
          40.17245163943608,
          40.17245163943608,
          41.64217652148391,
          41.64217652148391,
          41.6062303655233,
          41.6062303655233,
          40.17568251579937,
          40.17568251579937,
          37.42789137344088,
          37.42789137344088,
          33.62496708511679,
          33.62496708511679,
          29.17790907617099,
          29.17790907617099,
          24.423408559611943,
          24.423408559611943,
          19.740990883383123,
          19.740990883383123,
          15.388739403308893,
          15.388739403308893,
          11.570634025292449,
          11.570634025292449,
          8.419367907022663,
          8.419367907022663,
          5.894019106972982,
          5.894019106972982,
          3.9795875689489413,
          3.9795875689489413,
          2.608513194573175,
          2.608513194573175,
          1.6393849923284536,
          1.6393849923284536,
          0.9936605079054143,
          0.9936605079054143,
          0.5870955956861574,
          0.5870955956861574,
          0.3311404907044538,
          0.3311404907044538,
          0.1801129550042376,
          0.1801129550042376,
          0.09598994408993576,
          0.09598994408993576,
          0.048574265962994426,
          0.048574265962994426,
          0.02369984432214786,
          0.02369984432214786,
          0.011400984642326632,
          0.011400984642326632,
          0.0051744390059736516,
          0.0051744390059736516,
          0.0022637316801655994,
          0.0022637316801655994,
          0.0009836870224181594,
          0.0009836870224181594,
          0.00040029812939628497,
          0.00040029812939628497,
          0.00015695208864050338,
          0.00015695208864050338,
          6.165487488761766e-05,
          6.165487488761766e-05,
          2.2488841378601263e-05,
          2.2488841378601263e-05,
          7.898671476316832e-06,
          7.898671476316832e-06,
          2.807187534703152e-06,
          2.807187534703152e-06,
          9.175158900731644e-07,
          9.175158900731644e-07,
          2.885134372243777e-07,
          2.885134372243777e-07,
          9.284666031940775e-08,
          9.284666031940775e-08,
          2.718458261953615e-08,
          2.718458261953615e-08,
          7.648587582026529e-09,
          7.648587582026529e-09,
          2.230740408986155e-09,
          2.230740408986155e-09,
          5.849162690587626e-10,
          5.849162690587626e-10,
          1.4715515641826652e-10,
          1.4715515641826652e-10,
          3.8932869839440156e-11,
          3.8932869839440156e-11,
          9.139573402418744e-12,
          9.139573402418744e-12,
          2.0545749467370086e-12,
          2.0545749467370086e-12,
          4.935883611477953e-13,
          4.935883611477953e-13,
          1.0370947423478672e-13,
          1.0370947423478672e-13,
          2.081570026210523e-14,
          2.081570026210523e-14,
          4.545594817490605e-15,
          4.545594817490605e-15,
          8.546143564588019e-16,
          8.546143564588019e-16,
          1.5302046786914372e-16,
          1.5302046786914372e-16,
          3.040813648934722e-17,
          3.040813648934722e-17,
          5.11422726470359e-18,
          5.11422726470359e-18,
          8.161323812529787e-19,
          8.161323812529787e-19,
          1.4776033905001372e-19,
          1.4776033905001372e-19,
          2.2225251696138786e-20,
          2.2225251696138786e-20,
          3.1577885276299982e-21,
          3.1577885276299982e-21,
          5.215433655598911e-22,
          5.215433655598911e-22,
          7.014049449417065e-23,
          7.014049449417065e-23,
          8.862792404225321e-24,
          8.862792404225321e-24,
          1.337157956159709e-24,
          1.337157956159709e-24,
          1.6074778292564793e-25,
          1.6074778292564793e-25,
          1.80414384589141e-26,
          1.80414384589141e-26,
          2.490174636187103e-27,
          2.490174636187103e-27,
          2.675307352892012e-28,
          2.675307352892012e-28,
          2.663336160576891e-29,
          2.663336160576891e-29,
          3.368422617252095e-30,
          3.368422617252095e-30,
          3.2333545178332518e-31,
          3.2333545178332518e-31,
          2.8508102543711136e-32,
          2.8508102543711136e-32,
          3.3095406063189995e-33,
          3.3095406063189995e-33,
          2.8378033081296692e-34,
          2.8378033081296692e-34,
          2.2121880290553455e-35,
          2.2121880290553455e-35,
          2.3618251841857804e-36,
          2.3618251841857804e-36,
          1.8086682213331358e-37,
          1.8086682213331358e-37,
          1.2442278138921776e-38,
          1.2442278138921776e-38,
          1.224224458252515e-39,
          1.224224458252515e-39,
          8.371079512386546e-41,
          8.371079512386546e-41,
          5.071089322174979e-42,
          5.071089322174979e-42,
          4.608948452067579e-43,
          4.608948452067579e-43,
          2.8135084708099284e-44,
          2.8135084708099284e-44,
          1.497301296682379e-45,
          1.497301296682379e-45,
          1.2602718735360864e-46,
          1.2602718735360864e-46,
          6.866847820641572e-48,
          6.866847820641572e-48,
          3.2017463174718112e-49,
          3.2017463174718112e-49,
          2.5028925641327795e-50,
          2.5028925641327795e-50,
          1.217046779329446e-51,
          1.217046779329446e-51,
          4.956475174964421e-53,
          4.956475174964421e-53,
          3.610186272068931e-54,
          3.610186272068931e-54,
          1.5663758430695064e-55,
          1.5663758430695064e-55,
          5.552324057533861e-57,
          5.552324057533861e-57,
          3.781988619119448e-58,
          3.781988619119448e-58,
          1.4639348021619084e-59,
          1.4639348021619084e-59,
          4.572782487496749e-61,
          4.572782487496749e-61,
          2.8774494611534463e-62,
          2.8774494611534463e-62,
          9.935340163184449e-64,
          9.935340163184449e-64,
          2.7464134341600177e-65,
          2.7464134341600177e-65,
          1.589958038125516e-66,
          1.589958038125516e-66,
          4.8964033690527995e-68,
          4.8964033690527995e-68,
          1.1976067194742777e-69,
          1.1976067194742777e-69,
          6.380395606675256e-71,
          6.380395606675256e-71,
          1.7522790817419308e-72,
          1.7522790817419308e-72,
          3.791647933952443e-74,
          3.791647933952443e-74,
          1.8594606150880922e-75,
          1.8594606150880922e-75,
          4.5536454607032246e-77,
          4.5536454607032246e-77,
          8.715846636155748e-79,
          8.715846636155748e-79,
          3.935475147804347e-80,
          3.935475147804347e-80,
          8.592968511727324e-82,
          8.592968511727324e-82,
          1.4546585917370767e-83,
          1.4546585917370767e-83,
          6.048831675423223e-85,
          6.048831675423223e-85,
          1.1774799708755907e-86,
          1.1774799708755907e-86,
          1.7627245104506166e-88,
          1.7627245104506166e-88,
          6.751545903832128e-90,
          6.751545903832128e-90,
          1.1716243472710903e-91,
          1.1716243472710903e-91,
          1.550891672389114e-93,
          1.550891672389114e-93,
          5.4724973824508386e-95,
          5.4724973824508386e-95,
          8.465372389150157e-97,
          8.465372389150157e-97,
          9.90726476154769e-99,
          9.90726476154769e-99,
          3.2211553633848863e-100,
          3.2211553633848863e-100,
          4.44145078867102e-102,
          4.44145078867102e-102,
          4.595183398628425e-104,
          4.595183398628425e-104,
          1.3768120627174189e-105,
          1.3768120627174189e-105,
          1.6920884436809173e-107,
          1.6920884436809173e-107,
          1.5474978860729683e-109,
          1.5474978860729683e-109,
          4.273341383576945e-111,
          4.273341383576945e-111,
          4.681004029571688e-113,
          4.681004029571688e-113,
          3.783873906031635e-115,
          3.783873906031635e-115,
          9.631267675837815e-117,
          9.631267675837815e-117,
          9.403100503442765e-119,
          9.403100503442765e-119,
          6.717748684999947e-121,
          6.717748684999947e-121,
          1.576214074138538e-122,
          1.576214074138538e-122,
          1.3715689034155284e-124,
          1.3715689034155284e-124
         ],
         "yaxis": "y1",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "𝕟₂ = 𝓛𝓝 (N₂,Dₘ,σ)",
         "line": {
          "color": "rgba(204, 0, 0, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "𝕟₂ = 𝓛𝓝 (N₂,Dₘ,σ)",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.090350448414474,
          10.273507681793024,
          10.273507681793024,
          10.459989534302535,
          10.459989534302535,
          10.649856353504289,
          10.649856353504289,
          10.84316958237171,
          10.84316958237171,
          11.039991779173976,
          11.039991779173976,
          11.240386637720556,
          11.240386637720556,
          11.44441900797323,
          11.44441900797323,
          11.652154917032231,
          11.652154917032231,
          11.863661590503344,
          11.863661590503344,
          12.079007474252842,
          12.079007474252842,
          12.298262256557319,
          12.298262256557319,
          12.521496890655566,
          12.521496890655566,
          12.748783617709826,
          12.748783617709826,
          12.98019599018381,
          12.98019599018381,
          13.215808895645086,
          13.215808895645086,
          13.455698580999508,
          13.455698580999508,
          13.699942677165545,
          13.699942677165545,
          13.948620224196498,
          13.948620224196498,
          14.201811696858716,
          14.201811696858716,
          14.459599030674116,
          14.459599030674116,
          14.722065648435406,
          14.722065648435406,
          14.989296487202608,
          14.989296487202608,
          15.261378025789629,
          15.261378025789629,
          15.538398312749738,
          15.538398312749738,
          15.820446994869037,
          15.820446994869037,
          16.10761534617715,
          16.10761534617715,
          16.39999629748447,
          16.39999629748447,
          16.69768446645562,
          16.69768446645562,
          17.00077618822873,
          17.00077618822873,
          17.309369546590553,
          17.309369546590553,
          17.623564405717435,
          17.623564405717435,
          17.94346244249247,
          17.94346244249247,
          18.269167179409244,
          18.269167179409244,
          18.600784018072822,
          18.600784018072822,
          18.938420273308882,
          18.938420273308882,
          19.282185207891956,
          19.282185207891956,
          19.632190067904055,
          19.632190067904055,
          19.988548118735103,
          19.988548118735103,
          20.35137468173687,
          20.35137468173687,
          20.72078717154221,
          20.72078717154221,
          21.096905134061714,
          21.096905134061714,
          21.479850285170084,
          21.479850285170084,
          21.869746550094703,
          21.869746550094703,
          22.266720103519187,
          22.266720103519187,
          22.67089941041491,
          22.67089941041491,
          23.08241526761366,
          23.08241526761366,
          23.501400846134892,
          23.501400846134892,
          23.927991734281377,
          23.927991734281377,
          24.36232598151701,
          24.36232598151701,
          24.804544143141136,
          24.804544143141136,
          25.25478932577379,
          25.25478932577379,
          25.713207233666548,
          25.713207233666548,
          26.179946215854002,
          26.179946215854002,
          26.65515731416115,
          26.65515731416115,
          27.138994312082165,
          27.138994312082165,
          27.6316137845464,
          27.6316137845464,
          28.133175148587764,
          28.133175148587764,
          28.6438407149338,
          28.6438407149338,
          29.163775740531204,
          29.163775740531204,
          29.693148482024785,
          29.693148482024785,
          30.232130250207152,
          30.232130250207152,
          30.78089546545674,
          30.78089546545674,
          31.339621714182158,
          31.339621714182158,
          31.90848980629108,
          31.90848980629108,
          32.48768383370232,
          32.48768383370232,
          33.07739122991996,
          33.07739122991996,
          33.6778028306889,
          33.6778028306889,
          34.289112935751355,
          34.289112935751355,
          34.911519371724424,
          34.911519371724424,
          35.54522355611888,
          35.54522355611888,
          36.19043056252011,
          36.19043056252011,
          36.847349186952165,
          36.847349186952165,
          37.51619201544639,
          37.51619201544639,
          38.19717549283665,
          38.19717549283665,
          38.89051999280318,
          38.89051999280318,
          39.59644988918792,
          39.59644988918792,
          40.31519362860439,
          40.31519362860439,
          41.04698380436544,
          41.04698380436544,
          41.792057231753,
          41.792057231753,
          42.55065502465411,
          42.55065502465411,
          43.323022673587985,
          43.323022673587985,
          44.10941012514944,
          44.10941012514944,
          44.910071862894306,
          44.910071862894306,
          45.72526698969311,
          45.72526698969311,
          46.55525931157958,
          46.55525931157958,
          47.400317423121166,
          47.400317423121166,
          48.26071479433915,
          48.26071479433915,
          49.13672985920654,
          49.13672985920654,
          50.02864610575234,
          50.02864610575234,
          50.93675216780135,
          50.93675216780135,
          51.861341918379274,
          51.861341918379274,
          52.80271456481317,
          52.80271456481317,
          53.76117474555825,
          53.76117474555825,
          54.73703262878217,
          54.73703262878217,
          55.73060401273886,
          55.73060401273886,
          56.74221042796429,
          56.74221042796429,
          57.77217924132721,
          57.77217924132721,
          58.8208437619687,
          58.8208437619687,
          59.888543349164614,
          59.888543349164614,
          60.975623522145916,
          60.975623522145916,
          62.08243607191253,
          62.08243607191253,
          63.20933917507671,
          63.20933917507671,
          64.35669750977287,
          64.35669750977287,
          65.52488237367147,
          65.52488237367147,
          66.71427180413495,
          66.71427180413495,
          67.92525070055476,
          67.92525070055476,
          69.15821094890896,
          69.15821094890896,
          70.41355154858087,
          70.41355154858087,
          71.69167874147956,
          71.69167874147956,
          72.9930061435042,
          72.9930061435042,
          74.31795487839462,
          74.31795487839462,
          75.66695371401163,
          75.66695371401163,
          77.04043920109092,
          77.04043920109092,
          78.43885581451562,
          78.43885581451562,
          79.8626560971533,
          79.8626560971533,
          81.31230080630368,
          81.31230080630368,
          82.78825906280481,
          82.78825906280481,
          84.29100850284559,
          84.29100850284559,
          85.82103543253415,
          85.82103543253415,
          87.37883498527172,
          87.37883498527172,
          88.9649112819833,
          88.9649112819833,
          90.5797775942566,
          90.5797775942566,
          92.22395651044235,
          92.22395651044235,
          93.8979801047696,
          93.8979801047696,
          95.60239010953076,
          95.60239010953076,
          97.33773809039202,
          97.33773809039202,
          99.10458562488608,
          99.10458562488608,
          100.90350448414475,
          100.90350448414475,
          102.73507681793026,
          102.73507681793026,
          104.59989534302535,
          104.59989534302535,
          106.4985635350429,
          106.4985635350429,
          108.4316958237171,
          108.4316958237171,
          110.39991779173975,
          110.39991779173975,
          112.40386637720557,
          112.40386637720557,
          114.44419007973231,
          114.44419007973231,
          116.5215491703223,
          116.5215491703223,
          118.63661590503344,
          118.63661590503344,
          120.79007474252845,
          120.79007474252845,
          122.98262256557321,
          122.98262256557321,
          125.21496890655568,
          125.21496890655568,
          127.48783617709826,
          127.48783617709826,
          129.8019599018381,
          129.8019599018381,
          132.15808895645085,
          132.15808895645085,
          134.55698580999507,
          134.55698580999507,
          136.99942677165546,
          136.99942677165546,
          139.48620224196497,
          139.48620224196497,
          142.01811696858715,
          142.01811696858715,
          144.59599030674116,
          144.59599030674116,
          147.22065648435404,
          147.22065648435404,
          149.89296487202606,
          149.89296487202606,
          152.6137802578963,
          152.6137802578963,
          155.38398312749737,
          155.38398312749737,
          158.20446994869036,
          158.20446994869036,
          161.07615346177147,
          161.07615346177147,
          163.9999629748447,
          163.9999629748447,
          166.9768446645562,
          166.9768446645562,
          170.0077618822873,
          170.0077618822873,
          173.0936954659055,
          173.0936954659055,
          176.23564405717434,
          176.23564405717434,
          179.43462442492472,
          179.43462442492472,
          182.69167179409243,
          182.69167179409243,
          186.00784018072818,
          186.00784018072818,
          189.3842027330888,
          189.3842027330888,
          192.8218520789196,
          192.8218520789196,
          196.32190067904054,
          196.32190067904054,
          199.88548118735102,
          199.88548118735102,
          203.51374681736868,
          203.51374681736868,
          207.2078717154221,
          207.2078717154221,
          210.96905134061717,
          210.96905134061717,
          214.79850285170085,
          214.79850285170085,
          218.69746550094703,
          218.69746550094703,
          222.66720103519188,
          222.66720103519188,
          226.70899410414913,
          226.70899410414913,
          230.82415267613658,
          230.82415267613658,
          235.01400846134894,
          235.01400846134894,
          239.27991734281375,
          239.27991734281375,
          243.6232598151701,
          243.6232598151701,
          248.04544143141135,
          248.04544143141135,
          252.5478932577379,
          252.5478932577379,
          257.13207233666543,
          257.13207233666543,
          261.79946215854,
          261.79946215854,
          266.5515731416115,
          266.5515731416115,
          271.3899431208216,
          271.3899431208216,
          276.31613784546397,
          276.31613784546397,
          281.33175148587765,
          281.33175148587765,
          286.438407149338,
          286.438407149338,
          291.637757405312,
          291.637757405312,
          296.9314848202479,
          296.9314848202479,
          302.32130250207155,
          302.32130250207155,
          307.8089546545674,
          307.8089546545674,
          313.3962171418216,
          313.3962171418216,
          319.08489806291084,
          319.08489806291084,
          324.8768383370232,
          324.8768383370232,
          330.7739122991996,
          330.7739122991996,
          336.7780283068889,
          336.7780283068889,
          342.89112935751353,
          342.89112935751353,
          349.1151937172442,
          349.1151937172442,
          355.4522355611888,
          355.4522355611888,
          361.9043056252011,
          361.9043056252011,
          368.4734918695216,
          368.4734918695216,
          375.16192015446387,
          375.16192015446387,
          381.97175492836647,
          381.97175492836647,
          388.9051999280318,
          388.9051999280318,
          395.96449889187926,
          395.96449889187926,
          403.15193628604396,
          403.15193628604396,
          410.4698380436544,
          410.4698380436544,
          417.92057231753,
          417.92057231753,
          425.5065502465411,
          425.5065502465411,
          433.23022673587985,
          433.23022673587985,
          441.09410125149435,
          441.09410125149435,
          449.100718628943,
          449.100718628943,
          457.2526698969311,
          457.2526698969311,
          465.55259311579584,
          465.55259311579584,
          474.0031742312117,
          474.0031742312117,
          482.6071479433915,
          482.6071479433915,
          491.36729859206537,
          491.36729859206537,
          500.2864610575233,
          500.2864610575233,
          509.36752167801353,
          509.36752167801353,
          518.6134191837928,
          518.6134191837928,
          528.0271456481318,
          528.0271456481318,
          537.6117474555825,
          537.6117474555825,
          547.3703262878216,
          547.3703262878216,
          557.3060401273885,
          557.3060401273885,
          567.4221042796428,
          567.4221042796428,
          577.7217924132722,
          577.7217924132722,
          588.2084376196871,
          588.2084376196871,
          598.8854334916462,
          598.8854334916462,
          609.7562352214592,
          609.7562352214592,
          620.8243607191254,
          620.8243607191254,
          632.093391750767,
          632.093391750767,
          643.5669750977287,
          643.5669750977287,
          655.2488237367147,
          655.2488237367147,
          667.1427180413494,
          667.1427180413494,
          679.2525070055476,
          679.2525070055476,
          691.5821094890896,
          691.5821094890896,
          704.1355154858088,
          704.1355154858088,
          716.9167874147956,
          716.9167874147956,
          729.9300614350419,
          729.9300614350419,
          743.1795487839462,
          743.1795487839462,
          756.6695371401163,
          756.6695371401163,
          770.4043920109092,
          770.4043920109092,
          784.3885581451563,
          784.3885581451563,
          798.626560971533,
          798.626560971533,
          813.1230080630369,
          813.1230080630369,
          827.8825906280481,
          827.8825906280481,
          842.9100850284559,
          842.9100850284559,
          858.2103543253414,
          858.2103543253414,
          873.7883498527173,
          873.7883498527173,
          889.649112819833,
          889.649112819833,
          905.797775942566,
          905.797775942566,
          922.2395651044235,
          922.2395651044235,
          938.9798010476961,
          938.9798010476961,
          956.0239010953076,
          956.0239010953076,
          973.3773809039202,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x1",
         "y": [
          1.4202150199510995e-124,
          1.6782974567143423e-122,
          1.6782974567143423e-122,
          2.0449534555641076e-120,
          2.0449534555641076e-120,
          1.014505345157839e-118,
          1.014505345157839e-118,
          1.0382463170160425e-116,
          1.0382463170160425e-116,
          1.1235242987725681e-114,
          1.1235242987725681e-114,
          5.237111716708587e-113,
          5.237111716708587e-113,
          4.663776041334063e-111,
          4.663776041334063e-111,
          4.482463144580841e-109,
          4.482463144580841e-109,
          1.9550511099379785e-107,
          1.9550511099379785e-107,
          1.5211835931811033e-105,
          1.5211835931811033e-105,
          1.2986470964156302e-103,
          1.2986470964156302e-103,
          5.280707700380181e-102,
          5.280707700380181e-102,
          3.602741169449861e-100,
          3.602741169449861e-100,
          2.732188885714984e-98,
          2.732188885714984e-98,
          1.0325053358026363e-96,
          1.0325053358026363e-96,
          6.195734424015478e-95,
          6.195734424015478e-95,
          4.174269335146588e-93,
          4.174269335146588e-93,
          1.4619257059035145e-91,
          1.4619257059035145e-91,
          7.736804678572611e-90,
          7.736804678572611e-90,
          4.631327085302431e-88,
          4.631327085302431e-88,
          1.4994518589303162e-86,
          1.4994518589303162e-86,
          7.015205079895578e-85,
          7.015205079895578e-85,
          3.731563013191362e-83,
          3.731563013191362e-83,
          1.1143844485441725e-81,
          1.1143844485441725e-81,
          4.6188066634598426e-80,
          4.6188066634598426e-80,
          2.1834415947473206e-78,
          2.1834415947473206e-78,
          6.002571540284237e-77,
          6.002571540284237e-77,
          2.2081604244235665e-75,
          2.2081604244235665e-75,
          9.27818480685239e-74,
          9.27818480685239e-74,
          2.3438525377594127e-72,
          2.3438525377594127e-72,
          7.66555517396153e-71,
          7.66555517396153e-71,
          2.863256739034833e-69,
          2.863256739034833e-69,
          6.635801304464058e-68,
          6.635801304464058e-68,
          1.9322773229346407e-66,
          1.9322773229346407e-66,
          6.4170971668990354e-65,
          6.4170971668990354e-65,
          1.3623748253382482e-63,
          1.3623748253382482e-63,
          3.5367862605268624e-62,
          3.5367862605268624e-62,
          1.0444874508441393e-60,
          1.0444874508441393e-60,
          2.0286258260525147e-59,
          2.0286258260525147e-59,
          4.700697568724928e-58,
          4.700697568724928e-58,
          1.234694103713601e-56,
          1.234694103713601e-56,
          2.191111593237911e-55,
          2.191111593237911e-55,
          4.5366003595827154e-54,
          4.5366003595827154e-54,
          1.0600157414998921e-52,
          1.0600157414998921e-52,
          1.716854419804713e-51,
          1.716854419804713e-51,
          3.179171657600222e-50,
          3.179171657600222e-50,
          6.609480168014251e-49,
          6.609480168014251e-49,
          9.760071783268042e-48,
          9.760071783268042e-48,
          1.6177564662686821e-46,
          1.6177564662686821e-46,
          2.993157631734781e-45,
          2.993157631734781e-45,
          4.025898677429563e-44,
          4.025898677429563e-44,
          5.977621668442231e-43,
          5.977621668442231e-43,
          9.844743416664452e-42,
          9.844743416664452e-42,
          1.2050326457545537e-40,
          1.2050326457545537e-40,
          1.6038367006604474e-39,
          1.6038367006604474e-39,
          2.3517813726336996e-38,
          2.3517813726336996e-38,
          2.6175403407776073e-37,
          2.6175403407776073e-37,
          3.1247016675653036e-36,
          3.1247016675653036e-36,
          4.0804906962899773e-35,
          4.0804906962899773e-35,
          4.126444433642735e-34,
          4.126444433642735e-34,
          4.4205246362707417e-33,
          4.4205246362707417e-33,
          5.142281669963391e-32,
          5.142281669963391e-32,
          4.721428740912952e-31,
          4.721428740912952e-31,
          4.5410467065885745e-30,
          4.5410467065885745e-30,
          4.706872343698685e-29,
          4.706872343698685e-29,
          3.921119539372039e-28,
          3.921119539372039e-28,
          3.3873101253620954e-27,
          3.3873101253620954e-27,
          3.129299006486512e-26,
          3.129299006486512e-26,
          2.3637860773357074e-25,
          2.3637860773357074e-25,
          1.8347234250696204e-24,
          1.8347234250696204e-24,
          1.5111400024290828e-23,
          1.5111400024290828e-23,
          1.0343988036928088e-22,
          1.0343988036928088e-22,
          7.216100690514762e-22,
          7.216100690514762e-22,
          5.300418469727466e-21,
          5.300418469727466e-21,
          3.286004517917331e-20,
          3.286004517917331e-20,
          2.0608691790603819e-19,
          2.0608691790603819e-19,
          1.3504177640557073e-18,
          1.3504177640557073e-18,
          7.578191491861891e-18,
          7.578191491861891e-18,
          4.2737930399158443e-17,
          4.2737930399158443e-17,
          2.4990977424030313e-16,
          2.4990977424030313e-16,
          1.268807625970479e-15,
          1.268807625970479e-15,
          6.4356283290461176e-15,
          6.4356283290461176e-15,
          3.3593860313947895e-14,
          3.3593860313947895e-14,
          1.5423145536484121e-13,
          1.5423145536484121e-13,
          7.036906942754797e-13,
          7.036906942754797e-13,
          3.2802160987820615e-12,
          3.2802160987820615e-12,
          1.36116279586707e-11,
          1.36116279586707e-11,
          5.587078986444879e-11,
          5.587078986444879e-11,
          2.3265640503849465e-10,
          2.3265640503849465e-10,
          8.722057853970727e-10,
          8.722057853970727e-10,
          3.221057602306762e-09,
          3.221057602306762e-09,
          1.1986752719498052e-08,
          1.1986752719498052e-08,
          4.0579850312541633e-08,
          4.0579850312541633e-08,
          1.3484073657348888e-07,
          1.3484073657348888e-07,
          4.486067707620454e-07,
          4.486067707620454e-07,
          1.3708639282186604e-06,
          1.3708639282186604e-06,
          4.098742837991392e-06,
          4.098742837991392e-06,
          1.2195831344010667e-05,
          1.2195831344010667e-05,
          3.36263433755741e-05,
          3.36263433755741e-05,
          9.046588428742004e-05,
          9.046588428742004e-05,
          0.00024084722488786802,
          0.00024084722488786802,
          0.0005989277745083023,
          0.0005989277745083023,
          0.0014498428943030507,
          0.0014498428943030507,
          0.003455092221278016,
          0.003455092221278016,
          0.007746154207422218,
          0.007746154207422218,
          0.0168715888745378,
          0.0168715888745378,
          0.03600545179568573,
          0.03600545179568573,
          0.0727480475255022,
          0.0727480475255022,
          0.14255633876666246,
          0.14255633876666246,
          0.27256501706757347,
          0.27256501706757347,
          0.4961192039037285,
          0.4961192039037285,
          0.8745985269226506,
          0.8745985269226506,
          1.4988822904807737,
          1.4988822904807737,
          2.4568892397179956,
          2.4568892397179956,
          3.8959941022508118,
          3.8959941022508118,
          5.987734850272692,
          5.987734850272692,
          8.83536978389316,
          8.83536978389316,
          12.601154937681114,
          12.601154937681114,
          17.376286778879926,
          17.376286778879926,
          23.073194094019435,
          23.073194094019435,
          29.59235573564629,
          29.59235573564629,
          36.631292152675826,
          36.631292152675826,
          43.75606518832477,
          43.75606518832477,
          50.456818660937465,
          50.456818660937465,
          56.09827508367051,
          56.09827508367051,
          60.25867745915413,
          60.25867745915413,
          62.46326478222587,
          62.46326478222587,
          62.40934554828494,
          62.40934554828494,
          60.26352377369906,
          60.26352377369906,
          56.141837060161315,
          56.141837060161315,
          50.43745062767519,
          50.43745062767519,
          43.766863614256486,
          43.766863614256486,
          36.63511283941791,
          36.63511283941791,
          29.611486325074683,
          29.611486325074683,
          23.08310910496334,
          23.08310910496334,
          17.355951037938674,
          17.355951037938674,
          12.629051860533995,
          12.629051860533995,
          8.841028660459473,
          8.841028660459473,
          5.969381353423412,
          5.969381353423412,
          3.9127697918597626,
          3.9127697918597626,
          2.4590774884926803,
          2.4590774884926803,
          1.4904907618581216,
          1.4904907618581216,
          0.880643393529236,
          0.880643393529236,
          0.4967107360566806,
          0.4967107360566806,
          0.2701694325063564,
          0.2701694325063564,
          0.14398491613490363,
          0.14398491613490363,
          0.07286139894449163,
          0.07286139894449163,
          0.03554976648322179,
          0.03554976648322179,
          0.017101476963489952,
          0.017101476963489952,
          0.0077616585089604765,
          0.0077616585089604765,
          0.0033955975202483997,
          0.0033955975202483997,
          0.0014755305336272388,
          0.0014755305336272388,
          0.0006004471940944275,
          0.0006004471940944275,
          0.00023542813296075507,
          0.00023542813296075507,
          9.248231233142651e-05,
          9.248231233142651e-05,
          3.373326206790189e-05,
          3.373326206790189e-05,
          1.1848007214475246e-05,
          1.1848007214475246e-05,
          4.210781302054727e-06,
          4.210781302054727e-06,
          1.3762738351097466e-06,
          1.3762738351097466e-06,
          4.327701558365666e-07,
          4.327701558365666e-07,
          1.3926999047911163e-07,
          1.3926999047911163e-07,
          4.077687392930422e-08,
          4.077687392930422e-08,
          1.1472881373039791e-08,
          1.1472881373039791e-08,
          3.3461106134792327e-09,
          3.3461106134792327e-09,
          8.773744035881437e-10,
          8.773744035881437e-10,
          2.2073273462739983e-10,
          2.2073273462739983e-10,
          5.839930475916024e-11,
          5.839930475916024e-11,
          1.3709360103628115e-11,
          1.3709360103628115e-11,
          3.081862420105513e-12,
          3.081862420105513e-12,
          7.403825417216929e-13,
          7.403825417216929e-13,
          1.5556421135218007e-13,
          1.5556421135218007e-13,
          3.1223550393157846e-14,
          3.1223550393157846e-14,
          6.818392226235908e-15,
          6.818392226235908e-15,
          1.281921534688203e-15,
          1.281921534688203e-15,
          2.295307018037156e-16,
          2.295307018037156e-16,
          4.561220473402082e-17,
          4.561220473402082e-17,
          7.671340897055385e-18,
          7.671340897055385e-18,
          1.224198571879468e-18,
          1.224198571879468e-18,
          2.216405085750206e-19,
          2.216405085750206e-19,
          3.3337877544208174e-20,
          3.3337877544208174e-20,
          4.736682791444998e-21,
          4.736682791444998e-21,
          7.823150483398365e-22,
          7.823150483398365e-22,
          1.0521074174125596e-22,
          1.0521074174125596e-22,
          1.329418860633798e-23,
          1.329418860633798e-23,
          2.005736934239564e-24,
          2.005736934239564e-24,
          2.411216743884719e-25,
          2.411216743884719e-25,
          2.7062157688371144e-26,
          2.7062157688371144e-26,
          3.7352619542806544e-27,
          3.7352619542806544e-27,
          4.0129610293380184e-28,
          4.0129610293380184e-28,
          3.995004240865337e-29,
          3.995004240865337e-29,
          5.052633925878142e-30,
          5.052633925878142e-30,
          4.850031776749878e-31,
          4.850031776749878e-31,
          4.27621538155667e-32,
          4.27621538155667e-32,
          4.9643109094784996e-33,
          4.9643109094784996e-33,
          4.2567049621945045e-34,
          4.2567049621945045e-34,
          3.3182820435830176e-35,
          3.3182820435830176e-35,
          3.542737776278671e-36,
          3.542737776278671e-36,
          2.713002331999704e-37,
          2.713002331999704e-37,
          1.866341720838266e-38,
          1.866341720838266e-38,
          1.8363366873787724e-39,
          1.8363366873787724e-39,
          1.255661926857982e-40,
          1.255661926857982e-40,
          7.60663398326247e-42,
          7.60663398326247e-42,
          6.91342267810137e-43,
          6.91342267810137e-43,
          4.2202627062148934e-44,
          4.2202627062148934e-44,
          2.2459519450235686e-45,
          2.2459519450235686e-45,
          1.8904078103041295e-46,
          1.8904078103041295e-46,
          1.0300271730962361e-47,
          1.0300271730962361e-47,
          4.802619476207716e-49,
          4.802619476207716e-49,
          3.754338846199169e-50,
          3.754338846199169e-50,
          1.825570168994169e-51,
          1.825570168994169e-51,
          7.434712762446631e-53,
          7.434712762446631e-53,
          5.415279408103395e-54,
          5.415279408103395e-54,
          2.3495637646042592e-55,
          2.3495637646042592e-55,
          8.328486086300793e-57,
          8.328486086300793e-57,
          5.672982928679171e-58,
          5.672982928679171e-58,
          2.1959022032428622e-59,
          2.1959022032428622e-59,
          6.859173731245125e-61,
          6.859173731245125e-61,
          4.3161741917301705e-62,
          4.3161741917301705e-62,
          1.4903010244776674e-63,
          1.4903010244776674e-63,
          4.119620151240026e-65,
          4.119620151240026e-65,
          2.3849370571882746e-66,
          2.3849370571882746e-66,
          7.344605053579199e-68,
          7.344605053579199e-68,
          1.7964100792114164e-69,
          1.7964100792114164e-69,
          9.570593410012883e-71,
          9.570593410012883e-71,
          2.628418622612896e-72,
          2.628418622612896e-72,
          5.687471900928664e-74,
          5.687471900928664e-74,
          2.789190922632138e-75,
          2.789190922632138e-75,
          6.830468191054835e-77,
          6.830468191054835e-77,
          1.3073769954233622e-78,
          1.3073769954233622e-78,
          5.9032127217065225e-80,
          5.9032127217065225e-80,
          1.2889452767590985e-81,
          1.2889452767590985e-81,
          2.181987887605615e-83,
          2.181987887605615e-83,
          9.073247513134835e-85,
          9.073247513134835e-85,
          1.766219956313386e-86,
          1.766219956313386e-86,
          2.6440867656759255e-88,
          2.6440867656759255e-88,
          1.0127318855748192e-89,
          1.0127318855748192e-89,
          1.7574365209066355e-91,
          1.7574365209066355e-91,
          2.3263375085836714e-93,
          2.3263375085836714e-93,
          8.208746073676256e-95,
          8.208746073676256e-95,
          1.2698058583725236e-96,
          1.2698058583725236e-96,
          1.486089714232154e-98,
          1.486089714232154e-98,
          4.831733045077329e-100,
          4.831733045077329e-100,
          6.6621761830065304e-102,
          6.6621761830065304e-102,
          6.892775097942637e-104,
          6.892775097942637e-104,
          2.0652180940761283e-105,
          2.0652180940761283e-105,
          2.538132665521376e-107,
          2.538132665521376e-107,
          2.3212468291094527e-109,
          2.3212468291094527e-109,
          6.410012075365417e-111,
          6.410012075365417e-111,
          7.021506044357532e-113,
          7.021506044357532e-113,
          5.6758108590474545e-115,
          5.6758108590474545e-115,
          1.4446901513756723e-116,
          1.4446901513756723e-116,
          1.4104650755164148e-118,
          1.4104650755164148e-118,
          1.0076623027499921e-120,
          1.0076623027499921e-120,
          2.364321111207807e-122,
          2.364321111207807e-122,
          2.0573533551232925e-124,
          2.0573533551232925e-124
         ],
         "yaxis": "y1",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "𝕟₁₂ (partMC)",
         "line": {
          "color": "rgba(0, 0, 204, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 1.5
         },
         "mode": "lines",
         "name": "𝕟₁₂ (partMC)",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.090350448414474,
          10.273507681793024,
          10.273507681793024,
          10.459989534302535,
          10.459989534302535,
          10.649856353504289,
          10.649856353504289,
          10.84316958237171,
          10.84316958237171,
          11.039991779173976,
          11.039991779173976,
          11.240386637720556,
          11.240386637720556,
          11.44441900797323,
          11.44441900797323,
          11.652154917032231,
          11.652154917032231,
          11.863661590503344,
          11.863661590503344,
          12.079007474252842,
          12.079007474252842,
          12.298262256557319,
          12.298262256557319,
          12.521496890655566,
          12.521496890655566,
          12.748783617709826,
          12.748783617709826,
          12.98019599018381,
          12.98019599018381,
          13.215808895645086,
          13.215808895645086,
          13.455698580999508,
          13.455698580999508,
          13.699942677165545,
          13.699942677165545,
          13.948620224196498,
          13.948620224196498,
          14.201811696858716,
          14.201811696858716,
          14.459599030674116,
          14.459599030674116,
          14.722065648435406,
          14.722065648435406,
          14.989296487202608,
          14.989296487202608,
          15.261378025789629,
          15.261378025789629,
          15.538398312749738,
          15.538398312749738,
          15.820446994869037,
          15.820446994869037,
          16.10761534617715,
          16.10761534617715,
          16.39999629748447,
          16.39999629748447,
          16.69768446645562,
          16.69768446645562,
          17.00077618822873,
          17.00077618822873,
          17.309369546590553,
          17.309369546590553,
          17.623564405717435,
          17.623564405717435,
          17.94346244249247,
          17.94346244249247,
          18.269167179409244,
          18.269167179409244,
          18.600784018072822,
          18.600784018072822,
          18.938420273308882,
          18.938420273308882,
          19.282185207891956,
          19.282185207891956,
          19.632190067904055,
          19.632190067904055,
          19.988548118735103,
          19.988548118735103,
          20.35137468173687,
          20.35137468173687,
          20.72078717154221,
          20.72078717154221,
          21.096905134061714,
          21.096905134061714,
          21.479850285170084,
          21.479850285170084,
          21.869746550094703,
          21.869746550094703,
          22.266720103519187,
          22.266720103519187,
          22.67089941041491,
          22.67089941041491,
          23.08241526761366,
          23.08241526761366,
          23.501400846134892,
          23.501400846134892,
          23.927991734281377,
          23.927991734281377,
          24.36232598151701,
          24.36232598151701,
          24.804544143141136,
          24.804544143141136,
          25.25478932577379,
          25.25478932577379,
          25.713207233666548,
          25.713207233666548,
          26.179946215854002,
          26.179946215854002,
          26.65515731416115,
          26.65515731416115,
          27.138994312082165,
          27.138994312082165,
          27.6316137845464,
          27.6316137845464,
          28.133175148587764,
          28.133175148587764,
          28.6438407149338,
          28.6438407149338,
          29.163775740531204,
          29.163775740531204,
          29.693148482024785,
          29.693148482024785,
          30.232130250207152,
          30.232130250207152,
          30.78089546545674,
          30.78089546545674,
          31.339621714182158,
          31.339621714182158,
          31.90848980629108,
          31.90848980629108,
          32.48768383370232,
          32.48768383370232,
          33.07739122991996,
          33.07739122991996,
          33.6778028306889,
          33.6778028306889,
          34.289112935751355,
          34.289112935751355,
          34.911519371724424,
          34.911519371724424,
          35.54522355611888,
          35.54522355611888,
          36.19043056252011,
          36.19043056252011,
          36.847349186952165,
          36.847349186952165,
          37.51619201544639,
          37.51619201544639,
          38.19717549283665,
          38.19717549283665,
          38.89051999280318,
          38.89051999280318,
          39.59644988918792,
          39.59644988918792,
          40.31519362860439,
          40.31519362860439,
          41.04698380436544,
          41.04698380436544,
          41.792057231753,
          41.792057231753,
          42.55065502465411,
          42.55065502465411,
          43.323022673587985,
          43.323022673587985,
          44.10941012514944,
          44.10941012514944,
          44.910071862894306,
          44.910071862894306,
          45.72526698969311,
          45.72526698969311,
          46.55525931157958,
          46.55525931157958,
          47.400317423121166,
          47.400317423121166,
          48.26071479433915,
          48.26071479433915,
          49.13672985920654,
          49.13672985920654,
          50.02864610575234,
          50.02864610575234,
          50.93675216780135,
          50.93675216780135,
          51.861341918379274,
          51.861341918379274,
          52.80271456481317,
          52.80271456481317,
          53.76117474555825,
          53.76117474555825,
          54.73703262878217,
          54.73703262878217,
          55.73060401273886,
          55.73060401273886,
          56.74221042796429,
          56.74221042796429,
          57.77217924132721,
          57.77217924132721,
          58.8208437619687,
          58.8208437619687,
          59.888543349164614,
          59.888543349164614,
          60.975623522145916,
          60.975623522145916,
          62.08243607191253,
          62.08243607191253,
          63.20933917507671,
          63.20933917507671,
          64.35669750977287,
          64.35669750977287,
          65.52488237367147,
          65.52488237367147,
          66.71427180413495,
          66.71427180413495,
          67.92525070055476,
          67.92525070055476,
          69.15821094890896,
          69.15821094890896,
          70.41355154858087,
          70.41355154858087,
          71.69167874147956,
          71.69167874147956,
          72.9930061435042,
          72.9930061435042,
          74.31795487839462,
          74.31795487839462,
          75.66695371401163,
          75.66695371401163,
          77.04043920109092,
          77.04043920109092,
          78.43885581451562,
          78.43885581451562,
          79.8626560971533,
          79.8626560971533,
          81.31230080630368,
          81.31230080630368,
          82.78825906280481,
          82.78825906280481,
          84.29100850284559,
          84.29100850284559,
          85.82103543253415,
          85.82103543253415,
          87.37883498527172,
          87.37883498527172,
          88.9649112819833,
          88.9649112819833,
          90.5797775942566,
          90.5797775942566,
          92.22395651044235,
          92.22395651044235,
          93.8979801047696,
          93.8979801047696,
          95.60239010953076,
          95.60239010953076,
          97.33773809039202,
          97.33773809039202,
          99.10458562488608,
          99.10458562488608,
          100.90350448414475,
          100.90350448414475,
          102.73507681793026,
          102.73507681793026,
          104.59989534302535,
          104.59989534302535,
          106.4985635350429,
          106.4985635350429,
          108.4316958237171,
          108.4316958237171,
          110.39991779173975,
          110.39991779173975,
          112.40386637720557,
          112.40386637720557,
          114.44419007973231,
          114.44419007973231,
          116.5215491703223,
          116.5215491703223,
          118.63661590503344,
          118.63661590503344,
          120.79007474252845,
          120.79007474252845,
          122.98262256557321,
          122.98262256557321,
          125.21496890655568,
          125.21496890655568,
          127.48783617709826,
          127.48783617709826,
          129.8019599018381,
          129.8019599018381,
          132.15808895645085,
          132.15808895645085,
          134.55698580999507,
          134.55698580999507,
          136.99942677165546,
          136.99942677165546,
          139.48620224196497,
          139.48620224196497,
          142.01811696858715,
          142.01811696858715,
          144.59599030674116,
          144.59599030674116,
          147.22065648435404,
          147.22065648435404,
          149.89296487202606,
          149.89296487202606,
          152.6137802578963,
          152.6137802578963,
          155.38398312749737,
          155.38398312749737,
          158.20446994869036,
          158.20446994869036,
          161.07615346177147,
          161.07615346177147,
          163.9999629748447,
          163.9999629748447,
          166.9768446645562,
          166.9768446645562,
          170.0077618822873,
          170.0077618822873,
          173.0936954659055,
          173.0936954659055,
          176.23564405717434,
          176.23564405717434,
          179.43462442492472,
          179.43462442492472,
          182.69167179409243,
          182.69167179409243,
          186.00784018072818,
          186.00784018072818,
          189.3842027330888,
          189.3842027330888,
          192.8218520789196,
          192.8218520789196,
          196.32190067904054,
          196.32190067904054,
          199.88548118735102,
          199.88548118735102,
          203.51374681736868,
          203.51374681736868,
          207.2078717154221,
          207.2078717154221,
          210.96905134061717,
          210.96905134061717,
          214.79850285170085,
          214.79850285170085,
          218.69746550094703,
          218.69746550094703,
          222.66720103519188,
          222.66720103519188,
          226.70899410414913,
          226.70899410414913,
          230.82415267613658,
          230.82415267613658,
          235.01400846134894,
          235.01400846134894,
          239.27991734281375,
          239.27991734281375,
          243.6232598151701,
          243.6232598151701,
          248.04544143141135,
          248.04544143141135,
          252.5478932577379,
          252.5478932577379,
          257.13207233666543,
          257.13207233666543,
          261.79946215854,
          261.79946215854,
          266.5515731416115,
          266.5515731416115,
          271.3899431208216,
          271.3899431208216,
          276.31613784546397,
          276.31613784546397,
          281.33175148587765,
          281.33175148587765,
          286.438407149338,
          286.438407149338,
          291.637757405312,
          291.637757405312,
          296.9314848202479,
          296.9314848202479,
          302.32130250207155,
          302.32130250207155,
          307.8089546545674,
          307.8089546545674,
          313.3962171418216,
          313.3962171418216,
          319.08489806291084,
          319.08489806291084,
          324.8768383370232,
          324.8768383370232,
          330.7739122991996,
          330.7739122991996,
          336.7780283068889,
          336.7780283068889,
          342.89112935751353,
          342.89112935751353,
          349.1151937172442,
          349.1151937172442,
          355.4522355611888,
          355.4522355611888,
          361.9043056252011,
          361.9043056252011,
          368.4734918695216,
          368.4734918695216,
          375.16192015446387,
          375.16192015446387,
          381.97175492836647,
          381.97175492836647,
          388.9051999280318,
          388.9051999280318,
          395.96449889187926,
          395.96449889187926,
          403.15193628604396,
          403.15193628604396,
          410.4698380436544,
          410.4698380436544,
          417.92057231753,
          417.92057231753,
          425.5065502465411,
          425.5065502465411,
          433.23022673587985,
          433.23022673587985,
          441.09410125149435,
          441.09410125149435,
          449.100718628943,
          449.100718628943,
          457.2526698969311,
          457.2526698969311,
          465.55259311579584,
          465.55259311579584,
          474.0031742312117,
          474.0031742312117,
          482.6071479433915,
          482.6071479433915,
          491.36729859206537,
          491.36729859206537,
          500.2864610575233,
          500.2864610575233,
          509.36752167801353,
          509.36752167801353,
          518.6134191837928,
          518.6134191837928,
          528.0271456481318,
          528.0271456481318,
          537.6117474555825,
          537.6117474555825,
          547.3703262878216,
          547.3703262878216,
          557.3060401273885,
          557.3060401273885,
          567.4221042796428,
          567.4221042796428,
          577.7217924132722,
          577.7217924132722,
          588.2084376196871,
          588.2084376196871,
          598.8854334916462,
          598.8854334916462,
          609.7562352214592,
          609.7562352214592,
          620.8243607191254,
          620.8243607191254,
          632.093391750767,
          632.093391750767,
          643.5669750977287,
          643.5669750977287,
          655.2488237367147,
          655.2488237367147,
          667.1427180413494,
          667.1427180413494,
          679.2525070055476,
          679.2525070055476,
          691.5821094890896,
          691.5821094890896,
          704.1355154858088,
          704.1355154858088,
          716.9167874147956,
          716.9167874147956,
          729.9300614350419,
          729.9300614350419,
          743.1795487839462,
          743.1795487839462,
          756.6695371401163,
          756.6695371401163,
          770.4043920109092,
          770.4043920109092,
          784.3885581451563,
          784.3885581451563,
          798.626560971533,
          798.626560971533,
          813.1230080630369,
          813.1230080630369,
          827.8825906280481,
          827.8825906280481,
          842.9100850284559,
          842.9100850284559,
          858.2103543253414,
          858.2103543253414,
          873.7883498527173,
          873.7883498527173,
          889.649112819833,
          889.649112819833,
          905.797775942566,
          905.797775942566,
          922.2395651044235,
          922.2395651044235,
          938.9798010476961,
          938.9798010476961,
          956.0239010953076,
          956.0239010953076,
          973.3773809039202,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x2",
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0.001660429349534434,
          0.001660429349534434,
          0.00285707455268562,
          0.00285707455268562,
          0.005074205387940568,
          0.005074205387940568,
          0.015911629435727482,
          0.015911629435727482,
          0.023630103722488985,
          0.023630103722488985,
          0.05358106669684123,
          0.05358106669684123,
          0.07406248316300047,
          0.07406248316300047,
          0.13235319643972215,
          0.13235319643972215,
          0.2179175293910647,
          0.2179175293910647,
          0.3004779122703456,
          0.3004779122703456,
          0.39675690579819173,
          0.39675690579819173,
          0.5207364988538564,
          0.5207364988538564,
          0.5855901707876983,
          0.5855901707876983,
          0.6085888788531155,
          0.6085888788531155,
          0.6425247127634108,
          0.6425247127634108,
          0.547214360658466,
          0.547214360658466,
          0.5445809230674346,
          0.5445809230674346,
          0.3952345454823395,
          0.3952345454823395,
          0.32283374399326803,
          0.32283374399326803,
          0.22188514183780128,
          0.22188514183780128,
          0.14015032000210698,
          0.14015032000210698,
          0.08619421842064146,
          0.08619421842064146,
          0.0634584598940785,
          0.0634584598940785,
          0.03835521616850645,
          0.03835521616850645,
          0.022223937534490618,
          0.022223937534490618,
          0.007604436589863831,
          0.007604436589863831,
          0.002141637636578918,
          0.002141637636578918,
          0.00216143414043382,
          0.00216143414043382,
          0.00030154005301095304,
          0.00030154005301095304,
          0.000510872965720734,
          0.000510872965720734,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
         ],
         "yaxis": "y2",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "f⋅[(β₁₂ᵇt)*(𝕟₁*𝕟₂)]",
         "line": {
          "color": "rgba(165, 42, 42, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "f⋅[(β₁₂ᵇt)*(𝕟₁*𝕟₂)]",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.273507681793024,
          10.459989534302535,
          10.649856353504289,
          10.84316958237171,
          11.039991779173976,
          11.240386637720556,
          11.44441900797323,
          11.652154917032231,
          11.863661590503344,
          12.079007474252842,
          12.298262256557319,
          12.521496890655566,
          12.748783617709826,
          12.98019599018381,
          13.215808895645086,
          13.455698580999508,
          13.699942677165545,
          13.948620224196498,
          14.201811696858716,
          14.459599030674116,
          14.722065648435406,
          14.989296487202608,
          15.261378025789629,
          15.538398312749738,
          15.820446994869037,
          16.10761534617715,
          16.39999629748447,
          16.69768446645562,
          17.00077618822873,
          17.309369546590553,
          17.623564405717435,
          17.94346244249247,
          18.269167179409244,
          18.600784018072822,
          18.938420273308882,
          19.282185207891956,
          19.632190067904055,
          19.988548118735103,
          20.35137468173687,
          20.72078717154221,
          21.096905134061714,
          21.479850285170084,
          21.869746550094703,
          22.266720103519187,
          22.67089941041491,
          23.08241526761366,
          23.501400846134892,
          23.927991734281377,
          24.36232598151701,
          24.804544143141136,
          25.25478932577379,
          25.713207233666548,
          26.179946215854002,
          26.65515731416115,
          27.138994312082165,
          27.6316137845464,
          28.133175148587764,
          28.6438407149338,
          29.163775740531204,
          29.693148482024785,
          30.232130250207152,
          30.78089546545674,
          31.339621714182158,
          31.90848980629108,
          32.48768383370232,
          33.07739122991996,
          33.6778028306889,
          34.289112935751355,
          34.911519371724424,
          35.54522355611888,
          36.19043056252011,
          36.847349186952165,
          37.51619201544639,
          38.19717549283665,
          38.89051999280318,
          39.59644988918792,
          40.31519362860439,
          41.04698380436544,
          41.792057231753,
          42.55065502465411,
          43.323022673587985,
          44.10941012514944,
          44.910071862894306,
          45.72526698969311,
          46.55525931157958,
          47.400317423121166,
          48.26071479433915,
          49.13672985920654,
          50.02864610575234,
          50.93675216780135,
          51.861341918379274,
          52.80271456481317,
          53.76117474555825,
          54.73703262878217,
          55.73060401273886,
          56.74221042796429,
          57.77217924132721,
          58.8208437619687,
          59.888543349164614,
          60.975623522145916,
          62.08243607191253,
          63.20933917507671,
          64.35669750977287,
          65.52488237367147,
          66.71427180413495,
          67.92525070055476,
          69.15821094890896,
          70.41355154858087,
          71.69167874147956,
          72.9930061435042,
          74.31795487839462,
          75.66695371401163,
          77.04043920109092,
          78.43885581451562,
          79.8626560971533,
          81.31230080630368,
          82.78825906280481,
          84.29100850284559,
          85.82103543253415,
          87.37883498527172,
          88.9649112819833,
          90.5797775942566,
          92.22395651044235,
          93.8979801047696,
          95.60239010953076,
          97.33773809039202,
          99.10458562488608,
          100.90350448414475,
          102.73507681793026,
          104.59989534302535,
          106.4985635350429,
          108.4316958237171,
          110.39991779173975,
          112.40386637720557,
          114.44419007973231,
          116.5215491703223,
          118.63661590503344,
          120.79007474252845,
          122.98262256557321,
          125.21496890655568,
          127.48783617709826,
          129.8019599018381,
          132.15808895645085,
          134.55698580999507,
          136.99942677165546,
          139.48620224196497,
          142.01811696858715,
          144.59599030674116,
          147.22065648435404,
          149.89296487202606,
          152.6137802578963,
          155.38398312749737,
          158.20446994869036,
          161.07615346177147,
          163.9999629748447,
          166.9768446645562,
          170.0077618822873,
          173.0936954659055,
          176.23564405717434,
          179.43462442492472,
          182.69167179409243,
          186.00784018072818,
          189.3842027330888,
          192.8218520789196,
          196.32190067904054,
          199.88548118735102,
          203.51374681736868,
          207.2078717154221,
          210.96905134061717,
          214.79850285170085,
          218.69746550094703,
          222.66720103519188,
          226.70899410414913,
          230.82415267613658,
          235.01400846134894,
          239.27991734281375,
          243.6232598151701,
          248.04544143141135,
          252.5478932577379,
          257.13207233666543,
          261.79946215854,
          266.5515731416115,
          271.3899431208216,
          276.31613784546397,
          281.33175148587765,
          286.438407149338,
          291.637757405312,
          296.9314848202479,
          302.32130250207155,
          307.8089546545674,
          313.3962171418216,
          319.08489806291084,
          324.8768383370232,
          330.7739122991996,
          336.7780283068889,
          342.89112935751353,
          349.1151937172442,
          355.4522355611888,
          361.9043056252011,
          368.4734918695216,
          375.16192015446387,
          381.97175492836647,
          388.9051999280318,
          395.96449889187926,
          403.15193628604396,
          410.4698380436544,
          417.92057231753,
          425.5065502465411,
          433.23022673587985,
          441.09410125149435,
          449.100718628943,
          457.2526698969311,
          465.55259311579584,
          474.0031742312117,
          482.6071479433915,
          491.36729859206537,
          500.2864610575233,
          509.36752167801353,
          518.6134191837928,
          528.0271456481318,
          537.6117474555825,
          547.3703262878216,
          557.3060401273885,
          567.4221042796428,
          577.7217924132722,
          588.2084376196871,
          598.8854334916462,
          609.7562352214592,
          620.8243607191254,
          632.093391750767,
          643.5669750977287,
          655.2488237367147,
          667.1427180413494,
          679.2525070055476,
          691.5821094890896,
          704.1355154858088,
          716.9167874147956,
          729.9300614350419,
          743.1795487839462,
          756.6695371401163,
          770.4043920109092,
          784.3885581451563,
          798.626560971533,
          813.1230080630369,
          827.8825906280481,
          842.9100850284559,
          858.2103543253414,
          873.7883498527173,
          889.649112819833,
          905.797775942566,
          922.2395651044235,
          938.9798010476961,
          956.0239010953076,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x2",
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.428320220902363e-248,
          2.6011538762290837e-245,
          5.082517348795381e-241,
          5.333453530973188e-237,
          8.256990827587541e-234,
          1.2596463430767196e-229,
          1.0501110333470017e-225,
          1.3819087591965063e-222,
          1.6461145945762073e-218,
          1.0902419946888113e-214,
          1.2193933541752307e-211,
          1.134276903471339e-207,
          5.9688333253244175e-204,
          5.67311209412967e-201,
          4.121282512163238e-197,
          1.7232711693791454e-193,
          1.3916164336944924e-190,
          7.896008557684633e-187,
          2.623827738249029e-183,
          1.7998966345091971e-180,
          7.977257836743746e-177,
          2.1069580605112442e-173,
          1.2274860580461422e-170,
          4.2499208336087735e-167,
          8.92356765673105e-164,
          4.414078714482218e-161,
          1.19399240983854e-157,
          1.9934653933464053e-154,
          8.370172870759755e-152,
          1.769011095491662e-148,
          2.3490638517520287e-145,
          8.369882593094965e-143,
          1.3822468899352927e-139,
          1.4602556651501059e-136,
          4.413861213653756e-134,
          5.696241846846968e-131,
          4.789029011469954e-128,
          1.227611536543043e-125,
          1.238127749254181e-122,
          8.286910955978269e-120,
          1.816453503779961e-117,
          1.4196305889495828e-114,
          7.566823544376118e-112,
          1.4526345665732377e-109,
          8.589013958469697e-107,
          3.6464304141581246e-104,
          6.0874578375898365e-102,
          2.7419057400268988e-99,
          9.275211363929551e-97,
          1.3381585506573132e-94,
          4.619266050598122e-92,
          1.2455531391372576e-89,
          1.5444238019065183e-87,
          4.1076164811640776e-85,
          8.832422060039479e-83,
          9.366417174621206e-81,
          1.9284425108361593e-78,
          3.308199634357488e-76,
          2.987217774749749e-74,
          4.7813272377619e-72,
          6.546895542694674e-70,
          5.01386298734379e-68,
          6.262757572016024e-66,
          6.848169283463627e-64,
          4.4321270048756904e-62,
          4.3354852483586696e-60,
          3.787936153636911e-58,
          2.064960170982087e-56,
          1.5870019492096616e-54,
          1.1085306515325207e-52,
          5.07465479094339e-51,
          3.0735047536851484e-49,
          1.7174138497546534e-47,
          6.583357779734459e-46,
          3.151336370739219e-44,
          1.4095791553500177e-42,
          4.5123649624760346e-41,
          1.7119343012929605e-39,
          6.133894316887858e-38,
          1.6355623662912352e-36,
          4.931453950425548e-35,
          1.4164385752346329e-33,
          3.1379522056030814e-32,
          7.539694001215332e-31,
          1.7373472090240245e-29,
          3.1898333394795165e-28,
          6.124058053025845e-27,
          1.1330115797770408e-25,
          1.7197547799750305e-24,
          2.645164964968553e-23,
          3.932545307544117e-22,
          4.9223554947964996e-21,
          6.081344542540695e-20,
          7.271375226082907e-19,
          7.486858539907457e-18,
          7.448099291086568e-17,
          7.168487519931627e-16,
          6.056499923561379e-15,
          4.862843878104405e-14,
          3.7704868232022443e-13,
          2.6077019928529966e-12,
          1.693342794847077e-11,
          1.0585684443349417e-10,
          5.979325890109996e-10,
          3.1456639879122196e-09,
          1.5866069876577182e-08,
          7.303969390404848e-08,
          3.117303446436826e-07,
          1.2694132469024808e-06,
          4.753731049931211e-06,
          1.6474641098790166e-05,
          5.419448726652532e-05,
          0.00016483020672010724,
          0.0004640766589280157,
          0.0012338318538313835,
          0.0030439046432489012,
          0.006962780848393107,
          0.014967643633200595,
          0.029922938199832928,
          0.05559265984962449,
          0.09665830374904037,
          0.15648860387315455,
          0.23598381546840624,
          0.33195213854204125,
          0.43506310027781286,
          0.5320529340673477,
          0.6056463571168386,
          0.6425065777813807,
          0.6365349193130792,
          0.5864627861802459,
          0.5036393079239253,
          0.40373359238330186,
          0.30111829276190694,
          0.20938676523234392,
          0.1356489084107456,
          0.0819110341811878,
          0.04613782679568445,
          0.024125036396816252,
          0.011795847137814773,
          0.0053846842398697,
          0.0022697126500595224,
          0.0008986909845210169,
          0.00033266325534829364,
          0.00011289753128085174,
          3.620242626221446e-05,
          1.0873450477077215e-05,
          2.967590507696957e-06,
          7.707221005141965e-07,
          1.8795489084164763e-07,
          4.120568213475952e-08,
          8.66780131608724e-09,
          1.7174993916086823e-09,
          3.0213426440507495e-10,
          5.147738047900595e-11,
          8.293806506908903e-12,
          1.1695352948718417e-12,
          1.6139451048813152e-13,
          2.1159476884437836e-14,
          2.3894550204096556e-15,
          2.6706298161388107e-16,
          2.851332649168858e-17,
          2.576178120284437e-18,
          2.331819375593988e-19,
          2.029070242811584e-20,
          1.4654750865067167e-21,
          1.0741103845887947e-22,
          7.623956171982208e-24,
          4.397974437265305e-25,
          2.609771356747055e-26,
          1.5122968327889706e-27,
          6.962334002311575e-29,
          3.344184633383014e-30,
          1.5834912657305577e-31,
          5.813655083137964e-33,
          2.2597116000957406e-34,
          8.751301802788624e-36,
          2.5603948937773476e-37,
          8.050741617911747e-39,
          2.5525292850055857e-40,
          5.94708792893869e-42,
          1.5121224537390521e-43,
          3.928961540724439e-45,
          7.284878184353445e-47,
          1.4971181712397808e-48,
          3.1912870908882595e-50,
          4.705926015592895e-52,
          7.812567346009867e-54,
          1.367761884822375e-55,
          1.6030975208258373e-57,
          2.148573917418882e-59,
          3.0930706902904774e-61,
          2.8797599984981886e-63,
          3.1136857768233395e-65,
          3.690492456711227e-67,
          2.7278810924063497e-69,
          2.377466492709984e-71,
          2.3231437989926457e-73,
          1.3625740258266482e-75,
          9.563428524319065e-78,
          7.715227593946453e-80,
          3.5888409196291957e-82,
          2.026344847409195e-84,
          1.3517207829819662e-86,
          4.98428155993595e-89,
          2.2612586639333951e-91,
          1.2493280094413272e-93,
          3.650066200964439e-96,
          1.328788059673696e-98,
          6.091209998365277e-101,
          1.4094343943122624e-103,
          4.1110720789679417e-106,
          1.5665896334487404e-108,
          2.8696671854996758e-111,
          6.695245450979264e-114,
          2.1252937336457638e-116,
          3.0807587518158134e-119,
          5.738517351694725e-122,
          1.5208366460802909e-124,
          1.7438959750530325e-127,
          2.5879425250696506e-130,
          5.740295603789154e-133,
          5.20496288561242e-136,
          6.1393128785796325e-139,
          1.1427796420942714e-141,
          8.191180577079527e-145,
          7.658965864707007e-148,
          1.1999302075491526e-150,
          6.796806756795694e-154,
          5.0230193716995935e-157,
          6.645132477893773e-160,
          2.973656268263522e-163,
          1.7311878139146936e-166,
          1.9408615627645946e-169,
          6.859650266448632e-173,
          3.1341937793601447e-176,
          2.9896337678381914e-179,
          8.343274910716416e-183,
          2.9792047952440938e-186,
          2.4286411025674965e-189,
          5.350477745989938e-193,
          1.48602188838742e-196,
          1.0404474537316912e-199,
          1.8091230030634097e-203
         ],
         "yaxis": "y2",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "f⋅[(β₁₂ᶻ⁽¹ ⁻¹⁾t)*(𝕟₁*𝕟₂)]",
         "line": {
          "color": "rgba(165, 42, 42, 1.000)",
          "dash": "dash",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "f⋅[(β₁₂ᶻ⁽¹ ⁻¹⁾t)*(𝕟₁*𝕟₂)]",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.273507681793024,
          10.459989534302535,
          10.649856353504289,
          10.84316958237171,
          11.039991779173976,
          11.240386637720556,
          11.44441900797323,
          11.652154917032231,
          11.863661590503344,
          12.079007474252842,
          12.298262256557319,
          12.521496890655566,
          12.748783617709826,
          12.98019599018381,
          13.215808895645086,
          13.455698580999508,
          13.699942677165545,
          13.948620224196498,
          14.201811696858716,
          14.459599030674116,
          14.722065648435406,
          14.989296487202608,
          15.261378025789629,
          15.538398312749738,
          15.820446994869037,
          16.10761534617715,
          16.39999629748447,
          16.69768446645562,
          17.00077618822873,
          17.309369546590553,
          17.623564405717435,
          17.94346244249247,
          18.269167179409244,
          18.600784018072822,
          18.938420273308882,
          19.282185207891956,
          19.632190067904055,
          19.988548118735103,
          20.35137468173687,
          20.72078717154221,
          21.096905134061714,
          21.479850285170084,
          21.869746550094703,
          22.266720103519187,
          22.67089941041491,
          23.08241526761366,
          23.501400846134892,
          23.927991734281377,
          24.36232598151701,
          24.804544143141136,
          25.25478932577379,
          25.713207233666548,
          26.179946215854002,
          26.65515731416115,
          27.138994312082165,
          27.6316137845464,
          28.133175148587764,
          28.6438407149338,
          29.163775740531204,
          29.693148482024785,
          30.232130250207152,
          30.78089546545674,
          31.339621714182158,
          31.90848980629108,
          32.48768383370232,
          33.07739122991996,
          33.6778028306889,
          34.289112935751355,
          34.911519371724424,
          35.54522355611888,
          36.19043056252011,
          36.847349186952165,
          37.51619201544639,
          38.19717549283665,
          38.89051999280318,
          39.59644988918792,
          40.31519362860439,
          41.04698380436544,
          41.792057231753,
          42.55065502465411,
          43.323022673587985,
          44.10941012514944,
          44.910071862894306,
          45.72526698969311,
          46.55525931157958,
          47.400317423121166,
          48.26071479433915,
          49.13672985920654,
          50.02864610575234,
          50.93675216780135,
          51.861341918379274,
          52.80271456481317,
          53.76117474555825,
          54.73703262878217,
          55.73060401273886,
          56.74221042796429,
          57.77217924132721,
          58.8208437619687,
          59.888543349164614,
          60.975623522145916,
          62.08243607191253,
          63.20933917507671,
          64.35669750977287,
          65.52488237367147,
          66.71427180413495,
          67.92525070055476,
          69.15821094890896,
          70.41355154858087,
          71.69167874147956,
          72.9930061435042,
          74.31795487839462,
          75.66695371401163,
          77.04043920109092,
          78.43885581451562,
          79.8626560971533,
          81.31230080630368,
          82.78825906280481,
          84.29100850284559,
          85.82103543253415,
          87.37883498527172,
          88.9649112819833,
          90.5797775942566,
          92.22395651044235,
          93.8979801047696,
          95.60239010953076,
          97.33773809039202,
          99.10458562488608,
          100.90350448414475,
          102.73507681793026,
          104.59989534302535,
          106.4985635350429,
          108.4316958237171,
          110.39991779173975,
          112.40386637720557,
          114.44419007973231,
          116.5215491703223,
          118.63661590503344,
          120.79007474252845,
          122.98262256557321,
          125.21496890655568,
          127.48783617709826,
          129.8019599018381,
          132.15808895645085,
          134.55698580999507,
          136.99942677165546,
          139.48620224196497,
          142.01811696858715,
          144.59599030674116,
          147.22065648435404,
          149.89296487202606,
          152.6137802578963,
          155.38398312749737,
          158.20446994869036,
          161.07615346177147,
          163.9999629748447,
          166.9768446645562,
          170.0077618822873,
          173.0936954659055,
          176.23564405717434,
          179.43462442492472,
          182.69167179409243,
          186.00784018072818,
          189.3842027330888,
          192.8218520789196,
          196.32190067904054,
          199.88548118735102,
          203.51374681736868,
          207.2078717154221,
          210.96905134061717,
          214.79850285170085,
          218.69746550094703,
          222.66720103519188,
          226.70899410414913,
          230.82415267613658,
          235.01400846134894,
          239.27991734281375,
          243.6232598151701,
          248.04544143141135,
          252.5478932577379,
          257.13207233666543,
          261.79946215854,
          266.5515731416115,
          271.3899431208216,
          276.31613784546397,
          281.33175148587765,
          286.438407149338,
          291.637757405312,
          296.9314848202479,
          302.32130250207155,
          307.8089546545674,
          313.3962171418216,
          319.08489806291084,
          324.8768383370232,
          330.7739122991996,
          336.7780283068889,
          342.89112935751353,
          349.1151937172442,
          355.4522355611888,
          361.9043056252011,
          368.4734918695216,
          375.16192015446387,
          381.97175492836647,
          388.9051999280318,
          395.96449889187926,
          403.15193628604396,
          410.4698380436544,
          417.92057231753,
          425.5065502465411,
          433.23022673587985,
          441.09410125149435,
          449.100718628943,
          457.2526698969311,
          465.55259311579584,
          474.0031742312117,
          482.6071479433915,
          491.36729859206537,
          500.2864610575233,
          509.36752167801353,
          518.6134191837928,
          528.0271456481318,
          537.6117474555825,
          547.3703262878216,
          557.3060401273885,
          567.4221042796428,
          577.7217924132722,
          588.2084376196871,
          598.8854334916462,
          609.7562352214592,
          620.8243607191254,
          632.093391750767,
          643.5669750977287,
          655.2488237367147,
          667.1427180413494,
          679.2525070055476,
          691.5821094890896,
          704.1355154858088,
          716.9167874147956,
          729.9300614350419,
          743.1795487839462,
          756.6695371401163,
          770.4043920109092,
          784.3885581451563,
          798.626560971533,
          813.1230080630369,
          827.8825906280481,
          842.9100850284559,
          858.2103543253414,
          873.7883498527173,
          889.649112819833,
          905.797775942566,
          922.2395651044235,
          938.9798010476961,
          956.0239010953076,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x2",
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.5732759659204021e-248,
          2.865136835034455e-245,
          5.598326113580841e-241,
          5.874729022832347e-237,
          9.09496696172356e-234,
          1.3874839046037687e-229,
          1.1566835126572157e-225,
          1.5221543503495396e-222,
          1.8131736083393208e-218,
          1.2008872395556997e-214,
          1.3431457659508242e-211,
          1.2493911132915762e-207,
          6.574591522190305e-204,
          6.248858469585925e-201,
          4.5395385644391197e-197,
          1.8981605622266735e-193,
          1.532847226323116e-190,
          8.697349732022197e-187,
          2.8901117962851175e-183,
          1.982562505784135e-180,
          8.786844745900319e-177,
          2.3207866340437384e-173,
          1.3520597729872665e-170,
          4.681231986169679e-167,
          9.82919258521041e-164,
          4.862049736149758e-161,
          1.315166959341652e-157,
          2.1957759516031867e-154,
          9.219635495915501e-152,
          1.9485424901604065e-148,
          2.587462983643151e-145,
          9.219315758879804e-143,
          1.5225267969178134e-139,
          1.608452438367332e-136,
          4.861810161843534e-134,
          6.274335588452742e-131,
          5.275052564250058e-128,
          1.3521979859037573e-125,
          1.3637814561009984e-122,
          9.127923590220106e-120,
          2.000799679852932e-117,
          1.5637044504409351e-114,
          8.334756762882346e-112,
          1.6000578983689258e-109,
          9.460686080099219e-107,
          4.016495214477758e-104,
          6.705254864615232e-102,
          3.020173164585054e-99,
          1.0216523510731468e-96,
          1.4739640701928723e-94,
          5.0880608922604226e-92,
          1.3719604255433364e-89,
          1.701162535667157e-87,
          4.5244856107625845e-85,
          9.728796907423441e-83,
          1.0316985513448765e-80,
          2.1241541004306202e-78,
          3.64393845234029e-76,
          3.2903811492739954e-74,
          5.266569161654115e-72,
          7.211319463226327e-70,
          5.522704236044751e-68,
          6.898345219963355e-66,
          7.543168532208407e-64,
          4.881929690999143e-62,
          4.7754800653427166e-60,
          4.1723619281906805e-58,
          2.2745265102643113e-56,
          1.7480618057644e-54,
          1.2210319548934095e-52,
          5.589665609361849e-51,
          3.385425123408298e-49,
          1.891708801581497e-47,
          7.251482138485623e-46,
          3.471155627470285e-44,
          1.5526329283313823e-42,
          4.970310747571603e-41,
          1.8856731509110673e-39,
          6.75640403673532e-38,
          1.801550467460475e-36,
          5.431931764115308e-35,
          1.560188489253011e-33,
          3.456413145340268e-32,
          8.304873927369243e-31,
          1.9136651350420328e-29,
          3.5135595329765977e-28,
          6.745569521265967e-27,
          1.2479973758591597e-25,
          1.8942873054769956e-24,
          2.913614471305719e-23,
          4.331647012140946e-22,
          5.421909934725303e-21,
          6.6985211504014e-20,
          8.009324320254985e-19,
          8.246676360599879e-18,
          8.203983557029185e-17,
          7.895994863101304e-16,
          6.671155128867437e-15,
          5.356358670474777e-14,
          4.1531417198700846e-13,
          2.8723494995026073e-12,
          1.8651948507137323e-11,
          1.1659992397935515e-10,
          6.586148944508096e-10,
          3.4649075722788668e-09,
          1.7476267608017636e-08,
          8.045226364213006e-08,
          3.433668808288298e-07,
          1.3982420209040605e-06,
          5.236172323165322e-06,
          1.8146600817228667e-05,
          5.969451601541946e-05,
          0.00018155830807086435,
          0.0005111743453263036,
          0.0013590495837085988,
          0.0033528209904859782,
          0.007669411665842796,
          0.016486662899513577,
          0.03295972346437623,
          0.06123458475421324,
          0.10646785221518915,
          0.17237014208097676,
          0.2599330736829342,
          0.3656409212453299,
          0.4792162914934256,
          0.5860493196944037,
          0.6671115087183952,
          0.7077125577138437,
          0.7011348543337653,
          0.6459810572598257,
          0.5547520836391356,
          0.44470724998212635,
          0.3316778450437379,
          0.23063677213345496,
          0.1494154912062625,
          0.09022392845459581,
          0.050820210310815565,
          0.026573410769251085,
          0.012992970713437474,
          0.005931158975894991,
          0.002500058677057859,
          0.000989896317397939,
          0.0003664242070686813,
          0.0001243551480799574,
          3.987649709976416e-05,
          1.1976962905001612e-05,
          3.268761972370269e-06,
          8.489402722147429e-07,
          2.070298439460171e-07,
          4.538751773815595e-08,
          9.547469319840617e-09,
          1.8918030248103318e-09,
          3.3279692446644827e-10,
          5.67016585713494e-11,
          9.135518949014434e-12,
          1.288227768388695e-12,
          1.7777393379059562e-13,
          2.330688591155216e-14,
          2.6319533254828372e-15,
          2.9416636704528097e-16,
          3.1407054679569386e-17,
          2.8376263678553356e-18,
          2.5684684196180106e-19,
          2.234994225708688e-20,
          1.6142015624476302e-21,
          1.183118482878768e-22,
          8.39768760189669e-24,
          4.844311086284616e-25,
          2.874628876656008e-26,
          1.6657751010913355e-27,
          7.668919470752191e-29,
          3.683575456194203e-30,
          1.7441948340161891e-31,
          6.403664726298915e-33,
          2.489042651861459e-34,
          9.639444009372735e-36,
          2.8202413511308685e-37,
          8.867786165831724e-39,
          2.8115774863638156e-40,
          6.550639253642664e-42,
          1.6655830248578813e-43,
          4.327699540052858e-45,
          8.024197651462494e-47,
          1.6490560047285504e-48,
          3.51516082106195e-50,
          5.183515705640888e-52,
          8.605440333153465e-54,
          1.5065717540101453e-55,
          1.7657908665246558e-57,
          2.3666259539076025e-59,
          3.406976745629566e-61,
          3.1720178199212646e-63,
          3.4296839927180594e-65,
          4.0650289757055894e-67,
          3.004725199409589e-69,
          2.61874811966089e-71,
          2.5589123859235715e-73,
          1.500857395455868e-75,
          1.0533990927891025e-77,
          8.49822187456911e-80,
          3.9530611425477057e-82,
          2.2319922384641897e-84,
          1.4889026909925733e-86,
          5.4901206822328675e-89,
          2.490746722361833e-91,
          1.3761183956098156e-93,
          4.0204999858979725e-96,
          1.4636425974323134e-98,
          6.709387820434158e-101,
          1.5524734759493684e-103,
          4.528291906362931e-106,
          1.7255779080183136e-108,
          3.1609007189471863e-111,
          7.374724938997852e-114,
          2.3409831372083358e-116,
          3.3934153070861544e-119,
          6.320901501859826e-122,
          1.6751815932826968e-124,
          1.920878514821369e-127,
          2.850584705230299e-130,
          6.322860223188958e-133,
          5.7331982643698045e-136,
          6.762372511279591e-139,
          1.2587567682225912e-141,
          9.022477835041553e-145,
          8.436250318668557e-148,
          1.321707365541812e-150,
          7.486593383601638e-154,
          5.532789873166524e-157,
          7.31952615725239e-160,
          3.275443327975789e-163,
          1.9068806422173105e-166,
          2.1378335230366943e-169,
          7.555814684192475e-173,
          3.452273288191175e-176,
          3.2930423339329056e-179,
          9.190007746165005e-183,
          3.2815549575789044e-186,
          2.6751162803687965e-189,
          5.893480972102932e-193,
          1.6368335948885183e-196,
          1.1460392066178312e-199,
          1.992725229581391e-203
         ],
         "yaxis": "y2",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "f⋅[(β₁₂ᶻ⁽² ⁻²⁾t)*(𝕟₁*𝕟₂)]",
         "line": {
          "color": "rgba(165, 42, 42, 1.000)",
          "dash": "dot",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "f⋅[(β₁₂ᶻ⁽² ⁻²⁾t)*(𝕟₁*𝕟₂)]",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.273507681793024,
          10.459989534302535,
          10.649856353504289,
          10.84316958237171,
          11.039991779173976,
          11.240386637720556,
          11.44441900797323,
          11.652154917032231,
          11.863661590503344,
          12.079007474252842,
          12.298262256557319,
          12.521496890655566,
          12.748783617709826,
          12.98019599018381,
          13.215808895645086,
          13.455698580999508,
          13.699942677165545,
          13.948620224196498,
          14.201811696858716,
          14.459599030674116,
          14.722065648435406,
          14.989296487202608,
          15.261378025789629,
          15.538398312749738,
          15.820446994869037,
          16.10761534617715,
          16.39999629748447,
          16.69768446645562,
          17.00077618822873,
          17.309369546590553,
          17.623564405717435,
          17.94346244249247,
          18.269167179409244,
          18.600784018072822,
          18.938420273308882,
          19.282185207891956,
          19.632190067904055,
          19.988548118735103,
          20.35137468173687,
          20.72078717154221,
          21.096905134061714,
          21.479850285170084,
          21.869746550094703,
          22.266720103519187,
          22.67089941041491,
          23.08241526761366,
          23.501400846134892,
          23.927991734281377,
          24.36232598151701,
          24.804544143141136,
          25.25478932577379,
          25.713207233666548,
          26.179946215854002,
          26.65515731416115,
          27.138994312082165,
          27.6316137845464,
          28.133175148587764,
          28.6438407149338,
          29.163775740531204,
          29.693148482024785,
          30.232130250207152,
          30.78089546545674,
          31.339621714182158,
          31.90848980629108,
          32.48768383370232,
          33.07739122991996,
          33.6778028306889,
          34.289112935751355,
          34.911519371724424,
          35.54522355611888,
          36.19043056252011,
          36.847349186952165,
          37.51619201544639,
          38.19717549283665,
          38.89051999280318,
          39.59644988918792,
          40.31519362860439,
          41.04698380436544,
          41.792057231753,
          42.55065502465411,
          43.323022673587985,
          44.10941012514944,
          44.910071862894306,
          45.72526698969311,
          46.55525931157958,
          47.400317423121166,
          48.26071479433915,
          49.13672985920654,
          50.02864610575234,
          50.93675216780135,
          51.861341918379274,
          52.80271456481317,
          53.76117474555825,
          54.73703262878217,
          55.73060401273886,
          56.74221042796429,
          57.77217924132721,
          58.8208437619687,
          59.888543349164614,
          60.975623522145916,
          62.08243607191253,
          63.20933917507671,
          64.35669750977287,
          65.52488237367147,
          66.71427180413495,
          67.92525070055476,
          69.15821094890896,
          70.41355154858087,
          71.69167874147956,
          72.9930061435042,
          74.31795487839462,
          75.66695371401163,
          77.04043920109092,
          78.43885581451562,
          79.8626560971533,
          81.31230080630368,
          82.78825906280481,
          84.29100850284559,
          85.82103543253415,
          87.37883498527172,
          88.9649112819833,
          90.5797775942566,
          92.22395651044235,
          93.8979801047696,
          95.60239010953076,
          97.33773809039202,
          99.10458562488608,
          100.90350448414475,
          102.73507681793026,
          104.59989534302535,
          106.4985635350429,
          108.4316958237171,
          110.39991779173975,
          112.40386637720557,
          114.44419007973231,
          116.5215491703223,
          118.63661590503344,
          120.79007474252845,
          122.98262256557321,
          125.21496890655568,
          127.48783617709826,
          129.8019599018381,
          132.15808895645085,
          134.55698580999507,
          136.99942677165546,
          139.48620224196497,
          142.01811696858715,
          144.59599030674116,
          147.22065648435404,
          149.89296487202606,
          152.6137802578963,
          155.38398312749737,
          158.20446994869036,
          161.07615346177147,
          163.9999629748447,
          166.9768446645562,
          170.0077618822873,
          173.0936954659055,
          176.23564405717434,
          179.43462442492472,
          182.69167179409243,
          186.00784018072818,
          189.3842027330888,
          192.8218520789196,
          196.32190067904054,
          199.88548118735102,
          203.51374681736868,
          207.2078717154221,
          210.96905134061717,
          214.79850285170085,
          218.69746550094703,
          222.66720103519188,
          226.70899410414913,
          230.82415267613658,
          235.01400846134894,
          239.27991734281375,
          243.6232598151701,
          248.04544143141135,
          252.5478932577379,
          257.13207233666543,
          261.79946215854,
          266.5515731416115,
          271.3899431208216,
          276.31613784546397,
          281.33175148587765,
          286.438407149338,
          291.637757405312,
          296.9314848202479,
          302.32130250207155,
          307.8089546545674,
          313.3962171418216,
          319.08489806291084,
          324.8768383370232,
          330.7739122991996,
          336.7780283068889,
          342.89112935751353,
          349.1151937172442,
          355.4522355611888,
          361.9043056252011,
          368.4734918695216,
          375.16192015446387,
          381.97175492836647,
          388.9051999280318,
          395.96449889187926,
          403.15193628604396,
          410.4698380436544,
          417.92057231753,
          425.5065502465411,
          433.23022673587985,
          441.09410125149435,
          449.100718628943,
          457.2526698969311,
          465.55259311579584,
          474.0031742312117,
          482.6071479433915,
          491.36729859206537,
          500.2864610575233,
          509.36752167801353,
          518.6134191837928,
          528.0271456481318,
          537.6117474555825,
          547.3703262878216,
          557.3060401273885,
          567.4221042796428,
          577.7217924132722,
          588.2084376196871,
          598.8854334916462,
          609.7562352214592,
          620.8243607191254,
          632.093391750767,
          643.5669750977287,
          655.2488237367147,
          667.1427180413494,
          679.2525070055476,
          691.5821094890896,
          704.1355154858088,
          716.9167874147956,
          729.9300614350419,
          743.1795487839462,
          756.6695371401163,
          770.4043920109092,
          784.3885581451563,
          798.626560971533,
          813.1230080630369,
          827.8825906280481,
          842.9100850284559,
          858.2103543253414,
          873.7883498527173,
          889.649112819833,
          905.797775942566,
          922.2395651044235,
          938.9798010476961,
          956.0239010953076,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x2",
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          3.4014950734334996e-248,
          6.194557750954432e-245,
          1.210383880979135e-240,
          1.270143462544449e-236,
          1.9663737312127937e-233,
          2.9998040828246994e-229,
          2.5008030091678994e-225,
          3.290967786881761e-222,
          3.9201648214575713e-218,
          2.5963735019038184e-214,
          2.9039429856871925e-211,
          2.7012411100850096e-207,
          1.4214569571387848e-203,
          1.3510319714599338e-200,
          9.814691380966712e-197,
          4.1039105286417724e-193,
          3.314086277046756e-190,
          1.880407055484024e-186,
          6.248554767049204e-183,
          4.286391416558319e-180,
          1.8997562895279827e-176,
          5.017647554014364e-173,
          2.9232154793092955e-170,
          1.012103908244734e-166,
          2.12511669145487e-163,
          1.0511975382924509e-160,
          2.843451517627441e-157,
          4.747368702967826e-154,
          1.993327642290815e-151,
          4.2128385764661194e-148,
          5.594214099879671e-145,
          1.993258513671598e-142,
          3.2917730335101606e-139,
          3.477548226421826e-136,
          1.0511457412244227e-133,
          1.3565402418580048e-130,
          1.1404906512318214e-127,
          2.923514301998202e-125,
          2.9485582978785626e-122,
          1.9734991060291822e-119,
          4.3258210265518024e-117,
          3.380801016285266e-114,
          1.8020127861436616e-111,
          3.45939884445271e-109,
          2.0454438884110249e-106,
          8.683847576939683e-104,
          1.449706973357442e-101,
          6.529753433462085e-99,
          2.20885942086074e-96,
          3.186778182456965e-94,
          1.1000621908203173e-91,
          2.9662416063803852e-89,
          3.677991725244619e-87,
          9.782146202065816e-85,
          2.1034106836861306e-82,
          2.230579768384783e-80,
          4.592518963194965e-78,
          7.878362704332755e-76,
          7.113955536990774e-74,
          1.1386565005321909e-71,
          1.55912046954644e-69,
          1.1940340828855556e-67,
          1.4914539971899662e-65,
          1.630867766124868e-63,
          1.0554956760600804e-61,
          1.032480776889016e-59,
          9.02083858823795e-58,
          4.917631036543387e-56,
          3.7793901064816147e-54,
          2.6399273039456963e-52,
          1.2085114400932087e-50,
          7.319444984983604e-49,
          4.089961525081738e-47,
          1.567803824850255e-45,
          7.504798281879118e-44,
          3.356863875741063e-42,
          1.0746040674057907e-40,
          4.0769121704452035e-39,
          1.4607656598654314e-37,
          3.895035055737107e-36,
          1.1744086565293632e-34,
          3.3731993463187955e-33,
          7.4729243567562e-32,
          1.795551979522328e-30,
          4.1374321289137766e-29,
          7.596477477899683e-28,
          1.4584231877378234e-26,
          2.698227785587135e-25,
          4.095536369220563e-24,
          6.299368632529133e-23,
          9.36522027337435e-22,
          1.1722418908737938e-20,
          1.4482511133417538e-19,
          1.731652793725879e-18,
          1.782969397639689e-17,
          1.773739016945999e-16,
          1.7071504433097123e-15,
          1.4423344534903596e-14,
          1.1580694057386093e-13,
          8.979283612932251e-13,
          6.210151863612472e-12,
          4.032637142578253e-11,
          2.5209440401415455e-10,
          1.4239557250553572e-09,
          7.4912896988889e-09,
          3.778449519242514e-08,
          1.7394149809260089e-07,
          7.423750052879047e-07,
          3.023063625579781e-06,
          1.132084564100994e-05,
          3.923378645351438e-05,
          0.00012906229201731763,
          0.00039253742116544344,
          0.0011051824695458333,
          0.002938327771906313,
          0.00724895334848043,
          0.01658162112851951,
          0.03564492425030253,
          0.07126043962682542,
          0.13239199153681125,
          0.23018839836986,
          0.3726721832634534,
          0.5619872728670797,
          0.7905325061862674,
          1.0360876857801242,
          1.267065611444308,
          1.4423257962940346,
          1.5301071335328935,
          1.5158858359814786,
          1.3966407873746358,
          1.1993995461384674,
          0.961477549203783,
          0.7171027717462723,
          0.49864732008767176,
          0.32304317121848275,
          0.1950682873138426,
          0.10987563450253544,
          0.057452937548087744,
          0.02809140089111316,
          0.012823438782054348,
          0.00540524196486532,
          0.002140201413977114,
          0.0007922260061995731,
          0.0002688615555775097,
          8.62148226813347e-05,
          2.5894745231314318e-05,
          7.067213881157565e-06,
          1.835447954541397e-06,
          4.476080544611282e-07,
          9.812990303414067e-08,
          2.0642068244013595e-08,
          4.090165240040606e-09,
          7.195222729816473e-10,
          1.2259159642925062e-10,
          1.9751412575702656e-11,
          2.7852077464813146e-12,
          3.8435542973533095e-13,
          5.0390560411848496e-14,
          5.690404267314493e-15,
          6.360012292496802e-16,
          6.790349822773354e-17,
          6.135078854305247e-18,
          5.553146977929623e-19,
          4.832160417230357e-20,
          3.489978097378542e-21,
          2.5579566318779283e-22,
          1.8156187232780984e-23,
          1.0473623605211858e-24,
          6.215079981962805e-26,
          3.601482462420734e-27,
          1.6580556980072493e-28,
          7.964059731590068e-30,
          3.7710295355229457e-31,
          1.3845017969039305e-32,
          5.381424811202486e-34,
          2.0840921757383737e-35,
          6.0974916477243354e-37,
          1.9172561971791062e-38,
          6.078759973205438e-40,
          1.416278366400275e-41,
          3.601067184760634e-43,
          9.356685656974558e-45,
          1.7348684764111657e-46,
          3.565335006321382e-48,
          7.599939536465034e-50,
          1.1206999609561633e-51,
          1.8605358202890384e-53,
          3.2572774961585146e-55,
          3.8177211521080144e-57,
          5.116754274045682e-59,
          7.366040584483057e-61,
          6.85804856937053e-63,
          7.4151346981515156e-65,
          8.788779803254528e-67,
          6.4963542215138e-69,
          5.661854004347277e-71,
          5.5324863931134136e-73,
          3.2449227898696937e-75,
          2.2774973381006535e-77,
          1.8373546958991762e-79,
          8.546700192862236e-82,
          4.825669982593419e-84,
          3.21907616841415e-86,
          1.1869893685336623e-88,
          5.385109090081311e-91,
          2.9752313291009884e-93,
          8.692506077133651e-96,
          3.164462683138269e-98,
          1.4506005374340135e-100,
          3.356519132349811e-103,
          9.790375588399215e-106,
          3.7307788843746574e-108,
          6.834012885222729e-111,
          1.59444948574251e-113,
          5.061313323722332e-116,
          7.336720129970745e-119,
          1.366608006730486e-121,
          3.6218197316222555e-124,
          4.153027788107529e-127,
          6.1630953763240275e-130,
          1.3670314912999827e-132,
          1.239543860943849e-135,
          1.4620560715413245e-138,
          2.7214900872494755e-141,
          1.9507012482773482e-144,
          1.823956160190571e-147,
          2.857592176958675e-150,
          1.618635958518749e-153,
          1.1962146440665103e-156,
          1.582515254988729e-159,
          7.08165927959263e-163,
          4.122763743062259e-166,
          4.622094504682853e-169,
          1.6336019224079033e-172,
          7.463973794996921e-176,
          7.119709140746799e-179,
          1.986921986385795e-182,
          7.094872904179773e-186,
          5.783724563041208e-189,
          1.274197720312498e-192,
          3.5389095935159225e-196,
          2.4777895294368316e-199,
          4.308363693309402e-203
         ],
         "yaxis": "y2",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "f*Dₘ",
         "line": {
          "color": "rgba(128, 128, 128, 1.000)",
          "dash": "dashdot",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "f*Dₘ",
         "showlegend": true,
         "text": [
          null,
          null
         ],
         "type": "scatter",
         "x": [
          125.99210498948732,
          125.99210498948732
         ],
         "xaxis": "x2",
         "y": [
          0,
          1.6066124902095382
         ],
         "yaxis": "y2",
         "zmax": 0.1,
         "zmin": -0.1
        }
       ],
       "layout": {
        "annotations": [],
        "height": 288,
        "legend": {
         "bgcolor": "rgba(255, 255, 255, 1.000)",
         "bordercolor": "rgba(0, 0, 0, 1.000)",
         "font": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 14
         },
         "tracegroupgap": 0,
         "x": 1,
         "y": 1
        },
        "margin": {
         "b": 20,
         "l": 0,
         "r": 0,
         "t": 20
        },
        "paper_bgcolor": "rgba(255, 255, 255, 1.000)",
        "plot_bgcolor": "rgba(255, 255, 255, 1.000)",
        "showlegend": true,
        "width": 792,
        "xaxis1": {
         "anchor": "y1",
         "domain": [
          0.09890572390572391,
          0.4971334075664785
         ],
         "gridcolor": "rgba(0, 0, 0, 0.100)",
         "gridwidth": 0.5,
         "linecolor": "rgba(0, 0, 0, 1.000)",
         "mirror": false,
         "range": [
          1.6020599913279623,
          2.6020599913279625
         ],
         "showgrid": true,
         "showline": true,
         "showticklabels": true,
         "tickangle": 0,
         "tickcolor": "rgb(0, 0, 0)",
         "tickfont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "tickmode": "array",
         "ticks": "inside",
         "ticktext": [
          "10^1.7781513",
          "10^1.9030900",
          "10^2.0000000",
          "10^2.0791812",
          "10^2.1461280",
          "10^2.2041200"
         ],
         "tickvals": [
          60,
          79.99999999999999,
          100,
          119.99999999999996,
          140.00000000000006,
          159.99999999999991
         ],
         "title": "Diameter (nm)",
         "titlefont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "type": "log",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1.000)"
        },
        "xaxis2": {
         "anchor": "y2",
         "domain": [
          0.5968013468013469,
          0.9950290304621014
         ],
         "gridcolor": "rgba(0, 0, 0, 0.100)",
         "gridwidth": 0.5,
         "linecolor": "rgba(0, 0, 0, 1.000)",
         "mirror": false,
         "range": [
          1.954242509439325,
          2.255272505103306
         ],
         "showgrid": true,
         "showline": true,
         "showticklabels": true,
         "tickangle": 0,
         "tickcolor": "rgb(0, 0, 0)",
         "tickfont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "tickmode": "array",
         "ticks": "inside",
         "ticktext": [
          "10^2.0000000",
          "10^2.0791812",
          "10^2.1461280",
          "10^2.2041200"
         ],
         "tickvals": [
          100,
          119.99999999999996,
          140.00000000000006,
          159.99999999999991
         ],
         "title": "Diameter (nm)",
         "titlefont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "type": "log",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1.000)"
        },
        "yaxis1": {
         "anchor": "x1",
         "domain": [
          0.1294109069699621,
          0.9863298337707787
         ],
         "gridcolor": "rgba(0, 0, 0, 0.100)",
         "gridwidth": 0.5,
         "linecolor": "rgba(0, 0, 0, 1.000)",
         "mirror": false,
         "range": [
          -1.873897943466776,
          64.33716272569265
         ],
         "showgrid": true,
         "showline": true,
         "showticklabels": true,
         "tickangle": 0,
         "tickcolor": "rgb(0, 0, 0)",
         "tickfont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "tickmode": "array",
         "ticks": "inside",
         "ticktext": [
          "0",
          "10",
          "20",
          "30",
          "40",
          "50",
          "60"
         ],
         "tickvals": [
          0,
          10,
          20,
          30,
          40,
          50,
          60
         ],
         "title": "dN/dlnD (m⁻³) × 10⁻¹⁰",
         "titlefont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "type": "-",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1.000)"
        },
        "yaxis2": {
         "anchor": "x2",
         "domain": [
          0.1294109069699621,
          0.9863298337707787
         ],
         "gridcolor": "rgba(0, 0, 0, 0.100)",
         "gridwidth": 0.5,
         "linecolor": "rgba(0, 0, 0, 1.000)",
         "mirror": false,
         "range": [
          -0.04819837470628614,
          1.6548108649158244
         ],
         "showgrid": true,
         "showline": true,
         "showticklabels": true,
         "tickangle": 0,
         "tickcolor": "rgb(0, 0, 0)",
         "tickfont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "tickmode": "array",
         "ticks": "inside",
         "ticktext": [
          "0.0",
          "0.5",
          "1.0",
          "1.5"
         ],
         "tickvals": [
          0,
          0.5,
          1,
          1.5
         ],
         "title": "",
         "titlefont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "type": "-",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1.000)"
        }
       }
      },
      "image/svg+xml": [
       "<svg class=\"main-svg\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"792\" height=\"288\" viewBox=\"0 0 792 288\"><rect x=\"0\" y=\"0\" width=\"792\" height=\"288\" style=\"fill: rgb(255, 255, 255); fill-opacity: 1;\"/><defs id=\"defs-66de9d\"><g class=\"clips\"><clipPath id=\"clip66de9dxyplot\" class=\"plotclip\"><rect width=\"244.91002545136405\" height=\"212.51589384660252\"/></clipPath><clipPath id=\"clip66de9dx2y2plot\" class=\"plotclip\"><rect width=\"244.91002545136405\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip66de9dx\"><rect x=\"60.82702020202021\" y=\"0\" width=\"244.91002545136405\" height=\"288\"/></clipPath><clipPath class=\"axesclip\" id=\"clip66de9dy\"><rect x=\"0\" y=\"23.390201224846894\" width=\"792\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip66de9dxy\"><rect x=\"60.82702020202021\" y=\"23.390201224846894\" width=\"244.91002545136405\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip66de9dy2\"><rect x=\"0\" y=\"23.390201224846894\" width=\"792\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip66de9dxy2\"><rect x=\"60.82702020202021\" y=\"23.390201224846894\" width=\"244.91002545136405\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip66de9dx2\"><rect x=\"367.03282828282835\" y=\"0\" width=\"244.91002545136405\" height=\"288\"/></clipPath><clipPath class=\"axesclip\" id=\"clip66de9dx2y\"><rect x=\"367.03282828282835\" y=\"23.390201224846894\" width=\"244.91002545136405\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip66de9dx2y2\"><rect x=\"367.03282828282835\" y=\"23.390201224846894\" width=\"244.91002545136405\" height=\"212.51589384660252\"/></clipPath></g><g class=\"gradients\"/></defs><g class=\"bglayer\"/><g class=\"layer-below\"><g class=\"imagelayer\"/><g class=\"shapelayer\"/></g><g class=\"cartesianlayer\"><g class=\"subplot xy\"><g class=\"layer-subplot\"><g class=\"shapelayer\"/><g class=\"imagelayer\"/></g><g class=\"gridlayer\"><g class=\"x\"><path class=\"xgrid crisp\" transform=\"translate(84.55702020202021,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(103.9570202020202,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(120.34702020202022,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(134.55702020202023,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(147.0770202020202,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(158.2870202020202,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(232.00702020202021,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(275.1370202020202,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/></g><g class=\"y\"><path class=\"ygrid crisp\" transform=\"translate(0,229.8902012248469)\" d=\"M60.82702020202021,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,197.7902012248469)\" d=\"M60.82702020202021,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,165.7002012248469)\" d=\"M60.82702020202021,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,133.6002012248469)\" d=\"M60.82702020202021,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,101.50020122484689)\" d=\"M60.82702020202021,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,69.4102012248469)\" d=\"M60.82702020202021,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,37.31020122484689)\" d=\"M60.82702020202021,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/></g></g><g class=\"zerolinelayer\"/><path class=\"xlines-below\"/><path class=\"ylines-below\"/><g class=\"overlines-below\"/><g class=\"xaxislayer-below\"/><g class=\"yaxislayer-below\"/><g class=\"overaxes-below\"/><g class=\"plot\" transform=\"translate(60.82702020202021, 23.390201224846894)\" clip-path=\"url('#clip66de9dxyplot')\"><g class=\"scatterlayer mlayer\"><g class=\"trace scatter trace1fa484\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-146.49,206.5L63.98,205.92L63.98,205.44L65.89,205.44L65.89,204.63L67.8,204.63L67.8,203.29L69.72,203.29L69.72,201.24L71.63,201.24L71.63,198.16L73.54,198.16L73.54,193.69L75.46,193.69L75.46,187.6L77.37,187.6L77.37,179.54L79.28,179.54L79.28,169.32L81.2,169.32L81.2,157.13L83.11,157.13L83.11,143.18L85.02,143.18L85.02,128.12L86.94,128.12L86.94,112.87L88.85,112.87L88.85,98.53L90.76,98.53L90.76,86.46L92.68,86.46L92.68,77.56L94.59,77.56L94.59,72.84L98.42,72.96L98.42,77.55L100.33,77.55L100.33,86.37L102.24,86.37L102.24,98.58L104.16,98.58L104.16,112.85L106.07,112.85L106.07,128.11L107.98,128.11L107.98,143.14L109.9,143.14L109.9,157.11L111.81,157.11L111.81,169.36L113.72,169.36L113.72,179.48L115.64,179.48L115.64,187.58L117.55,187.58L117.55,193.73L119.46,193.73L119.46,198.13L121.38,198.13L121.38,201.24L123.29,201.24L123.29,203.31L125.2,203.31L125.2,204.62L127.12,204.62L127.12,205.44L132.86,206.19L132.86,206.35L341.41,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace387151\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-146.49,206.5L62.06,206.04L62.06,205.63L65.89,204.91L65.89,203.69L67.8,203.69L67.8,201.69L69.72,201.69L69.72,198.62L71.63,198.62L71.63,194L73.54,194L73.54,187.28L75.46,187.28L75.46,178.14L77.37,178.14L77.37,166.06L79.28,166.06L79.28,150.73L81.2,150.73L81.2,132.44L83.11,132.44L83.11,111.52L85.02,111.52L85.02,88.93L86.94,88.93L86.94,66.06L88.85,66.06L88.85,44.55L90.76,44.55L90.76,26.44L92.68,26.44L92.68,13.09L94.59,13.09L94.59,6.01L98.42,6.19L98.42,13.08L100.33,13.08L100.33,26.3L102.24,26.3L102.24,44.61L104.16,44.61L104.16,66.02L106.07,66.02L106.07,88.91L107.98,88.91L107.98,111.46L109.9,111.46L109.9,132.41L111.81,132.41L111.81,150.79L113.72,150.79L113.72,165.97L115.64,165.97L115.64,178.12L117.55,178.12L117.55,187.34L119.46,187.34L119.46,193.94L121.38,193.94L121.38,198.61L123.29,198.61L123.29,201.72L125.2,201.72L125.2,203.67L127.12,203.67L127.12,204.91L130.94,205.63L130.94,206.04L341.41,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(204, 0, 0); stroke-opacity: 1; stroke-width: 1px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g></g></g><g class=\"overplot\"/><path class=\"xlines-above crisp\" d=\"M59.82702020202021,236.4060950714494H305.73704565338426\" style=\"fill: none; stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 1;\"/><path class=\"ylines-above crisp\" d=\"M60.32702020202021,23.390201224846894V235.9060950714494\" style=\"fill: none; stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 1;\"/><g class=\"overlines-above\"/><g class=\"xaxislayer-above\"><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(84.55702020202021,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(103.9570202020202,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(120.34702020202022,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(134.55702020202023,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(147.0770202020202,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(158.2870202020202,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(232.00702020202021,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(275.1370202020202,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(60.82702020202021,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">4</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(84.55702020202021,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">5</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(103.9570202020202,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">6</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(120.34702020202022,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">7</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(134.55702020202023,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">8</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(147.0770202020202,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">9</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"4.25\" y=\"265.8060950714494\" transform=\"translate(158.2870202020202,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">100</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(232.00702020202021,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">2</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(275.1370202020202,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">3</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(305.7370202020202,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">4</text></g></g><g class=\"yaxislayer-above\"><path class=\"ytick ticks crisp\" d=\"M60.82702020202021,0h5\" transform=\"translate(0,229.8902012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M60.82702020202021,0h5\" transform=\"translate(0,197.7902012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M60.82702020202021,0h5\" transform=\"translate(0,165.7002012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M60.82702020202021,0h5\" transform=\"translate(0,133.6002012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M60.82702020202021,0h5\" transform=\"translate(0,101.50020122484689)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M60.82702020202021,0h5\" transform=\"translate(0,69.4102012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M60.82702020202021,0h5\" transform=\"translate(0,37.31020122484689)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"ytick\"><text text-anchor=\"end\" x=\"56.42702020202021\" y=\"5.949999999999999\" transform=\"translate(0,229.8902012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">0</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"56.42702020202021\" y=\"5.949999999999999\" transform=\"translate(0,197.7902012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">10</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"56.42702020202021\" y=\"5.949999999999999\" transform=\"translate(0,165.7002012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">20</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"56.42702020202021\" y=\"5.949999999999999\" transform=\"translate(0,133.6002012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">30</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"56.42702020202021\" y=\"5.949999999999999\" transform=\"translate(0,101.50020122484689)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">40</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"56.42702020202021\" y=\"5.949999999999999\" transform=\"translate(0,69.4102012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">50</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"56.42702020202021\" y=\"5.949999999999999\" transform=\"translate(0,37.31020122484689)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">60</text></g></g><g class=\"overaxes-above\"/></g><g class=\"subplot x2y2\"><g class=\"layer-subplot\"><g class=\"shapelayer\"/><g class=\"imagelayer\"/></g><g class=\"gridlayer\"><g class=\"x2\"><path class=\"x2grid crisp\" transform=\"translate(404.26282828282837,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"x2grid crisp\" transform=\"translate(468.6828282828284,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"x2grid crisp\" transform=\"translate(523.1428282828283,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"x2grid crisp\" transform=\"translate(570.3228282828284,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/></g><g class=\"y2\"><path class=\"y2grid crisp\" transform=\"translate(0,229.8902012248469)\" d=\"M367.03282828282835,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"y2grid crisp\" transform=\"translate(0,167.5002012248469)\" d=\"M367.03282828282835,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"y2grid crisp\" transform=\"translate(0,105.10020122484688)\" d=\"M367.03282828282835,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"y2grid crisp\" transform=\"translate(0,42.7102012248469)\" d=\"M367.03282828282835,0h244.91002545136405\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/></g></g><g class=\"zerolinelayer\"/><path class=\"xlines-below\"/><path class=\"ylines-below\"/><g class=\"overlines-below\"/><g class=\"xaxislayer-below\"/><g class=\"yaxislayer-below\"/><g class=\"overaxes-below\"/><g class=\"plot\" transform=\"translate(367.03282828282835, 23.390201224846894)\" clip-path=\"url('#clip66de9dx2y2plot')\"><g class=\"scatterlayer mlayer\"><g class=\"trace scatter trace569145\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-773.17,206.5L46.76,205.87L46.76,204.52L53.12,204.52L53.12,203.55L59.47,203.55L59.47,199.81L65.83,199.81L65.83,197.26L72.19,197.26L72.19,189.99L78.54,189.99L78.54,179.31L84.9,179.31L84.9,169.01L91.25,169.01L91.25,156.99L97.61,156.99L97.61,141.52L103.97,141.52L103.97,133.43L110.32,133.43L110.32,130.56L116.68,130.56L116.68,126.32L123.03,126.32L123.03,138.22L135.75,138.54L135.75,157.18L142.1,157.18L142.1,166.22L148.46,166.22L148.46,178.81L154.81,178.81L154.81,189.01L161.17,189.01L161.17,195.75L167.53,195.75L167.53,198.58L173.88,198.58L173.88,201.72L180.24,201.72L180.24,203.73L186.59,203.73L186.59,205.55L205.66,206.23L205.66,206.46L847.62,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(0, 0, 204); stroke-opacity: 1; stroke-width: 1.5px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace783d18\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-773.17,206.5L40.41,206.12L46.76,205.63L53.12,204.63L59.47,202.77L65.83,199.56L72.19,194.44L78.54,186.97L84.9,177.05L103.97,140.11L110.32,130.92L116.68,126.32L123.03,127.07L129.39,133.32L135.75,143.65L154.81,180.37L161.17,189.57L167.53,196.28L173.88,200.74L180.24,203.49L186.59,205.03L199.31,206.22L205.66,206.39L847.62,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-width: 1px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace74ebc9\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-773.17,206.5L40.41,206.08L46.76,205.54L53.12,204.44L59.47,202.39L65.83,198.86L72.19,193.22L78.54,184.99L84.9,174.06L103.97,133.37L110.32,123.25L116.68,118.19L123.03,119.01L129.39,125.89L135.75,137.27L154.81,177.72L161.17,187.86L167.53,195.24L173.88,200.16L180.24,203.19L186.59,204.88L199.31,206.19L205.66,206.38L847.62,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-width: 1px; opacity: 1; stroke-dasharray: 9px, 9px;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace637d2d\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-773.17,206.5L34.05,206.13L40.41,205.6L46.76,204.43L53.12,202.05L59.47,197.61L65.83,189.98L72.19,177.78L78.54,160L84.9,136.37L91.25,107.85L103.97,48.39L110.32,26.52L116.68,15.56L123.03,17.34L129.39,32.22L135.75,56.83L154.81,144.28L161.17,166.19L167.53,182.16L173.88,192.79L180.24,199.33L186.59,203L192.95,204.9L199.31,205.83L218.37,206.47L224.73,206.49L847.62,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-width: 1px; opacity: 1; stroke-dasharray: 3px, 3px;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace3c2cf7\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M118.86,206.5L118.86,6.01\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(128, 128, 128); stroke-opacity: 1; stroke-width: 1px; opacity: 1; stroke-dasharray: 9px, 3px, 3px, 3px;\"/></g><g class=\"points\"/><g class=\"text\"/></g></g></g><g class=\"overplot\"/><path class=\"xlines-above crisp\" d=\"M366.03282828282835,236.4060950714494H611.9428537341923\" style=\"fill: none; stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 1;\"/><path class=\"ylines-above crisp\" d=\"M366.53282828282835,23.390201224846894V235.9060950714494\" style=\"fill: none; stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 1;\"/><g class=\"overlines-above\"/><g class=\"xaxislayer-above\"><path class=\"x2tick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(404.26282828282837,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"x2tick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(468.6828282828284,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"x2tick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(523.1428282828283,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"x2tick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(570.3228282828284,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"x2tick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(404.26282828282837,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">100</text></g><g class=\"x2tick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(468.6828282828284,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">120</text></g><g class=\"x2tick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(523.1428282828283,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">140</text></g><g class=\"x2tick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(570.3228282828284,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">160</text></g><g class=\"x2tick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(611.9428282828284,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">180</text></g></g><g class=\"yaxislayer-above\"><path class=\"y2tick ticks crisp\" d=\"M367.03282828282835,0h5\" transform=\"translate(0,229.8902012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"y2tick ticks crisp\" d=\"M367.03282828282835,0h5\" transform=\"translate(0,167.5002012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"y2tick ticks crisp\" d=\"M367.03282828282835,0h5\" transform=\"translate(0,105.10020122484688)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"y2tick ticks crisp\" d=\"M367.03282828282835,0h5\" transform=\"translate(0,42.7102012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"y2tick\"><text text-anchor=\"end\" x=\"362.63282828282837\" y=\"5.949999999999999\" transform=\"translate(0,229.8902012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">0.0</text></g><g class=\"y2tick\"><text text-anchor=\"end\" x=\"362.63282828282837\" y=\"5.949999999999999\" transform=\"translate(0,167.5002012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">0.5</text></g><g class=\"y2tick\"><text text-anchor=\"end\" x=\"362.63282828282837\" y=\"5.949999999999999\" transform=\"translate(0,105.10020122484688)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">1.0</text></g><g class=\"y2tick\"><text text-anchor=\"end\" x=\"362.63282828282837\" y=\"5.949999999999999\" transform=\"translate(0,42.7102012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">1.5</text></g></g><g class=\"overaxes-above\"/></g></g><g class=\"polarlayer\"/><g class=\"ternarylayer\"/><g class=\"geolayer\"/><g class=\"pielayer\"/><g class=\"sunburstlayer\"/><g class=\"glimages\"/><defs id=\"topdefs-66de9d\"><g class=\"clips\"/><clipPath id=\"legend66de9d\"><rect width=\"177\" height=\"159\" x=\"0\" y=\"0\"/></clipPath></defs><g class=\"layer-above\"><g class=\"imagelayer\"/><g class=\"shapelayer\"/></g><g class=\"infolayer\"><g class=\"legend\" pointer-events=\"all\" transform=\"translate(615, 20)\"><rect class=\"bg\" shape-rendering=\"crispEdges\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; fill: rgb(255, 255, 255); fill-opacity: 1; stroke-width: 0px;\" width=\"177\" height=\"159\" x=\"0\" y=\"0\"/><g class=\"scrollbox\" transform=\"translate(0, 0)\" clip-path=\"url('#legend66de9d')\"><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 15.6)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">𝕟₁ = 𝓛𝓝 (N₁,Dₘ,σ)</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"217\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 36.8)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">𝕟₂ = 𝓛𝓝 (N₂,Dₘ,σ)</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(204, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"217\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 58)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">𝕟₁₂ (partMC)</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(0, 0, 204); stroke-opacity: 1; stroke-width: 1.5px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"217\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 79.19999999999999)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">f⋅[(β₁₂ᵇt)*(𝕟₁*𝕟₂)]</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"217\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 100.39999999999999)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">f⋅[(β₁₂ᶻ⁽¹ ⁻¹⁾t)*(𝕟₁*𝕟₂)]</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-dasharray: 9px, 9px; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"217\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 121.6)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">f⋅[(β₁₂ᶻ⁽² ⁻²⁾t)*(𝕟₁*𝕟₂)]</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-dasharray: 3px, 3px; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"217\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 142.79999999999998)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">f*Dₘ</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(128, 128, 128); stroke-opacity: 1; stroke-dasharray: 9px, 3px, 3px, 3px; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"217\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g></g><rect class=\"scrollbar\" rx=\"20\" ry=\"3\" width=\"0\" height=\"0\" style=\"fill: rgb(128, 139, 164); fill-opacity: 1;\" x=\"0\" y=\"0\"/></g><g class=\"g-gtitle\"/><g class=\"g-xtitle\" transform=\"translate(0,-13.906095071449386)\"><text class=\"xtitle\" x=\"183.28203292770223\" y=\"296.9060950714494\" text-anchor=\"middle\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); opacity: 1; font-weight: normal; white-space: pre;\">Diameter (nm)</text></g><g class=\"g-x2title\" transform=\"translate(0,-13.906095071449386)\"><text class=\"x2title\" x=\"489.4878410085104\" y=\"296.9060950714494\" text-anchor=\"middle\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); opacity: 1; font-weight: normal; white-space: pre;\">Diameter (nm)</text></g><g class=\"g-ytitle\"><text class=\"ytitle\" transform=\"rotate(-90,16.827020202020208,129.64814814814815)\" x=\"16.827020202020208\" y=\"129.64814814814815\" text-anchor=\"middle\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); opacity: 1; font-weight: normal; white-space: pre;\">dN/dlnD (m⁻³) × 10⁻¹⁰</text></g><g class=\"g-y2title\"/></g></svg>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure(\"Nimbus Sans L\", 2, 5.5, 2, 8)\n",
    "pre = 1e-10\n",
    "p1 = plot(𝕟₁.Dp, pre*𝕟₁.S, xlim = (40, 400), color = :black, label = \"𝕟₁ = 𝓛𝓝 (N₁,Dₘ,σ)\", \n",
    "    xlabel = \"Diameter (nm)\", ylabel = \"dN/dlnD (m⁻³) × 10⁻¹⁰\",  t = :steppre, \n",
    "    xticks = [60,80,100,120,140,160])\n",
    "\n",
    "p1 = plot!(𝕟₂.Dp, pre*𝕟₂.S, color = RGBA(0.8,0,0,1), label = \"𝕟₂ = 𝓛𝓝 (N₂,Dₘ,σ)\", t = :steppre)\n",
    "\n",
    "p2 = plot(𝕟₁₂.Dp, pre*𝕟₁₂.S, color = RGBA(0.0,0.0,0.8), xlim = (90, 180), label = \"𝕟₁₂ (partMC)\", \n",
    "    xlabel = \"Diameter (nm)\", t = :steppre, lw = 1.5, xticks = [60,80,100,120,140, 160])\n",
    "p2 = plot!(𝕟ₚᵇ.Dp,pre*𝕟ₚᵇ.S, color = :brown, label = \"f⋅[(β₁₂ᵇt)*(𝕟₁*𝕟₂)]\", lw = 1)\n",
    "p2 = plot!(𝕟ₚᶻ¹.Dp,pre*𝕟ₚᶻ¹.S, color = :brown, label = \"f⋅[(β₁₂ᶻ⁽¹ ⁻¹⁾t)*(𝕟₁*𝕟₂)]\", lw = 1, ls = :dash)\n",
    "p2 = plot!(𝕟ₚᶻ².Dp,pre*𝕟ₚᶻ².S, color = :brown, label = \"f⋅[(β₁₂ᶻ⁽² ⁻²⁾t)*(𝕟₁*𝕟₂)]\", lw = 1, ls = :dot)\n",
    "p2 = plot!([f*Dm, f*Dm], [0,1.05*maximum(pre*𝕟ₚᶻ².S)], color = :grey, ls = :dashdot, label = \"f*Dₘ\") \n",
    "\n",
    "plot(p1,p2, layout = grid(1,2), left_margin = 35px, xaxis = :log10, fmt = :svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Figure 3. </b> Comparison of assumed PartMC inferred size distribution and size distribution obtained from 𝕟ₚᵇ = f$⋅$((β₁₂$*$t)$*$(𝕟₁$.*$𝕟₂)). Left: Input size distributions to PartMC. Right: Blue histogram shows output size distribution from PartMC. The dark-red solid line corresponds to the analytical prediction. Note that the diameter is shifted by f$*$Dm due to the larger sphere equivalent volume of the dimers. Enhancement of concentration due to +1/-1 charge on the input size distribution is negligible and approximately a factor of two for +2/-2 charges. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The DMA particle size distribution is not lognormal. To test of the analytical approximation holds, the model as also initialized with DMA type size distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "t,p = 295.15, 1e5                                # Temperature [K], Pressure [Pa]\n",
    "qsa,β = 1.66e-5, 1/3                             # Qsample [m3 s-1], Sample-to-sheath ratio,\n",
    "r₁,r₂,l = 9.37e-3,1.961e-2,0.44369               # DMA geometry [m]\n",
    "leff = 13.0                                      # DMA effective diffusion length [m]\n",
    "n = 6                                            # Upper number of charges\n",
    "Λ = DMAconfig(t,p,qsa,qsa/β,r₁,r₂,l,leff,:-,n,:cylindrical)   # Specify DMA with negative polarity\n",
    "bins,z₁,z₂ = 512, dtoz(Λ,500e-9),dtoz(Λ,20e-9)   # bins, upper, lower mobility limit\n",
    "δ = setupDMA(Λ, z₁, z₂, bins);                   # Compute matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The API for Triangular size distributions is\n",
    "```julia\n",
    "ics = InitialConditionTriangular(N1, N2, Dm, Λ, δ)\n",
    "```\n",
    "where N1, N2, Dm are as above, and Λ, δ define the DMA. The width of the distribution is set by β."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1     0s  999372       0       0        0         0       0     0s     0s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    10s  998722    2984       0        0         0       0    19s    97s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    20s  998050    2965       0        0         0       0    20s    40s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    30s  997444    2951       0        0         0       0    21s    21s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    40s  996810    2938       0        0         0       0    21s    11s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    50s  996200    2908       0        0         0       0    22s     4s\n",
      "repeat  t_sim  n_part  n_coag  n_emit n_dil_in n_dil_out   n_nuc t_wall  t_rem\n",
      "     1    60s  995468    2994       0        0         0       0    23s     0s\n"
     ]
    }
   ],
   "source": [
    "cd(\"PartMC\")         # Descend into directory PartMC\n",
    "Random.seed!(30)     # Pick a random seed \n",
    "ics = InitialConditionTriangular(1e11, 1.5e11, 100.0, Λ, δ)    # Set initial conditions\n",
    "x = runSimulation(ics,1,\"triangular\"; verbose = true, repeat = 1)  # Run simulations\n",
    "cd(\"..\")      # Come back "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>Input</th><th>PartMC</th></tr><tr><th></th><th>Float64</th><th>String</th></tr></thead><tbody><p>2 rows × 2 columns</p><tr><th>1</th><td>1.0e11</td><td>1.0E+11</td></tr><tr><th>2</th><td>1.5e11</td><td>1.5E+11</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& Input & PartMC\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & String\\\\\n",
       "\t\\hline\n",
       "\t1 & 1.0e11 & 1.0E+11 \\\\\n",
       "\t2 & 1.5e11 & 1.5E+11 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "2×2 DataFrame\n",
       "│ Row │ Input   │ PartMC  │\n",
       "│     │ \u001b[90mFloat64\u001b[39m │ \u001b[90mString\u001b[39m  │\n",
       "├─────┼─────────┼─────────┤\n",
       "│ 1   │ 1.0e11  │ 1.0E+11 │\n",
       "│ 2   │ 1.5e11  │ 1.5E+11 │"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = 1                    # repeat number\n",
    "Dm  = ics.Dm             # recover Dm from initial condition\n",
    "N₁  = ics.Nt1            # recover N₁ from initial condition\n",
    "N₂  = ics.Nt2            # recover N₂ from initial condition\n",
    "t   = x[r].r[end,end].t  # end time of simulation. \n",
    "𝕟₁  = (𝕟0 + x[r].s1)            # reconstructed size distribution for 𝕟₁ from model output \n",
    "𝕟₂  = (𝕟0 + x[r].s2)            # reconstructed size distribution for 𝕟₂ from model output \n",
    "𝕟₁₂ = (𝕟0 + x[r].r[end,1].sc12) # reconstructed dimer size distribution 𝕟₁₂ from model output \n",
    "\n",
    "DataFrame(Input = [N₁,N₂], PartMC = [@sprintf(\"%.1E\", sum(𝕟₁.N)), @sprintf(\"%.1E\", sum(𝕟₂.N))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Table 3. </b> Comparison of assumed input number concentration and reconstructed output number concentration from PartMC simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>PartMC</th><th>Analytical</th></tr><tr><th></th><th>String</th><th>String</th></tr></thead><tbody><p>1 rows × 2 columns</p><tr><th>1</th><td>1.046E+09</td><td>1.097E+09</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& PartMC & Analytical\\\\\n",
       "\t\\hline\n",
       "\t& String & String\\\\\n",
       "\t\\hline\n",
       "\t1 & 1.046E+09 & 1.097E+09 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "1×2 DataFrame\n",
       "│ Row │ PartMC    │ Analytical │\n",
       "│     │ \u001b[90mString\u001b[39m    │ \u001b[90mString\u001b[39m     │\n",
       "├─────┼───────────┼────────────┤\n",
       "│ 1   │ 1.046E+09 │ 1.097E+09  │"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "β₁₂ = β12(Dm*1e-9, Dm*1e-9, 0,0)         # Zebel-Brownian coagulation rate for no charge\n",
    "β₁₂ᶻ⁽¹⁻¹⁾ = β12(Dm*1e-9, Dm*1e-9, 1,-1)  # +1 -1 charge\n",
    "β₁₂ᶻ⁽²⁻²⁾ = β12(Dm*1e-9, Dm*1e-9, 2,-2)  # +1 -1 charge\n",
    "f   = (Dm^3.0+Dm^3.0)^(1.0/3.0)/Dm \t     # diameter shift for larger particles\n",
    "\n",
    "𝕟ₚᵇ = f⋅((β₁₂*t)*(𝕟₁*𝕟₂))              # Semi-analytical estimate using Browninan Kernel\n",
    "𝕟ₚᶻ¹ = f⋅((β₁₂ᶻ⁽¹⁻¹⁾*t)*(𝕟₁*𝕟₂))       # Estimated enhancement for +1/-1 charged case\n",
    "𝕟ₚᶻ² = f⋅((β₁₂ᶻ⁽²⁻²⁾*t)*(𝕟₁*𝕟₂))       # Estimated enhancement for +2/-2 charged caseprintln()\n",
    "\n",
    "DataFrame(PartMC = [@sprintf(\"%.3E\",sum(𝕟₁₂.N))], Analytical = [@sprintf(\"%.3E\",sum(𝕟ₚᵇ.N))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Table 4. </b> Comparison of assumed PartMC inferred number concentration and number concentration obtained from f$⋅$((β₁₂$*$t)$*$(𝕟₁$.*$𝕟₂))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "𝕟₁ = Λ(N₁,Dₘ,β)",
         "line": {
          "color": "rgba(0, 0, 0, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "𝕟₁ = Λ(N₁,Dₘ,β)",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.090350448414474,
          10.273507681793024,
          10.273507681793024,
          10.459989534302535,
          10.459989534302535,
          10.649856353504289,
          10.649856353504289,
          10.84316958237171,
          10.84316958237171,
          11.039991779173976,
          11.039991779173976,
          11.240386637720556,
          11.240386637720556,
          11.44441900797323,
          11.44441900797323,
          11.652154917032231,
          11.652154917032231,
          11.863661590503344,
          11.863661590503344,
          12.079007474252842,
          12.079007474252842,
          12.298262256557319,
          12.298262256557319,
          12.521496890655566,
          12.521496890655566,
          12.748783617709826,
          12.748783617709826,
          12.98019599018381,
          12.98019599018381,
          13.215808895645086,
          13.215808895645086,
          13.455698580999508,
          13.455698580999508,
          13.699942677165545,
          13.699942677165545,
          13.948620224196498,
          13.948620224196498,
          14.201811696858716,
          14.201811696858716,
          14.459599030674116,
          14.459599030674116,
          14.722065648435406,
          14.722065648435406,
          14.989296487202608,
          14.989296487202608,
          15.261378025789629,
          15.261378025789629,
          15.538398312749738,
          15.538398312749738,
          15.820446994869037,
          15.820446994869037,
          16.10761534617715,
          16.10761534617715,
          16.39999629748447,
          16.39999629748447,
          16.69768446645562,
          16.69768446645562,
          17.00077618822873,
          17.00077618822873,
          17.309369546590553,
          17.309369546590553,
          17.623564405717435,
          17.623564405717435,
          17.94346244249247,
          17.94346244249247,
          18.269167179409244,
          18.269167179409244,
          18.600784018072822,
          18.600784018072822,
          18.938420273308882,
          18.938420273308882,
          19.282185207891956,
          19.282185207891956,
          19.632190067904055,
          19.632190067904055,
          19.988548118735103,
          19.988548118735103,
          20.35137468173687,
          20.35137468173687,
          20.72078717154221,
          20.72078717154221,
          21.096905134061714,
          21.096905134061714,
          21.479850285170084,
          21.479850285170084,
          21.869746550094703,
          21.869746550094703,
          22.266720103519187,
          22.266720103519187,
          22.67089941041491,
          22.67089941041491,
          23.08241526761366,
          23.08241526761366,
          23.501400846134892,
          23.501400846134892,
          23.927991734281377,
          23.927991734281377,
          24.36232598151701,
          24.36232598151701,
          24.804544143141136,
          24.804544143141136,
          25.25478932577379,
          25.25478932577379,
          25.713207233666548,
          25.713207233666548,
          26.179946215854002,
          26.179946215854002,
          26.65515731416115,
          26.65515731416115,
          27.138994312082165,
          27.138994312082165,
          27.6316137845464,
          27.6316137845464,
          28.133175148587764,
          28.133175148587764,
          28.6438407149338,
          28.6438407149338,
          29.163775740531204,
          29.163775740531204,
          29.693148482024785,
          29.693148482024785,
          30.232130250207152,
          30.232130250207152,
          30.78089546545674,
          30.78089546545674,
          31.339621714182158,
          31.339621714182158,
          31.90848980629108,
          31.90848980629108,
          32.48768383370232,
          32.48768383370232,
          33.07739122991996,
          33.07739122991996,
          33.6778028306889,
          33.6778028306889,
          34.289112935751355,
          34.289112935751355,
          34.911519371724424,
          34.911519371724424,
          35.54522355611888,
          35.54522355611888,
          36.19043056252011,
          36.19043056252011,
          36.847349186952165,
          36.847349186952165,
          37.51619201544639,
          37.51619201544639,
          38.19717549283665,
          38.19717549283665,
          38.89051999280318,
          38.89051999280318,
          39.59644988918792,
          39.59644988918792,
          40.31519362860439,
          40.31519362860439,
          41.04698380436544,
          41.04698380436544,
          41.792057231753,
          41.792057231753,
          42.55065502465411,
          42.55065502465411,
          43.323022673587985,
          43.323022673587985,
          44.10941012514944,
          44.10941012514944,
          44.910071862894306,
          44.910071862894306,
          45.72526698969311,
          45.72526698969311,
          46.55525931157958,
          46.55525931157958,
          47.400317423121166,
          47.400317423121166,
          48.26071479433915,
          48.26071479433915,
          49.13672985920654,
          49.13672985920654,
          50.02864610575234,
          50.02864610575234,
          50.93675216780135,
          50.93675216780135,
          51.861341918379274,
          51.861341918379274,
          52.80271456481317,
          52.80271456481317,
          53.76117474555825,
          53.76117474555825,
          54.73703262878217,
          54.73703262878217,
          55.73060401273886,
          55.73060401273886,
          56.74221042796429,
          56.74221042796429,
          57.77217924132721,
          57.77217924132721,
          58.8208437619687,
          58.8208437619687,
          59.888543349164614,
          59.888543349164614,
          60.975623522145916,
          60.975623522145916,
          62.08243607191253,
          62.08243607191253,
          63.20933917507671,
          63.20933917507671,
          64.35669750977287,
          64.35669750977287,
          65.52488237367147,
          65.52488237367147,
          66.71427180413495,
          66.71427180413495,
          67.92525070055476,
          67.92525070055476,
          69.15821094890896,
          69.15821094890896,
          70.41355154858087,
          70.41355154858087,
          71.69167874147956,
          71.69167874147956,
          72.9930061435042,
          72.9930061435042,
          74.31795487839462,
          74.31795487839462,
          75.66695371401163,
          75.66695371401163,
          77.04043920109092,
          77.04043920109092,
          78.43885581451562,
          78.43885581451562,
          79.8626560971533,
          79.8626560971533,
          81.31230080630368,
          81.31230080630368,
          82.78825906280481,
          82.78825906280481,
          84.29100850284559,
          84.29100850284559,
          85.82103543253415,
          85.82103543253415,
          87.37883498527172,
          87.37883498527172,
          88.9649112819833,
          88.9649112819833,
          90.5797775942566,
          90.5797775942566,
          92.22395651044235,
          92.22395651044235,
          93.8979801047696,
          93.8979801047696,
          95.60239010953076,
          95.60239010953076,
          97.33773809039202,
          97.33773809039202,
          99.10458562488608,
          99.10458562488608,
          100.90350448414475,
          100.90350448414475,
          102.73507681793026,
          102.73507681793026,
          104.59989534302535,
          104.59989534302535,
          106.4985635350429,
          106.4985635350429,
          108.4316958237171,
          108.4316958237171,
          110.39991779173975,
          110.39991779173975,
          112.40386637720557,
          112.40386637720557,
          114.44419007973231,
          114.44419007973231,
          116.5215491703223,
          116.5215491703223,
          118.63661590503344,
          118.63661590503344,
          120.79007474252845,
          120.79007474252845,
          122.98262256557321,
          122.98262256557321,
          125.21496890655568,
          125.21496890655568,
          127.48783617709826,
          127.48783617709826,
          129.8019599018381,
          129.8019599018381,
          132.15808895645085,
          132.15808895645085,
          134.55698580999507,
          134.55698580999507,
          136.99942677165546,
          136.99942677165546,
          139.48620224196497,
          139.48620224196497,
          142.01811696858715,
          142.01811696858715,
          144.59599030674116,
          144.59599030674116,
          147.22065648435404,
          147.22065648435404,
          149.89296487202606,
          149.89296487202606,
          152.6137802578963,
          152.6137802578963,
          155.38398312749737,
          155.38398312749737,
          158.20446994869036,
          158.20446994869036,
          161.07615346177147,
          161.07615346177147,
          163.9999629748447,
          163.9999629748447,
          166.9768446645562,
          166.9768446645562,
          170.0077618822873,
          170.0077618822873,
          173.0936954659055,
          173.0936954659055,
          176.23564405717434,
          176.23564405717434,
          179.43462442492472,
          179.43462442492472,
          182.69167179409243,
          182.69167179409243,
          186.00784018072818,
          186.00784018072818,
          189.3842027330888,
          189.3842027330888,
          192.8218520789196,
          192.8218520789196,
          196.32190067904054,
          196.32190067904054,
          199.88548118735102,
          199.88548118735102,
          203.51374681736868,
          203.51374681736868,
          207.2078717154221,
          207.2078717154221,
          210.96905134061717,
          210.96905134061717,
          214.79850285170085,
          214.79850285170085,
          218.69746550094703,
          218.69746550094703,
          222.66720103519188,
          222.66720103519188,
          226.70899410414913,
          226.70899410414913,
          230.82415267613658,
          230.82415267613658,
          235.01400846134894,
          235.01400846134894,
          239.27991734281375,
          239.27991734281375,
          243.6232598151701,
          243.6232598151701,
          248.04544143141135,
          248.04544143141135,
          252.5478932577379,
          252.5478932577379,
          257.13207233666543,
          257.13207233666543,
          261.79946215854,
          261.79946215854,
          266.5515731416115,
          266.5515731416115,
          271.3899431208216,
          271.3899431208216,
          276.31613784546397,
          276.31613784546397,
          281.33175148587765,
          281.33175148587765,
          286.438407149338,
          286.438407149338,
          291.637757405312,
          291.637757405312,
          296.9314848202479,
          296.9314848202479,
          302.32130250207155,
          302.32130250207155,
          307.8089546545674,
          307.8089546545674,
          313.3962171418216,
          313.3962171418216,
          319.08489806291084,
          319.08489806291084,
          324.8768383370232,
          324.8768383370232,
          330.7739122991996,
          330.7739122991996,
          336.7780283068889,
          336.7780283068889,
          342.89112935751353,
          342.89112935751353,
          349.1151937172442,
          349.1151937172442,
          355.4522355611888,
          355.4522355611888,
          361.9043056252011,
          361.9043056252011,
          368.4734918695216,
          368.4734918695216,
          375.16192015446387,
          375.16192015446387,
          381.97175492836647,
          381.97175492836647,
          388.9051999280318,
          388.9051999280318,
          395.96449889187926,
          395.96449889187926,
          403.15193628604396,
          403.15193628604396,
          410.4698380436544,
          410.4698380436544,
          417.92057231753,
          417.92057231753,
          425.5065502465411,
          425.5065502465411,
          433.23022673587985,
          433.23022673587985,
          441.09410125149435,
          441.09410125149435,
          449.100718628943,
          449.100718628943,
          457.2526698969311,
          457.2526698969311,
          465.55259311579584,
          465.55259311579584,
          474.0031742312117,
          474.0031742312117,
          482.6071479433915,
          482.6071479433915,
          491.36729859206537,
          491.36729859206537,
          500.2864610575233,
          500.2864610575233,
          509.36752167801353,
          509.36752167801353,
          518.6134191837928,
          518.6134191837928,
          528.0271456481318,
          528.0271456481318,
          537.6117474555825,
          537.6117474555825,
          547.3703262878216,
          547.3703262878216,
          557.3060401273885,
          557.3060401273885,
          567.4221042796428,
          567.4221042796428,
          577.7217924132722,
          577.7217924132722,
          588.2084376196871,
          588.2084376196871,
          598.8854334916462,
          598.8854334916462,
          609.7562352214592,
          609.7562352214592,
          620.8243607191254,
          620.8243607191254,
          632.093391750767,
          632.093391750767,
          643.5669750977287,
          643.5669750977287,
          655.2488237367147,
          655.2488237367147,
          667.1427180413494,
          667.1427180413494,
          679.2525070055476,
          679.2525070055476,
          691.5821094890896,
          691.5821094890896,
          704.1355154858088,
          704.1355154858088,
          716.9167874147956,
          716.9167874147956,
          729.9300614350419,
          729.9300614350419,
          743.1795487839462,
          743.1795487839462,
          756.6695371401163,
          756.6695371401163,
          770.4043920109092,
          770.4043920109092,
          784.3885581451563,
          784.3885581451563,
          798.626560971533,
          798.626560971533,
          813.1230080630369,
          813.1230080630369,
          827.8825906280481,
          827.8825906280481,
          842.9100850284559,
          842.9100850284559,
          858.2103543253414,
          858.2103543253414,
          873.7883498527173,
          873.7883498527173,
          889.649112819833,
          889.649112819833,
          905.797775942566,
          905.797775942566,
          922.2395651044235,
          922.2395651044235,
          938.9798010476961,
          938.9798010476961,
          956.0239010953076,
          956.0239010953076,
          973.3773809039202,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x1",
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          2.879295754192845e-13,
          2.879295754192845e-13,
          7.98629143769524e-16,
          7.98629143769524e-16,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          2.0087932375700155e-13,
          2.0087932375700155e-13,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          9.359918905212538e-14,
          9.359918905212538e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          2.6255915461265948e-14,
          2.6255915461265948e-14,
          2.0358201742982285e-13,
          2.0358201742982285e-13,
          1.333308304749645e-13,
          1.333308304749645e-13,
          1.86137851517955e-13,
          1.86137851517955e-13,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          2.0212451720925313e-13,
          2.0212451720925313e-13,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          8.313697342016117e-14,
          8.313697342016117e-14,
          0,
          0,
          7.322080843553106e-14,
          7.322080843553106e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          6.737762009220397e-14,
          6.737762009220397e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          3.4219734445789547e-14,
          3.4219734445789547e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          3.039573917254629e-15,
          3.039573917254629e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          2.3081375380844478e-14,
          2.3081375380844478e-14,
          2.89999938679599e-14,
          2.89999938679599e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          8.513176103683918e-15,
          8.513176103683918e-15,
          0,
          0,
          0,
          0,
          3.0749467209554194e-13,
          3.0749467209554194e-13,
          1.4877283676497799e-05,
          1.4877283676497799e-05,
          0.15249772700137998,
          0.15249772700137998,
          3.95853958122214,
          3.95853958122214,
          10.312317667014637,
          10.312317667014637,
          16.482380694456616,
          16.482380694456616,
          22.417865417197365,
          22.417865417197365,
          28.126708857190987,
          28.126708857190987,
          33.616585927342946,
          33.616585927342946,
          38.894909460793784,
          38.894909460793784,
          43.96782178223359,
          43.96782178223359,
          48.465718459647704,
          48.465718459647704,
          48.36290607467809,
          48.36290607467809,
          44.0142833576386,
          44.0142833576386,
          39.43661932049587,
          39.43661932049587,
          35.02538714336563,
          35.02538714336563,
          30.7772868764537,
          30.7772868764537,
          26.68670909293412,
          26.68670909293412,
          22.748235855983808,
          22.748235855983808,
          18.956634756585085,
          18.956634756585085,
          15.30685247797967,
          15.30685247797967,
          11.794008609168017,
          11.794008609168017,
          8.416117069953417,
          8.416117069953417,
          5.174681296364537,
          5.174681296364537,
          2.2693618968384763,
          2.2693618968384763,
          0.5025988361859374,
          0.5025988361859374,
          0.03927658173121001,
          0.03927658173121001,
          0.0008562116243944005,
          0.0008562116243944005,
          5.404597596774551e-06,
          5.404597596774551e-06,
          1.798489140322821e-08,
          1.798489140322821e-08,
          1.539350030326486e-11,
          1.539350030326486e-11,
          0,
          0,
          0,
          0,
          2.1040632136072264e-16,
          2.1040632136072264e-16,
          0,
          0,
          5.17730690154359e-15,
          5.17730690154359e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          5.444968921673138e-15,
          5.444968921673138e-15,
          2.1817475890228234e-15,
          2.1817475890228234e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          7.0884971447365185e-15,
          7.0884971447365185e-15,
          0,
          0,
          0,
          0,
          7.79839610527883e-15,
          7.79839610527883e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.839858959450457e-14,
          1.839858959450457e-14,
          0,
          0,
          3.246957681480402e-17,
          3.246957681480402e-17,
          9.468813230051754e-15,
          9.468813230051754e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.6730660139569572e-14,
          1.6730660139569572e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.1796209897745128e-14,
          1.1796209897745128e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          1.829709332412506e-14,
          1.829709332412506e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          4.6850625794977315e-15,
          4.6850625794977315e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          5.53291155730977e-15,
          5.53291155730977e-15,
          9.549144450367065e-15,
          9.549144450367065e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.7052628737853258e-14,
          1.7052628737853258e-14,
          0,
          0,
          1.60044287284556e-14,
          1.60044287284556e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
         ],
         "yaxis": "y1",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "𝕟₂ = Λ(N₂,Dₘ,,β)",
         "line": {
          "color": "rgba(204, 0, 0, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "𝕟₂ = Λ(N₂,Dₘ,,β)",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.090350448414474,
          10.273507681793024,
          10.273507681793024,
          10.459989534302535,
          10.459989534302535,
          10.649856353504289,
          10.649856353504289,
          10.84316958237171,
          10.84316958237171,
          11.039991779173976,
          11.039991779173976,
          11.240386637720556,
          11.240386637720556,
          11.44441900797323,
          11.44441900797323,
          11.652154917032231,
          11.652154917032231,
          11.863661590503344,
          11.863661590503344,
          12.079007474252842,
          12.079007474252842,
          12.298262256557319,
          12.298262256557319,
          12.521496890655566,
          12.521496890655566,
          12.748783617709826,
          12.748783617709826,
          12.98019599018381,
          12.98019599018381,
          13.215808895645086,
          13.215808895645086,
          13.455698580999508,
          13.455698580999508,
          13.699942677165545,
          13.699942677165545,
          13.948620224196498,
          13.948620224196498,
          14.201811696858716,
          14.201811696858716,
          14.459599030674116,
          14.459599030674116,
          14.722065648435406,
          14.722065648435406,
          14.989296487202608,
          14.989296487202608,
          15.261378025789629,
          15.261378025789629,
          15.538398312749738,
          15.538398312749738,
          15.820446994869037,
          15.820446994869037,
          16.10761534617715,
          16.10761534617715,
          16.39999629748447,
          16.39999629748447,
          16.69768446645562,
          16.69768446645562,
          17.00077618822873,
          17.00077618822873,
          17.309369546590553,
          17.309369546590553,
          17.623564405717435,
          17.623564405717435,
          17.94346244249247,
          17.94346244249247,
          18.269167179409244,
          18.269167179409244,
          18.600784018072822,
          18.600784018072822,
          18.938420273308882,
          18.938420273308882,
          19.282185207891956,
          19.282185207891956,
          19.632190067904055,
          19.632190067904055,
          19.988548118735103,
          19.988548118735103,
          20.35137468173687,
          20.35137468173687,
          20.72078717154221,
          20.72078717154221,
          21.096905134061714,
          21.096905134061714,
          21.479850285170084,
          21.479850285170084,
          21.869746550094703,
          21.869746550094703,
          22.266720103519187,
          22.266720103519187,
          22.67089941041491,
          22.67089941041491,
          23.08241526761366,
          23.08241526761366,
          23.501400846134892,
          23.501400846134892,
          23.927991734281377,
          23.927991734281377,
          24.36232598151701,
          24.36232598151701,
          24.804544143141136,
          24.804544143141136,
          25.25478932577379,
          25.25478932577379,
          25.713207233666548,
          25.713207233666548,
          26.179946215854002,
          26.179946215854002,
          26.65515731416115,
          26.65515731416115,
          27.138994312082165,
          27.138994312082165,
          27.6316137845464,
          27.6316137845464,
          28.133175148587764,
          28.133175148587764,
          28.6438407149338,
          28.6438407149338,
          29.163775740531204,
          29.163775740531204,
          29.693148482024785,
          29.693148482024785,
          30.232130250207152,
          30.232130250207152,
          30.78089546545674,
          30.78089546545674,
          31.339621714182158,
          31.339621714182158,
          31.90848980629108,
          31.90848980629108,
          32.48768383370232,
          32.48768383370232,
          33.07739122991996,
          33.07739122991996,
          33.6778028306889,
          33.6778028306889,
          34.289112935751355,
          34.289112935751355,
          34.911519371724424,
          34.911519371724424,
          35.54522355611888,
          35.54522355611888,
          36.19043056252011,
          36.19043056252011,
          36.847349186952165,
          36.847349186952165,
          37.51619201544639,
          37.51619201544639,
          38.19717549283665,
          38.19717549283665,
          38.89051999280318,
          38.89051999280318,
          39.59644988918792,
          39.59644988918792,
          40.31519362860439,
          40.31519362860439,
          41.04698380436544,
          41.04698380436544,
          41.792057231753,
          41.792057231753,
          42.55065502465411,
          42.55065502465411,
          43.323022673587985,
          43.323022673587985,
          44.10941012514944,
          44.10941012514944,
          44.910071862894306,
          44.910071862894306,
          45.72526698969311,
          45.72526698969311,
          46.55525931157958,
          46.55525931157958,
          47.400317423121166,
          47.400317423121166,
          48.26071479433915,
          48.26071479433915,
          49.13672985920654,
          49.13672985920654,
          50.02864610575234,
          50.02864610575234,
          50.93675216780135,
          50.93675216780135,
          51.861341918379274,
          51.861341918379274,
          52.80271456481317,
          52.80271456481317,
          53.76117474555825,
          53.76117474555825,
          54.73703262878217,
          54.73703262878217,
          55.73060401273886,
          55.73060401273886,
          56.74221042796429,
          56.74221042796429,
          57.77217924132721,
          57.77217924132721,
          58.8208437619687,
          58.8208437619687,
          59.888543349164614,
          59.888543349164614,
          60.975623522145916,
          60.975623522145916,
          62.08243607191253,
          62.08243607191253,
          63.20933917507671,
          63.20933917507671,
          64.35669750977287,
          64.35669750977287,
          65.52488237367147,
          65.52488237367147,
          66.71427180413495,
          66.71427180413495,
          67.92525070055476,
          67.92525070055476,
          69.15821094890896,
          69.15821094890896,
          70.41355154858087,
          70.41355154858087,
          71.69167874147956,
          71.69167874147956,
          72.9930061435042,
          72.9930061435042,
          74.31795487839462,
          74.31795487839462,
          75.66695371401163,
          75.66695371401163,
          77.04043920109092,
          77.04043920109092,
          78.43885581451562,
          78.43885581451562,
          79.8626560971533,
          79.8626560971533,
          81.31230080630368,
          81.31230080630368,
          82.78825906280481,
          82.78825906280481,
          84.29100850284559,
          84.29100850284559,
          85.82103543253415,
          85.82103543253415,
          87.37883498527172,
          87.37883498527172,
          88.9649112819833,
          88.9649112819833,
          90.5797775942566,
          90.5797775942566,
          92.22395651044235,
          92.22395651044235,
          93.8979801047696,
          93.8979801047696,
          95.60239010953076,
          95.60239010953076,
          97.33773809039202,
          97.33773809039202,
          99.10458562488608,
          99.10458562488608,
          100.90350448414475,
          100.90350448414475,
          102.73507681793026,
          102.73507681793026,
          104.59989534302535,
          104.59989534302535,
          106.4985635350429,
          106.4985635350429,
          108.4316958237171,
          108.4316958237171,
          110.39991779173975,
          110.39991779173975,
          112.40386637720557,
          112.40386637720557,
          114.44419007973231,
          114.44419007973231,
          116.5215491703223,
          116.5215491703223,
          118.63661590503344,
          118.63661590503344,
          120.79007474252845,
          120.79007474252845,
          122.98262256557321,
          122.98262256557321,
          125.21496890655568,
          125.21496890655568,
          127.48783617709826,
          127.48783617709826,
          129.8019599018381,
          129.8019599018381,
          132.15808895645085,
          132.15808895645085,
          134.55698580999507,
          134.55698580999507,
          136.99942677165546,
          136.99942677165546,
          139.48620224196497,
          139.48620224196497,
          142.01811696858715,
          142.01811696858715,
          144.59599030674116,
          144.59599030674116,
          147.22065648435404,
          147.22065648435404,
          149.89296487202606,
          149.89296487202606,
          152.6137802578963,
          152.6137802578963,
          155.38398312749737,
          155.38398312749737,
          158.20446994869036,
          158.20446994869036,
          161.07615346177147,
          161.07615346177147,
          163.9999629748447,
          163.9999629748447,
          166.9768446645562,
          166.9768446645562,
          170.0077618822873,
          170.0077618822873,
          173.0936954659055,
          173.0936954659055,
          176.23564405717434,
          176.23564405717434,
          179.43462442492472,
          179.43462442492472,
          182.69167179409243,
          182.69167179409243,
          186.00784018072818,
          186.00784018072818,
          189.3842027330888,
          189.3842027330888,
          192.8218520789196,
          192.8218520789196,
          196.32190067904054,
          196.32190067904054,
          199.88548118735102,
          199.88548118735102,
          203.51374681736868,
          203.51374681736868,
          207.2078717154221,
          207.2078717154221,
          210.96905134061717,
          210.96905134061717,
          214.79850285170085,
          214.79850285170085,
          218.69746550094703,
          218.69746550094703,
          222.66720103519188,
          222.66720103519188,
          226.70899410414913,
          226.70899410414913,
          230.82415267613658,
          230.82415267613658,
          235.01400846134894,
          235.01400846134894,
          239.27991734281375,
          239.27991734281375,
          243.6232598151701,
          243.6232598151701,
          248.04544143141135,
          248.04544143141135,
          252.5478932577379,
          252.5478932577379,
          257.13207233666543,
          257.13207233666543,
          261.79946215854,
          261.79946215854,
          266.5515731416115,
          266.5515731416115,
          271.3899431208216,
          271.3899431208216,
          276.31613784546397,
          276.31613784546397,
          281.33175148587765,
          281.33175148587765,
          286.438407149338,
          286.438407149338,
          291.637757405312,
          291.637757405312,
          296.9314848202479,
          296.9314848202479,
          302.32130250207155,
          302.32130250207155,
          307.8089546545674,
          307.8089546545674,
          313.3962171418216,
          313.3962171418216,
          319.08489806291084,
          319.08489806291084,
          324.8768383370232,
          324.8768383370232,
          330.7739122991996,
          330.7739122991996,
          336.7780283068889,
          336.7780283068889,
          342.89112935751353,
          342.89112935751353,
          349.1151937172442,
          349.1151937172442,
          355.4522355611888,
          355.4522355611888,
          361.9043056252011,
          361.9043056252011,
          368.4734918695216,
          368.4734918695216,
          375.16192015446387,
          375.16192015446387,
          381.97175492836647,
          381.97175492836647,
          388.9051999280318,
          388.9051999280318,
          395.96449889187926,
          395.96449889187926,
          403.15193628604396,
          403.15193628604396,
          410.4698380436544,
          410.4698380436544,
          417.92057231753,
          417.92057231753,
          425.5065502465411,
          425.5065502465411,
          433.23022673587985,
          433.23022673587985,
          441.09410125149435,
          441.09410125149435,
          449.100718628943,
          449.100718628943,
          457.2526698969311,
          457.2526698969311,
          465.55259311579584,
          465.55259311579584,
          474.0031742312117,
          474.0031742312117,
          482.6071479433915,
          482.6071479433915,
          491.36729859206537,
          491.36729859206537,
          500.2864610575233,
          500.2864610575233,
          509.36752167801353,
          509.36752167801353,
          518.6134191837928,
          518.6134191837928,
          528.0271456481318,
          528.0271456481318,
          537.6117474555825,
          537.6117474555825,
          547.3703262878216,
          547.3703262878216,
          557.3060401273885,
          557.3060401273885,
          567.4221042796428,
          567.4221042796428,
          577.7217924132722,
          577.7217924132722,
          588.2084376196871,
          588.2084376196871,
          598.8854334916462,
          598.8854334916462,
          609.7562352214592,
          609.7562352214592,
          620.8243607191254,
          620.8243607191254,
          632.093391750767,
          632.093391750767,
          643.5669750977287,
          643.5669750977287,
          655.2488237367147,
          655.2488237367147,
          667.1427180413494,
          667.1427180413494,
          679.2525070055476,
          679.2525070055476,
          691.5821094890896,
          691.5821094890896,
          704.1355154858088,
          704.1355154858088,
          716.9167874147956,
          716.9167874147956,
          729.9300614350419,
          729.9300614350419,
          743.1795487839462,
          743.1795487839462,
          756.6695371401163,
          756.6695371401163,
          770.4043920109092,
          770.4043920109092,
          784.3885581451563,
          784.3885581451563,
          798.626560971533,
          798.626560971533,
          813.1230080630369,
          813.1230080630369,
          827.8825906280481,
          827.8825906280481,
          842.9100850284559,
          842.9100850284559,
          858.2103543253414,
          858.2103543253414,
          873.7883498527173,
          873.7883498527173,
          889.649112819833,
          889.649112819833,
          905.797775942566,
          905.797775942566,
          922.2395651044235,
          922.2395651044235,
          938.9798010476961,
          938.9798010476961,
          956.0239010953076,
          956.0239010953076,
          973.3773809039202,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x1",
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          4.318943631289267e-13,
          4.318943631289267e-13,
          1.197943715654286e-15,
          1.197943715654286e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          3.0131898563550233e-13,
          3.0131898563550233e-13,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.4039878357818805e-13,
          1.4039878357818805e-13,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          3.938387319189893e-14,
          3.938387319189893e-14,
          3.0537302614473423e-13,
          3.0537302614473423e-13,
          1.9999624571244673e-13,
          1.9999624571244673e-13,
          2.792067772769325e-13,
          2.792067772769325e-13,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          3.0318677581387974e-13,
          3.0318677581387974e-13,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.2470546013024176e-13,
          1.2470546013024176e-13,
          0,
          0,
          1.0983121265329658e-13,
          1.0983121265329658e-13,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.0106643013830595e-13,
          1.0106643013830595e-13,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          5.132960166868431e-14,
          5.132960166868431e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          4.559360875881943e-15,
          4.559360875881943e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          3.462206307126671e-14,
          3.462206307126671e-14,
          4.3499990801939846e-14,
          4.3499990801939846e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.2769764155525873e-14,
          1.2769764155525873e-14,
          0,
          0,
          0,
          0,
          4.612420081433129e-13,
          4.612420081433129e-13,
          2.23159255147467e-05,
          2.23159255147467e-05,
          0.22874659050206997,
          0.22874659050206997,
          5.93780937183321,
          5.93780937183321,
          15.468476500521952,
          15.468476500521952,
          24.72357104168492,
          24.72357104168492,
          33.62679812579604,
          33.62679812579604,
          42.19006328578648,
          42.19006328578648,
          50.42487889101441,
          50.42487889101441,
          58.342364191190676,
          58.342364191190676,
          65.95173267335039,
          65.95173267335039,
          72.69857768947155,
          72.69857768947155,
          72.54435911201713,
          72.54435911201713,
          66.02142503645791,
          66.02142503645791,
          59.154928980743804,
          59.154928980743804,
          52.53808071504844,
          52.53808071504844,
          46.16593031468055,
          46.16593031468055,
          40.03006363940118,
          40.03006363940118,
          34.12235378397572,
          34.12235378397572,
          28.434952134877626,
          28.434952134877626,
          22.9602787169695,
          22.9602787169695,
          17.69101291375203,
          17.69101291375203,
          12.624175604930123,
          12.624175604930123,
          7.762021944546807,
          7.762021944546807,
          3.4040428452577145,
          3.4040428452577145,
          0.753898254278906,
          0.753898254278906,
          0.058914872596815014,
          0.058914872596815014,
          0.0012843174365916006,
          0.0012843174365916006,
          8.106896395161825e-06,
          8.106896395161825e-06,
          2.697733710484231e-08,
          2.697733710484231e-08,
          2.309025045489729e-11,
          2.309025045489729e-11,
          0,
          0,
          0,
          0,
          3.1560948204108392e-16,
          3.1560948204108392e-16,
          0,
          0,
          7.765960352315384e-15,
          7.765960352315384e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          8.167453382509707e-15,
          8.167453382509707e-15,
          3.2726213835342358e-15,
          3.2726213835342358e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.0632745717104777e-14,
          1.0632745717104777e-14,
          0,
          0,
          0,
          0,
          1.1697594157918246e-14,
          1.1697594157918246e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          2.759788439175685e-14,
          2.759788439175685e-14,
          0,
          0,
          4.870436522220602e-17,
          4.870436522220602e-17,
          1.4203219845077629e-14,
          1.4203219845077629e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          2.5095990209354358e-14,
          2.5095990209354358e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.769431484661769e-14,
          1.769431484661769e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          2.744563998618759e-14,
          2.744563998618759e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          7.027593869246598e-15,
          7.027593869246598e-15,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          8.299367335964653e-15,
          8.299367335964653e-15,
          1.4323716675550596e-14,
          1.4323716675550596e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          2.5578943106779885e-14,
          2.5578943106779885e-14,
          0,
          0,
          2.4006643092683396e-14,
          2.4006643092683396e-14,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
         ],
         "yaxis": "y1",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "𝕟₁₂ (partMC)",
         "line": {
          "color": "rgba(0, 0, 204, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 1.5
         },
         "mode": "lines",
         "name": "𝕟₁₂ (partMC)",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.090350448414474,
          10.273507681793024,
          10.273507681793024,
          10.459989534302535,
          10.459989534302535,
          10.649856353504289,
          10.649856353504289,
          10.84316958237171,
          10.84316958237171,
          11.039991779173976,
          11.039991779173976,
          11.240386637720556,
          11.240386637720556,
          11.44441900797323,
          11.44441900797323,
          11.652154917032231,
          11.652154917032231,
          11.863661590503344,
          11.863661590503344,
          12.079007474252842,
          12.079007474252842,
          12.298262256557319,
          12.298262256557319,
          12.521496890655566,
          12.521496890655566,
          12.748783617709826,
          12.748783617709826,
          12.98019599018381,
          12.98019599018381,
          13.215808895645086,
          13.215808895645086,
          13.455698580999508,
          13.455698580999508,
          13.699942677165545,
          13.699942677165545,
          13.948620224196498,
          13.948620224196498,
          14.201811696858716,
          14.201811696858716,
          14.459599030674116,
          14.459599030674116,
          14.722065648435406,
          14.722065648435406,
          14.989296487202608,
          14.989296487202608,
          15.261378025789629,
          15.261378025789629,
          15.538398312749738,
          15.538398312749738,
          15.820446994869037,
          15.820446994869037,
          16.10761534617715,
          16.10761534617715,
          16.39999629748447,
          16.39999629748447,
          16.69768446645562,
          16.69768446645562,
          17.00077618822873,
          17.00077618822873,
          17.309369546590553,
          17.309369546590553,
          17.623564405717435,
          17.623564405717435,
          17.94346244249247,
          17.94346244249247,
          18.269167179409244,
          18.269167179409244,
          18.600784018072822,
          18.600784018072822,
          18.938420273308882,
          18.938420273308882,
          19.282185207891956,
          19.282185207891956,
          19.632190067904055,
          19.632190067904055,
          19.988548118735103,
          19.988548118735103,
          20.35137468173687,
          20.35137468173687,
          20.72078717154221,
          20.72078717154221,
          21.096905134061714,
          21.096905134061714,
          21.479850285170084,
          21.479850285170084,
          21.869746550094703,
          21.869746550094703,
          22.266720103519187,
          22.266720103519187,
          22.67089941041491,
          22.67089941041491,
          23.08241526761366,
          23.08241526761366,
          23.501400846134892,
          23.501400846134892,
          23.927991734281377,
          23.927991734281377,
          24.36232598151701,
          24.36232598151701,
          24.804544143141136,
          24.804544143141136,
          25.25478932577379,
          25.25478932577379,
          25.713207233666548,
          25.713207233666548,
          26.179946215854002,
          26.179946215854002,
          26.65515731416115,
          26.65515731416115,
          27.138994312082165,
          27.138994312082165,
          27.6316137845464,
          27.6316137845464,
          28.133175148587764,
          28.133175148587764,
          28.6438407149338,
          28.6438407149338,
          29.163775740531204,
          29.163775740531204,
          29.693148482024785,
          29.693148482024785,
          30.232130250207152,
          30.232130250207152,
          30.78089546545674,
          30.78089546545674,
          31.339621714182158,
          31.339621714182158,
          31.90848980629108,
          31.90848980629108,
          32.48768383370232,
          32.48768383370232,
          33.07739122991996,
          33.07739122991996,
          33.6778028306889,
          33.6778028306889,
          34.289112935751355,
          34.289112935751355,
          34.911519371724424,
          34.911519371724424,
          35.54522355611888,
          35.54522355611888,
          36.19043056252011,
          36.19043056252011,
          36.847349186952165,
          36.847349186952165,
          37.51619201544639,
          37.51619201544639,
          38.19717549283665,
          38.19717549283665,
          38.89051999280318,
          38.89051999280318,
          39.59644988918792,
          39.59644988918792,
          40.31519362860439,
          40.31519362860439,
          41.04698380436544,
          41.04698380436544,
          41.792057231753,
          41.792057231753,
          42.55065502465411,
          42.55065502465411,
          43.323022673587985,
          43.323022673587985,
          44.10941012514944,
          44.10941012514944,
          44.910071862894306,
          44.910071862894306,
          45.72526698969311,
          45.72526698969311,
          46.55525931157958,
          46.55525931157958,
          47.400317423121166,
          47.400317423121166,
          48.26071479433915,
          48.26071479433915,
          49.13672985920654,
          49.13672985920654,
          50.02864610575234,
          50.02864610575234,
          50.93675216780135,
          50.93675216780135,
          51.861341918379274,
          51.861341918379274,
          52.80271456481317,
          52.80271456481317,
          53.76117474555825,
          53.76117474555825,
          54.73703262878217,
          54.73703262878217,
          55.73060401273886,
          55.73060401273886,
          56.74221042796429,
          56.74221042796429,
          57.77217924132721,
          57.77217924132721,
          58.8208437619687,
          58.8208437619687,
          59.888543349164614,
          59.888543349164614,
          60.975623522145916,
          60.975623522145916,
          62.08243607191253,
          62.08243607191253,
          63.20933917507671,
          63.20933917507671,
          64.35669750977287,
          64.35669750977287,
          65.52488237367147,
          65.52488237367147,
          66.71427180413495,
          66.71427180413495,
          67.92525070055476,
          67.92525070055476,
          69.15821094890896,
          69.15821094890896,
          70.41355154858087,
          70.41355154858087,
          71.69167874147956,
          71.69167874147956,
          72.9930061435042,
          72.9930061435042,
          74.31795487839462,
          74.31795487839462,
          75.66695371401163,
          75.66695371401163,
          77.04043920109092,
          77.04043920109092,
          78.43885581451562,
          78.43885581451562,
          79.8626560971533,
          79.8626560971533,
          81.31230080630368,
          81.31230080630368,
          82.78825906280481,
          82.78825906280481,
          84.29100850284559,
          84.29100850284559,
          85.82103543253415,
          85.82103543253415,
          87.37883498527172,
          87.37883498527172,
          88.9649112819833,
          88.9649112819833,
          90.5797775942566,
          90.5797775942566,
          92.22395651044235,
          92.22395651044235,
          93.8979801047696,
          93.8979801047696,
          95.60239010953076,
          95.60239010953076,
          97.33773809039202,
          97.33773809039202,
          99.10458562488608,
          99.10458562488608,
          100.90350448414475,
          100.90350448414475,
          102.73507681793026,
          102.73507681793026,
          104.59989534302535,
          104.59989534302535,
          106.4985635350429,
          106.4985635350429,
          108.4316958237171,
          108.4316958237171,
          110.39991779173975,
          110.39991779173975,
          112.40386637720557,
          112.40386637720557,
          114.44419007973231,
          114.44419007973231,
          116.5215491703223,
          116.5215491703223,
          118.63661590503344,
          118.63661590503344,
          120.79007474252845,
          120.79007474252845,
          122.98262256557321,
          122.98262256557321,
          125.21496890655568,
          125.21496890655568,
          127.48783617709826,
          127.48783617709826,
          129.8019599018381,
          129.8019599018381,
          132.15808895645085,
          132.15808895645085,
          134.55698580999507,
          134.55698580999507,
          136.99942677165546,
          136.99942677165546,
          139.48620224196497,
          139.48620224196497,
          142.01811696858715,
          142.01811696858715,
          144.59599030674116,
          144.59599030674116,
          147.22065648435404,
          147.22065648435404,
          149.89296487202606,
          149.89296487202606,
          152.6137802578963,
          152.6137802578963,
          155.38398312749737,
          155.38398312749737,
          158.20446994869036,
          158.20446994869036,
          161.07615346177147,
          161.07615346177147,
          163.9999629748447,
          163.9999629748447,
          166.9768446645562,
          166.9768446645562,
          170.0077618822873,
          170.0077618822873,
          173.0936954659055,
          173.0936954659055,
          176.23564405717434,
          176.23564405717434,
          179.43462442492472,
          179.43462442492472,
          182.69167179409243,
          182.69167179409243,
          186.00784018072818,
          186.00784018072818,
          189.3842027330888,
          189.3842027330888,
          192.8218520789196,
          192.8218520789196,
          196.32190067904054,
          196.32190067904054,
          199.88548118735102,
          199.88548118735102,
          203.51374681736868,
          203.51374681736868,
          207.2078717154221,
          207.2078717154221,
          210.96905134061717,
          210.96905134061717,
          214.79850285170085,
          214.79850285170085,
          218.69746550094703,
          218.69746550094703,
          222.66720103519188,
          222.66720103519188,
          226.70899410414913,
          226.70899410414913,
          230.82415267613658,
          230.82415267613658,
          235.01400846134894,
          235.01400846134894,
          239.27991734281375,
          239.27991734281375,
          243.6232598151701,
          243.6232598151701,
          248.04544143141135,
          248.04544143141135,
          252.5478932577379,
          252.5478932577379,
          257.13207233666543,
          257.13207233666543,
          261.79946215854,
          261.79946215854,
          266.5515731416115,
          266.5515731416115,
          271.3899431208216,
          271.3899431208216,
          276.31613784546397,
          276.31613784546397,
          281.33175148587765,
          281.33175148587765,
          286.438407149338,
          286.438407149338,
          291.637757405312,
          291.637757405312,
          296.9314848202479,
          296.9314848202479,
          302.32130250207155,
          302.32130250207155,
          307.8089546545674,
          307.8089546545674,
          313.3962171418216,
          313.3962171418216,
          319.08489806291084,
          319.08489806291084,
          324.8768383370232,
          324.8768383370232,
          330.7739122991996,
          330.7739122991996,
          336.7780283068889,
          336.7780283068889,
          342.89112935751353,
          342.89112935751353,
          349.1151937172442,
          349.1151937172442,
          355.4522355611888,
          355.4522355611888,
          361.9043056252011,
          361.9043056252011,
          368.4734918695216,
          368.4734918695216,
          375.16192015446387,
          375.16192015446387,
          381.97175492836647,
          381.97175492836647,
          388.9051999280318,
          388.9051999280318,
          395.96449889187926,
          395.96449889187926,
          403.15193628604396,
          403.15193628604396,
          410.4698380436544,
          410.4698380436544,
          417.92057231753,
          417.92057231753,
          425.5065502465411,
          425.5065502465411,
          433.23022673587985,
          433.23022673587985,
          441.09410125149435,
          441.09410125149435,
          449.100718628943,
          449.100718628943,
          457.2526698969311,
          457.2526698969311,
          465.55259311579584,
          465.55259311579584,
          474.0031742312117,
          474.0031742312117,
          482.6071479433915,
          482.6071479433915,
          491.36729859206537,
          491.36729859206537,
          500.2864610575233,
          500.2864610575233,
          509.36752167801353,
          509.36752167801353,
          518.6134191837928,
          518.6134191837928,
          528.0271456481318,
          528.0271456481318,
          537.6117474555825,
          537.6117474555825,
          547.3703262878216,
          547.3703262878216,
          557.3060401273885,
          557.3060401273885,
          567.4221042796428,
          567.4221042796428,
          577.7217924132722,
          577.7217924132722,
          588.2084376196871,
          588.2084376196871,
          598.8854334916462,
          598.8854334916462,
          609.7562352214592,
          609.7562352214592,
          620.8243607191254,
          620.8243607191254,
          632.093391750767,
          632.093391750767,
          643.5669750977287,
          643.5669750977287,
          655.2488237367147,
          655.2488237367147,
          667.1427180413494,
          667.1427180413494,
          679.2525070055476,
          679.2525070055476,
          691.5821094890896,
          691.5821094890896,
          704.1355154858088,
          704.1355154858088,
          716.9167874147956,
          716.9167874147956,
          729.9300614350419,
          729.9300614350419,
          743.1795487839462,
          743.1795487839462,
          756.6695371401163,
          756.6695371401163,
          770.4043920109092,
          770.4043920109092,
          784.3885581451563,
          784.3885581451563,
          798.626560971533,
          798.626560971533,
          813.1230080630369,
          813.1230080630369,
          827.8825906280481,
          827.8825906280481,
          842.9100850284559,
          842.9100850284559,
          858.2103543253414,
          858.2103543253414,
          873.7883498527173,
          873.7883498527173,
          889.649112819833,
          889.649112819833,
          905.797775942566,
          905.797775942566,
          922.2395651044235,
          922.2395651044235,
          938.9798010476961,
          938.9798010476961,
          956.0239010953076,
          956.0239010953076,
          973.3773809039202,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x2",
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0.015792948989228776,
          0.015792948989228776,
          0.03787796640629062,
          0.03787796640629062,
          0.08601540799184956,
          0.08601540799184956,
          0.21552412829822407,
          0.21552412829822407,
          0.2731740555921125,
          0.2731740555921125,
          0.46298713017445164,
          0.46298713017445164,
          0.577338420459175,
          0.577338420459175,
          0.619159822923045,
          0.619159822923045,
          0.6330471575141582,
          0.6330471575141582,
          0.6604623925544546,
          0.6604623925544546,
          0.5942497468911792,
          0.5942497468911792,
          0.5132919805738363,
          0.5132919805738363,
          0.40359186313669176,
          0.40359186313669176,
          0.3079567853992242,
          0.3079567853992242,
          0.201887132529441,
          0.201887132529441,
          0.1180648644587022,
          0.1180648644587022,
          0.06352676076991295,
          0.06352676076991295,
          0.022126315209840944,
          0.022126315209840944,
          0.00724152242500706,
          0.00724152242500706,
          0.001750072303297965,
          0.001750072303297965,
          0.0012775751129169397,
          0.0012775751129169397,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
         ],
         "yaxis": "y2",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "f⋅[(β₁₂ᵇt)*(𝕟₁*𝕟₂)]",
         "line": {
          "color": "rgba(165, 42, 42, 1.000)",
          "dash": "solid",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "f⋅[(β₁₂ᵇt)*(𝕟₁*𝕟₂)]",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.273507681793024,
          10.459989534302535,
          10.649856353504289,
          10.84316958237171,
          11.039991779173976,
          11.240386637720556,
          11.44441900797323,
          11.652154917032231,
          11.863661590503344,
          12.079007474252842,
          12.298262256557319,
          12.521496890655566,
          12.748783617709826,
          12.98019599018381,
          13.215808895645086,
          13.455698580999508,
          13.699942677165545,
          13.948620224196498,
          14.201811696858716,
          14.459599030674116,
          14.722065648435406,
          14.989296487202608,
          15.261378025789629,
          15.538398312749738,
          15.820446994869037,
          16.10761534617715,
          16.39999629748447,
          16.69768446645562,
          17.00077618822873,
          17.309369546590553,
          17.623564405717435,
          17.94346244249247,
          18.269167179409244,
          18.600784018072822,
          18.938420273308882,
          19.282185207891956,
          19.632190067904055,
          19.988548118735103,
          20.35137468173687,
          20.72078717154221,
          21.096905134061714,
          21.479850285170084,
          21.869746550094703,
          22.266720103519187,
          22.67089941041491,
          23.08241526761366,
          23.501400846134892,
          23.927991734281377,
          24.36232598151701,
          24.804544143141136,
          25.25478932577379,
          25.713207233666548,
          26.179946215854002,
          26.65515731416115,
          27.138994312082165,
          27.6316137845464,
          28.133175148587764,
          28.6438407149338,
          29.163775740531204,
          29.693148482024785,
          30.232130250207152,
          30.78089546545674,
          31.339621714182158,
          31.90848980629108,
          32.48768383370232,
          33.07739122991996,
          33.6778028306889,
          34.289112935751355,
          34.911519371724424,
          35.54522355611888,
          36.19043056252011,
          36.847349186952165,
          37.51619201544639,
          38.19717549283665,
          38.89051999280318,
          39.59644988918792,
          40.31519362860439,
          41.04698380436544,
          41.792057231753,
          42.55065502465411,
          43.323022673587985,
          44.10941012514944,
          44.910071862894306,
          45.72526698969311,
          46.55525931157958,
          47.400317423121166,
          48.26071479433915,
          49.13672985920654,
          50.02864610575234,
          50.93675216780135,
          51.861341918379274,
          52.80271456481317,
          53.76117474555825,
          54.73703262878217,
          55.73060401273886,
          56.74221042796429,
          57.77217924132721,
          58.8208437619687,
          59.888543349164614,
          60.975623522145916,
          62.08243607191253,
          63.20933917507671,
          64.35669750977287,
          65.52488237367147,
          66.71427180413495,
          67.92525070055476,
          69.15821094890896,
          70.41355154858087,
          71.69167874147956,
          72.9930061435042,
          74.31795487839462,
          75.66695371401163,
          77.04043920109092,
          78.43885581451562,
          79.8626560971533,
          81.31230080630368,
          82.78825906280481,
          84.29100850284559,
          85.82103543253415,
          87.37883498527172,
          88.9649112819833,
          90.5797775942566,
          92.22395651044235,
          93.8979801047696,
          95.60239010953076,
          97.33773809039202,
          99.10458562488608,
          100.90350448414475,
          102.73507681793026,
          104.59989534302535,
          106.4985635350429,
          108.4316958237171,
          110.39991779173975,
          112.40386637720557,
          114.44419007973231,
          116.5215491703223,
          118.63661590503344,
          120.79007474252845,
          122.98262256557321,
          125.21496890655568,
          127.48783617709826,
          129.8019599018381,
          132.15808895645085,
          134.55698580999507,
          136.99942677165546,
          139.48620224196497,
          142.01811696858715,
          144.59599030674116,
          147.22065648435404,
          149.89296487202606,
          152.6137802578963,
          155.38398312749737,
          158.20446994869036,
          161.07615346177147,
          163.9999629748447,
          166.9768446645562,
          170.0077618822873,
          173.0936954659055,
          176.23564405717434,
          179.43462442492472,
          182.69167179409243,
          186.00784018072818,
          189.3842027330888,
          192.8218520789196,
          196.32190067904054,
          199.88548118735102,
          203.51374681736868,
          207.2078717154221,
          210.96905134061717,
          214.79850285170085,
          218.69746550094703,
          222.66720103519188,
          226.70899410414913,
          230.82415267613658,
          235.01400846134894,
          239.27991734281375,
          243.6232598151701,
          248.04544143141135,
          252.5478932577379,
          257.13207233666543,
          261.79946215854,
          266.5515731416115,
          271.3899431208216,
          276.31613784546397,
          281.33175148587765,
          286.438407149338,
          291.637757405312,
          296.9314848202479,
          302.32130250207155,
          307.8089546545674,
          313.3962171418216,
          319.08489806291084,
          324.8768383370232,
          330.7739122991996,
          336.7780283068889,
          342.89112935751353,
          349.1151937172442,
          355.4522355611888,
          361.9043056252011,
          368.4734918695216,
          375.16192015446387,
          381.97175492836647,
          388.9051999280318,
          395.96449889187926,
          403.15193628604396,
          410.4698380436544,
          417.92057231753,
          425.5065502465411,
          433.23022673587985,
          441.09410125149435,
          449.100718628943,
          457.2526698969311,
          465.55259311579584,
          474.0031742312117,
          482.6071479433915,
          491.36729859206537,
          500.2864610575233,
          509.36752167801353,
          518.6134191837928,
          528.0271456481318,
          537.6117474555825,
          547.3703262878216,
          557.3060401273885,
          567.4221042796428,
          577.7217924132722,
          588.2084376196871,
          598.8854334916462,
          609.7562352214592,
          620.8243607191254,
          632.093391750767,
          643.5669750977287,
          655.2488237367147,
          667.1427180413494,
          679.2525070055476,
          691.5821094890896,
          704.1355154858088,
          716.9167874147956,
          729.9300614350419,
          743.1795487839462,
          756.6695371401163,
          770.4043920109092,
          784.3885581451563,
          798.626560971533,
          813.1230080630369,
          827.8825906280481,
          842.9100850284559,
          858.2103543253414,
          873.7883498527173,
          889.649112819833,
          905.797775942566,
          922.2395651044235,
          938.9798010476961,
          956.0239010953076,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x2",
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.2948692500253121e-32,
          7.066063534901799e-32,
          1.47003690501054e-32,
          8.021948292657387e-32,
          0,
          0,
          0,
          4.6097193984596395e-33,
          2.67026832968744e-32,
          8.445096972341087e-33,
          0,
          0,
          0,
          0,
          1.1096253157011322e-33,
          6.0551928162063975e-33,
          0,
          0,
          0,
          0,
          1.6924263187054677e-32,
          9.235520803261726e-32,
          0,
          0,
          7.034456481825688e-33,
          3.838682278779354e-32,
          0,
          0,
          0,
          0,
          1.415049780713496e-32,
          7.721885167460305e-32,
          0,
          0,
          0,
          0,
          0,
          4.532488016685056e-33,
          2.473370752179979e-32,
          2.908375257307287e-37,
          1.7112545975806762e-32,
          9.338266169084031e-32,
          0,
          0,
          0,
          0,
          0,
          0,
          3.0743700821115573e-33,
          1.6776747404866052e-32,
          0,
          2.5401180553342097e-33,
          1.3861349757739948e-32,
          0,
          0,
          0,
          0,
          2.4063266085478563e-34,
          2.811900148395201e-33,
          8.178769995138152e-33,
          0,
          0,
          1.3550439573819136e-33,
          7.39443514876823e-33,
          2.2380157104004096e-36,
          1.2212786118358615e-35,
          0,
          1.1978993607162498e-26,
          1.635170109544413e-20,
          1.4767212840645759e-15,
          3.7068261758588255e-11,
          7.81875695597435e-08,
          1.3195493810636216e-05,
          0.0003300324363077736,
          0.002774377513328843,
          0.010967646657888314,
          0.026571658608021666,
          0.05021701445382377,
          0.08280154781138495,
          0.125293521122834,
          0.17875817201440947,
          0.2443516634288891,
          0.3233281947564421,
          0.41704764612945167,
          0.5269726234677785,
          0.6526637679853796,
          0.7639858859297045,
          0.7457145030778874,
          0.6097715209846679,
          0.4744614812412556,
          0.35174146169420495,
          0.24364620567228734,
          0.15237272345425376,
          0.08032002002725151,
          0.030128762841548234,
          0.0043239957934242765,
          6.415402754945914e-06,
          6.10582668683794e-14,
          2.6083890896977585e-29,
          0,
          3.663775031190361e-33,
          1.999311293203752e-32,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          4.2514920969691745e-32,
          2.5893469754032075e-31,
          1.469672448944772e-31,
          0,
          0,
          4.670581795834117e-34,
          2.5487227929519276e-33,
          0,
          0,
          0,
          0,
          0,
          0,
          5.919688222234659e-32,
          3.2303565077557613e-31,
          0,
          0,
          0,
          0,
          0,
          2.29496939114495e-31,
          1.2523580684434624e-30,
          0,
          0,
          0,
          2.710282764317869e-31,
          1.4789933585838696e-30,
          3.4940891703857583e-31,
          1.9067142164412235e-30,
          0,
          0,
          0,
          2.065301950112675e-30,
          1.1270292192024783e-29,
          0,
          0,
          0,
          0,
          0,
          1.7515194225687576e-30,
          1.0456673564784727e-29,
          6.999283832116371e-30,
          1.1468265943096313e-29,
          1.9017416376797924e-31,
          0,
          0,
          0,
          4.428837400659248e-31,
          2.4168035852420076e-30,
          0,
          0,
          0,
          0,
          0,
          0,
          2.0399336376869543e-30,
          1.1131858054856826e-29,
          0,
          0,
          0,
          3.2243031906369405e-35,
          4.1911803575261916e-30,
          2.2870188185520317e-29,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
         ],
         "yaxis": "y2",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "f⋅[(β₁₂ᶻ⁽¹ ⁻¹⁾t)*(𝕟₁*𝕟₂)]",
         "line": {
          "color": "rgba(165, 42, 42, 1.000)",
          "dash": "dash",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "f⋅[(β₁₂ᶻ⁽¹ ⁻¹⁾t)*(𝕟₁*𝕟₂)]",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.273507681793024,
          10.459989534302535,
          10.649856353504289,
          10.84316958237171,
          11.039991779173976,
          11.240386637720556,
          11.44441900797323,
          11.652154917032231,
          11.863661590503344,
          12.079007474252842,
          12.298262256557319,
          12.521496890655566,
          12.748783617709826,
          12.98019599018381,
          13.215808895645086,
          13.455698580999508,
          13.699942677165545,
          13.948620224196498,
          14.201811696858716,
          14.459599030674116,
          14.722065648435406,
          14.989296487202608,
          15.261378025789629,
          15.538398312749738,
          15.820446994869037,
          16.10761534617715,
          16.39999629748447,
          16.69768446645562,
          17.00077618822873,
          17.309369546590553,
          17.623564405717435,
          17.94346244249247,
          18.269167179409244,
          18.600784018072822,
          18.938420273308882,
          19.282185207891956,
          19.632190067904055,
          19.988548118735103,
          20.35137468173687,
          20.72078717154221,
          21.096905134061714,
          21.479850285170084,
          21.869746550094703,
          22.266720103519187,
          22.67089941041491,
          23.08241526761366,
          23.501400846134892,
          23.927991734281377,
          24.36232598151701,
          24.804544143141136,
          25.25478932577379,
          25.713207233666548,
          26.179946215854002,
          26.65515731416115,
          27.138994312082165,
          27.6316137845464,
          28.133175148587764,
          28.6438407149338,
          29.163775740531204,
          29.693148482024785,
          30.232130250207152,
          30.78089546545674,
          31.339621714182158,
          31.90848980629108,
          32.48768383370232,
          33.07739122991996,
          33.6778028306889,
          34.289112935751355,
          34.911519371724424,
          35.54522355611888,
          36.19043056252011,
          36.847349186952165,
          37.51619201544639,
          38.19717549283665,
          38.89051999280318,
          39.59644988918792,
          40.31519362860439,
          41.04698380436544,
          41.792057231753,
          42.55065502465411,
          43.323022673587985,
          44.10941012514944,
          44.910071862894306,
          45.72526698969311,
          46.55525931157958,
          47.400317423121166,
          48.26071479433915,
          49.13672985920654,
          50.02864610575234,
          50.93675216780135,
          51.861341918379274,
          52.80271456481317,
          53.76117474555825,
          54.73703262878217,
          55.73060401273886,
          56.74221042796429,
          57.77217924132721,
          58.8208437619687,
          59.888543349164614,
          60.975623522145916,
          62.08243607191253,
          63.20933917507671,
          64.35669750977287,
          65.52488237367147,
          66.71427180413495,
          67.92525070055476,
          69.15821094890896,
          70.41355154858087,
          71.69167874147956,
          72.9930061435042,
          74.31795487839462,
          75.66695371401163,
          77.04043920109092,
          78.43885581451562,
          79.8626560971533,
          81.31230080630368,
          82.78825906280481,
          84.29100850284559,
          85.82103543253415,
          87.37883498527172,
          88.9649112819833,
          90.5797775942566,
          92.22395651044235,
          93.8979801047696,
          95.60239010953076,
          97.33773809039202,
          99.10458562488608,
          100.90350448414475,
          102.73507681793026,
          104.59989534302535,
          106.4985635350429,
          108.4316958237171,
          110.39991779173975,
          112.40386637720557,
          114.44419007973231,
          116.5215491703223,
          118.63661590503344,
          120.79007474252845,
          122.98262256557321,
          125.21496890655568,
          127.48783617709826,
          129.8019599018381,
          132.15808895645085,
          134.55698580999507,
          136.99942677165546,
          139.48620224196497,
          142.01811696858715,
          144.59599030674116,
          147.22065648435404,
          149.89296487202606,
          152.6137802578963,
          155.38398312749737,
          158.20446994869036,
          161.07615346177147,
          163.9999629748447,
          166.9768446645562,
          170.0077618822873,
          173.0936954659055,
          176.23564405717434,
          179.43462442492472,
          182.69167179409243,
          186.00784018072818,
          189.3842027330888,
          192.8218520789196,
          196.32190067904054,
          199.88548118735102,
          203.51374681736868,
          207.2078717154221,
          210.96905134061717,
          214.79850285170085,
          218.69746550094703,
          222.66720103519188,
          226.70899410414913,
          230.82415267613658,
          235.01400846134894,
          239.27991734281375,
          243.6232598151701,
          248.04544143141135,
          252.5478932577379,
          257.13207233666543,
          261.79946215854,
          266.5515731416115,
          271.3899431208216,
          276.31613784546397,
          281.33175148587765,
          286.438407149338,
          291.637757405312,
          296.9314848202479,
          302.32130250207155,
          307.8089546545674,
          313.3962171418216,
          319.08489806291084,
          324.8768383370232,
          330.7739122991996,
          336.7780283068889,
          342.89112935751353,
          349.1151937172442,
          355.4522355611888,
          361.9043056252011,
          368.4734918695216,
          375.16192015446387,
          381.97175492836647,
          388.9051999280318,
          395.96449889187926,
          403.15193628604396,
          410.4698380436544,
          417.92057231753,
          425.5065502465411,
          433.23022673587985,
          441.09410125149435,
          449.100718628943,
          457.2526698969311,
          465.55259311579584,
          474.0031742312117,
          482.6071479433915,
          491.36729859206537,
          500.2864610575233,
          509.36752167801353,
          518.6134191837928,
          528.0271456481318,
          537.6117474555825,
          547.3703262878216,
          557.3060401273885,
          567.4221042796428,
          577.7217924132722,
          588.2084376196871,
          598.8854334916462,
          609.7562352214592,
          620.8243607191254,
          632.093391750767,
          643.5669750977287,
          655.2488237367147,
          667.1427180413494,
          679.2525070055476,
          691.5821094890896,
          704.1355154858088,
          716.9167874147956,
          729.9300614350419,
          743.1795487839462,
          756.6695371401163,
          770.4043920109092,
          784.3885581451563,
          798.626560971533,
          813.1230080630369,
          827.8825906280481,
          842.9100850284559,
          858.2103543253414,
          873.7883498527173,
          889.649112819833,
          905.797775942566,
          922.2395651044235,
          938.9798010476961,
          956.0239010953076,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x2",
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.4262814740431077e-32,
          7.783176188673087e-32,
          1.619226345621548e-32,
          8.836070696192152e-32,
          0,
          0,
          0,
          5.077545380301215e-33,
          2.9412654978738427e-32,
          9.302163409867192e-33,
          0,
          0,
          0,
          0,
          1.222237713099467e-33,
          6.669715367281501e-33,
          0,
          0,
          0,
          0,
          1.8641853642793655e-32,
          1.0172804879391818e-31,
          0,
          0,
          7.748361434789117e-33,
          4.2282581186120113e-32,
          0,
          0,
          0,
          0,
          1.5586587503263117e-32,
          8.505555104364089e-32,
          0,
          0,
          0,
          0,
          0,
          4.992476027516997e-33,
          2.724385402005191e-32,
          3.2035371517098355e-37,
          1.88492446619819e-32,
          1.0285977550542415e-31,
          0,
          0,
          0,
          0,
          0,
          0,
          3.386378271306068e-33,
          1.8479366945962677e-32,
          0,
          2.7979066798711667e-33,
          1.526809472408889e-32,
          0,
          0,
          0,
          0,
          2.650537158251073e-34,
          3.097271086201747e-33,
          9.008807742014997e-33,
          0,
          0,
          1.4925631239525545e-33,
          8.144873209009443e-33,
          2.465144914283145e-36,
          1.3452223525058784e-35,
          0,
          1.319470414425449e-26,
          1.8011184018051594e-20,
          1.626589101367016e-15,
          4.083020352844236e-11,
          8.612258107244344e-08,
          1.4534663142701882e-05,
          0.00036352639444475786,
          0.0030559403964418507,
          0.012080718761134467,
          0.029268333004647793,
          0.05531338194635767,
          0.09120481752359505,
          0.13800916810066624,
          0.19689977893364863,
          0.26915014832071155,
          0.35614176041936324,
          0.4593725053368092,
          0.5804534242861155,
          0.7189005693343318,
          0.8415204203132075,
          0.821394732050716,
          0.6716553225451287,
          0.5226130907257439,
          0.3874386008143147,
          0.26837309586623287,
          0.16783655385132326,
          0.08847144725801528,
          0.033186436604235224,
          0.004762824581617655,
          7.0664818843490216e-06,
          6.725487910833257e-14,
          2.873106327653819e-29,
          0,
          4.0356000823607255e-33,
          2.202215133524822e-32,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          4.6829627121265575e-32,
          2.85213168882878e-31,
          1.618824902051321e-31,
          0,
          0,
          5.144584511734268e-34,
          2.8073846853554364e-33,
          0,
          0,
          0,
          0,
          0,
          0,
          6.520458836534596e-32,
          3.558195270662707e-31,
          0,
          0,
          0,
          0,
          0,
          2.5278786456795127e-31,
          1.3794559658084426e-30,
          0,
          0,
          0,
          2.9853408721300264e-31,
          1.6290917616120178e-30,
          3.8486933350826274e-31,
          2.100220669501246e-30,
          0,
          0,
          0,
          2.274902975488242e-30,
          1.24140788424958e-29,
          0,
          0,
          0,
          0,
          0,
          1.929275642145079e-30,
          1.1517888609430811e-29,
          7.709619223038836e-30,
          1.2632144329412435e-29,
          2.0947434392978796e-31,
          0,
          0,
          0,
          4.878306235155431e-31,
          2.6620774104908702e-30,
          0,
          0,
          0,
          0,
          0,
          0,
          2.2469601125004645e-30,
          1.2261595458390467e-29,
          0,
          0,
          0,
          3.5515276213514633e-35,
          4.616530123173534e-30,
          2.519121194379243e-29,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
         ],
         "yaxis": "y2",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "f⋅[(β₁₂ᶻ⁽² ⁻²⁾*t)*(𝕟₁*𝕟₂)]",
         "line": {
          "color": "rgba(165, 42, 42, 1.000)",
          "dash": "dot",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "f⋅[(β₁₂ᶻ⁽² ⁻²⁾*t)*(𝕟₁*𝕟₂)]",
         "showlegend": true,
         "text": [
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null,
          null
         ],
         "type": "scatter",
         "x": [
          10.090350448414474,
          10.273507681793024,
          10.459989534302535,
          10.649856353504289,
          10.84316958237171,
          11.039991779173976,
          11.240386637720556,
          11.44441900797323,
          11.652154917032231,
          11.863661590503344,
          12.079007474252842,
          12.298262256557319,
          12.521496890655566,
          12.748783617709826,
          12.98019599018381,
          13.215808895645086,
          13.455698580999508,
          13.699942677165545,
          13.948620224196498,
          14.201811696858716,
          14.459599030674116,
          14.722065648435406,
          14.989296487202608,
          15.261378025789629,
          15.538398312749738,
          15.820446994869037,
          16.10761534617715,
          16.39999629748447,
          16.69768446645562,
          17.00077618822873,
          17.309369546590553,
          17.623564405717435,
          17.94346244249247,
          18.269167179409244,
          18.600784018072822,
          18.938420273308882,
          19.282185207891956,
          19.632190067904055,
          19.988548118735103,
          20.35137468173687,
          20.72078717154221,
          21.096905134061714,
          21.479850285170084,
          21.869746550094703,
          22.266720103519187,
          22.67089941041491,
          23.08241526761366,
          23.501400846134892,
          23.927991734281377,
          24.36232598151701,
          24.804544143141136,
          25.25478932577379,
          25.713207233666548,
          26.179946215854002,
          26.65515731416115,
          27.138994312082165,
          27.6316137845464,
          28.133175148587764,
          28.6438407149338,
          29.163775740531204,
          29.693148482024785,
          30.232130250207152,
          30.78089546545674,
          31.339621714182158,
          31.90848980629108,
          32.48768383370232,
          33.07739122991996,
          33.6778028306889,
          34.289112935751355,
          34.911519371724424,
          35.54522355611888,
          36.19043056252011,
          36.847349186952165,
          37.51619201544639,
          38.19717549283665,
          38.89051999280318,
          39.59644988918792,
          40.31519362860439,
          41.04698380436544,
          41.792057231753,
          42.55065502465411,
          43.323022673587985,
          44.10941012514944,
          44.910071862894306,
          45.72526698969311,
          46.55525931157958,
          47.400317423121166,
          48.26071479433915,
          49.13672985920654,
          50.02864610575234,
          50.93675216780135,
          51.861341918379274,
          52.80271456481317,
          53.76117474555825,
          54.73703262878217,
          55.73060401273886,
          56.74221042796429,
          57.77217924132721,
          58.8208437619687,
          59.888543349164614,
          60.975623522145916,
          62.08243607191253,
          63.20933917507671,
          64.35669750977287,
          65.52488237367147,
          66.71427180413495,
          67.92525070055476,
          69.15821094890896,
          70.41355154858087,
          71.69167874147956,
          72.9930061435042,
          74.31795487839462,
          75.66695371401163,
          77.04043920109092,
          78.43885581451562,
          79.8626560971533,
          81.31230080630368,
          82.78825906280481,
          84.29100850284559,
          85.82103543253415,
          87.37883498527172,
          88.9649112819833,
          90.5797775942566,
          92.22395651044235,
          93.8979801047696,
          95.60239010953076,
          97.33773809039202,
          99.10458562488608,
          100.90350448414475,
          102.73507681793026,
          104.59989534302535,
          106.4985635350429,
          108.4316958237171,
          110.39991779173975,
          112.40386637720557,
          114.44419007973231,
          116.5215491703223,
          118.63661590503344,
          120.79007474252845,
          122.98262256557321,
          125.21496890655568,
          127.48783617709826,
          129.8019599018381,
          132.15808895645085,
          134.55698580999507,
          136.99942677165546,
          139.48620224196497,
          142.01811696858715,
          144.59599030674116,
          147.22065648435404,
          149.89296487202606,
          152.6137802578963,
          155.38398312749737,
          158.20446994869036,
          161.07615346177147,
          163.9999629748447,
          166.9768446645562,
          170.0077618822873,
          173.0936954659055,
          176.23564405717434,
          179.43462442492472,
          182.69167179409243,
          186.00784018072818,
          189.3842027330888,
          192.8218520789196,
          196.32190067904054,
          199.88548118735102,
          203.51374681736868,
          207.2078717154221,
          210.96905134061717,
          214.79850285170085,
          218.69746550094703,
          222.66720103519188,
          226.70899410414913,
          230.82415267613658,
          235.01400846134894,
          239.27991734281375,
          243.6232598151701,
          248.04544143141135,
          252.5478932577379,
          257.13207233666543,
          261.79946215854,
          266.5515731416115,
          271.3899431208216,
          276.31613784546397,
          281.33175148587765,
          286.438407149338,
          291.637757405312,
          296.9314848202479,
          302.32130250207155,
          307.8089546545674,
          313.3962171418216,
          319.08489806291084,
          324.8768383370232,
          330.7739122991996,
          336.7780283068889,
          342.89112935751353,
          349.1151937172442,
          355.4522355611888,
          361.9043056252011,
          368.4734918695216,
          375.16192015446387,
          381.97175492836647,
          388.9051999280318,
          395.96449889187926,
          403.15193628604396,
          410.4698380436544,
          417.92057231753,
          425.5065502465411,
          433.23022673587985,
          441.09410125149435,
          449.100718628943,
          457.2526698969311,
          465.55259311579584,
          474.0031742312117,
          482.6071479433915,
          491.36729859206537,
          500.2864610575233,
          509.36752167801353,
          518.6134191837928,
          528.0271456481318,
          537.6117474555825,
          547.3703262878216,
          557.3060401273885,
          567.4221042796428,
          577.7217924132722,
          588.2084376196871,
          598.8854334916462,
          609.7562352214592,
          620.8243607191254,
          632.093391750767,
          643.5669750977287,
          655.2488237367147,
          667.1427180413494,
          679.2525070055476,
          691.5821094890896,
          704.1355154858088,
          716.9167874147956,
          729.9300614350419,
          743.1795487839462,
          756.6695371401163,
          770.4043920109092,
          784.3885581451563,
          798.626560971533,
          813.1230080630369,
          827.8825906280481,
          842.9100850284559,
          858.2103543253414,
          873.7883498527173,
          889.649112819833,
          905.797775942566,
          922.2395651044235,
          938.9798010476961,
          956.0239010953076,
          973.3773809039202,
          991.0458562488608
         ],
         "xaxis": "x2",
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          3.0836862142293453e-32,
          1.6827585264704841e-31,
          3.5008419099463216e-32,
          1.9103991666220086e-31,
          0,
          0,
          0,
          1.0977886887203248e-32,
          6.359151425048833e-32,
          2.0111705572534927e-32,
          0,
          0,
          0,
          0,
          2.6425342087014404e-33,
          1.442023170406682e-32,
          0,
          0,
          0,
          0,
          4.030454586429442e-32,
          2.1994072514803946e-31,
          0,
          0,
          1.675231416390349e-32,
          9.141688725442343e-32,
          0,
          0,
          0,
          0,
          3.369891980328644e-32,
          1.838940173943734e-31,
          0,
          0,
          0,
          0,
          0,
          1.0793963029810305e-32,
          5.890246672416055e-32,
          6.926194815877269e-37,
          4.07529347962581e-32,
          2.223875704040836e-31,
          0,
          0,
          0,
          0,
          0,
          0,
          7.321505734622415e-33,
          3.995324214470464e-32,
          0,
          6.0492030601514694e-33,
          3.301032375100296e-32,
          0,
          0,
          0,
          0,
          5.730583369376658e-34,
          6.69644268965861e-33,
          1.947745711226605e-32,
          0,
          0,
          3.2269901930034256e-33,
          1.7609590875544977e-32,
          5.3297568022837284e-36,
          2.9084326614272287e-35,
          0,
          2.852755785653752e-26,
          3.894100909897603e-20,
          3.5167605268562618e-15,
          8.827677988968301e-11,
          1.8620098544371634e-07,
          3.1424610904160506e-05,
          0.0007859608018886166,
          0.006607083835493665,
          0.026119070169291308,
          0.06327948349778419,
          0.11959007844844952,
          0.19718901464207947,
          0.298382175506279,
          0.4257063875066126,
          0.5819150125967889,
          0.7699948831301777,
          0.9931845064828351,
          1.254967027931271,
          1.554296129763026,
          1.8194058931132775,
          1.775893228484047,
          1.4521497309889189,
          1.1299135637500808,
          0.8376600930001976,
          0.5802349894139761,
          0.36287035678025226,
          0.19127934228094357,
          0.07175060387328795,
          0.010297446030406136,
          1.5278059181472533e-05,
          1.4540814511046376e-13,
          6.211788160920476e-29,
          0,
          8.725153180908847e-33,
          4.76129051074843e-32,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1.0124780991650371e-31,
          6.166440026088529e-31,
          3.4999739704646493e-31,
          0,
          0,
          1.1122828575906534e-33,
          6.069694944384797e-33,
          0,
          0,
          0,
          0,
          0,
          0,
          1.409753221268016e-31,
          7.692981997848636e-31,
          0,
          0,
          0,
          0,
          0,
          5.465390017883007e-31,
          2.9824473095353093e-30,
          0,
          0,
          0,
          6.454444413462624e-31,
          3.5221713935308016e-30,
          8.321052187930162e-31,
          4.5407737836078595e-30,
          0,
          0,
          0,
          4.918444971690339e-30,
          2.6839810013407973e-29,
          0,
          0,
          0,
          0,
          0,
          4.1711827639930745e-30,
          2.4902205468075447e-29,
          1.6668551718371314e-29,
          2.7311277636063006e-29,
          4.528931759731322e-31,
          0,
          0,
          0,
          1.0547122682239366e-30,
          5.755533926043227e-30,
          0,
          0,
          0,
          0,
          0,
          0,
          4.858031215394923e-30,
          2.6510133916493e-29,
          0,
          0,
          0,
          7.678566233052846e-35,
          9.981150675714703e-30,
          5.446456004970482e-29,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
         ],
         "yaxis": "y2",
         "zmax": 0.1,
         "zmin": -0.1
        },
        {
         "colorbar": {
          "title": ""
         },
         "hoverinfo": "text",
         "legendgroup": "f*Dₘ",
         "line": {
          "color": "rgba(128, 128, 128, 1.000)",
          "dash": "dashdot",
          "shape": "linear",
          "width": 1
         },
         "mode": "lines",
         "name": "f*Dₘ",
         "showlegend": true,
         "text": [
          null,
          null
         ],
         "type": "scatter",
         "x": [
          125.9921049894873,
          125.9921049894873
         ],
         "xaxis": "x2",
         "y": [
          0,
          1.9103761877689414
         ],
         "yaxis": "y2",
         "zmax": 0.1,
         "zmin": -0.1
        }
       ],
       "layout": {
        "annotations": [],
        "height": 288,
        "legend": {
         "bgcolor": "rgba(255, 255, 255, 1.000)",
         "bordercolor": "rgba(0, 0, 0, 1.000)",
         "font": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 14
         },
         "tracegroupgap": 0,
         "x": 1,
         "y": 1
        },
        "margin": {
         "b": 20,
         "l": 0,
         "r": 0,
         "t": 20
        },
        "paper_bgcolor": "rgba(255, 255, 255, 1.000)",
        "plot_bgcolor": "rgba(255, 255, 255, 1.000)",
        "showlegend": true,
        "width": 792,
        "xaxis1": {
         "anchor": "y1",
         "domain": [
          0.09890572390572391,
          0.4971334075664785
         ],
         "gridcolor": "rgba(0, 0, 0, 0.100)",
         "gridwidth": 0.5,
         "linecolor": "rgba(0, 0, 0, 1.000)",
         "mirror": false,
         "range": [
          1.6020599913279623,
          2.6020599913279625
         ],
         "showgrid": true,
         "showline": true,
         "showticklabels": true,
         "tickangle": 0,
         "tickcolor": "rgb(0, 0, 0)",
         "tickfont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "tickmode": "array",
         "ticks": "inside",
         "ticktext": [
          "10^1.7781513",
          "10^1.9030900",
          "10^2.0000000",
          "10^2.0791812",
          "10^2.1461280",
          "10^2.2041200"
         ],
         "tickvals": [
          60,
          79.99999999999999,
          100,
          119.99999999999996,
          140.00000000000006,
          159.99999999999991
         ],
         "title": "Diameter (nm)",
         "titlefont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "type": "log",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1.000)"
        },
        "xaxis2": {
         "anchor": "y2",
         "domain": [
          0.5968013468013469,
          0.9950290304621014
         ],
         "gridcolor": "rgba(0, 0, 0, 0.100)",
         "gridwidth": 0.5,
         "linecolor": "rgba(0, 0, 0, 1.000)",
         "mirror": false,
         "range": [
          1.954242509439325,
          2.255272505103306
         ],
         "showgrid": true,
         "showline": true,
         "showticklabels": true,
         "tickangle": 0,
         "tickcolor": "rgb(0, 0, 0)",
         "tickfont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "tickmode": "array",
         "ticks": "inside",
         "ticktext": [
          "10^2.0000000",
          "10^2.0791812",
          "10^2.1461280",
          "10^2.2041200"
         ],
         "tickvals": [
          100,
          119.99999999999996,
          140.00000000000006,
          159.99999999999991
         ],
         "title": "Diameter (nm)",
         "titlefont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "type": "log",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1.000)"
        },
        "yaxis1": {
         "anchor": "x1",
         "domain": [
          0.1294109069699621,
          0.9863298337707787
         ],
         "gridcolor": "rgba(0, 0, 0, 0.100)",
         "gridwidth": 0.5,
         "linecolor": "rgba(0, 0, 0, 1.000)",
         "mirror": false,
         "range": [
          -2.1809573306841465,
          74.8795350201557
         ],
         "showgrid": true,
         "showline": true,
         "showticklabels": true,
         "tickangle": 0,
         "tickcolor": "rgb(0, 0, 0)",
         "tickfont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "tickmode": "array",
         "ticks": "inside",
         "ticktext": [
          "0",
          "20",
          "40",
          "60"
         ],
         "tickvals": [
          0,
          20,
          40,
          60
         ],
         "title": "dN/dlnD (m⁻³) × 10⁻¹⁰",
         "titlefont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "type": "-",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1.000)"
        },
        "yaxis2": {
         "anchor": "x2",
         "domain": [
          0.1294109069699621,
          0.9863298337707787
         ],
         "gridcolor": "rgba(0, 0, 0, 0.100)",
         "gridwidth": 0.5,
         "linecolor": "rgba(0, 0, 0, 1.000)",
         "mirror": false,
         "range": [
          -0.05731128563306824,
          1.9676874734020096
         ],
         "showgrid": true,
         "showline": true,
         "showticklabels": true,
         "tickangle": 0,
         "tickcolor": "rgb(0, 0, 0)",
         "tickfont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "tickmode": "array",
         "ticks": "inside",
         "ticktext": [
          "0.0",
          "0.5",
          "1.0",
          "1.5"
         ],
         "tickvals": [
          0,
          0.5,
          1,
          1.5
         ],
         "title": "",
         "titlefont": {
          "color": "rgba(0, 0, 0, 1.000)",
          "family": "Nimbus Sans L",
          "size": 17
         },
         "type": "-",
         "visible": true,
         "zeroline": false,
         "zerolinecolor": "rgba(0, 0, 0, 1.000)"
        }
       }
      },
      "image/svg+xml": [
       "<svg class=\"main-svg\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"792\" height=\"288\" viewBox=\"0 0 792 288\"><rect x=\"0\" y=\"0\" width=\"792\" height=\"288\" style=\"fill: rgb(255, 255, 255); fill-opacity: 1;\"/><defs id=\"defs-7e11e8\"><g class=\"clips\"><clipPath id=\"clip7e11e8xyplot\" class=\"plotclip\"><rect width=\"242.52065934939952\" height=\"212.51589384660252\"/></clipPath><clipPath id=\"clip7e11e8x2y2plot\" class=\"plotclip\"><rect width=\"242.52065934939952\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip7e11e8x\"><rect x=\"60.23358585858586\" y=\"0\" width=\"242.52065934939952\" height=\"288\"/></clipPath><clipPath class=\"axesclip\" id=\"clip7e11e8y\"><rect x=\"0\" y=\"23.390201224846894\" width=\"792\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip7e11e8xy\"><rect x=\"60.23358585858586\" y=\"23.390201224846894\" width=\"242.52065934939952\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip7e11e8y2\"><rect x=\"0\" y=\"23.390201224846894\" width=\"792\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip7e11e8xy2\"><rect x=\"60.23358585858586\" y=\"23.390201224846894\" width=\"242.52065934939952\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip7e11e8x2\"><rect x=\"363.45202020202026\" y=\"0\" width=\"242.52065934939952\" height=\"288\"/></clipPath><clipPath class=\"axesclip\" id=\"clip7e11e8x2y\"><rect x=\"363.45202020202026\" y=\"23.390201224846894\" width=\"242.52065934939952\" height=\"212.51589384660252\"/></clipPath><clipPath class=\"axesclip\" id=\"clip7e11e8x2y2\"><rect x=\"363.45202020202026\" y=\"23.390201224846894\" width=\"242.52065934939952\" height=\"212.51589384660252\"/></clipPath></g><g class=\"gradients\"/></defs><g class=\"bglayer\"/><g class=\"layer-below\"><g class=\"imagelayer\"/><g class=\"shapelayer\"/></g><g class=\"cartesianlayer\"><g class=\"subplot xy\"><g class=\"layer-subplot\"><g class=\"shapelayer\"/><g class=\"imagelayer\"/></g><g class=\"gridlayer\"><g class=\"x\"><path class=\"xgrid crisp\" transform=\"translate(83.73358585858585,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(102.94358585858586,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(119.17358585858585,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(133.24358585858587,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(145.64358585858585,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(156.74358585858587,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(229.74358585858585,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"xgrid crisp\" transform=\"translate(272.4535858585859,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/></g><g class=\"y\"><path class=\"ygrid crisp\" transform=\"translate(0,229.8902012248469)\" d=\"M60.23358585858586,0h242.52065934939952\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,174.74020122484688)\" d=\"M60.23358585858586,0h242.52065934939952\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,119.58020122484689)\" d=\"M60.23358585858586,0h242.52065934939952\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"ygrid crisp\" transform=\"translate(0,64.42020122484689)\" d=\"M60.23358585858586,0h242.52065934939952\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/></g></g><g class=\"zerolinelayer\"/><path class=\"xlines-below\"/><path class=\"ylines-below\"/><g class=\"overlines-below\"/><g class=\"xaxislayer-below\"/><g class=\"yaxislayer-below\"/><g class=\"overaxes-below\"/><g class=\"plot\" transform=\"translate(60.23358585858586, 23.390201224846894)\" clip-path=\"url('#clip7e11e8xyplot')\"><g class=\"scatterlayer mlayer\"><g class=\"trace scatter tracee9d280\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-145.06,206.5L78.51,206.08L78.51,195.58L80.4,195.58L80.4,178.06L82.3,178.06L82.3,161.05L84.19,161.05L84.19,144.68L86.09,144.68L86.09,128.93L87.98,128.93L87.98,113.79L89.88,113.79L89.88,99.24L91.77,99.24L91.77,85.25L93.67,85.25L93.67,72.84L97.46,73.13L97.46,85.12L99.35,85.12L99.35,97.74L101.25,97.74L101.25,109.91L103.14,109.91L103.14,121.62L105.03,121.62L105.03,132.91L106.93,132.91L106.93,143.77L108.82,143.77L108.82,154.22L110.72,154.22L110.72,164.29L112.61,164.29L112.61,173.98L114.51,173.98L114.51,183.29L116.4,183.29L116.4,192.23L118.3,192.23L118.3,200.24L120.19,200.24L120.19,205.12L122.09,205.12L122.09,206.39L338.08,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace5694e2\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-145.06,206.5L78.51,205.87L78.51,190.13L80.4,190.13L80.4,163.84L82.3,163.84L82.3,138.32L84.19,138.32L84.19,113.77L86.09,113.77L86.09,90.15L87.98,90.15L87.98,67.44L89.88,67.44L89.88,45.61L91.77,45.61L91.77,24.62L93.67,24.62L93.67,6.01L97.46,6.44L97.46,24.43L99.35,24.43L99.35,43.37L101.25,43.37L101.25,61.61L103.14,61.61L103.14,79.19L105.03,79.19L105.03,96.11L106.93,96.11L106.93,112.4L108.82,112.4L108.82,128.08L110.72,128.08L110.72,143.18L112.61,143.18L112.61,157.71L114.51,157.71L114.51,171.69L116.4,171.69L116.4,185.1L118.3,185.1L118.3,197.11L120.19,197.11L120.19,204.42L122.09,204.42L122.09,206.34L338.08,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(204, 0, 0); stroke-opacity: 1; stroke-width: 1px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g></g></g><g class=\"overplot\"/><path class=\"xlines-above crisp\" d=\"M59.23358585858586,236.4060950714494H302.7542452079854\" style=\"fill: none; stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 1;\"/><path class=\"ylines-above crisp\" d=\"M59.73358585858586,23.390201224846894V235.9060950714494\" style=\"fill: none; stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 1;\"/><g class=\"overlines-above\"/><g class=\"xaxislayer-above\"><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(83.73358585858585,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(102.94358585858586,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(119.17358585858585,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(133.24358585858587,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(145.64358585858585,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(156.74358585858587,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(229.74358585858585,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(272.4535858585859,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(60.23358585858586,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">4</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(83.73358585858585,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">5</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(102.94358585858586,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">6</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(119.17358585858585,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">7</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(133.24358585858587,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">8</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(145.64358585858585,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">9</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"4.25\" y=\"265.8060950714494\" transform=\"translate(156.74358585858587,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">100</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(229.74358585858585,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">2</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(272.4535858585859,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">3</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"253.05609507144942\" transform=\"translate(302.7535858585859,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 12.75px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">4</text></g></g><g class=\"yaxislayer-above\"><path class=\"ytick ticks crisp\" d=\"M60.23358585858586,0h5\" transform=\"translate(0,229.8902012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M60.23358585858586,0h5\" transform=\"translate(0,174.74020122484688)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M60.23358585858586,0h5\" transform=\"translate(0,119.58020122484689)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M60.23358585858586,0h5\" transform=\"translate(0,64.42020122484689)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"ytick\"><text text-anchor=\"end\" x=\"55.83358585858586\" y=\"5.949999999999999\" transform=\"translate(0,229.8902012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">0</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"55.83358585858586\" y=\"5.949999999999999\" transform=\"translate(0,174.74020122484688)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">20</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"55.83358585858586\" y=\"5.949999999999999\" transform=\"translate(0,119.58020122484689)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">40</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"55.83358585858586\" y=\"5.949999999999999\" transform=\"translate(0,64.42020122484689)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">60</text></g></g><g class=\"overaxes-above\"/></g><g class=\"subplot x2y2\"><g class=\"layer-subplot\"><g class=\"shapelayer\"/><g class=\"imagelayer\"/></g><g class=\"gridlayer\"><g class=\"x2\"><path class=\"x2grid crisp\" transform=\"translate(400.3120202020203,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"x2grid crisp\" transform=\"translate(464.1120202020203,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"x2grid crisp\" transform=\"translate(518.0420202020202,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"x2grid crisp\" transform=\"translate(564.7620202020203,0)\" d=\"M0,23.390201224846894v212.51589384660252\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/></g><g class=\"y2\"><path class=\"y2grid crisp\" transform=\"translate(0,229.8902012248469)\" d=\"M363.45202020202026,0h242.52065934939952\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"y2grid crisp\" transform=\"translate(0,177.4202012248469)\" d=\"M363.45202020202026,0h242.52065934939952\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"y2grid crisp\" transform=\"translate(0,124.9502012248469)\" d=\"M363.45202020202026,0h242.52065934939952\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/><path class=\"y2grid crisp\" transform=\"translate(0,72.47020122484689)\" d=\"M363.45202020202026,0h242.52065934939952\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 0.1; stroke-width: 0.5px;\"/></g></g><g class=\"zerolinelayer\"/><path class=\"xlines-below\"/><path class=\"ylines-below\"/><g class=\"overlines-below\"/><g class=\"xaxislayer-below\"/><g class=\"yaxislayer-below\"/><g class=\"overaxes-below\"/><g class=\"plot\" transform=\"translate(363.45202020202026, 23.390201224846894)\" clip-path=\"url('#clip7e11e8x2y2plot')\"><g class=\"scatterlayer mlayer\"><g class=\"trace scatter trace856afe\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-765.63,206.5L65.19,206.5L65.19,204.84L71.48,204.84L71.48,202.53L77.78,202.53L77.78,197.47L84.07,197.47L84.07,183.88L90.36,183.88L90.36,177.83L96.66,177.83L96.66,157.91L102.95,157.91L102.95,145.91L109.25,145.91L109.25,141.52L115.54,141.52L115.54,140.07L121.83,140.07L121.83,137.19L128.13,137.19L128.13,144.14L134.42,144.14L134.42,152.63L140.72,152.63L140.72,164.15L147.01,164.15L147.01,174.18L153.3,174.18L153.3,185.31L159.6,185.31L159.6,194.11L165.89,194.11L165.89,199.83L172.19,199.83L172.19,204.18L178.48,204.18L178.48,205.74L197.36,206.37L197.36,206.5L839.35,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(0, 0, 204); stroke-opacity: 1; stroke-width: 1.5px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace0d8a8f\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-765.63,206.5L40.01,206.21L46.3,205.35L52.6,203.71L58.89,201.23L65.19,197.81L71.48,193.35L77.78,187.74L84.07,180.86L90.36,172.57L96.66,162.73L102.95,151.2L109.25,138.01L115.54,126.32L121.83,128.24L140.72,169.59L147.01,180.93L153.3,190.51L159.6,198.07L165.89,203.34L172.19,206.05L184.77,206.5L191.07,206.5L839.35,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-width: 1px; opacity: 1;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace81e557\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-765.63,206.5L40.01,206.18L46.3,205.23L52.6,203.43L58.89,200.7L65.19,196.93L71.48,192.02L77.78,185.84L84.07,178.26L90.36,169.13L96.66,158.29L102.95,145.58L109.25,131.06L115.54,118.19L121.83,120.3L140.72,165.84L147.01,178.34L153.3,188.89L159.6,197.22L165.89,203.02L172.19,206L184.77,206.5L191.07,206.5L839.35,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-width: 1px; opacity: 1; stroke-dasharray: 9px, 9px;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter traceab112a\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M-765.63,206.5L40.01,205.81L46.3,203.76L52.6,199.86L58.89,193.95L65.19,185.81L71.48,175.19L77.78,161.83L84.07,145.43L90.36,125.69L96.66,102.27L102.95,74.8L109.25,43.38L115.54,15.56L121.83,20.13L140.72,118.59L147.01,145.61L153.3,168.42L159.6,186.43L165.89,198.97L172.19,205.42L178.48,206.5L184.77,206.5L839.35,206.5\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-width: 1px; opacity: 1; stroke-dasharray: 3px, 3px;\"/></g><g class=\"points\"/><g class=\"text\"/></g><g class=\"trace scatter trace1a9ff1\" style=\"stroke-miterlimit: 2; opacity: 1;\"><g class=\"fills\"/><g class=\"errorbars\"/><g class=\"lines\"><path class=\"js-line\" d=\"M117.7,206.5L117.7,6.01\" style=\"vector-effect: non-scaling-stroke; fill: none; stroke: rgb(128, 128, 128); stroke-opacity: 1; stroke-width: 1px; opacity: 1; stroke-dasharray: 9px, 3px, 3px, 3px;\"/></g><g class=\"points\"/><g class=\"text\"/></g></g></g><g class=\"overplot\"/><path class=\"xlines-above crisp\" d=\"M362.45202020202026,236.4060950714494H605.9726795514198\" style=\"fill: none; stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 1;\"/><path class=\"ylines-above crisp\" d=\"M362.95202020202026,23.390201224846894V235.9060950714494\" style=\"fill: none; stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 1;\"/><g class=\"overlines-above\"/><g class=\"xaxislayer-above\"><path class=\"x2tick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(400.3120202020203,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"x2tick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(464.1120202020203,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"x2tick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(518.0420202020202,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"x2tick ticks crisp\" d=\"M0,235.9060950714494v-5\" transform=\"translate(564.7620202020203,0)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"x2tick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(400.3120202020203,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">100</text></g><g class=\"x2tick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(464.1120202020203,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">120</text></g><g class=\"x2tick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(518.0420202020202,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">140</text></g><g class=\"x2tick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(564.7620202020203,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">160</text></g><g class=\"x2tick\"><text text-anchor=\"middle\" x=\"0\" y=\"257.3060950714494\" transform=\"translate(605.9720202020203,0)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">180</text></g></g><g class=\"yaxislayer-above\"><path class=\"y2tick ticks crisp\" d=\"M363.45202020202026,0h5\" transform=\"translate(0,229.8902012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"y2tick ticks crisp\" d=\"M363.45202020202026,0h5\" transform=\"translate(0,177.4202012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"y2tick ticks crisp\" d=\"M363.45202020202026,0h5\" transform=\"translate(0,124.9502012248469)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"y2tick ticks crisp\" d=\"M363.45202020202026,0h5\" transform=\"translate(0,72.47020122484689)\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"y2tick\"><text text-anchor=\"end\" x=\"359.0520202020203\" y=\"5.949999999999999\" transform=\"translate(0,229.8902012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">0.0</text></g><g class=\"y2tick\"><text text-anchor=\"end\" x=\"359.0520202020203\" y=\"5.949999999999999\" transform=\"translate(0,177.4202012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">0.5</text></g><g class=\"y2tick\"><text text-anchor=\"end\" x=\"359.0520202020203\" y=\"5.949999999999999\" transform=\"translate(0,124.9502012248469)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">1.0</text></g><g class=\"y2tick\"><text text-anchor=\"end\" x=\"359.0520202020203\" y=\"5.949999999999999\" transform=\"translate(0,72.47020122484689)\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">1.5</text></g></g><g class=\"overaxes-above\"/></g></g><g class=\"polarlayer\"/><g class=\"ternarylayer\"/><g class=\"geolayer\"/><g class=\"pielayer\"/><g class=\"sunburstlayer\"/><g class=\"glimages\"/><defs id=\"topdefs-7e11e8\"><g class=\"clips\"/><clipPath id=\"legend7e11e8\"><rect width=\"183\" height=\"159\" x=\"0\" y=\"0\"/></clipPath></defs><g class=\"layer-above\"><g class=\"imagelayer\"/><g class=\"shapelayer\"/></g><g class=\"infolayer\"><g class=\"legend\" pointer-events=\"all\" transform=\"translate(609, 20)\"><rect class=\"bg\" shape-rendering=\"crispEdges\" style=\"stroke: rgb(0, 0, 0); stroke-opacity: 1; fill: rgb(255, 255, 255); fill-opacity: 1; stroke-width: 0px;\" width=\"183\" height=\"159\" x=\"0\" y=\"0\"/><g class=\"scrollbox\" transform=\"translate(0, 0)\" clip-path=\"url('#legend7e11e8')\"><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 15.6)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">𝕟₁ = Λ(N₁,Dₘ,β)</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(0, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"223\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 36.8)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">𝕟₂ = Λ(N₂,Dₘ,,β)</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(204, 0, 0); stroke-opacity: 1; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"223\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 58)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">𝕟₁₂ (partMC)</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(0, 0, 204); stroke-opacity: 1; stroke-width: 1.5px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"223\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 79.19999999999999)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">f⋅[(β₁₂ᵇt)*(𝕟₁*𝕟₂)]</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"223\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 100.39999999999999)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">f⋅[(β₁₂ᶻ⁽¹ ⁻¹⁾t)*(𝕟₁*𝕟₂)]</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-dasharray: 9px, 9px; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"223\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 121.6)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">f⋅[(β₁₂ᶻ⁽² ⁻²⁾*t)*(𝕟₁*𝕟₂)]</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(165, 42, 42); stroke-opacity: 1; stroke-dasharray: 3px, 3px; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"223\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g><g class=\"groups\" transform=\"translate(0, 0)\"><g class=\"traces\" transform=\"translate(0, 142.79999999999998)\" style=\"opacity: 1;\"><text class=\"legendtext user-select-none\" text-anchor=\"start\" x=\"40\" y=\"5.46\" style=\"font-family: 'Nimbus Sans L'; font-size: 14px; fill: rgb(0, 0, 0); fill-opacity: 1; white-space: pre;\">f*Dₘ</text><g class=\"layers\" style=\"opacity: 1;\"><g class=\"legendfill\"/><g class=\"legendlines\"><path class=\"js-line\" d=\"M5,0h30\" style=\"fill: none; stroke: rgb(128, 128, 128); stroke-opacity: 1; stroke-dasharray: 9px, 3px, 3px, 3px; stroke-width: 1px;\"/></g><g class=\"legendsymbols\"><g class=\"legendpoints\"/></g></g><rect class=\"legendtoggle\" pointer-events=\"all\" x=\"0\" y=\"-10.6\" width=\"223\" height=\"21.2\" style=\"cursor: pointer; fill: rgb(0, 0, 0); fill-opacity: 0;\"/></g></g></g><rect class=\"scrollbar\" rx=\"20\" ry=\"3\" width=\"0\" height=\"0\" style=\"fill: rgb(128, 139, 164); fill-opacity: 1;\" x=\"0\" y=\"0\"/></g><g class=\"g-gtitle\"/><g class=\"g-xtitle\" transform=\"translate(0,-13.906095071449386)\"><text class=\"xtitle\" x=\"181.49391553328562\" y=\"296.9060950714494\" text-anchor=\"middle\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); opacity: 1; font-weight: normal; white-space: pre;\">Diameter (nm)</text></g><g class=\"g-x2title\" transform=\"translate(0,-13.906095071449386)\"><text class=\"x2title\" x=\"484.71234987672005\" y=\"296.9060950714494\" text-anchor=\"middle\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); opacity: 1; font-weight: normal; white-space: pre;\">Diameter (nm)</text></g><g class=\"g-ytitle\"><text class=\"ytitle\" transform=\"rotate(-90,16.23358585858586,129.64814814814815)\" x=\"16.23358585858586\" y=\"129.64814814814815\" text-anchor=\"middle\" style=\"font-family: 'Nimbus Sans L'; font-size: 17px; fill: rgb(0, 0, 0); opacity: 1; font-weight: normal; white-space: pre;\">dN/dlnD (m⁻³) × 10⁻¹⁰</text></g><g class=\"g-y2title\"/></g></svg>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pre = 1e-10\n",
    "p1 = plot(𝕟₁.Dp, pre*𝕟₁.S, xlim = (40, 400), color = :black, label = \"𝕟₁ = Λ(N₁,Dₘ,β)\", \n",
    "    xlabel = \"Diameter (nm)\", ylabel = \"dN/dlnD (m⁻³) × 10⁻¹⁰\",  t = :steppre, \n",
    "    xticks = [60,80,100,120,140,160])\n",
    "\n",
    "p1 = plot!(𝕟₂.Dp, pre*𝕟₂.S, color = RGBA(0.8,0.0,0.0,1.0), label = \"𝕟₂ = Λ(N₂,Dₘ,,β)\", t = :steppre)\n",
    "\n",
    "p2 = plot(𝕟₁₂.Dp, pre*𝕟₁₂.S, color = RGBA(0.0,0.0,0.8), xlim = (90, 180), label = \"𝕟₁₂ (partMC)\", \n",
    "    xlabel = \"Diameter (nm)\", t = :steppre, lw = 1.5, xticks = [60,80,100,120,140, 160])\n",
    "p2 = plot!(𝕟ₚᵇ.Dp,pre*𝕟ₚᵇ.S, color = :brown, label = \"f⋅[(β₁₂ᵇt)*(𝕟₁*𝕟₂)]\", lw = 1)\n",
    "p2 = plot!(𝕟ₚᶻ¹.Dp,pre*𝕟ₚᶻ¹.S, color = :brown, label = \"f⋅[(β₁₂ᶻ⁽¹ ⁻¹⁾t)*(𝕟₁*𝕟₂)]\", lw = 1, ls = :dash)\n",
    "p2 = plot!(𝕟ₚᶻ².Dp,pre*𝕟ₚᶻ².S, color = :brown, label = \"f⋅[(β₁₂ᶻ⁽² ⁻²⁾*t)*(𝕟₁*𝕟₂)]\", lw = 1, ls = :dot)\n",
    "p2 = plot!([f*Dm, f*Dm], [0,1.05*maximum(pre*𝕟ₚᶻ².S)], color = :grey, ls = :dashdot, \n",
    "    label = \"f*Dₘ\") \n",
    "\n",
    "plot(p1,p2, layout = grid(1,2), left_margin = 35px, xaxis = :log10, fmt = :svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Figure 4. </b> Comparison of assumed PartMC inferred size distribution and size distribution obtained from 𝕟ₚᵇ = f$⋅$((k₁₂$*$t)$*$(𝕟₁$.*$𝕟₂)). Left: Input size distributions to PartMC. Right: Blue histogram shows output size distribution from PartMC. The dark-red solid line corresponds to the analytical prediction. Note that the diameter is shifted by f$*$Dm due to the larger sphere equivalent volume of the dimers. Enhancement of concentration due to +1/-1 charge on the input size distribution is negligible and approximately a factor of two for +2/-2 charges. Fpr the triangular case, the number concentration is predicted well (Table 4). However, the shape of the analytical prediction of the size distribution does not fit exactly the modeled shape. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generalization \n",
    "The predicted number of dimers by the analytical approximation is \n",
    "<center> $N = β_{1,2}^B N_1N_2t$ </center> <br> \n",
    "How accurate is this estimate relative to the PartMC prediction? The average coagulation coefficient is enhanced for polydisperse coagulation because coagulation is more efficient for particles of dissimilar size (e.g. Table 12.4, Hinds 1999). To test how this might affect the dimer formation rate, a Monte-Carlo simulation is used. PartMC is is run for a range of sizes and geometric standard deviations. Number concentration for N1 and N2 are picked randomly within an interval where coagulated number concentration after time t remains small relative to the total particle number. This assumption mimicks the physics in the coagulation system described in Notebook 9a. After the simulation is completed the effective coagulation rate concentration is computed from the dimer size distribution  \n",
    "\n",
    "```julia\n",
    "β12eff = sum(𝕟₁₂)/(N₁*N₂*t) \n",
    "```\n",
    "where sum(𝕟₁₂) is the number concentration of the dimers formed, N₁ and N₂ are the initial concentrations, and t is the total simulation time. This effectively observed coagulation rate is compared to the underlying Brownian coagulation rate computed from Eq. (15.33). The calculations are performed for lognormal distributions and triangular distributions.\n",
    "\n",
    "### Step 1. Monte-Carlo Simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mSimulate...100%|████████████████████████████████████████| Time: 0:57:56\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "Random.seed!(10)\n",
    "Narr = exp10.(range(10, stop=12, length=100))\n",
    "Dgs = collect([20:20:100;200:200:1000])\n",
    "σs = collect(1.05:0.05:1.3)\n",
    "\n",
    "ics = InitialConditionLogNormal[]\n",
    "for Dg in Dgs\n",
    "    for σ in σs\n",
    "        N = Narr[randperm(100)]\n",
    "        push!(ics, InitialConditionLogNormal(N[1], N[2], Dg, σ))\n",
    "    end\n",
    "end\n",
    "\n",
    "cd(\"PartMC\")  # Descend into directory PartMC\n",
    "l = Simulation[]\n",
    "@showprogress 1 \"Simulate...\" for i = 1:length(ics)\n",
    "    x = runSimulation(ics[i],1,\"logn\"; verbose = false, repeat=2)\n",
    "    push!(l,x[1])\n",
    "end\n",
    "cd(\"..\")      # Come back "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2. Collate the Results\n",
    "The code below extracts the effective $\\beta$12 from the five repeats and multiple 5 time steps (10..60s) in the model and computes an average $\\beta$12eff from these points for each simulation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>Dₘ</th><th>σ₁</th><th>σ₂</th><th>σ₃</th><th>σ₄</th><th>σ₅</th><th>σ₆</th></tr><tr><th></th><th>Float64</th><th>Float64</th><th>Float64</th><th>Float64</th><th>Float64</th><th>Float64</th><th>Float64</th></tr></thead><tbody><p>11 rows × 7 columns</p><tr><th>1</th><td>NaN</td><td>1.05</td><td>1.1</td><td>1.15</td><td>1.2</td><td>1.25</td><td>1.3</td></tr><tr><th>2</th><td>20.0</td><td>1.21</td><td>1.2</td><td>1.21</td><td>1.24</td><td>1.16</td><td>1.25</td></tr><tr><th>3</th><td>40.0</td><td>0.85</td><td>0.93</td><td>0.94</td><td>0.96</td><td>1.02</td><td>1.01</td></tr><tr><th>4</th><td>60.0</td><td>0.91</td><td>0.84</td><td>0.94</td><td>0.91</td><td>1.01</td><td>0.91</td></tr><tr><th>5</th><td>80.0</td><td>0.92</td><td>0.91</td><td>0.88</td><td>0.95</td><td>0.96</td><td>0.94</td></tr><tr><th>6</th><td>100.0</td><td>0.91</td><td>0.92</td><td>0.94</td><td>0.96</td><td>0.98</td><td>1.04</td></tr><tr><th>7</th><td>200.0</td><td>0.99</td><td>0.97</td><td>1.04</td><td>1.01</td><td>1.04</td><td>1.03</td></tr><tr><th>8</th><td>400.0</td><td>1.01</td><td>1.01</td><td>1.01</td><td>1.0</td><td>1.03</td><td>1.06</td></tr><tr><th>9</th><td>600.0</td><td>0.95</td><td>0.97</td><td>1.0</td><td>1.01</td><td>1.03</td><td>1.04</td></tr><tr><th>10</th><td>800.0</td><td>0.97</td><td>0.98</td><td>0.99</td><td>0.99</td><td>1.05</td><td>1.04</td></tr><tr><th>11</th><td>1000.0</td><td>0.96</td><td>0.98</td><td>1.01</td><td>1.0</td><td>1.07</td><td>1.05</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccc}\n",
       "\t& Dₘ & σ₁ & σ₂ & σ₃ & σ₄ & σ₅ & σ₆\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & NaN & 1.05 & 1.1 & 1.15 & 1.2 & 1.25 & 1.3 \\\\\n",
       "\t2 & 20.0 & 1.21 & 1.2 & 1.21 & 1.24 & 1.16 & 1.25 \\\\\n",
       "\t3 & 40.0 & 0.85 & 0.93 & 0.94 & 0.96 & 1.02 & 1.01 \\\\\n",
       "\t4 & 60.0 & 0.91 & 0.84 & 0.94 & 0.91 & 1.01 & 0.91 \\\\\n",
       "\t5 & 80.0 & 0.92 & 0.91 & 0.88 & 0.95 & 0.96 & 0.94 \\\\\n",
       "\t6 & 100.0 & 0.91 & 0.92 & 0.94 & 0.96 & 0.98 & 1.04 \\\\\n",
       "\t7 & 200.0 & 0.99 & 0.97 & 1.04 & 1.01 & 1.04 & 1.03 \\\\\n",
       "\t8 & 400.0 & 1.01 & 1.01 & 1.01 & 1.0 & 1.03 & 1.06 \\\\\n",
       "\t9 & 600.0 & 0.95 & 0.97 & 1.0 & 1.01 & 1.03 & 1.04 \\\\\n",
       "\t10 & 800.0 & 0.97 & 0.98 & 0.99 & 0.99 & 1.05 & 1.04 \\\\\n",
       "\t11 & 1000.0 & 0.96 & 0.98 & 1.01 & 1.0 & 1.07 & 1.05 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "11×7 DataFrame\n",
       "│ Row │ Dₘ      │ σ₁      │ σ₂      │ σ₃      │ σ₄      │ σ₅      │ σ₆      │\n",
       "│     │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┼─────────┤\n",
       "│ 1   │ NaN     │ 1.05    │ 1.1     │ 1.15    │ 1.2     │ 1.25    │ 1.3     │\n",
       "│ 2   │ 20.0    │ 1.21    │ 1.2     │ 1.21    │ 1.24    │ 1.16    │ 1.25    │\n",
       "│ 3   │ 40.0    │ 0.85    │ 0.93    │ 0.94    │ 0.96    │ 1.02    │ 1.01    │\n",
       "│ 4   │ 60.0    │ 0.91    │ 0.84    │ 0.94    │ 0.91    │ 1.01    │ 0.91    │\n",
       "│ 5   │ 80.0    │ 0.92    │ 0.91    │ 0.88    │ 0.95    │ 0.96    │ 0.94    │\n",
       "│ 6   │ 100.0   │ 0.91    │ 0.92    │ 0.94    │ 0.96    │ 0.98    │ 1.04    │\n",
       "│ 7   │ 200.0   │ 0.99    │ 0.97    │ 1.04    │ 1.01    │ 1.04    │ 1.03    │\n",
       "│ 8   │ 400.0   │ 1.01    │ 1.01    │ 1.01    │ 1.0     │ 1.03    │ 1.06    │\n",
       "│ 9   │ 600.0   │ 0.95    │ 0.97    │ 1.0     │ 1.01    │ 1.03    │ 1.04    │\n",
       "│ 10  │ 800.0   │ 0.97    │ 0.98    │ 0.99    │ 0.99    │ 1.05    │ 1.04    │\n",
       "│ 11  │ 1000.0  │ 0.96    │ 0.98    │ 1.01    │ 1.0     │ 1.07    │ 1.05    │"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "β12eff = Array{Float64}(undef,length(Dgs)+1, length(σs)+1)\n",
    "Dm = Array{Float64}(undef,length(Dgs)+1, length(σs)+1)\n",
    "σk = Array{Float64}(undef,length(Dgs)+1, length(σs)+1)\n",
    "mDm, mσ = Float64[], Float64[]\n",
    "for i = 1:length(l)\n",
    "    push!(mDm, l[i].case.Dm)\n",
    "    push!(mσ, l[i].case.σ)\n",
    "end\n",
    "β12eff[2:end,1] = map(x -> x, mDm[1:length(σs):end])\n",
    "β12eff[1,2:end] = map(x -> x, mσ[1:length(σs)])\n",
    "β12eff[1,1] = NaN\n",
    "\n",
    "# Compute the Browninan Kernel\n",
    "f = collect([10e-9:20e-9:100e-9; 200e-9:200e-9:1000e-9])\n",
    "g = map(x->β12brown(x, x), f)\n",
    "\n",
    "for i = 1:length(σs)\n",
    "    β12eff[2:end,i+1] = map(x -> mean(x.k12), l[i:length(σs):end]) # average the different runs\n",
    "    β12eff[2:end,i+1] = β12eff[2:end,i+1]./g                       # Compute the ratio\n",
    "end\n",
    "table = DataFrame(round.(β12eff,digits=2))\n",
    "rename!(table,f => t for (f, t) = zip([:x1, :x2, :x3, :x4, :x5, :x6, :x7],[:Dₘ, :σ₁, :σ₂, :σ₃, :σ₄, :σ₅, :σ₆]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Table 5. </b> Column Dₘ: Mode diameter for simulation. Row 1: List of geometric standard deviation for simulation. All other entries, ratio of effective $\\beta_{1,2}$ derived as average from five PartMC repeat runs and Brownian coagulation kernel computed via Eq. (15.33) in Jacobson (2005), the same kernel that is used in PartMC. The table shows that the analytical approximation of number concentrion fir distributions with σg < 1.3 and sizes 10 < D < 1000 nm is within a few % of the model simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mSimulate...100%|████████████████████████████████████████| Time: 0:10:48\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "Random.seed!(10)\n",
    "Narr = exp10.(range(10, stop=12, length=100))\n",
    "\n",
    "t,p = 295.15, 1e5                                # Temperature [K], Pressure [Pa]\n",
    "qsa,β = 1.66e-5, 1/3                             # Qsample [m3 s-1], Sample-to-sheath ratio,\n",
    "r₁,r₂,l = 9.37e-3,1.961e-2,0.44369               # DMA geometry [m]\n",
    "leff = 13.0                                      # DMA effective diffusion length [m]\n",
    "m = 6                                            # Upper number of charges\n",
    "Λ = DMAconfig(t,p,qsa,qsa/β,r₁,r₂,l,leff,:-,m,:cylindrical)   # Specify DMA with negative polarity\n",
    "bins,z₁,z₂ = 512, dtoz(Λ,900e-9),dtoz(Λ,10e-9)   # bins, upper, lower mobility limit\n",
    "δ = setupDMA(Λ, z₁, z₂, bins);                   # Compute matrices\n",
    "\n",
    "Dgs = collect([40:20:100;200:200:600])           # Stay within grid for simulations\n",
    "\n",
    "Λs,δs = DMAconfig[], DifferentialMobilityAnalyzer[]\n",
    "β = [1.0/10.0, 1.0/5.0, 1.0/3.0]                 # Three sheath-to-sample flow ratios\n",
    "for i = 1:length(β)\n",
    "    push!(Λs, DMAconfig(t,p,qsa,qsa/β[i],r₁,r₂,l,leff,:-,n,:cylindrical))\n",
    "    push!(δs, setupDMA(Λs[i], z₁, z₂, bins))          \n",
    "end\n",
    "\n",
    "# Setup simulation initial conditions as a list\n",
    "ics = InitialConditionTriangular[]\n",
    "for Dg in Dgs\n",
    "    for i in 1:length(Λs)\n",
    "        N = Narr[randperm(100)]\n",
    "        push!(ics, InitialConditionTriangular(N[1], N[2], Dg, Λs[i], δs[i]))\n",
    "    end\n",
    "end\n",
    "\n",
    "# Run simulations\n",
    "cd(\"PartMC\")  # Descend into directory PartMC\n",
    "l = Simulation[]\n",
    "@showprogress 1 \"Simulate...\" for i = 1:length(ics)\n",
    "    x = runSimulation(ics[i],1,\"triangular\"; verbose = false)\n",
    "    push!(l,x[1])\n",
    "end\n",
    "cd(\"..\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>Dₘ</th><th>β₁</th><th>β₂</th><th>β₃</th></tr><tr><th></th><th>Float64</th><th>Float64</th><th>Float64</th><th>Float64</th></tr></thead><tbody><p>8 rows × 4 columns</p><tr><th>1</th><td>NaN</td><td>0.1</td><td>0.2</td><td>0.33</td></tr><tr><th>2</th><td>40.0</td><td>0.96</td><td>0.97</td><td>0.96</td></tr><tr><th>3</th><td>60.0</td><td>0.97</td><td>0.91</td><td>0.96</td></tr><tr><th>4</th><td>80.0</td><td>0.93</td><td>0.98</td><td>0.99</td></tr><tr><th>5</th><td>100.0</td><td>0.98</td><td>1.01</td><td>1.01</td></tr><tr><th>6</th><td>200.0</td><td>0.99</td><td>0.94</td><td>0.99</td></tr><tr><th>7</th><td>400.0</td><td>0.97</td><td>0.93</td><td>0.97</td></tr><tr><th>8</th><td>600.0</td><td>1.03</td><td>0.99</td><td>0.91</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& Dₘ & β₁ & β₂ & β₃\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & NaN & 0.1 & 0.2 & 0.33 \\\\\n",
       "\t2 & 40.0 & 0.96 & 0.97 & 0.96 \\\\\n",
       "\t3 & 60.0 & 0.97 & 0.91 & 0.96 \\\\\n",
       "\t4 & 80.0 & 0.93 & 0.98 & 0.99 \\\\\n",
       "\t5 & 100.0 & 0.98 & 1.01 & 1.01 \\\\\n",
       "\t6 & 200.0 & 0.99 & 0.94 & 0.99 \\\\\n",
       "\t7 & 400.0 & 0.97 & 0.93 & 0.97 \\\\\n",
       "\t8 & 600.0 & 1.03 & 0.99 & 0.91 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "8×4 DataFrame\n",
       "│ Row │ Dₘ      │ β₁      │ β₂      │ β₃      │\n",
       "│     │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼─────────┼─────────┼─────────┼─────────┤\n",
       "│ 1   │ NaN     │ 0.1     │ 0.2     │ 0.33    │\n",
       "│ 2   │ 40.0    │ 0.96    │ 0.97    │ 0.96    │\n",
       "│ 3   │ 60.0    │ 0.97    │ 0.91    │ 0.96    │\n",
       "│ 4   │ 80.0    │ 0.93    │ 0.98    │ 0.99    │\n",
       "│ 5   │ 100.0   │ 0.98    │ 1.01    │ 1.01    │\n",
       "│ 6   │ 200.0   │ 0.99    │ 0.94    │ 0.99    │\n",
       "│ 7   │ 400.0   │ 0.97    │ 0.93    │ 0.97    │\n",
       "│ 8   │ 600.0   │ 1.03    │ 0.99    │ 0.91    │"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "β12eff = Array{Float64}(undef,length(Dgs)+1, length(β)+1)\n",
    "Dm = Array{Float64}(undef,length(Dgs)+1, length(β)+1)\n",
    "mDm = Float64[]\n",
    "for i = 1:length(l)\n",
    "    push!(mDm, l[i].case.Dm)\n",
    "end\n",
    "\n",
    "β12eff[2:end,1] = map(x -> x, mDm[1:length(β):end])\n",
    "β12eff[1,2:end] = map(x -> x, β[1:length(β)])\n",
    "β12eff[1,1] = NaN\n",
    "\n",
    "# Compute the Browninan Kernel\n",
    "f = collect([40:20:100; 200:200:600])\n",
    "g = map(x->β12brown(x*1e-9, x*1e-9), f)\n",
    "\n",
    "for i = 1:length(β)\n",
    "    β12eff[2:end,i+1] = (map(x -> mean(x.k12), l[i:length(β):end]))   # Average rate\n",
    "    β12eff[2:end,i+1] = β12eff[2:end,i+1]./g                          # Compute the ratio\n",
    "end\n",
    "\n",
    "table = DataFrame(round.(β12eff,digits=2))\n",
    "rename!(table, f => t for (f, t) = zip([:x1, :x2, :x3, :x4], [:Dₘ, :β₁, :β₂, :β₃]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Table 6. </b> Column Dₘ: Mode diameter for simulation. Row 1: List of sample-to-sheath flow ratios. All other entries, ratio of effective $\\beta_{1,2}$ derived as average from five PartMC repeat runs and Brownian coagulation kernel computed via Eq. (15.33) in Jacobson (2005), the same kernel that is used in PartMC. The table shows that the analytical approximation of number concentrion fir distributions with sheath-to-sample flow ratio < 1/10 and sizes 40 < D < 600 nm is within a few % of the model simulation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "\n",
    "Jacobson, M. Z. (2005) Fundamentals of Atmospheric Modeling. Second Edition, Cambridge University Press. \n",
    "\n",
    "Hinds, W. C. (1999) Aerosol Technology, Properties, Behavior, and Measurement of Airborne Particles, Second Edition, John Wiley & Sons, Inc.\n",
    "\n",
    "Riemer, N.,  M. West, R. A. Zaveri, and R. C. Easter (2009) Simulating the evolution of soot mixing state with a particle-resolved aerosol model, Journal of Geophysical Research 114(D09202), DOI:10.1029/2008JD011073. \n",
    "\n",
    "Tian, J., B. T. Brem, M. West, T. C. Bond, M. J. Rood & N. Riemer (2017) Simulating aerosol chamber experiments with the particle-resolved aerosol model PartMC, Aerosol Science and Technology, 51:7, 856-867, DOI:10.1080/02786826.2017.1311988\n",
    "\n",
    "Zebel, G. (1957) Zur Theorie des Verhaltens elektrisch geladener Aerosole, Kolloid-Zeitschrift, (1), 37–50, DOI:10.1007/BF01734032."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.1.0",
   "language": "julia",
   "name": "julia-1.1"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.1.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}