150 lines
4.2 KiB
Text
150 lines
4.2 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "6d6ace33-bd89-49ac-a148-06c99d7d071c",
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"metadata": {},
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"source": [
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"# Getting Started with CHEG231MD\n",
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"\n",
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"Eric M. Furst\\\n",
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"October 2024\n",
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"\n",
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"Test run of the simple MD simulation.\n",
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"\n",
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"The temperature will depend on density. At any density, change temp by \n",
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"scaling max velocity by sqrt(Tnew/Told) \n",
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"\n",
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"$$ \\langle v^2 \\rangle = v_\\mathrm{max}^2/2 $$\n",
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"\n",
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"Without a thermostat, both the temperature and pressure equilibrate.\n",
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"This makes calculating an isotherm difficult, but it shows the\n",
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"combined contributions of potential and kinetic energy\n",
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"\n",
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"rho and vmax values that give results close to T+ = 2:\\\n",
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"0.7 5.8\\\n",
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"0.6 5.47\\\n",
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"0.4 5.04"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c7f0016e-5ba0-45b9-9d0e-df7bde2c901f",
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"import CHEG231MD as md\n",
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"\n",
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"# create a simulation with # particles, density, and max speed\n",
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"# N^(1/3), rho+, max vel+\n",
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"\n",
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"#sim = md.MDSimulation(8,0.4,5.04)\n",
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"#sim = md.MDSimulation(8,0.6,5.47)\n",
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"sim = md.MDSimulation(8,0.7,5.8)\n",
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"\n",
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"# initialize variables and lists\n",
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"pres=[]\n",
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"temp=[]\n",
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"time=[]\n",
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"Pavg = 0\n",
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"Tavg = 0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "a14e5dc1-7601-4972-911e-0f42eb32a6c3",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Run time steps of the simulation\n",
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"for timestep in range(1,1001):\n",
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"\n",
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" # advance simulation one timestep\n",
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" sim.move()\n",
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" \n",
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" # only average after an equilibration time\n",
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" if timestep > 100:\n",
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" # production stage\n",
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" Pavg += (sim.P-Pavg)/(timestep+1)\n",
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" Tavg += (sim.T-Tavg)/(timestep+1)\n",
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" else:\n",
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" # equilibration stage\n",
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" Pavg = sim.P\n",
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" Tavg = sim.T\n",
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"\n",
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" # print timestep, ke, pe, total e, Tavg, Pavg \n",
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" if timestep%50==0: # only print every 50 timesteps\n",
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" # timestep, <ke>, <pe>, <e>, T, P, Tavg, Pavg\n",
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" print(\"%4d %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f\" % \n",
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" (timestep,sim.ke/sim.N,sim.pe/sim.N,\n",
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" (sim.ke+sim.pe)/sim.N,sim.T,sim.P,Tavg,Pavg))\n",
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"\n",
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" pres.append(sim.P)\n",
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" temp.append(sim.T)\n",
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" time.append(timestep)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d3993efe-4dc7-4b09-9630-90201f989487",
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"metadata": {},
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"outputs": [],
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"source": [
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"# A different way to calculate the average pressure and temperature\n",
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"# with standard deviations\n",
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"\n",
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"import numpy as np\n",
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"\n",
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"print(\"Pressure: {:.2f}+/-{:.2f}\"\n",
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" .format(np.mean(pres[200:]),np.std(pres[200:])))\n",
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"print(\"Temperature: {:.2f}+/-{:.2f}\"\n",
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" .format(np.mean(temp[200:]),np.std(temp[200:])))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "77d0de84-eb9b-4ea5-b5d3-4780335f3d7c",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Plot pressure and temperature\n",
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"\n",
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"fig, ax = plt.subplots()\n",
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"ax.plot(time[0:],pres[0:],label=\"P*\")\n",
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"ax.plot(time[0:],temp[0:],label=\"T*\")\n",
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"ax.set_xlabel(\"time step\")\n",
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"ax.legend(frameon=False)\n",
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"ax.set_xscale('linear')\n",
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"plt.title(\"Dimensionless instantaneous pressure and temperature\")\n",
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"\n",
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"plt.show()"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.4"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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