sdt_intro.ipynb

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    "# Shock and Detonation Toolbox Tutorial\n",
    "\n",
    "2019 US National Combustion Meeting Cantera Workshop  \n",
    "March 24, 2019  \n",
    "\n",
    "Joe Shepherd  \n",
    "Graduate Aerospace Laboratories  \n",
    "California Institute of Technology  \n",
    "Pasadena, CA 91125 USA    \n",
    "\n",
    "<a href=\"mailto:jeshep@caltech.edu\">jeshep@caltech.edu</a>\n",
    "\n",
    "### What is the SDT?\n",
    "The Shock & Detonation Toolbox is an open-source software library that enables the solution of standard problems\n",
    "    for gas-phase explosions using realistic thermochemistry\n",
    "    and detailed chemical kinetics.\n",
    "    The SD Toolbox uses the <a href=\"http://www.cantera.org/\">Cantera</a>\n",
    "    software package and is implemented as routines that can be called from either MATLAB or Python. A set of demonstration programs and a library of contemporary reaction mechanisms and thermodynamic data are provided.  \n",
    "   \n",
    "### How to download\n",
    "The SDT home page is located on the <a href=\"http://shepherd.caltech.edu/EDL/\">Explosion Dynamics Laboratory</a> site under the Public Resources page at http://shepherd.caltech.edu/EDL/PublicResources/sdt/\n",
    "\n",
    "Python and Matlab libraries and demonstration programs can be downloaded as <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox.zip\">(ZIP)</a> archives.   Installation instructions are available in a <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/sdt-install.pdf\">(PDF)</a> file.\n",
    "\n",
    "### Additional resources\n",
    "* Quick reference to SDT functions and demonstation programs <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/doc/QuickReferenceSDT.pdf\">(PDF)</a> \n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/cti_mech.html\"> Cantera format (.CTI) data sets </a>\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/thermo.html\">  Thermodynamic data sources and software tools </a>\n",
    "\n",
    "\n"
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    "# Toolbox Capabilities"
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    "   The SD Toolbox includes numerical routines for the computation of:\n",
    "    <ul>\n",
    "      <li> CJ detonation speed and post-detonation state\n",
    "      <li> Postshock gas state for frozen composition\n",
    "      <li> Postshock gas state for equilibrium composition\n",
    "      <li> Frozen and equilibrium Hugoniot curves\n",
    "      <li> Oblique shock waves, shock-expansion solutions\n",
    "      <li> Shock tube and shock tunnel performance\n",
    "      <li> Constant-volume explosion structure\n",
    "      <li> ZND detonation structure\n",
    "      <li> Effective activation energies and\n",
    "       chemical time scales from detailed reaction mechanisms\n",
    "      <li> Creating and modifying thermodynamic databases.\n",
    "    </ul>\n"
   ]
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    "# 2018 Release \n",
    "\n",
    "This is the third update of the SDT since 2007 and is now compatible with Cantera 2.3 and 2.4, Python 3.5 and 3.6 and Matlab R2017b and R2018a.  Python 2.X versions are not available.\n",
    " \n",
    "The SDT interfaces are similar to earlier versions, but the underlying routines have been restructured and the demonstration programs rewritten. Plotting and error control are now more flexible and additional demonstration programs have been added.   Programs that used earlier versions of the Matlab libraries will require some minor coding changes for certain routines.  The Python code base has been completely rewritten.\n",
    "\n",
    "Both Matlab and Python versions of all demonstration programs are now available, in particular  shock and detonation structure programs are available as Python scripts.  The Python and Matlab code structures have been made as similar as possible.   The chemical reaction mechanisms and thermodynamic databases have been updated to reference contemporary reaction data sets.\n",
    "\n",
    "Contributors: S. Browne, J. Ziegler, N. Bitter, B. Schmidt, J. Lawson, \n",
    "J. E. Shepherd "
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    "# Components\n",
    "\n",
    "## Libraries\n",
    "The core Python and Matlab libraries which must be installed in the appropriate systems directories as described in the installation instructions\n",
    "\n",
    "## Demonstration Programs\n",
    "There are over 30 demonstration programs provided that illustrate how to use the libraries to solve various problems.  Both Python 3 and Matlab versions are available.  \n",
    "\n",
    "## Cantera input (.cti) files\n",
    "Reaction mechanism and associated thermodynamic data (.cti files) used by the demonstration programs are provided.\n",
    "\n",
    "## Thermodynamics ultilities\n",
    "Primary sources, references and programs for checking and fitting thermodynamic data are provided.  "
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    "# Fundamental Library Functions\n",
    "\n",
    "Non-reactive shock wave.  \n",
    "\n",
    "    PostShock_fr\n",
    "\n",
    "Reactive shock wave. \n",
    "\n",
    "    PostShock_eq\n",
    "\n",
    "Chapman-Jouguet (CJ) detonation.  \n",
    "\n",
    "    CJSpeed\n",
    "\n",
    "Reflected shock wave.  \n",
    "\n",
    "    reflected_eq and reflected_fr\n",
    "\n",
    "ZND detonation structure. \n",
    "\n",
    "    zndsolve\n",
    "\n",
    "CV explosion structure.  \n",
    "\n",
    "    cvsolve"
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    "# Shock Wave Physics  \n",
    "\n",
    "Transformation from laboratory to wave frame  \n",
    "\n",
    "<img src=\"images/shockframe.png\" width=\"50%\" alt=\"Laboratory and wave frame\"/>   \n",
    "\n",
    "\\begin{align}\n",
    "    \\textrm{w}_1 &= \\textrm{U}_s - \\textrm{u}_1\\\\\n",
    "    \\textrm{w}_2 &= \\textrm{U}_s - \\textrm{u}_2\n",
    "\\end{align}  \n",
    "\n",
    "Conservation or jump equations\n",
    "\n",
    "Mass $$\\rho_1 \\textrm{w}_1 = \\rho_2 \\textrm{w}_2 $$\n",
    "\n",
    "Momentum $$P_1 + \\rho_1 \\textrm{w}^2_1 = P_2 + \\rho_2 \\textrm{w}^2_2 $$\n",
    "\n",
    "Energy $$ h_1 + \\dfrac{\\textrm{w}^2_1}{2} = h_2 + \\dfrac{\\textrm{w}^2_2}{2} $$\n",
    "\n",
    "Entropy  $$ s_2 > s_1 $$  \n",
    "\n",
    "Equation of state  (EoS)\n",
    "\n",
    "$$ h(P, \\rho, Y) \\quad \\textrm{or} \\quad h(T, Y) \\;\\textrm{and} \\;  P(\\rho, T, Y)$$\n",
    "\n",
    "Species mass fractions\n",
    "\n",
    "$$  Y = (Y_1, Y_2, \\dots, Y_k) $$"
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    "# Issues  \n",
    "* Iterative solution required except for simplest EoS models (perfect gas)\n",
    "* Chemical composition of downstream state\n",
    "    * nonreactive,  frozen  $Y$ = constant\n",
    "    * reactive, equilibrium $Y$ = $Y^{eq}(T,P,composition)$\n",
    "    * varies with distance (ZND model)\n",
    "* Limits on solutions for shocks\n",
    "    * upstream state supersonic $\\textrm{w}_1$ $>$ $a_1$\n",
    "    * downstream state subsonic for nonreactive case\n",
    "    * solutions multivalued for reactive case, require $\\textrm{w}_1$ $>$ $\\textrm{w}_{min}$"
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    "# Ideal gas model  \n",
    "\n",
    "The methods in the SDT can be used with any equation of state but the current implmentation is specific to ideal gases.  \n",
    "\n",
    "\\begin{align}\n",
    "    P  &= \\rho RT \\\\\n",
    "    R & = \\dfrac{\\mathcal{R}}{\\overline{W}}\\\\\n",
    "    \\overline{W} & = \\left(\\sum_{i=1}^K \\dfrac{Y_i}{W_i} \\right)^{-1}\\\\\n",
    "    h & = \\sum_{i=1}^K Y_i h_i(T) \\; \\label{eq:h-sum}\\\\\n",
    "    h_i & = \\Delta_f h_i + \\int_{T_\\circ}^T c_{P, i}(T') \\; dT'\n",
    "\\end{align}\n",
    "\n",
    "All quantities are computed from the Cantera gas object using thermodynamic properties in .cti file"
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    "# Graphical Interpretation  \n",
    "Rayleigh Line  \n",
    "\n",
    "\\begin{align}\n",
    " P_2 &= P_1 - \\rho^2_1\\textrm{w}_1^2 \\left(v_2-v_1\\right)\\label{eq:RL} \\\\\n",
    "\\dfrac{P_2 - P_1}{v_2-v_1} = \\dfrac{\\Delta P}{\\Delta v} &= - \\left(\\dfrac{\\textrm{ w}_1}{v_1}\\right)^2 =\n",
    "    - \\left(\\dfrac{\\textrm{w}_2}{v_2}\\right)^2 \\label{eq:Rayleigh-slope}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "Hugoniot or Shock Adiabat  \n",
    "\n",
    "\\begin{align}\n",
    "    h_2 - h_1 &= (P_2 - P_1)\\dfrac{(v_2 + v_1)}{2}  \\label{eq:RH1}\\\\\n",
    "    e_2 - e_1 & = \\dfrac{(P_2 + P_1)}{2}(v_1 - v_2) \\label{eq:RH2}\n",
    "\\end{align}\n",
    "\n"
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    "# Hugoniot and Rayleigh line  \n",
    "\n",
    "Example: Shock wave in air (frozen),  $U_s$ = 1000 m/s\n",
    "\n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_RH_air.py\">demo_RH_air.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_RH_air.m\">demo_RH_air.m</a> \n",
    "\n",
    "<img src=\"images/air-shock-1000.png\"  width=\"50%\" alt=\"P-V diagram, air shock  1000 m/s\"/>"
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    "## Nonreactive Shock waves\n",
    "\n",
    "Matlab: \n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/SDToolbox/PostShock/PostShock_fr.m\">PostShock_fr.m </a> \n",
    "Python: PostShock_fr in <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/sdtoolbox/postshock.py\">PostShock.py</a> \n",
    "\n",
    "Calculates frozen post-shock state for a specified shock velocity, pressure, temperature,\n",
    "and composition and gas object.\n",
    "\n",
    "FUNCTION SYNTAX:  \n",
    "\n",
    "    [gas] = PostShock_fr(U1,P1,T1,q,mech)  \n",
    "    \n",
    "INPUT:  \n",
    "\n",
    "    U1 = shock speed (m/s)  \n",
    "    P1 = initial pressure (Pa)  \n",
    "    T1 = initial temperature (K)  \n",
    "    q = reactant species mole fractions in one of Cantera's recognized formats  \n",
    "    mech = cti file containing mechanism data (e.g. 'gri30.cti')  \n",
    "    \n",
    "OUTPUT:  \n",
    "\n",
    "    gas = gas object at frozen post-shock state"
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    "## Reactive Shock waves\n",
    "\n",
    "Equilibrium postshock state\n",
    "\n",
    "Matlab: \n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/SDToolbox/PostShock/PostShock_eq.m\">PostShock_eq.m </a> \n",
    "Python: PostShock_eq in <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/sdtoolbox/postshock.py\">PostShock.py</a> \n",
    "\n",
    "Calculates equilibrium post-shock state for a specified shock velocity, pressure, temperature, and composition and gas object.\n",
    "\n",
    "FUNCTION SYNTAX:  \n",
    "\n",
    "    [gas] = PostShock_eq(U1,P1,T1,q,mech)  \n",
    "    \n",
    "INPUT:  \n",
    "\n",
    "    U1 = shock speed (m/s)  \n",
    "    P1 = initial pressure (Pa)  \n",
    "    T1 = initial temperature (K)  \n",
    "    q = reactant species mole fractions in one of Cantera's recognized formats  \n",
    "    mech = cti file containing mechanism data (e.g. 'gri30.cti')  \n",
    "    \n",
    "OUTPUT:  \n",
    "\n",
    "    gas = gas object at frozen post-shock state"
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    "# Example with endothermic shock  \n",
    "\n",
    "Shock wave in air (frozen vs equilibrium),  $U_s$ < 3500 m/s  \n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_RH_air_eq.py\">demo_RH_air_eq.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_RH_air_eq.m\">demo_RH_air_eq.m</a>\n",
    "\n",
    "Uses <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/cti/airNASA9ions.cti\">airNASA9ions.cti</a> high-temperature thermodynamic data (20,000 K) with molecules, atoms and ions.\n",
    "\n",
    "<img src=\"images/air-shock-3500.png\"  width=\"50%\" alt=\"P-V diagram, air shock  1000 m/s\"/>\n"
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    "# Solution Method \n",
    "The solution method is based on an iterative solution of the jump conditions in the following form:  \n",
    "\n",
    "$$ \\mathcal{H} = \\left(h_2+\\dfrac{1}{2}\\textrm{w}_2^2\\right)\n",
    "    - \\left(h_1+\\dfrac{1}{2}\\textrm{w}_1^2\\right) $$  \n",
    "$$ \\mathcal{P} = \\left(P_2 + \\rho_2\\textrm{w}_2^2\\right) - \\left(P_1 + \\rho_1\\textrm{ w}_1^2\\right)$$  \n",
    "\n",
    "The exact solution to the jump conditions then occurs when both $\\mathcal{H}$ and $\\mathcal{P}$\n",
    "are identically zero.  We can construct an approximate solution by simultaneously iterating these two\n",
    "equations until $\\mathcal{H}$ and $\\mathcal{P}$ are less than a specified tolerance. An iteration algorithm\n",
    "can be developed by considering trial values of $(T, v)$ for the downstream thermodynamic state 2 that are\n",
    "close to but not equal to the exact solution,  $(T_2, v_2)$.  The expansion of $\\mathcal{P}$ and\n",
    "$\\mathcal{H}$ to first order in a Taylor series about the exact solution yields:  \n",
    "\n",
    "$$ \\mathcal{H}(T,v) =  \\mathcal{H}(T_2,v_2) + \\dfrac{\\partial \\mathcal{H}}{\\partial T}(T-T_2) + \\dfrac{\\partial \\mathcal{H}}{\\partial v}(v-v_2) + \\ldots $$\n",
    "\n",
    "$$ \\mathcal{P}(T,v)  = \\mathcal{P}(T_2,v_2) + \\dfrac{\\partial \\mathcal{P}}{\\partial T}(T-T_2) + \\dfrac{\\partial \\mathcal{P}}{\\partial v}(v-v_2) + \\ldots $$"
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    "## Numerical method\n",
    "The solver uses the Newton-Raphson scheme (see Press,et al. Numerical Recipes) with the variables temperature and specific volume.  The scheme  is an extension of the method used by Reynolds (1986) in STANJAN to solve the jump conditions for a Chapman-Jouguet detonation. Truncating the Taylor series expansions, the residuals computation can be represented as the matrix operation  \n",
    "\n",
    "$$\n",
    "\\left(\\begin{array}{c}\n",
    "\\mathcal{H}\\\\\\\n",
    "\\mathcal{P}\n",
    "\\end{array}\\right)\n",
    "= \\left(\\begin{array}{cc} \n",
    "        \\dfrac{\\partial \\mathcal{H}}{\\partial T} & \\dfrac{\\partial \\mathcal{H}}{\\partial v}\\\\\\ \n",
    "        \\dfrac{\\partial \\mathcal{P}}{\\partial T} & \\dfrac{\\partial \\mathcal{P}}{\\partial v} \n",
    "        \\end{array}\\right) \n",
    "\\left(\\begin{array}{c} \n",
    "      \\delta T\\\\\\\n",
    "      \\delta v  \n",
    "    \\end{array}\n",
    "      \\right) $$  \n",
    "      \n",
    "where $\\delta T$ = $T-T_2$ and $\\delta v$ = $v-v_2$.  This equation is used to relate the corrections,\n",
    "$\\delta T$ and $\\delta v$, to the current values of $(T, v)$ and through successive applications, approach the\n",
    "true solution to within a specified error tolerance.  At step $i$, we have values $(T^i, v^i)$ which we use to\n",
    "evaluate $\\mathcal{H}$ and $\\mathcal{P}$ to obtain $\\mathcal{H}^i$ and $\\mathcal{P}^i$; then we solve for $\\delta T^i$ and $\\delta v^i$  and compute the next approximation to the solution as\n",
    "\n",
    "$$\n",
    "\\begin{array}{cc}\n",
    "T^{i+1} &= T^i - \\delta T^i \\\\\\\n",
    "v^{i+1} &= v^i - \\delta v^i\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "The corrections can be formally obtained by inverting the Jacobian  \n",
    "\n",
    "$$ J = \\left(\\begin{array}{cc} \\dfrac{\\partial \\mathcal{H}}{\\partial T} & \\dfrac{\\partial \\mathcal{H}}{\\partial v}\\\\\\\n",
    "    \\dfrac{\\partial \\mathcal{P}}{\\partial T} & \\dfrac{\\partial \\mathcal{P}}{\\partial v}\\\\ \\end{array}\\right) $$  \n",
    "    \n",
    "and carrying out the matrix multiplication operation.\n",
    "\n",
    "\\begin{equation} \\left(\\begin{array}{c} \\delta T\\\\\\ \\delta v \\end{array}\\right) = J^{-1} \\left(\\begin{array}{c} \\mathcal{H}\\\\\\ \\mathcal{P} \\end{array}\\right) \\end{equation}  \n",
    "\n",
    "The derivatives needed to form the Jacobian are computed using finite differences. "
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    "# Algorithm  \n",
    "\n",
    "* Define known quantities: Upstream State ($P_1$, $\\rho_1$, $T_1$, $h_1$, $\\textrm{ w}_1$, $\\overline{W}$), $\\mathcal{R}$, error tolerances, increment values ($\\Delta T$, $\\Delta v$)\n",
    "\n",
    "* Seek unknown quantities: Downstream State ($P_2$, $\\rho_2$, $T_2$, $h_2$)\n",
    "\n",
    "* Establish preliminary guess ($i=1$)  \n",
    "\n",
    "\\begin{align}\n",
    "    \\rho^i_2 &= 5\\rho_1\\\\\n",
    "    v^i_2 &= \\dfrac{1}{\\rho^i_2}\\\\\n",
    "    P^i_2 &= P_1 + \\rho_1\\textrm{w}_1^2\\left(1-\\dfrac{\\rho_1}{\\rho^i_2}\\right)\\\\\n",
    "    T^i_2 &= T_1\\dfrac{P_1}{P^i_2}\\dfrac{\\rho_2^i}{\\rho_1}\n",
    "\\end{align}\n",
    "\n",
    "* Evaluate residuals $\\mathcal{H}$ and $\\mathcal{P}$  \n",
    "\n",
    "    * For frozen computations, hold composition of state 2 fixed and equal to state 1.  For equilibrium computations, find equilibrium state 2 for specified initial composition and $(T_2, v_2)$.  \n",
    "    \n",
    "    * Compute $\\mathcal{H}(T_2^i, v_2^i)$ and $\\mathcal{P}(T_2^i, v_2^i)$  \n",
    "\n",
    "    * Perturb temperature holding volume fixed and compute $\\mathcal{H}(T_2^i+\\Delta T)$ and $\\mathcal{P}(T_2^i+\\Delta T)$  \n",
    "\n",
    "    * Perturb specific volume holding temperature fixed and compute $\\mathcal{H}(v_2^i+\\Delta v)$ and $\\mathcal{P}(v_2^i+\\Delta v)$  "
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    "# Alogorithm (continued)\n",
    "\n",
    "* Evaluate the elements of the approximate Jacobian $\\tilde{J}$ by first order differences\n",
    "\n",
    "\\begin{align}\n",
    "\\dfrac{\\partial \\mathcal{H}}{\\partial T} &\\approx \\dfrac{\\mathcal{H}(T_2^i+\\Delta T)-\\mathcal{H}(T_2^i)}{\\Delta T}\\\\\n",
    "\\dfrac{\\partial \\mathcal{P}}{\\partial T} &\\approx \\dfrac{\\mathcal{P}(T_2^i+\\Delta T)-\\mathcal{P}(T_2^i)}{\\Delta T}\\\\\n",
    "\\dfrac{\\partial \\mathcal{H}}{\\partial v} &\\approx \\dfrac{\\mathcal{H}(v_2^i+\\Delta v)-\\mathcal{H}(v_2^i)}{\\Delta v}\\\\\n",
    "\\dfrac{\\partial \\mathcal{P}}{\\partial v} &\\approx \\dfrac{\\mathcal{P}(v_2^i+\\Delta v)-\\mathcal{P}(v_2^i)}{\\Delta v}\n",
    "\\end{align}\n",
    "\n",
    "* Update the post-shock state \n",
    "\n",
    "\\begin{equation} \n",
    "\\left(\\begin{array}{c} T_2\\\\\\  v_2 \\end{array}\\right)^{i+1} =  \\left(\\begin{array}{c} T_2\\\\\\  v_2 \\end{array}\\right)^{i} - \\tilde{J}^{-1} \\left(\\begin{array}{c} \\mathcal{H}\\\\\\ \\mathcal{P} \\end{array}\\right)^i \n",
    "\\end{equation}\n",
    "\n",
    "*  Check convergence\n",
    "\n",
    "\\begin{align*}\n",
    "    |T_2^{i+1}-T_2^i| &< T_{error}\\\\\n",
    "    |v_2^{i+1}-v_2^i| &< v_{error}\n",
    "\\end{align*}"
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    "# Reflected Shock Waves  \n",
    "\n",
    "Frozen:  Matlab: \n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/SDToolbox/Reflections/reflected_fr.m\">reflected_fr.m </a> \n",
    "Python: reflected_fr in <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/sdtoolbox/reflections.py\">PostShock.py</a> \n",
    "\n",
    "Equilibrium:  Matlab: \n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/SDToolbox/Reflections/reflected_eq.m\">reflected_eq.m </a> \n",
    "Python: reflected_eq in <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/sdtoolbox/reflections.py\">PostShock.py</a>   \n",
    "\n",
    "\n",
    "<img src=\"images/reflectiondiagram.png\"  width=\"50%\" alt=\"reflection of shock or detonation\"/> \n",
    "\n",
    "Transformation from laboratory frame to shock frame\n",
    "\n",
    "\\begin{align}\n",
    "    \\textrm{w}_2 &= \\textrm{U}_R+\\textrm{u}_2\\\\\n",
    "    \\textrm{w}_3 &= \\textrm{U}_R  \\\\\n",
    "\\end{align}\n",
    " \n",
    "Resulting conservation (jump) equations for reflected shock\n",
    "\n",
    "\\begin{align}\n",
    "  (\\textrm{U}_R+\\textrm{u}_2)\\rho_2 &= \\textrm{U}_R\\,\\rho_3 \\\\\n",
    "    P_2  + \\rho_2 (\\textrm{U}_R+\\textrm{u}_2)^2 &= P_3 + \\rho_3 \\textrm{U}_R^2 \\\\\n",
    "    h_2 + \\dfrac{1}{2} (\\textrm{U}_R+\\textrm{u}_2)^2 &= h_3 + \\dfrac{1}{2} \\textrm{U}_R^2 \\\\\n",
    "    h_3 &= h_3(P_3,\\rho_3, {\\bf Y}_3) \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Solution for state 3\n",
    "\n",
    "\\begin{align}\n",
    "\\textrm{U}_R &= \\dfrac{\\textrm{u}_2}{\\dfrac{\\rho_3}{\\rho_2} -1} \\\\\n",
    "P_3 &=  P_2 + \\dfrac{\\rho_3 \\textrm{u}_2^2}{\\dfrac{\\rho_3}{\\rho_2} -1} \\\\\n",
    "h_3 &= h_2 + \\dfrac{\\textrm{ u}_2^2}{2}\\dfrac{\\dfrac{\\rho_3}{\\rho_2}+1}{\\dfrac{\\rho_3}{\\rho_2}-1}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Reflection of shock wave  \n",
    "\n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_reflected_eq.py\">demo_reflected_eq.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_reflected_eq.m\">demo_reflected_eq.m</a>  \n",
    "\n",
    "Define namespaces and import modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import cantera as ct\n",
    "from sdtoolbox.postshock import PostShock_fr\n",
    "from sdtoolbox.reflections import reflected_fr\n",
    "from sdtoolbox.thermo import soundspeed_fr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Define incident state and gas objects for states 1, 2, 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "P1 = 100000; T1 = 300; P1atm = P1/ct.one_atm\n",
    "q = 'H2:2 O2:1 N2:3.76' \n",
    "mech = 'Mevel2017.cti'             \n",
    "gas1 = ct.Solution(mech)\n",
    "gas1.TPX = T1, P1, q\n",
    "gas2 = ct.Solution(mech)\n",
    "gas3 = ct.Solution(mech)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Set incident shock wave Mach number $M_s > 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Incident shock speed UI = 1226.22 m/s\n"
     ]
    }
   ],
   "source": [
    "a_fr = soundspeed_fr(gas1)\n",
    "UI = 3*a_fr\n",
    "print('Incident shock speed UI = %.2f m/s' % (UI))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Compute postshock state behind incident shock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Frozen Post-Incident-Shock State\n",
      "T2 = 790.68 K, P2 = 10.28 atm\n"
     ]
    }
   ],
   "source": [
    "gas2 = PostShock_fr(UI, P1, T1, q, mech);\n",
    "P2 = gas2.P/ct.one_atm;\n",
    "\n",
    "print ('Frozen Post-Incident-Shock State')\n",
    "print ('T2 = %.2f K, P2 = %.2f atm' % (gas2.T,P2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "compute reflected shock post-shock state gas3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Frozen Post-Reflected-Shock State\n",
      "T3 = 1332.58 K,  P3 = 51.54 atm\n",
      "Reflected Wave Speed = 463.44 m/s\n"
     ]
    }
   ],
   "source": [
    "[p3,UR,gas3]= reflected_fr(gas1,gas2,gas3,UI);\n",
    "P3 = gas3.P/ct.one_atm\n",
    "print ('Frozen Post-Reflected-Shock State')\n",
    "print ('T3 = %.2f K,  P3 = %.2f atm' % (gas3.T,P3))\n",
    "print (\"Reflected Wave Speed = %.2f m/s\" % (UR))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For equilibrium post-shock states, procedure is the same, subsitute PostShock_eq, reflected_eq  for frozen routines.  See \n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_reflected_fr.py\">demo_reflected_fr.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_reflected_fr.m\">demo_reflected_fr.m</a>  \n",
    "\n",
    "Reflection of detonation waves follows the same procedure, compute incident wave speed with CJspeed, post-CJ state with PostShock_eq.  See\n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_CJ_and_shock_state.py\">demo_CJ_and_shock_state.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_CJ_and_shock_state.m\">demo_CJ_and_shock_state.m</a>  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exothermic Shock Waves - Detonations  \n",
    "\n",
    "Multivalued solutions to jump conditions, two branches\n",
    "\n",
    "* detonation, supersonic waves, compressed final state\n",
    "* deflagration, subsonic waves, expanded final state\n",
    "\n",
    "<img src=\"images/CJ2b.png\"  width=\"50%\" alt=\"P-V exothermic solutions, detonation and deflagration\"/> \n",
    "\n",
    "Detonation branch has minimum wave speed for solution, $\\textrm{w}_1 > \\textrm{U}_\\textrm{CJ}$\n",
    "\n",
    "<img src=\"images/CJ3a.png\"  width=\"50%\" alt=\"P-V detonation solutions\"/> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Computing CJ speed  \n",
    "\n",
    "<img src=\"images/cj-isentrope.png\"  width=\"50%\" alt=\"detonation solutions with isentropes\"/> \n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_RH_CJ_isentropes.py\">demo_RH_CJ_isentropes.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_RH_CJ_isentropes.m\">demo_RH_CJ_isentropes.m</a>\n",
    "\n",
    "Equivalent conditions for CJ condition\n",
    "\n",
    "* Wave speed is a minimum for solutions to exist\n",
    "\n",
    "$$ \\textrm{w}_{1, \\textrm{min}}  = \\textrm{U}_\\textrm{CJ}$$  \n",
    "\n",
    "* Rayleigh line and shock adiabat (Hugoniot) are tangent  \n",
    "\n",
    "$$ \\left.\\dfrac{\\partial P}{\\partial v}\\right|_{\\mathcal{H}, \\textrm{CJ}} =\n",
    "    \\left.\\dfrac{\\Delta P}{\\Delta v}\\right|_\\textrm{CJ} $$  \n",
    "    \n",
    "* Isentropes (equilibrium) are tangent to shock adiabat (Hugoniot)  \n",
    "\n",
    "$$\\left.\\dfrac{\\partial P}{\\partial v}\\right|_{\\mathcal{H}, \\textrm{CJ}} =\n",
    "    \\left.\\dfrac{\\partial P}{\\partial v}\\right|_{s, \\textrm{CJ}} $$ \n",
    "    \n",
    "* Entropy (equilibrium state computation) is local minimum $s_3 > s_2  >  s_1$\n",
    "\n",
    "$$ \\left.\\dfrac{\\partial s}{\\partial v}\\right|_{\\mathcal{H}, \\textrm{CJ}}  = 0 \\quad \\left.\\dfrac{\\partial^2 s}{\\partial v^2}\\right|_{\\mathcal{H}, \\textrm{CJ}} > 0$$\n",
    "\n",
    "* Downstream speed (wave frame) is sonic w.r.t. equilibrium sound speed\n",
    "\n",
    "$$ \\textrm{w}_2 = a_2^{eq} \\qquad  a^{eq}_2 = - v^2 \\left(\\dfrac{\\partial P}{\\partial v }\\right)_{s, eq} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Chapman-Jouguet Speed \n",
    "\n",
    "Calculate detonation Chapman-Jouguet (CJ) speed based on the\n",
    "initial gas state and the minimum wave speed method.  Alogrithm computes solutions to equilibrium shock adiabat (Hugoniot) for range of states bracketing CJ point.  Newton-Raphson method is used with variables $(T_2, \\textrm{w}_1)$ to find $\\textrm{w}_1(v_2)$.  The minimum wave speed if found by fitting a parabola to an array of $\\textrm{w}_1$ vs $\\rho_2/\\rho_1$ results and determining the minimum analytically.   Theoretical analyis of CJ point shows this variation in wave speed is quadratic in volume difference from CJ point\n",
    "\n",
    "$$     \\textrm{w}_1 - \\textrm{w}_{1,\\textrm{CJ}} = \\dfrac{\\textrm{w}_{1,\\textrm{CJ}}}{4(P_2-P_1)}P_{2\\mathcal{H},vv}\\left(v_2 - v_{2, \\textrm{CJ}} \\right)^2  $$\n",
    "\n",
    "\n",
    "See \n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_CJ.py\">demo_CJ.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_CJ.m\">demo_CJ.m</a>  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "import cantera as ct\n",
    "from sdtoolbox.postshock import CJspeed\n",
    "from sdtoolbox.utilities import CJspeed_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Initial state specification:\n",
    "$P_1$ = Initial Pressure  \n",
    "$T_1$ = Initial Temperature  \n",
    "$U$ = Shock Speed  \n",
    "$q$ = Initial Composition  \n",
    "mech = Cantera mechanism File name "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "P1 = 100000 \n",
    "P1atm = P1/ct.one_atm\n",
    "T1 = 300\n",
    "U = 2000\n",
    "q = 'H2:2 O2:1 N2:3.76'\n",
    "mech = 'Mevel2017.cti'\n",
    "gas = ct.Solution(mech)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Compute CJ speed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "[cj_speed,R2,plot_data] = CJspeed(P1, T1, q, mech, fullOutput=True)\n",
    "dratio_cj = plot_data[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Outputs:\n",
    " cj_speed - detonation speed  \n",
    " R2 - R-squared value of wave speed - density fit \n",
    " plot_data - further values relating to the fit procedure "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CJ computation for Mevel2017.cti with composition H2:2 O2:1 N2:3.76\n",
      "CJ speed 1967.8455 (m/s) Density ratio 1.8042 R-squared 0.99999991\n"
     ]
    }
   ],
   "source": [
    "print('CJ computation for '+mech+' with composition '+q)\n",
    "print('CJ speed '+str(round(cj_speed,4))+' (m/s)'+' Density ratio '+str(round(dratio_cj,4))+' R-squared '+str(round(R2,8)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## diagnostic plots \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dcpS0D6HJ6x2JhPYycL6ZPStpJKGp8KXx3oPpwAgzmxHv01hs4R6M5DSnEbrdmZIx/GygxMxOjffHPEpIiE0ISay3mVU8NmKlmf2qqvhLSkqstLR041aCc841MpKmmVlJGvMu2inHmHQWZQzuRbjnBcI9MMfE9wcBMy30OYiZLcySzHYkdJaaPGKr0Bt4MtadT7jPp4SvOiptE28UbM9XvTo455xrQGr7GtoswuM8IHTsWdFNTk/AFB4GN13ShVnqDiN0O5PtkHIGcES883w7wl3y3S10IHsW4SbcuYTEd0uW+gBIOl3hgXOl5eXlNVk+55xzKanthDYSODueOmxHeA4YhGt5exN6RdgbOErSoIy6Q8nxmBBCDwxlhB4VriZ0bbQ2do9zFvAtQs8MM4Ff5grOzG4ysxIzK+ncOZVTwM4552qoVm+sttC/2kHw5bOqDotFZYQOURfEsonArsTTiLExSTPL/lgGLPQy/eVjHCS9SHg4ZP9Y/l4cfh+hax7nnHMNTK0eoSU6NG1C6D/whlg0CegbO2BtRujUdXai6jByH50R67WJ7w8E1prZbEKv6r1jp6UQHjyY69Hozjnn6rFiNtsfTejYspOkMkLP221ji0SAscAoADP7TNJVhA40DZhoZhMSkzuOjMcdSBpMaNl4GaGxyCRJ6wlJbESc7lxJVwBTJK0hPJ/plCIsrnPO1VslV05mwfLVGwzv1LYFpZccmEJENeM9heTgzfadc41Fj4sm5Cz78A+H5SzLpkE223fOOVe/fEOf8PNm99GcDR5+XS94QnPOOUdz1nJ1839wYtMn6MjytMOpkQb3+BjnnHPVd26zB+jT5ENOX30u5XRMO5wa8SM055xr5L6tNziz6XhGr92Px9fvlnY4NeYJzTnnGrPPF3NNy+v5yLrwm7UjvlbUqW2LlIKqGT/l6JxzjdmE89hSn8Hpk5ndbUDa0WwUP0JzzrnGauZ9MOsBGPhLqOfJDDyhOedc4/TZRzDhPOi+B3z352lHUxCe0JxzrrFZvw7GnQlmcPSN0KRp2hEVhF9Dc865xuaFq+HjF+GoG2HTHmlHUzB+hOacc41JWSk89VvY+Wjoe3za0RSUJzTnnGssVi2FB0ZC+63h+38DKe2ICspPOTrnXGMx4TxYUganPgqb1M/eQCrjR2jOOdcYzLgXXrsPBl4E23w77WiKwhOac841dAvfC0dn234Hvnte2tEUjSc055xryNauhgd/AE2awdE3NZgm+tn4NTTnnGvInr4S5r4Cx90JHbqlHU1R+RGac841VO89DS9cAwNOgd6D046m6DyhOedcQ7S8HMadAZ16wcG/TzuaWuGnHJ1zrqFZvx7GnQ6fL4YTx0KL1mlHVCs8oTnnXEPzwtXw3lPh5uktd0k7mlpTtFOOkm6VNF/SrMSwfpKmSnpN0nhJ7RNlfWPZ67G8laR2kl5NvBZIujrLvFpIGhXrzZA0MKPsJklvS3pT0jHFWmbnnEvdxy/BU1fCzkfBgFPTjqZWFfMa2m3AIRnDbgYuMrM+wDjgAgBJzYC7gDPNbGdgILDGzJaZWf+KF/ARMDbLvE4DiNM9EPirpIpluxiYb2Y9gd7As4VbROecq0NWLgpdW3XsDodf0+C6tqpK0RKamU0BFmUM7gVMie8nAxVHSwcBM81sRqy70MzWJStK2hHoAjyXZXa9gSdj3fnAYqAklo0Efh/L1pvZgo1YLOecq5vM4OEfw/L/wbG3QqsOaUdU62q7leMsoKLt6BCge3zfEzBJkyRNl3RhlrrDgDFmZlnKZgBHSGomaTtgANBdUkVnZb+J071f0haFWxznnKsjXroR3poAB14BW9f/p0/XRG0ntJHA2ZKmAe2A1XF4M2BvYHj8e5SkQRl1hwKjc0z3VqAMKAWuBl4E1sbpdgNeMLNdganAX3IFJ+l0SaWSSsvLy2uweM45l4K5r8DkS6HnIbDHj9KOJjW1mtDM7E0zO8jMBhCS03uxqAx41swWmNlKYCKwa0U9Sf2AZmY2Lcd015rZufFa2xFAR+AdYCGwknC9DuD+5HSzTOcmMysxs5LOnTtv3MI651xtWLUU7j8V2nSGI69vdNfNkmo1oUnqEv82AS4BbohFk4C+klrHBiL7ArMTVYeR++iMWK9NfH8gsNbMZsfTk+MJjUwABmVM1znn6i8z+PePYfHHcMwt0HqztCNKVdHuQ5M0mpBIOkkqAy4H2ko6O44yFhgFYGafSboKeBkwYKKZTUhM7jjg0IzpDwZKzOwyQmORSZLWA58AIxKj/gK4Mzb3LwcaVztW51zD9d+bYPbDcMAVsO2eaUeTOmVvY+FKSkqstLQ07TCccy67smlw68GwwwEw9B5oUjd6MpQ0zcxKqh6z8OrGGnDOOZe/lYvg/lOg3VZw5D/rTDJLm3d95Zxz9cn69fDQWbBsHoyc1OivmyV5QnPOufpk6t/h7cfge3+Cbo3zfrNc/DjVOefqi49ehCeugN5HwO6npx1NneMJzTnn6oPl5aGfxk23hcF/b9T3m+Xipxydc66uW7cWHhwJn38GJ9zXKPtpzIcnNOecq+uevhI+mAJH/AO26pt2NHWWn3J0zrm67M0J8PzfYNeT4Vsnph1NneYJzTnn6qqF78G4M2Gr/qFVo6uUJzTnnKuLVq+EMSOgSVM4/k5o3irtiOo8v4bmnHN1jRk8ci7Mnw0nPgAdt0k7onrBj9Ccc66uKb0FZt4LA38Z+mp0efGE5pxzdUlZKTx6Eex4EOxzQdrR1Cue0Jxzrq5Y9r9w3ax9VzjqRu90uJr8GppzztUFa1fD/SeHm6d/ONk7Ha4BT2jOOVcXPH4xfDw1PHl6yz5pR1Mv+fGsc86l7ZW7w9On9/wx9Dk27WjqLU9ozjmXpk+mhSb62+0DB1yRdjT1mic055xLy/Ly0Aik7RZw7G3Q1K8CbQxfe845l4Z1a+D+U2DlwvDk6Tabpx1RvecJzTnn0vD4JfDR86F5ftf+aUfTIPgpR+ecq23T74SXboBvnwX9hqYdTYNRtIQm6VZJ8yXNSgzrJ2mqpNckjZfUPlHWN5a9HstbSWon6dXEa4Gkq7PMq4WkUbHeDEkDs4zz72QszjmXio//ExqBbD8QDroy7WgalGIeod0GHJIx7GbgIjPrA4wDLgCQ1Ay4CzjTzHYGBgJrzGyZmfWveAEfAWOzzOs0gDjdA4G/Svpy2SQdDSwv4LI551z1LSmDMSdCh25w7ChvBFJgRUtoZjYFWJQxuBcwJb6fDBwT3x8EzDSzGbHuQjNbl6woaUegC/Bcltn1Bp6MdecDi4GSWK8t8HPAd4Wcc+lZvRLuPQHWrIJh93pPIEVQ29fQZgGD4/shQPf4vidgkiZJmi7pwix1hwFjzMyylM0AjpDUTNJ2wIDEtH8D/BVYWVVwkk6XVCqptLy8PP+lcs65ypjBw2fDvJlwzM3Q5ZtpR9Qg1XZCGwmcLWka0A5YHYc3A/YGhse/R0kalFF3KDA6x3RvBcqAUuBq4EVgraT+wA5mNi6f4MzsJjMrMbOSzp07V2OxnHOuEs9fBa+PhUGXQa/MKzGuUGr1BK6ZvUk4vYiknsBhsagMeNbMFsSyicCuxNOIkvoBzcxsWo7prgXOrfgs6UXgHWBfYICkDwnL2kXSM2Y2sOAL55xz2bz1KDz5G9jlWNj73KrHdzVWq0dokrrEv02AS4AbYtEkoK+k1rGByL7A7ETVYeQ+OiPWaxPfHwisNbPZZna9mXU1sx6EI7+3PZk552rN/16HB0+DrfrBEdeBlHZEDVrRjtAkjSa0VuwkqQy4HGgr6ew4ylhgFICZfSbpKuBlwICJZjYhMbnjgEMzpj8YKDGzywiNRSZJWg98Aowo1nI551xelpfDPUOhRRsYeg803yTtiBo8ZW9j4UpKSqy0tDTtMJxz9dGaVXD74fDpa3DqRNh617QjqjWSpplZSRrz9psgnHOukMzg3z+Bsv/CkNsbVTJLm3d95ZxzhfTcX+C1+2C/S2DnI9OOplHxhOacc4Xy+kPw1JXQ5zjY5/y0o2l0PKE551whfDIdxp0J3b8Ng//uLRpT4AnNOec21pJPQrdWbTrD8XdD81ZpR9QoeaMQ55zbGKuWwj3HwRfL4QeToK33MpQWT2jOOVdT69bCA6fC/Ddg+P2wxc5pR9SoeUJzzrmaMIOJ58O7T8Dh18IOmd3Putrm19Ccc64mXrwWpo0K/TMOODntaBye0JxzrvpeHweTL4Odj4b9L0s7Ghd5QnPOueqY818Ye0Zonn/k9dDEf0brCv9POOdcvha9D6OHQvuuMHS0N8+vY6psFBIf+fIdoCvwOeGp06Vmtr7IsTnnXN2xYgHcdQzYehj+ALTZPO2IXIacCU3SfsBFwGbAK8B8oBVwJPANSQ8AfzWzpbURqHPOpWb1inCv2dK5cPJ46LRD2hG5LCo7QjsUOM3MPs4siA/h/D5wIPBgkWJzzrn0rVsLD4yEua/AcXdC993TjsjlkDOhmdkFlZStBR4qSkTOOVdXmMGEn8Pbj8Fhf4Wdvp92RK4SVTYKkfQzSe0V3CJpuqSDaiM455xL1ZQ/w/Tb4bvnwW4/TDsaV4V8WjmOjNfJDgI6A6cCfyhqVM45l7bpd8LTv4V+w2D/S9OOxuUhn4RW8QyEQ4FRZjYjMcw55xqedybD+J/BN/b3R8HUI/kktGmSHicktEmS2gHeZN851zDN+S+MGRE6Gj7uDmjaPO2IXJ4qa7bfLDb++AHQH3jfzFZK2pxw2tE55xqW+W/A3UOg/VZw4oPQsl3aEblqqOwI7T+SHgJOBxaZ2WIAM1toZjOrmrCkWyXNlzQrMayfpKmSXpM0XlL7RFnfWPZ6LG8lqZ2kVxOvBZKuzjKvFpJGxXozJA2Mw1tLmiDpzThdv/bnnMtu8Ry482ho1hJGjIO2XdKOyFVTzoRmZiXAz+LHqyW9LOlvkg6S1DKPad8GHJIx7GbgIjPrA4wDLoAv72u7CzjTzHYGBgJrzGyZmfWveAEfAWOzzOu0GHMfwr1xf5VUsWx/MbNvAt8CviPpe3nE7pxrTFYshDuPCjdQnzgWNu2RdkSuBiq9hmZmH5nZDWZ2JLAXMB44AHhO0oQq6k4BFmUM7gVMie8nA8fE9wcBM2ODk4qjwHXJipJ2BLoAz2WZXW/gyVh3PrAYKDGzlWb2dBy+GpgOdKssbudcI/PFMrj7WFgyB064F7bcJe2IXA3l3Tmxma0xs6fM7EIz251wKrK6ZgGD4/shQPf4vidgkibF+9wuzFJ3GDDGzCxL2QzgCEnNJG0HDEhMGwBJHYHDiYkvG0mnSyqVVFpeXl6tBXPO1UNrv4AxJ8K8GTDkNth2r7Qjchshnxurvy/pFUmfSVoqaZmkpWb2SQ3mNxI4W9I0oB2wOg5vBuwNDI9/j5KU+fjXocDoHNO9FSgDSoGrgReBtYllaBbrXmtm7+cKzsxuMrMSMyvp3LlzdZfNOVefrF8H486A958JTfN7+dWI+q7K3vYJCeJo4LUcR0d5M7M3CacXkdQTOCwWlQHPmtmCWDYR2JV4NCWpH9DMzKblmO5a4NyKz5JeBN5JjHIT8I6ZbdCgxDnXCJnBI+eEB3Ue+Bv41vC0I3IFkM8pxznArI1NZvDlo2iIDTYuAW6IRZOAvrFVYjNgX2B2ouowch+dVbRmbBPfHwisNbPZ8fOVQAfgnI2N3znXAJjB45fA9DtgnwvgOz9NOyJXIPkcoV0ITJT0LPBFxUAzu6qySpJGE1ordpJUBlwOtJV0dhxlLDAqTuszSVcBLwMGTDSzZKOT4wg3dienP5jQ8OMyQmORSZLWA58AI+I43YCLgTeB6Qp3+19nZjfnsdzOuYbo2T/B1Otg9zNgv4vTjsYVkKo68Iq9hCwHXiPRQ4iZXVHc0NJVUlJipaWlaYfhnCuk/1wPj10E/YfD4OugSd7t4lyeJE2Lt33VunyO0DYzM+9d3zlXv02/MySznQbD4dd6MmuA8vmPPuGPi3HO1Wuvj4PxP4VvDIJjboam+ezLu/omn4R2NvCYpM+TzfaLHZhzzhXEW4/Cg6dB92/D8XeFrq1cg1TlboqZee+czrn66d0n4L6TYMs+cMIYaNE67YhcEeWPZZl2AAAgAElEQVQ8QpPUo7KK8QnW3o2Uc65uev9ZuHc4dO4FI8ZCqw5pR+SKrLIjtD/H+8UeBqYB5UArYAdgP2AQoSl+WbGDdM65avnoRRg9FDbbHkY8DJtsmnZErhbkTGhmNkRSb0J3VCOBrYCVwBvAROC3ZraqVqJ0zrl8zXk5PNOsQzc46WFos3naEblaUuk1tNjbht956JyrH+a+AncdE55ldtK//ZlmjYzfiOGcaxjmzYQ7joRNOsDJ48NTp12j4gnNOVf/zZsBtx8OLduFZNbB26s1Rp7QnHP129xX4fbBIZmd8og/bboRy3kNTdKulVU0s+mFD8c556ph7qtwxxHQsj2cMt6TWSNXWaOQv8a/rYASwlOhBfQFXiI8iNM559LxtWT2CGy6bdoRuZTlPOVoZvuZ2X7AR8Cu8UnOA4BvAe/WVoDOObeBua/AHYM9mbmvyeca2jfN7LWKD2Y2C+hfvJCcc64Sn0wPR2atOngyc1+TT5fTb0i6GbiL8PDNEwk3VzvnXO36+CW4+1jYpCOc7MnMfV0+Ce1U4CzgZ/HzFOD6okXknHPZfPAc3HM8tNsyNs3fOu2IXB2TT2/7qyTdAEw0s7dqISbnnPu6d58IHQ1vul3ozqrdFmlH5OqgKq+hSRoMvAo8Fj/3l/TvYgfmnHMAvDkBRg+DTjvCKRM8mbmc8mkUcjmwO7AYwMxeBXoUMSbnnAteH/fV88xOHu8dDbtK5ZPQ1prZkqJH4pxzSa+OhgdGQrfdYMRD/ggYV6V8EtosSScATSXtKOnvwItFjss515i9dCM8dCb0+C6c+CC0ap92RK4eyCeh/QTYGfgCuAdYApxTVSVJt0qaL2lWYlg/SVMlvSZpvKT2ibK+sez1WN5KUjtJryZeCyRdnWVeLSSNivVmSBqYKBsQh78r6VpJymOZnXNpMINn/giPXgjf/D4Mvx9atEk7KldPVJnQzGylmV0MDDSz3czskjwf7HkbcEjGsJuBi8ysDzAOuABAUjPCfW5nmtnOwEBgjZktM7P+FS9CryVjs8zrtBhrH+BA4K/xadsQbjE4HdgxvjJjcs7VBevXw2O/hGd+B/2Hw5DboVnLtKNy9Ug+rRz3kjSbeDN1PMr6Z1X1zGwKsChjcC/CfWwAk4Fj4vuDgJlmNiPWXWhm6zLi2BHoAjyXZXa9gSdj3fmEBiwlkrYC2pvZVDMz4A7gyKpid87VsnVr4eGz4aXrYY8fweDroGk+t8k695V8Tjn+DTgYWAgQk84+NZzfLGBwfD8E6B7f9wRM0iRJ0yVdmKXuMGBMTEyZZgBHSGomaTtgQJz21kBZYryyOCwrSadLKpVUWl5eXq0Fc87V0JpVcP/JMOMe2O9iOPh30MSfbOWqL6+txszmZAxal3XEqo0EzpY0DWgHrI7DmxF67x8e/x4laVBG3aHA6BzTvZWQrEqBqwmNVtYSng6QKVtCDAVmN8VOmEs6d+6c3xI552pu1VK4Zwi8+Qh870+w74Xgl7ldDeVzTD9H0l6EI6gWwE+pYV+OZvYm4fQiknoCh8WiMuBZM1sQyyYCuxJPI0rqBzQzs2k5prsWOLfis6QXgXeAz4Dko2u7AXNrErtzrsCW/Q/uPgbmvwFH3Qj9hqYdkavn8jlCOxM4m3Cq7hNCT/tn12RmkrrEv02AS4AbYtEkoK+k1rGByL7A7ETVYeQ+OiPWaxPfH0i4d262mc0DlknaI7ZuPAl4uCaxO+cKaMG7cMuBsPB9GDbGk5kriHz6clxAOBVYLZJGE1ordpJURuhxpK2kimQ4FhgV5/GZpKuAlwmnBCea2YTE5I4DDs2Y/mCgxMwuIzQWmSRpPSHpjkiMehahxeUmwKPx5ZxLyyfT4O4h4f0p42HrAenG4xoMZW9jkRhB2h64BtiDkGymAuea2fvFDy89JSUlVlpamnYYzjUs7zwB942ANp1hxDjY/BtpR+QKTNI0MytJY975nHK8B7gP2AroCtxPJaf/nHMuqxn3wujjQxL7wWRPZq7g8kloMrM7zWxtfFU86NM556pmBs/+GcadAdvuBadM9B7zXVHk08rxaUkXAfcSEtnxwARJmwGYWebN0845F6xbA4+cA6/cBX2Ph8F/994/XNHkk9COj3/PyBg+kpDgti9oRM65hmHVkvDol/efgX1/AQN/6feYuaLKp5XjdrURiHOuAVk8B+45Dha8DUf8E75V7YbSzlVbPn05DpHULr6/RNJYSd8qfmjOuXpp7qtw8wGwpCw8+sWTmasl+TQKudTMlknam9Cn4+18dUO0c8595a1HYdSh0LQ5jJwE2w9MOyLXiOST0Cr6bTwMuN7MHgZaFC8k51y9YwYvXAOjh0GnHeGHT8AWvdOOyjUy+TQK+UTSjcABwB8ltSTPTo2dc43A2i/gkXPh1buh95Fw5PXQonXaUblGKJ+EdhzhoZh/MbPF8RljFxQ3LOdcvbBiAYwZAR+/CPteFFoz+qNfXEryaeW4ksRTomOHv/OKGZRzrh6Y/wbcczws/x8ccwv0OTbtiFwj54+Edc5V39uT4IEfhFOLp0yEbt7BsEufJzTnXP7Wr4fn/gpP/xa27APD7oUOOR8C71yt8oTmnMvPF8vgobPgjfHQ5zg4/Bpv/OHqFE9ozrmqLXwP7h0OC96Cg34Le57t3Vi5OscTmnOucu88AQ+OBDWBE8fCN/ZLOyLnsvKE5pzLbv16eOFv8ORvYIudYejdsGmPtKNyLidPaM65DX3+GYw7C95+FHY+Go64Dlq0STsq5yrlCc0593XzZoSbpZd+Aof8Eb59hl8vc/WCJzTn3Fem3wETzofWm4f7y7b5dtoROZc3T2jOOVjzOUw8PzxZert9Q88fbTunHZVz1VLUTtck3SppvqRZiWH9JE2V9Jqk8ZLaJ8r6xrLXY3krSe0kvZp4LZB0dZZ5NZd0e6z3hqRfJsrOjdOcJWm0pFbFXG7n6pUF78ItB4Zk9t3zYcQ4T2auXip2L6K3ETo2TroZuMjM+gDjiB0dS2oG3AWcaWY7AwOBNWa2zMz6V7yAj0j0LZkwBGgZpzsAOENSD0lbAz8FSsxsF6ApMLTAy+lc/TRjDNy4T3gY57AxMOhSaNI07aicq5GiJjQzmwIsyhjcC5gS308GjonvDwJmmtmMWHehma1LVpS0I9AFeC7b7IA2MTFuAqwGlsayZsAmsaw1MHdjlsu5em/1CnjoRzDudNiqL5z5PPTK3Pd0rn5J4zkPs4DB8f0QoHt83xMwSZMkTZd0YZa6w4AxZmZZyh4AVhCeBPAx4XE3i8zsE+Avcdg8YImZPZ4tMEmnSyqVVFpeXl7T5XOubvt0Ftw0EF69B/a5AE5+BDp0Szsq5zZaGgltJHC2pGlAO8KRFISjqL2B4fHvUZIGZdQdCozOMd3dCU/X7gpsB5wnaXtJmwJHxGFdCUdxJ2abgJndZGYlZlbSubNfQ3ANjBmU3go3D4JVS+Ckh2D/S6Cptw1zDUOtb8lm9ibh9CKSegKHxaIy4FkzWxDLJgK7Ak/Gz/2AZmY2LcekTwAeM7M1wHxJLwAlhFORH5hZeZzOWGAvwvU65xqHFQth/E/hzUfgG/vDUTdC2y5pR+VcQdX6EZqkLvFvE+AS4IZYNAnoK6l1vNa1LzA7UXUYuY/OIJxS3F9BG2AP4M04fI84XQGDgDcKuUzO1WnvPgHX7wnvPA4HXQnDH/Rk5hqkoh6hSRpNaK3YSVIZcDnQVtLZcZSxwCgAM/tM0lXAy4SjqolmNiExueOAQzOmP5jQevEy4B9xWrMAAaPMbGYc7wFgOrAWeAW4qfBL61wds2YVPHE5vHQDdP4mnPhgeIaZcw2UsrevcCUlJVZaWpp2GM7VzKezYOxpMH827H4GHHgFNN8k7ahcIyBpmpmVpDFvvxrsXEOyfh1MvQ6euhJadQynF3c8IO2onKsVntCcaygWvBueKF32X/jm98MTpdt0Sjsq52qNJzTn6rv16+G/N8ITV0CzlnD0v6DPEO8h3zU6ntCcq88WfQAP/xg+eh52PDgclbXfKu2onEuFJzTn6qP166H0Fph8eeh78Yh/QP/hflTmGjVPaM7VN+Vvwb9/AnNeCjdJH34tdOxedT3nGjhPaM7VF2tXwwtXw5Q/Q4s2cOQN0G+oH5U5F3lCc64+KCsNR2XzZ8Mux8Ahf/RnljmXwROac3XZqqXw9O9Cbx/tu4ZnlvljXpzLyhOac3WRGbw+Fh77P1j+P9jthzDoMmjVvuq6zjVSntCcq2sWvAsTz4P3n4Gt+sOwe2DrAWlH5Vyd5wnNubpizefw3F/hhWug2SZw6F+gZGRolu+cq5InNOfSZgZvjIfHL4bFH0Pf48NjXvwRL85Viyc059L06Sx47CL48Dno0htOHg/b7ZN2VM7VS57QnEvDioXw9G9h2iho1SGcXhxwKjT1r6RzNeXfHudq07o18PIt8Mzv4IvlsNtpMPAiaL1Z2pE5V+95QnOuNpjB7IfhyV/Dovdg+4FwyB+gy05pR+Zcg+EJzbli+2gqTL4Uyl6GzjuFm6N7HuxdVjlXYJ7QnCuW8rfhiV/BWxOg3VYw+Drof4I3w3euSDyhOVdoiz+GZ/8Er94DzVvD/pfCHj+CFq3Tjsy5Bs0TmnOFsnRuuDF62u3hdOLup8E+F0CbTmlH5lyj4AnNuY21vBye/xu8fDPYOtj1JPju+dBh67Qjc65RKVpCk3Qr8H1gvpntEof1A24A2gIfAsPNbGks6wvcCLQH1gO7Ac2B5xKT7QbcZWbnZMyrOXAzsGtcpjvM7PexrGMs2wUwYKSZTS3CIrvGZvl8mHod/PdfsHYV9DsB9r0ANu2RdmTONUrFPEK7DbgOuCMx7GbgfDN7VtJI4ALgUknNgLuAEWY2Q9LmwBozWwX0r6gsaRowNsu8hgAtzayPpNbAbEmjzexD4BrgMTM7VlILwC9kuI2zeA68eC1MvwPWrQ7PJ9v3Iui0Q9qROdeoFS2hmdkUST0yBvcCpsT3k4FJwKXAQcBMM5sR6y7MnJ6kHYEufP2I7cvZAW1iYtwEWA0sldQe2Ac4JU53dSxzrvoWvgfPXwUz7g2f+w2Dvc+Fzb+RblzOOaD2r6HNAgYDDxOOqrrH4T0BkzQJ6Azca2Z/yqg7DBhjZpZlug8ARwDzCEdg55rZIkn9gXJgVDzdOQ34mZmtyBacpNOB0wG22Wabmi+la1g+mR5OLb4+Dpo0Dz3g7/VT6Ni96rrOuVrTpJbnNxI4O546bMdXR0vNgL2B4fHvUZIGZdQdCozOMd3dgXVAV2A74DxJ28fp7gpcb2bfAlYAF+UKzsxuMrMSMyvp3Nkfb9+orV8Pb06EUYfCv/aDtx+HPX8M57wGh/7Zk5lzdVCtHqGZ2ZuE04tI6gkcFovKgGfNbEEsm0hIRE/Gz/2AZmY2LcekTyBcJ1sDzJf0AlBCOL1ZZmYvxfEeoJKE5hyrV8KM0fCff8LCd6F9t/Aol11PCp0IO+fqrFpNaJK6mNl8SU2ASwgtHiFcS7swNuhYDewL/C1RdRi5j84APgb2l3QX4ZTjHsDVZvappDmSepnZW8AgYHZhl8o1CJ99CKW3wvQ74fNF4UnRx9wCvY+Aps3Tjs45l4diNtsfDQwEOkkqAy4H2ko6O44yFhgFYGafSboKeJnQwGOimU1ITO444NCM6Q8GSszsMuAfcVqzAAGjzGxmHPUnwN2xheP7wKmFXlZXT61fD+89BS//C96eFG6G7nUo7HEWbPsd72vRuXpG2dtYuJKSEistLU07DFcMKxaG04qlt8Ci96FNFxhwMgw4BTp0Szs65+o1SdPMrCSNeXtPIa5xWL8uHI29cmdo7LF+DWyzJ+x3Mew0GJq1SDtC59xG8oTmGrZFH8Ard4WOgpfNhdabw+6nw7dOhC16px2dc66APKG5hmfFQpj9ELx2P3w8FRDsMAgO+X24RuZHY841SJ7QXMOwegW89WhIYu8+AevXQqdesP8loUcPvzbmXIPnCc3VX18sh3cnwxvj4a3HYM0KaL91ePZYnyGwZR9vqehcI+IJzdUvKxfB24+FJPbuk7Dui3BdrM+x0Pc42GYvaFLbHeA45+oCT2iubjODBe/AO4/DO5PgwxfCM8fabw0lp8JOh4fWik2aph2pcy5lntBc3bN6JXz4fExij8Pij8Lwzt+EvX4CvQdD1139dKJz7ms8obn0rV0Nc6fDB1PCa85/w6nE5q1hu33hOz+DHQ+Ejv4EBOdcbp7QXO1bswrmvQof/ycksI//Exp0oNCQY/fTQjP7bfaC5q3SjtY5V094QnPFt+QTmPMSlL0cjr7mzQg9dUA4jdj/BNhuH+ixN7TeLN1YnXP1lie0Aim5cjILllf+MOxObVtQesmBtRRRYeRarqzLYgaffQDzZsKnM8PfeTNgxfxQ3qxVuPa154+g2+7QfXdo26UWlsI51xh4QiuQqpJZxTg9LppQ5XhQ3OSXT/KtjFhPqxWfwDuTofwtWPAWlL8N89+AL5bEkZpCl51ghwNgq37QfTfYoo/30uGcKxpPaAU2psWv2YxlzLHOfGxdmGOdKfvybyeW0obwhJvKVSf5FUMbPqebyummcrrHV8X7HvqU1voC7o4jt9489MrR51jYqi9s2Re69PbrX865WuUJrcBeXLczOzX5mG00n5Imb9Fen3+tfJU1p9w6Mp+OzLfwKreOLKENS6wNS2nDUmvNEtqw1NrwOS1YRQvW0pR8EmGmpqyjBWtozRe010o6sIL2WkF7VtJeK+nIcjprcXwtoQuf0UWLaaMvvjadldaSMuvEHOvC1PW9ede68vvTjw2JrM3mG7PKnHOuIDyhFdg1646BdRWfjA6soLvms43ms5UW0kWLw4vF7KC57NXkdTpoZZXTXWdiFS34guasogXryd4bRlPW05LVtGQNLVlDM62vctpLbRPKrSPldGSWbcf89ZtSbh34JCawOdaZhbQnM6H+ftu9qpy2c87VFk9oRSWW0JYl1pZZtn3OsZqzlvasoINW0CH+bc8K2mslrVhNK1bTUmvCX8LfJtrwwazCWGtN+YLmX72s+ZdJMNsR4FJas4qWxVwJzjlXKzyhFUinti1q3NBiDc1YSAcWWocwoB48RLxTW2/c4ZyrWzyhFUiuFokb26KwLqmPtx045xoPT2hFVp0EkEby8yTlnGsoPKHVIZ5YnHOu5or64ChJt0qaL2lWYlg/SVMlvSZpvKT2ibK+sez1WN5KUjtJryZeCyRdnWVezSXdHuu9IemXGeVNJb0i6ZFiLrNzzrl0FPtJiLcBh2QMuxm4yMz6AOOACwAkNQPuAs40s52BgcAaM1tmZv0rXsBHwNgs8xoCtIzTHQCcIalHovxnwBsFWi7nnHN1TFETmplNARZlDO4FTInvJwPHxPcHATPNbEasu9DM1iUrStoR6AI8l212QJuYGDcBVgNLY71uwGGEZOqcc64BSuNZ9bOAwfH9EKB7fN8TMEmTJE2XdGGWusOAMWaWrWH7A8AKYB7wMfAXM6tIplcDFwKV3mUs6XRJpZJKy8vLq7VQzjnn0pVGQhsJnC1pGtCOcCQFoYHK3sDw+PcoSYMy6g4FRueY7u6EPjq6AtsB50naXtL3gflmNq2qwMzsJjMrMbOSzp07V3e5nHPOpajWWzma2ZuE04tI6kk4FQhQBjxrZgti2URgV+DJ+Lkf0KySxHQC8JiZrQHmS3oBKAG+BQyWdCjQCmgv6S4zO7GyOKdNm7ZA0kcbsaidgAUbUb+YPLaaq8vxeWw1V5fjq2+xbZtGIJBCQpPUxczmS2oCXALcEIsmARdKak04atsX+Fui6jByH51BOM24v6S7gNbAHsDVZnYf8Ms474HA+VUlMwAz26hDNEmlZlayMdMoFo+t5upyfB5bzdXl+Dy2/BW72f5oYCrQS1KZpB8AwyS9DbwJzAVGAZjZZ8BVwMvAq8B0M0s+P+U4MhKapMGSfh0//gNoS7hG9zIwysxmFm3hnHPO1SlFPUIzs2E5iq7JMf5dhKb72co26N3XzP4N/Du+X05oZFJZPM8Az1Q2jnPOufopjUYhjcVNaQdQCY+t5upyfB5bzdXl+Dy2PCl7C3jnnHOufvEjNOeccw2CJzTnnHMNgie0LLJ1qpxR3iF2rDwjdqR8aqLsZEnvxNfJcVhrSRMkvRnH/0Ni/FMklSc6X/5hbccXhz8j6a1EHF3i8JaSxkh6V9JLGf1j1sa6y9k5dXXX3UbG9pikxZmdW0vaLq6Xd+J6alGT9VbE+O6O/9dZcfrN4/CBkpYk1t1lKcR2m6QPEjH0j8Ml6dq47mZK2jWF2J5LxDVX0kM1WW8bE5+k/vqqs/aZko5P1CnIdlek2AqyzdWImfkr4wXsQ7ipe1aO8v8D/hjfdyb0V9kC2Ax4P/7dNL7flHBf3H5x/BaEvii/Fz+fAlyXZnxxvGeAkizT+hFwQ3w/lND1WK3GllF/GrBPTdZdTWOLnwcBhwOPZNS5Dxga398AnFWT9VbE+A4FFF+jE/ENzBw3hdhuA47NMq1DgUdjzHsAL9V2bBn1HwROqsl628jvRE9gxzi8K6Fbv46F3O6KFFtBtrmavPwILQvL3qny10YB2kkS4d63RcBa4GBgspktsnBf3WTgEDNbaWZPx2mvBqYD3epKfFXM7gjg9vj+AWBQnG6tx6bKO6eu0kbEhpk9CSzLiEfA/oT1AmE9HRnfV2u9FSO+OHyiRcB/qeF2V4zYKnEEcEcM+z9AR0lbpRGbpHaE//FD1Yi/IPGZ2dtm9k6cxlxgPtC5kNtdoWOLnwuyzdWEJ7SauQ7YiXBj+GvAz8xsPbA1MCcxXlkc9iVJHQl7hE8mBh8TD9sfkNSdjVfT+EbFUwGXJr4EX9Yxs7XAEmDzFGKD7J1TF3Ld5Yotl82BxXG9ZMZc6PVWk/i+FE/7jAAeSwzeM55KelTSzinF9tv4//ubpJZxWD7bQm3EBnAU8KSZLU0MK+R6yys+SbsTjozeo3a3u+rGlhxe7G1uA57QauZgQm8mXYH+wHUKDyrNtif05Y+vwqNtRgPXmtn7cfB4oIeZ9QWe4Ku9q9qOb7iFZ8l9N75GVIRdSZ3aiq1CZufUhV53uWLLpbKYC73eoPrxJf0TmGJmFUe304Ftzawf8Hc24ghkI2L7JfBNYDfCqeZfxOG1tc3lI7PLvUKvtyrji0endwKnxmRSm9tddWNLKvY2twFPaDVzKjA2HlW/C3xA+GKW8dXjcCAcas9NfL4JeMfMvnzitoXnvn0RP/6L8HDSWo/PzD6Jf5cB9xCeXkCyTkzIHaj8FEXBY4vz3qBz6iKsu1yx5bKAcDqsosedZMyFXm81iY84/8sJp4N+XjHMzJZa6F0HM5sINJfUqTZjM7N5cfwvCF3gbbDNRZnfo6LHBiBp8xjTl13wFWG9VRpfTB4TgEvi6Veo3e2uurERy2pjm9uAJ7Sa+ZhwMRlJWxAeWvo+oYPlgyRtKmlTwlMFJsXxriRsXOckJ5RxbWAwhXmqdrXik9SsYsOKpwm+T+gTE0LXYhWtIY8Fnso45VfU2BL1NuicugjrLldsWcX18DRhvUBYTw/H94Veb9WOL473Q8Je9rDkHrSkLStOK8dTRk2AhbUc21bxrwjXgJLb3EkK9gCWmNm82owtGkJoxLAqEXOh11vO+BRaLo4jXE+8v2LkWt7uqhVbHK+2trkNWRFbnNTXF+GHcx6whrDH8wPgTOBM+6pVz+OEc8qzgBMTdUcC78bXqXFYN8Jh/xuEw/dXgR/Gst8DrwMzCBvpN1OIrw2h9eDMGMs1QNNY1gq4P47/X2D72owtUfZ+5rqp7rrbyNieA8qBz2Pdg+Pw7eN6eTeup5Y1WW9FjG8t4dpGxXZ3WRz+48S6+w+wVwqxPZUY/y6gbRwuQmfj78XyDVrfFju2WPYMoVFXcl7VWm8bEx9wYqzzauLVv5DbXZFiK8g2V5OXd33lnHOuQfBTjs455xoET2jOOecaBE9ozjnnGgRPaM455xoET2jOOecaBE9ozhWApF9JOr/A05woqWN8/aiQ086Yz/9lfH6xWPNyrpg8oTlXR5nZoWa2GOhI6EW9RiQ1rWKUryU0M9urpvNyLk2e0JyrIUkXKzz36QlCDwoVw7+h8JytaQrP1aroKug2hed8vSjpfUnHxuFbSZoSO4aeJem7cfiHsQeXPwDfiOV/lnSnpCMS87tb0uCM2AZKelrSPYSbYpH0UIzpdUmnx2F/ADaJ0747Dlse/yrOb5ak15R45pVzdVKh79T2l78aw4vQb+RrhGfdtSf0zHD+/7d3/yBVhXEYx79PCmEkQn+IhqiGIFoKl/5Q5uAWERbR4FZ7S9DS2OgU0VJEkUOEiOLUEmTQUlAqFA2BjRlERCpExK/h91493fRmDqmX5wOH855zzznve+/y3sM5PL/y2RMWakUdJuOHIOt/DZJ/JA8A78v+K8C10m4B2kv7A7AN2EOlXhVwEhgp7Q4yX6+1bnzdwCywt7JvS1m3kakPW8v2TN25M2V9jizj0wLsIGOQdq72b+/Fy1JLLdzSzP7NCWA4IuYAJI2W9WbgGDCohTJUGyvnjUTm270t2XgAL4FaZd+RiBhv1HFEjEm6pawqfhYYioVSIlUvImKqsn1ZUm9p7wL20ThL7zjwMCJ+AtOSxshk/NFG4zNbLZ7QzFZusdy4DWStqkNLnPO90hZkkUVJXcApYEBSf0Q8+EvfA0AfWVLn4hLHzM53JHUDPcDRiJiT9JTM/WukYUFSs7XGz9DMVuYZ0CupTVnV+DRkiQxgStJ5mH8OdbDRhSTtBj5FxB3gLtBZd8g3oL1u331K5YaIeLOM8XYAX8pkth84UvnsR7k7XOw7XpDUImk70EUG3pqtSZ7QzFYgIl4Bj8g08SEytb2mD7gkaYJMFz/z5xV+0w2MS3pNPre6UdfXZ+B5eXOAOAIAAAB9SURBVDmjv+ybJqs33FvmkB8DrZImgetk2nnNbWCy9lJIxTBZgWGCTMa/GhEfl9mf2X/ntH2zdUjSJvKllM6I+Lra4zFbC3yHZrbOSOoB3gE3PZmZLfAdmpmZNQXfoZmZWVPwhGZmZk3BE5qZmTUFT2hmZtYUPKGZmVlT+AWZqdZQpUCKBgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "CJspeed_plot(plot_data,cj_speed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Detonation modeling \n",
    "\n",
    "The conventional model of unsteady detonation is by the Euler equations\n",
    "\n",
    "\\begin{align}\n",
    "\\dfrac{\\partial}{\\partial t}\\rho + \\nabla \\cdot (\\rho {\\bf u})%\n",
    "&=0\\label{unsteady_mass_eqn}\\\\\n",
    "\\dfrac{\\partial}{\\partial t}(\\rho {\\bf u}) + \\nabla\\cdot(\\rho{\\bf u}\\otimes {\\bf u}\n",
    "+ {\\bf I}P)%\n",
    "&=0 \\label{unsteady_mom_eqn}\\\\\n",
    "\\dfrac{\\partial}{\\partial t}\\rho (e + \\dfrac{|{\\bf u}|^2}{2})%\n",
    "+ \\nabla\\cdot\\rho{\\bf u}(h + \\dfrac{|{\\bf u}|^2}{2}) &=0\\label{unsteady_energy_eqn}\\\\\n",
    "\\dfrac{\\partial}{\\partial t}(\\rho Y_k) + \\nabla \\cdot (\\rho {\\bf u} Y_k) &=%\n",
    "\\mathcal{W}_k\\dot{\\omega}_k \\qquad (k=1,\\dots, K) \n",
    "\\end{align}\n",
    "\n",
    "In terms of the material derivative, \n",
    "\n",
    "$$\\dfrac{\\textrm{D} }{\\textrm{D} t} = {\\partial/\\partial t} + {\\bf u}\\cdot\\nabla $$  \n",
    "\n",
    "these are:  \n",
    "\n",
    "\\begin{align}\n",
    "\\dfrac{\\textrm{D} \\rho}{\\textrm{D} t} &= -\\rho \\nabla\\cdot{\\bf u}\\\\\n",
    "\\dfrac{\\textrm{D} {\\bf u}}{t} &= -\\dfrac{1}{\\rho} \\nabla P\\\\\n",
    "\\dfrac{\\textrm{D} h }{\\textrm{D} t} &= \\dfrac{1}{\\rho} \\dfrac{\\textrm{D} P}{\\textrm{D} t}\\\\\n",
    "\\dfrac{\\textrm{D}  Y_k}{\\textrm{D} t} &= {1\\over\\rho} \\mathcal{W}_k\\dot{\\omega}_k\\qquad (k=1,\\dots, K)\n",
    "\\end{align}  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# ZND Model\n",
    "\n",
    "The ZND model considers a motion that is one-dimensional and steady in the wave frame.    \n",
    "\n",
    "$$ \\dfrac{\\partial }{\\partial t } = 0 \\; \\textrm{and} \\;  \\nabla = \\dfrac{\\textrm{d} }{\\textrm{d} x} \\; \\rightarrow \\dfrac{\\textrm{D} }{\\textrm{D} t} = \\textrm{w}\\dfrac{\\textrm{d} }{\\textrm{d} x}  =  \\dfrac{\\textrm{d} }{\\textrm{d} t} $$  \n",
    "\n",
    "Defining themicity\n",
    "\n",
    "$$   \\dot{\\sigma} =  \\sum_{k=1}^K \\left( \\dfrac{W}{{W}_k}\n",
    "  - \\dfrac{h_k}{c_p T}  \\right) \\dfrac{\\textrm{d}Y_k}{\\textrm{d} t}$$\n",
    "\n",
    "and the sonic parameter (based on the frozen sound speed $a_{fr}$)\n",
    "\n",
    "$$ \\eta = 1 - \\textrm{w}^2/a_{fr}^2  = 1 - M_2^2$$\n",
    "\n",
    "the resulting model can be rewritten in terms of a set of ordinary differential equations  (ODEs)\n",
    "\n",
    "\\begin{align}\n",
    "\\dfrac{\\textrm{d} P}{\\textrm{d} t} & = -\\rho \\textrm{w}^2\\dfrac{\\dot{\\sigma}}{{\\eta}}\\\\\n",
    "\\dfrac{\\textrm{d}\\rho}{\\textrm{d} t} &= -\\rho \\dfrac{\\dot{\\sigma}}{\\eta}\\\\\n",
    "\\dfrac{\\textrm{d}\\textrm{w}}{\\textrm{d} t} &= w \\dfrac{\\dot{\\sigma}}{\\eta}\\\\\n",
    "\\dfrac{\\textrm{d}Y_k}{\\textrm{d} t} &= \\dfrac{W_k \\dot{\\omega}_k}{\\rho} \\qquad (k=1,\\dots, K)\n",
    "\\end{align}  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# ZND model equivalence\n",
    "\n",
    "The ZND model is equivalent to steady flow in a constant area, adiabatic flow.  The differential equation formulation is mathematically equivalent to the differential-algebraic equation (DAE) set conserving mass, momentum and energy using the jump conditions as each point in the downstream flow\n",
    "\n",
    "\\begin{align}\n",
    "\\rho \\textrm{w} & = \\rho_1 w_1 \\\\\n",
    "P + \\rho \\textrm{w}^2  & = P_1 + \\rho_1 \\textrm{w}_1^2 \\\\\n",
    "h + \\dfrac{1}{2}\\textrm{w}^2 & = h_1 + \\dfrac{1}{2}\\textrm{w}_1^2\n",
    "\\end{align}  \n",
    "\n",
    "and computing the change in chemical composition with distance downstream from the shock.  \n",
    "\n",
    "$$ \\textrm{w}\\dfrac{\\textrm{d}Y_k}{x} = \\dfrac{W_k \\dot{\\omega}_k}{\\rho} \\qquad (k=1,\\dots, K) $$\n",
    "Following a parcel of gas downstream from the shock the distance traveled and time elapsed are related by integrating distance along the stream line.\n",
    "\n",
    "$$\\dfrac{\\textrm{d} x}{\\textrm{d} t}  = \\textrm{w}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Initial conditions for ZND model  \n",
    "\n",
    "The initial conditions for a znd computation have to be consistent with a compressible one-dimensional flow.  The standard way to insure this is to solve the frozen (non-reactive) shock jump conditions with specified upstream state $(P, \\rho, \\textrm{w}, {\\bf Y})_1$.   The state downstream of the shock is $(P, \\rho, \\textrm{w}, {\\bf Y})_2$, will be the initial conditions for starting the ODE or DAE solution.  In detonation modeling the state 2 is referred as the von Neumann  (vN) condition and the ZND solution is computed as follows for a CJ detonation:\n",
    "\n",
    "* Define initial state  $(P, \\rho, \\textrm{w}, {\\bf Y})_1$ of fuel-oxidizer-diluent mixture\n",
    "* Compute CJ shock speed $\\textrm{U}_\\textrm{CJ}$  using CJspeed function\n",
    "* Compute frozen postshock conditions corresponding to a nonreactive shock wave with $\\textrm{w}$ = $\\textrm{U}_\\textrm{CJ}$\n",
    "* Evaluate gas properties from gas object corresponding to postshock state 2 returned by PostShock_fr\n",
    "* Integrate from state 2 toward state 3\n",
    "* Solutions that extend to state 3 are only possible for certain exothermic cases  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* CJ detonations $\\textrm{w}_1$ = $\\textrm{U}_\\textrm{CJ}$  \n",
    "<img src=\"images/zndpath.png\"  width=\"50%\" alt=\"Hugoniots and Rayleigh line for CJ case\"/>\n",
    "\n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_RH.py\">demo_RH.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_RH.m\">demo_RH.m</a>  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Overdriven detonations  $w_1$ $>$ $\\textrm{U}_\\textrm{CJ}$\n",
    "<img src=\"images/zndpath2.png\"  width=\"50%\" alt=\"Hugoniots and Rayleigh line for CJ case\"/> \n",
    "* Exothermic cases may be singular if $\\eta$ $\\rightarrow$ 0 in the interior of the domain unless  $\\dot{\\sigma}$ vanishes simultaneously - known as an eigenvalue detonation.    Usually occurs when $w_1$ $<$ $\\textrm{U}_\\textrm{CJ}$ and in certain cases for CJ detonations, see Fickett and Davis, Detonation or Lee, The Detonation Phenomenon. \n",
    "* Endothermic cases are not ordinarily singular"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# ZND Example\n",
    "\n",
    "See \n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_CJ.py\">demo_ZNDCJ.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_CJ.m\">demo_ZNDCJ.m</a>  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reaction zone pulse width (exothermic length) = 4.383e-05 m\n",
      "Reaction zone induction length = 0.0001444 m\n",
      "Reaction zone pulse time (exothermic time) = 8.516e-08 s\n",
      "Reaction zone induction time = 3.811e-07 s\n"
     ]
    }
   ],
   "source": [
    "from sdtoolbox.postshock import CJspeed, PostShock_fr\n",
    "from sdtoolbox.znd import zndsolve\n",
    "from sdtoolbox.utilities import CJspeed_plot, znd_plot, znd_fileout\n",
    "import cantera as ct\n",
    "\n",
    "P1 = 100000 \n",
    "T1 = 300\n",
    "q = 'H2:2 O2:1 N2:3.76'\n",
    "mech = 'Mevel2017.cti'\n",
    "file_name = 'h2air'\n",
    "\n",
    "# Find CJ speed and related data, make CJ diagnostic plots\n",
    "cj_speed,R2,plot_data = CJspeed(P1,T1,q,mech,fullOutput=True)\n",
    "CJspeed_plot(plot_data,cj_speed)\n",
    "\n",
    "# Set up gas object\n",
    "gas1 = ct.Solution(mech)\n",
    "gas1.TPX = T1,P1,q\n",
    "\n",
    "# Find post shock state for given speed\n",
    "gas = PostShock_fr(cj_speed, P1, T1, q, mech)\n",
    "\n",
    "# Solve ZND ODEs, make ZND plots\n",
    "znd_out = zndsolve(gas,gas1,cj_speed,t_end=1e-5,advanced_output=True)\n",
    "znd_plot(znd_out,maxx=0.001,\n",
    "         major_species=['H2', 'O2', 'H2O'],\n",
    "         minor_species=['H', 'O', 'OH', 'H2O2', 'HO2'])\n",
    "         \n",
    "print('Reaction zone pulse width (exothermic length) = %.4g m' % znd_out['exo_len_ZND'])\n",
    "print('Reaction zone induction length = %.4g m' % znd_out['ind_len_ZND'])\n",
    "print('Reaction zone pulse time (exothermic time) = %.4g s' % znd_out['exo_time_ZND'])\n",
    "print('Reaction zone induction time = %.4g s' % znd_out['ind_time_ZND'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Applications\n",
    "\n",
    "The reaction mechanisms and thermodynamic data needed to run the demonstration programs are included with the zip archive as .cti files or can be downloaded individually from the SDT website\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_CJ.py\">demo_CJ.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_CJ.m\">demo_CJ.m</a> Computes CJ speed.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_CJ_and_shock_state.py\">demo_CJ_and_shock_state.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_CJ_and_shock_state.m\">demo_CJ_and_shock_state.m</a>  Computes 2 reflection conditions.\n",
    "    * equilibrium post-initial-shock state behind a shock traveling at CJ speed (CJ state) followed by equilibrium post-reflected-shock state\n",
    "    * frozen post-initial-shock state behind a CJ wave followed by frozen                                 post-reflected-shock state\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_CJstate.py\">demo_CJstate.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_CJstate.m\">demo_CJstate.m</a>  Computes CJ speed and CJ state.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_CJstate_isentrope.py\">demo_CJstate_isentrope.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_CJstate_isentrope.m\">demo_CJstate_isentrope.m</a> Computes CJ speed, CJ state, isentropic expansion in 1-D Taylor wave, plateau state conditions.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_cv_comp.py\">demo_cv_comp.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_cv_comp.m\">demo_cv_comp.m</a>  Generates plots and output files for a constant volume  explosion simulation where the initial conditions are adiabaically compressed reactants.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_cvCJ.py\">demo_cvCJ.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_cvCJ.m\">demo_cvCJ.m</a>  Generates plots and output files for a constant volume  explosion simulation where the initial conditions are given by the postshock conditions for a CJ speed shock wave.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_cvshk.py\">demo_cvshk.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_cvshk.m\">demo_cvshk.m</a>  Generates plots and output files for a constant volume  explosion simulation where the initial conditions are given by the postshock conditions for shock wave traveling at a user specified speed.\n",
    "\n",
    "*  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_detonation_pu.py\">demo_detonation_pu.py</a>    <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_detonation_pu.m\">demo_detonation_pu.m</a>    Computes the Hugoniot and pressure-velocity $(P-U)$ relationship for shock waves centered on the CJ state. Generates an output file.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_equil.py\">demo_equil.py</a>     <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_equil.m\">demo_equil.m</a>    Computes the equilibrium state at constant $(T,P)$ over a range of temperature for a fixed pressure and plots composition.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_EquivalenceRatioSeries.py\">demo_EquivalenceRatioSeries.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_EquivalenceRatioSeries.m\">demo_EquivalenceRatioSeries.m</a> - An example of how to vary the equivalence ratio over a specified range and for each resulting composition, compute constant volume explosion and ZND detonation structure.  This example creates a set of plots and an output file.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_exp_state.py\">demo_exp_state.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_exp_state.m\">demo_exp_state.m</a> Calculates mixture properties for explosion states (UV,HP, TP).\n",
    "\n",
    "*  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_ExplosionSeries.py\">demo_ExplosionSeries.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_ExplosionSeries.m\">demo_ExplosionSeries.m</a>   How to compute                                       basic explosion parameters as a functionof concentration of one component for                                       given mixture.  Creates plots and output file.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_g.py\">demo_g.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_g.m\">demo_g.m</a> Compares methods of computing ratio of specific heats and logarithmic isentrope slope using several approaches and compares the results graphically.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_GasPropAll.py\">demo_GasPropAll.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_GasPropAll.m\">demo_GasPropAll.m</a> Mixture thermodynamic and transport properties of gases at fixed pressure as a function of temperature. Edit to choose either frozen or equilibrium composition state.  The mechanism file must contain transport parameters\n",
    "for each species and specify the transport model 'Mix'.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_oblique.py\">demo_oblique.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_oblique.m\">demo_oblique.m</a> Calculates shock polar using  FROZEN post-shock state  based the initial gas properties and the shock speed.  Plots shock polar\n",
    " using three different sets of coordinates.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_overdriven.py\">demo_overdriven.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_overdriven.m\">demo_overdriven.m</a>  Computes\n",
    "detonation and reflected shock wave pressure for overdriven waves. Both the post-initial-shock and the post-reflected-shock states are equilibrium states. Creates output file.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_OverdriveSeries.py\">demo_OverdriveSeries.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_OverdriveSeries.m\">demo_OverdriveSeries.m</a>  This is a demonstration of how to vary the Overdrive ($U/U_{CJ})$) in a loop for constant volume explosions and ZND detonation\n",
    "    simulations.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_PrandtlMeyer.py\">demo_PrandtlMeyer.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_PrandtlMeyer.m\">demo_PrandtlMeyer.m</a> Calculates Prandtl-Meyer function and polar.  Creates plots of polars.\n",
    "\n",
    "*  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_PrandtlMeyer_CJ.py\">demo_PrandtlMeyer_CJ.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_PrandtlMeyer_CJ.m\">demo_PrandtlMeyer_CJ.m</a> Calculates Prandtl-Meyer function and polar expanded from CJ state.  Creates plots of polars and fluid element trajectories.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_PrandtlMeyerDetn.py\">demo_PrandtlMeyerDetn.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_PrandtlMeyerDetn.m\">demo_PrandtlMeyerDetn.m</a> Calculates Prandtl-Meyer function and polar  originating from CJ state. Calculates oblique shock wave moving into\n",
    "   expanded detonation products or a specified bounding atmosphere.  Creates a set of plots, evaluates axial flow model for rotating detonation engine.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_PrandtlMeyerLayer.py\">demo_PrandtlMeyerLayer.py</a>\n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_PrandtlMeyerLayer.m\">demo_PrandtlMeyerLayer.m</a>\n",
    "Calculates Prandtl-Meyer function and polar originating from lower layer\n",
    "postshock state. Calculates oblique shock wave moving into expanded\n",
    "detonation products or a specified bounding atmosphere.  Two-layer version\n",
    "with arbitrary flow in lower layer (1), oblique wave in upper layer (2).\n",
    "Upper and lower layers can have various compositions as set by user.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_precompression_detonation.py\">demo_precompression_detonation.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_precompression_detonation.m\">demo_precompression_detonation.m</a> Computes detonation and reflected shock  wave pressure for overdriven waves. Varies density of initial state and detonation wave speed. Creates an output file.\n",
    "\n",
    "*  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_PressureSeries.py\">demo_PressureSeries.py</a>\n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_PressureSeries.m\">demo_PressureSeries.m</a>\n",
    "Properties computed as a function of initial pressure for a constant volume explosions and ZND detonation simulations Creates a set of plots and an output file.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_PSeq.py\">demo_PSeq.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_PSeq.m\">demo_PSeq.m</a> Calculates the equilibrium post shock state based on the initial gas state and the shock speed.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_PSfr.py\">demo_PSfr.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_PSfr.m\">demo_PSfr.m</a> Calculates the frozen postshock state based on the initial gas state and the shock speed.\n"
   ]
  },
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   "source": [
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_quasi1d_eq.py\">demo_quasi1d_eq.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_quasi1d_eq.m\">demo_quasi1d_eq.m</a> Computes ideal quasi-one dimensional flow using equilibrium properties to determine exit conditions for expansion to a specified pressure.  Carries out computation for a range of helium dilutions.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_reflected_eq.py\">demo_reflected_eq.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_reflected_eq.m\">demo_reflected_eq.m</a> Calculates post-relected-shock state for a specified shock speed speed and a specified initial mixture.  In this demo, both shocks are reactive, i.e. the computed states behind both the incident and reflected shocks are equilibrium states.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_reflected_fr.py\">demo_reflected_fr.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_reflected_fr.m\">demo_reflected_fr.m</a> Calculates post-relected-shock state for a specified shock speed speed and a specified initial mixture.  In this demo, both shocks are frozen, i.e. there is no composition change across the incident and reflected shocks.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_RH.py\">demo_RH.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_RH.m\">demo_RH.m</a> Creates arrays for Rayleigh Line\n",
    "with specified shock speed, Reactant, and Product Hugoniot Curves for H$_2$-air mixture.  Options to creates output file and plots.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_RH_air.py\">demo_RH_air.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_RH_air.m\">demo_RH_air.m</a> Creates arrays for\n",
    "Rayleigh Line with specified shock speed and frozen Hugoniot Curve for a\n",
    "shock wave in air.  Options to create output file and plot.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_RH_air_eq.py\">demo_RH_air_eq.py</a>    <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_RH_air_eq.m\">demo_RH_air_eq.m</a>   Creates arrays\n",
    "for Rayleigh Line with specified shock speed in air, frozen and equilibrium Hugoniot curves. Options to create output file and plot.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_RH_air_isentropes.py\">demo_RH_air_isentropes.py</a>\n",
    "<a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_RH_air_isentropes.m\">demo_RH_air_isentropes.m</a>\n",
    "Creates arrays for frozen Hugoniot curve for shock wave in air, Rayleigh Line with specified shock speed, and four representative isentropes.  Options to create plot and output file.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_RH_CJ_isentropes.py\">demo_RH_CJ_isentropes.py</a>\n",
    " <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_RH_CJ_isentropes.m\">demo_RH_CJ_isentropes.m</a>\n",
    "Creates plot for equilibrium product Hugoniot curve near CJ point, Shows\n",
    "Rayleigh Line with slope $U_{CJ}$ and four isentropes bracketing CJ point. Creates plot showing Gruneisen coefficient, denominator in Jouguet's rule, isentrope\n",
    "slope.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_rocket_impulse.py\">demo_rocket_impulse.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_rocket_impulse.m\">demo_rocket_impulse.m</a>  Computes rocket performance using quasi-one dimensional isentropic flow using  both frozen and equilibrium properties for a range of helium dilutions in a hydrogen-oxygen mixture.  Plots impulse as a function of dilution.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_RZshock.py\">demo_RZshock.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_RZshock.m\">demo_RZshock.m</a> Generate plots and output files for a reaction zone behind a shock front traveling at a user specified speed.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_shock_adiabat.py\">demo_shock_adiabat.py</a>    <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_shock_adiabat.m\">demo_shock_adiabat.m</a>   Generates the points on a frozen shock adiabat and creates an output file.\n"
   ]
  },
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   "source": [
    "\n",
    "*  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_shock_point.py\">demo_shock_point.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_shock_point.m\">demo_shock_point.m</a>   This is a demonstration of how to compute frozen and equilibrium postshock  conditions for a single shock Mach number. Computes transport properties and thermodynamic states.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_shock_state_isentrope.py\">demo_shock_state_isentrope.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_shock_state_isentrope.m\">demo_shock_state_isentrope.m</a>  Computes frozen post-shock state and isentropic expansion for specified shock speed.  Create plots and output file.\n",
    "\n",
    "    * <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_ShockTube.py\">demo_ShockTube.py</a>   <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_ShockTube.m\">demo_ShockTube.m</a>   Calculates the solution to ideal shock tube problem. Three cases possible:\n",
    "    * conventional nonreactive driver (gas),\n",
    "    * constant volume combustion driver (uv),\n",
    "    * CJ detonation (initiate at diaphragm) driver (cj).\n",
    "\n",
    "*  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_STGshk.py\">demo_STGshk.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_STGshk.m\">demo_STGshk.m</a> Generate plots and output files for a steady reaction zone between a shock and a blunt body using the model of linear profile of mass flux $\\rho u$ on stagnation streamline.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_STG_RZ.py\">demo_STG_RZ.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_STG_RZ.m\">demo_STG_RZ.m</a> Compare propagating shock and stagnation point profiles using transformation methodology of Hornung.\n",
    "\n",
    "*  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_TP.py\">demo_TP.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_TP.m\">demo_TP.m</a> Explosion computation simulating constant temperature and pressure reaction.  Reguires function \\texttt{tpsys.m</a> for ODE solver\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_TransientCompression.py\">demo_TransientCompression.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_TransientCompression.m\">demo_TransientCompression.m</a> Explosion computation simulating adiabatic compression ignition with\n",
    " control volume approach and effective piston used for compression.\n",
    " Requires $\\textrm{adiasys.m}$  function for ODE solver.\n",
    "\n",
    "*  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_vN_state.m\">demo_vN_state.m</a> Calculates the frozen shock (vN = von Neumann) state of the gas behind the leading shock wave in a CJ detonation.\n",
    "\n",
    "*  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_vN_state.py\">demo_vN_state.py</a> <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_ZNDCJ.m\">demo_ZNDCJ.m</a> Solves ODEs for ZND model of detonation structure.  Generate plots and output files for a for a shock front traveling at the CJ speed.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_ZNDCJ.py\">demo_ZNDCJ.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_ZNDshk.m\">demo_ZNDshk.m</a> Solves ODEs for ZND model of detonation structure. Generate plots and output files for a for a shock front traveling at a user specified speed $U$.\n",
    "\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/Python3/demo/demo_ZNDshk.py\">demo_ZNDshk.py</a>  <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/MATLAB/Demo/demo_ZND_CJ_cell.m\">demo_ZND_CJ_cell.m</a>  Computes ZND and CV models of detonation with the shock front\n",
    " traveling at the CJ speed.  Evaluates various measures of the reaction\n",
    " zone thickness and exothermic pulse width, effective activation energy\n",
    " and Ng stability parameter.  Estimates cell size using three correlation methods: Westbrook; Gavrikov et al; and Ng et al.\n"
   ]
  },
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   "source": [
    "# Shock and Detonation Toolbox Resources\n",
    "\n",
    "\n",
    "## SDT home page \n",
    "The SDT home page is located on the <a href=\"http://shepherd.caltech.edu/EDL/\">Explosion Dynamics Laboratory</a> site under the Public Resources page at http://shepherd.caltech.edu/EDL/PublicResources/sdt/\n",
    "\n",
    "## Downloads\n",
    "Python and Matlab libraries and demonstration programs can be downloaded as <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox.zip\">(ZIP)</a> archives.   Installation instructions are available in a <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/SDToolbox/sdt-install.pdf\">(PDF)</a> file.\n",
    "\n",
    "## Quick reference\n",
    "Quick reference to SDT functions and demonstation programs <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/doc/QuickReferenceSDT.pdf\">(PDF)</a> \n",
    "\n",
    "## Reaction mechanisms \n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/cti_mech.html\"> Cantera format (.CTI) data sets </a>\n",
    "\n",
    "## Thermodynamic data and tools\n",
    "* <a href=\"http://shepherd.caltech.edu/EDL/PublicResources/sdt/thermo.html\">  Thermodynamic data sources and software tools </a>\n",
    "\n"
   ]
  }
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