{ "cells": [ { "cell_type": "markdown", "id": "daaff79b-8fbc-46f3-ad81-6fd0dde3f927", "metadata": {}, "source": [ "# Moliere Potential\n", "\n", "Simulation data from Figure 8 of [Vorberger et al](https://doi.org/10.1016/j.hedp.2012.12.009)\n", "\n", "The YAML input file can be found at [input_file](https://raw.githubusercontent.com/murillo-group/sarkas/master/docs/examples/Moliere/input_files/moliere_mks.yaml) and this notebook at [notebook](https://raw.githubusercontent.com/murillo-group/sarkas/master/docs/examples/Moliere/Moliere_Simulation.ipynb)." ] }, { "cell_type": "code", "execution_count": 1, "id": "a48c278f-e79b-42f5-ae97-3e0b1e94508a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Using matplotlib backend: Qt5Agg\n", "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "# Import the usual packages.\n", "%pylab\n", "%matplotlib inline\n", "import os\n", "import pandas as pd\n", "\n", "from sarkas.processes import PreProcess, Simulation, PostProcess\n", "\n", "# Set the plotting style\n", "plt.style.use('MSUstyle')\n", "\n", "# Link to the input file.\n", "input_file = os.path.join('input_files', 'moliere_mks.yaml')" ] }, { "cell_type": "markdown", "id": "02e7f164-c82e-476e-bfcd-885f936c409b", "metadata": {}, "source": [ "## Simulation" ] }, { "cell_type": "code", "execution_count": 2, "id": "3407ee8a-3508-4607-bdf6-a6134f0bfeb0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[38;2;83;80;84m\n", "\n", "\n", "\n", "\n", "\n", " __ _ \n", "/ _\\ __ _ _ __| | ____ _ ___ \n", "\\ \\ / _` | '__| |/ / _` / __|\n", "_\\ \\ (_| | | | < (_| \\__ \\\n", "\\__/\\__,_|_| |_|\\_\\__,_|___/\n", " \n", "\n", "\u001b[0m\n", "An open-source pure-python molecular dynamics suite for non-ideal plasmas.\n", "\n", "\n", "\n", "\n", "\n", "* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\n", " Simulation \n", "* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\n", "\n", "Job ID: Moliere_mks\n", "Job directory: Simulations/Moliere_mks\n", "\n", "Equilibration dumps directory: \n", " Simulations/Moliere_mks/Simulation/Equilibration/dumps\n", "Production dumps directory: \n", " Simulations/Moliere_mks/Simulation/Production/dumps\n", "\n", "Equilibration Thermodynamics file: \n", " Simulations/Moliere_mks/Simulation/Equilibration/EquilibrationEnergy_Moliere_mks.csv\n", "Production Thermodynamics file: \n", " Simulations/Moliere_mks/Simulation/Production/ProductionEnergy_Moliere_mks.csv\n", "Random Seed = 654984647\n", "\n", "PARTICLES:\n", "Total No. of particles = 10000\n", "No. of species = 1\n", "Species ID: 0\n", "\tName: Be\n", "\tNo. of particles = 10000 \n", "\tNumber density = 1.234875e+29 [N/m^3]\n", "\tAtomic weight = 9.0122 [a.u.]\n", "\tMass = 1.507397e-26 [kg]\n", "\tMass density = 1.848000e+06 [kg/m^3]\n", "\tCharge number/ionization degree = 4.0000 \n", "\tCharge = 6.408707e-19 [C]\n", "\tTemperature = 1.392542e+05 [K] = 1.200000e+01 [eV]\n", "\tDebye Length = 1.832054e-11 [1/m^3]\n", "\tPlasma Frequency = 6.164440e+14 [rad/s]\n", "\n", "SIMULATION AND INITIAL PARTICLE BOX:\n", "Units: mks\n", "Wigner-Seitz radius = 1.245746e-10 [m]\n", "No. of non-zero box dimensions = 3\n", "Box side along x axis = 3.472931e+01 a_ws = 4.326390e-09 [m]\n", "Box side along y axis = 3.472931e+01 a_ws = 4.326390e-09 [m]\n", "Box side along z axis = 3.472931e+01 a_ws = 4.326390e-09 [m]\n", "Box Volume = 8.097987e-26 [m^3]\n", "Initial particle box side along x axis = 3.472931e+01 a_ws = 4.326390e-09 [m]\n", "Initial particle box side along y axis = 3.472931e+01 a_ws = 4.326390e-09 [m]\n", "Initial particle box side along z axis = 3.472931e+01 a_ws = 4.326390e-09 [m]\n", "Initial particle box Volume = 8.097987e-26 [m^3]\n", "Boundary conditions: periodic\n", "\n", "ELECTRON PROPERTIES:\n", "Number density: n_e = 4.939499e+29 [N/m^3]\n", "Wigner-Seitz radius: a_e = 7.847708e-11 [m]\n", "Temperature: T_e = 1.392542e+05 [K] = 1.200000e+01 [eV]\n", "de Broglie wavelength: lambda_deB = 1.997449e-10 [m]\n", "Thomas-Fermi length: lambda_TF = 4.721828e-11 [m]\n", "Fermi wave number: k_F = 2.445502e+10 [1/m]\n", "Fermi Energy: E_F = 2.278552e+01 [eV]\n", "Relativistic parameter: x_F = 9.443531e-03 --> E_F = 2.278501e+01 [eV]\n", "Degeneracy parameter: Theta = 5.266503e-01 \n", "Coupling: r_s = 1.483002, Gamma_e = 1.529071\n", "Warm Dense Matter Parameter: W = 7.5544e-01\n", "Chemical potential: mu = 1.3549e+00 k_B T_e = 7.1357e-01 E_F\n", "\n", "POTENTIAL: moliere\n", "\n", "ALGORITHM: pp\n", "rcut = 5.3219 a_ws = 6.629755e-10 [m]\n", "No. of PP cells per dimension = 6, 6, 6\n", "No. of particles in PP loop = 971\n", "No. of PP neighbors per particle = 150\n", "Tot Force Error = 5.713963e-20\n", "\n", "THERMOSTAT: \n", "Type: berendsen\n", "First thermostating timestep, i.e. relaxation_timestep = 50\n", "Berendsen parameter tau: 2.000 [timesteps]\n", "Berendsen relaxation rate: 0.500 [1/timesteps] \n", "Thermostating temperatures: \n", "Species ID 0: T_eq = 1.392542e+05 [K] = 1.200000e+01 [eV]\n", "\n", "INTEGRATOR: \n", "Type: verlet\n", "Time step = 3.244415e-17 [s]\n", "Total plasma frequency = 6.164440e+14 [rad/s]\n", "w_p dt = 0.0200 ~ 1/49\n", "\n", "Equilibration: \n", "No. of equilibration steps = 1000 \n", "Total equilibration time = 3.2444e-14 [s] ~ 20 w_p T_eq \n", "snapshot interval step = 10 \n", "snapshot interval time = 3.2444e-16 [s] = 0.2000 w_p T_snap\n", "Total number of snapshots = 100 \n", "\n", "Production: \n", "No. of production steps = 5000 \n", "Total production time = 1.6222e-13 [s] ~ 100 w_p T_prod \n", "snapshot interval step = 10 \n", "snapshot interval time = 3.2444e-16 [s] = 0.2000 w_p T_snap\n", "Total number of snapshots = 500 \n", "\n", "\n", "------------------------ Initialization Times ------------------------ \n", "\n", "\n", "Potential Initialization Time: 1 sec 171 msec 420 usec 854 nsec\n", "\n", "Particles Initialization Time: 0 sec 1 msec 914 usec 956 nsec\n", "\n", "Total Simulation Initialization Time: 1 sec 171 msec 420 usec 854 nsec\n", "\n", "\n", "--------------------------- Equilibration ---------------------------- \n", "\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "7259e40cba224fbba80ee92a057ad3aa", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/1000 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "postproc = PostProcess(input_file)\n", "postproc.setup(read_yaml = True)\n", "postproc.run()" ] }, { "cell_type": "code", "execution_count": 4, "id": "460d4bfa-7b5d-4f5b-8392-1e9caa8aac5f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "postproc.rdf.plot(scaling= postproc.rdf.a_ws,\n", " xlabel = r'$r/a_{ws}$',\n", " title = 'Pair Distribution Function')" ] }, { "cell_type": "code", "execution_count": 5, "id": "e9dd9a42-9f21-4610-b3ca-7b6ad6a1155a", "metadata": {}, "outputs": [], "source": [ "from sarkas.potentials import moliere as mol\n", "from sarkas.potentials import coulomb as coul" ] }, { "cell_type": "code", "execution_count": 7, "id": "2441a2ff-f5bb-468f-a433-ac1ac2c09828", "metadata": {}, "outputs": [], "source": [ "r_array = postproc.parameters.box_lengths[0] * np.linspace(0.001, 1, 1000)\n", "mol_potential = np.zeros(len(r_array))\n", "coul_potential = np.zeros(len(r_array))\n", "\n", "# I need to do this, because Numba compiled the function to take in a float and an array not two arrays\n", "for (ir, r) in enumerate(r_array):\n", " mol_potential[ir], _ = mol.moliere_force(r, postproc.potential.matrix[:,0, 0])\n", " coul_potential[ir], _ = coul.coulomb_force(r, postproc.potential.matrix[:,0, 0])" ] }, { "cell_type": "code", "execution_count": 8, "id": "27ef4e05-06a5-4709-81af-68e5639bcba5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Potential Plot')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pot_const = postproc.potential.matrix[0,0,0]\n", "plt.plot(r_array/postproc.parameters.a_ws, mol_potential/pot_const, label = 'Moliere')\n", "plt.plot(r_array/postproc.parameters.a_ws, coul_potential/pot_const, label = 'Coulomb')\n", "plt.legend()\n", "plt.yscale('log')\n", "plt.ylabel(r'$U(r)$ [$Q^2/(4\\pi \\epsilon_0)$]')\n", "plt.xlabel(r'$r/a_{\\rm ws}$')\n", "plt.xlim(0,10)\n", "plt.ylim(1e5,1e11)\n", "plt.title('Potential Plot')" ] }, { "cell_type": "code", "execution_count": null, "id": "0a08575d-5e3a-4ea4-b41f-8c9ca1680438", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.10" } }, "nbformat": 4, "nbformat_minor": 5 }