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Fix more typos

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jngrad committed Jun 7, 2019
1 parent fc23107 commit 6e6899b865e0116adbdd7fec2ee5141d2f371072
@@ -151,7 +151,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"The aim of this tutorial is to introduce the basic features of **ESPResSo** for ferrofluids or dipolar fluids in general. In **part I** and **part II** we will do this for a monolayer-ferrofluid, in **part III** for a three dimensional system. In **part I** we will examine the clusters which are present in all interesting ferrofluid systems. In **part II** we will examine the influence of the dipole-dipole-interaction on the magnetization curve of a ferrofluid. In **part III** we calculate estimatiors for the initial susceptibility using fluctuation formulas and sample the magnetization curve.\n",
"The aim of this tutorial is to introduce the basic features of **ESPResSo** for ferrofluids or dipolar fluids in general. In **part I** and **part II** we will do this for a monolayer-ferrofluid, in **part III** for a three dimensional system. In **part I** we will examine the clusters which are present in all interesting ferrofluid systems. In **part II** we will examine the influence of the dipole-dipole-interaction on the magnetization curve of a ferrofluid. In **part III** we calculate estimators for the initial susceptibility using fluctuation formulas and sample the magnetization curve.\n",
"\n",
"We assume the reader is familiar with the basic concepts of Python and MD simulations."
]
@@ -273,7 +273,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we setting up all simulation parameters. "
"Now we set up all simulation parameters. "
]
},
{
@@ -799,8 +799,8 @@
"metadata": {},
"source": [
"<a id='[1]'></a>[1] Juan J. Cerdà, V. Ballenegger, O. Lenz, and Ch. Holm. *P3M algorithm for dipolar interactions. *Journal of Chemical Physics, 129:234104, 2008. \n",
"<a id='[2]'></a>[2] A. Bródka. “Ewald summation method with electrostatic layer correction for in-\n",
"teractions of point dipoles in slab geometry”. In: Chemical Physics Letters 400.1\n",
"<a id='[2]'></a>[2] A. Bródka. “Ewald summation method with electrostatic layer correction for\n",
"interactions of point dipoles in slab geometry”. In: Chemical Physics Letters 400.1\n",
"(2004), pp. 62–67. issn: 0009-2614. doi: https://doi.org/10.1016/j.cplett.\n",
"2004.10.086. url: http://www.sciencedirect.com/science/article/pii/S0009261404016847."
]
@@ -114,7 +114,7 @@
"Now we set up the system, where we, as we did in **part I**, only commit the orientation of the dipole moment to the particles and take the magnitude into account in the prefactor of Dipolar P3M (for more details see **part I**). \n",
"\n",
"**Hint:**\n",
"It should be noted that we seed both the Langevin thermostat and the random number generator of numpy. Latter means that the initial configuration of our system is the same every time this script will be executed. As the time evolution of the system depends not solely on the Langevin thermostat but also on the numeric accuracy and DP3M as well as DLC (the tuned parameters are slightly different every time) it is only partly predefined. You can change the seeds to simulate with a different initial configuration and a guaranteed different time evolution."
"It should be noted that we seed both the Langevin thermostat and the random number generator of numpy. The latter means that the initial configuration of our system is the same every time this script will be executed. As the time evolution of the system depends not solely on the Langevin thermostat but also on the numeric accuracy and DP3M as well as DLC (the tuned parameters are slightly different every time) it is only partly predefined. You can change the seeds to simulate with a different initial configuration and a guaranteed different time evolution."
]
},
{
@@ -565,7 +565,7 @@
"loops = 500\n",
"\n",
"for alpha in alphas:\n",
" print(\"Sample for alpha = {}\".format(alpha))\n",
" print(\"Sampling for alpha = {}\".format(alpha))\n",
" H_dipm = (alpha*kT)\n",
" H_field = [0,0,H_dipm]\n",
" print(\"Set magnetic field constraint...\")\n",
@@ -85,7 +85,7 @@
" \\chi = \\frac{\\beta\\mu_0}{V} \\left \\lbrack \\frac{1}{Z_c}\\sum_{\\alpha} \\mu_{\\alpha}^2~ e^{ -\\beta E_{\\alpha}(H=0) + \\beta\\mu_0\\mu_{\\boldsymbol{H},\\alpha}H } - \\frac{1}{Z_c}\\sum_{\\alpha} \\mu_{\\alpha}~ e^{ -\\beta E_{\\alpha}(H=0) + \\beta\\mu_0\\mu_{\\boldsymbol{H},\\alpha}H }~~ \\frac{1}{Z_c}\\sum_{\\alpha'}\\mu_{\\alpha'}~ e^{ -\\beta E_{\\alpha'}(H=0) + \\beta\\mu_0\\mu_{\\boldsymbol{H},\\alpha}H }\\right \\rbrack = \\frac{\\beta\\mu_0}{V} \\left \\lbrack \\langle \\mu_{\\boldsymbol{H}}^2 \\rangle - \\langle \\mu_{\\boldsymbol{H}} \\rangle^2 \\right \\rbrack = \\frac{\\beta\\mu_0}{V} \\left(\\Delta \\mu_{\\boldsymbol{H}}\\right)^2\n",
"\\end{equation}\n",
"\n",
"At zero external magentic field ($H = 0$) there is no distinct direction for the system, so we can take the fluctuations $\\Delta \\mu$ in all directions and divide it by the dimension. Thus we can use more data points of our simulation for the average and get a more precise estimatior for the susceptibility. Thus finally the fluctuation formular for the initial susceptibility in three dimensions reads\n",
"At zero external magentic field ($H = 0$) there is no distinct direction for the system, so we can take the fluctuations $\\Delta \\mu$ in all directions and divide it by the dimension. Thus we can use more data points of our simulation for the average and get a more precise estimator for the susceptibility. Thus finally the fluctuation formula for the initial susceptibility in three dimensions reads\n",
"\n",
"\\begin{equation}\n",
" \\chi_{init} = \\frac{\\beta\\mu_0}{3V} \\left \\lbrack \\langle \\boldsymbol{\\mu}^2 \\rangle - \\langle \\boldsymbol{\\mu} \\rangle^2 \\right \\rbrack = \\frac{V\\beta\\mu_0}{3} \\left \\lbrack \\langle \\boldsymbol{M}^2 \\rangle - \\langle \\boldsymbol{M} \\rangle^2 \\right \\rbrack\n",
@@ -2811,14 +2811,14 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Copared with the value $\\chi = 0.822 \\pm 0.017$ of Ref. <a href='#[1]'>[1]</a> (see table 1) it should be very similar."
"Compared with the value $\\chi = 0.822 \\pm 0.017$ of Ref. <a href='#[1]'>[1]</a> (see table 1) it should be very similar."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we want to compare the result with the theoretically expectations.\n",
"Now we want to compare the result with the theoretical expectations.\n",
"At first with the simple Langevin susceptibility"
]
},
@@ -3032,7 +3032,7 @@
" \\frac{\\partial M^*}{\\partial \\alpha} = \\frac{1}{M_{sat}}\\frac{\\partial M}{\\partial \\left( \\frac{\\mu_0\\mu}{k_BT} H\\right)} = \\frac{k_BT~V}{\\mu_0\\mu^2N}\\frac{\\partial M}{\\partial H} = \\frac{k_BT~V}{\\mu_0\\mu^2N}~\\chi\n",
"\\end{equation}\n",
"\n",
"we have to scale our calculated initial susceptibilit $\\chi_{init}$ by a factor to get it in our dimensionless units.\n",
"we have to scale our calculated initial susceptibility $\\chi_{init}$ by a factor to get it in our dimensionless units.\n",
"\n",
"Now we plot the resulting curves together with our simulation results and the linear approximation"
]
@@ -77,7 +77,7 @@ class ReactionEnsembleTest(ut.TestCase):
system.setup_type_map([0, 1, 2, 3])
# initialize wang_landau
# generate preliminary_energy_run_results here, this should be done in a
# seperate simulation without energy reweighting using the update energy
# separate simulation without energy reweighting using the update energy
# functions
np.savetxt("energy_boundaries.dat", np.c_[[0, 1], [0, 0], [9, 9]],
delimiter='\t', header="nbar E_potmin E_potmax")

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