2. IdealGas-MarkovChain.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maxwell's distribution of speed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math as math\n",
    "import random as random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Global constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 3.2  # mass is in unit of Kb\n",
    "Kb = 1.0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Input parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100\n",
    "u0 = 150.00\n",
    "dv = 0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Starter "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def starter(key):\n",
    "    u = [0.0  for k in range(N)]\n",
    "    \n",
    "    if key == 0:return u\n",
    "    else:\n",
    "        for k in range(N):\n",
    "            u[k] = u0\n",
    "     \n",
    "   \n",
    "    return u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hamiltonian(u):\n",
    "    H = 0.0\n",
    "    for k in range(N):\n",
    "          H = H + 0.5*u[k]**2\n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Pick a particle and change"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pick_random_particle():\n",
    "    n = random.randint(0, N-1)\n",
    "    return n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Thermalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thermalize(u,T,nruns):\n",
    "    irun = 0\n",
    "    h_stor = [0.0 for k in range(nrun)]\n",
    "    while irun < nrun:\n",
    "        L = len(u)\n",
    "        h_old = hamiltonian(u)\n",
    "        n = pick_random_particle()\n",
    "        ov = u[n] \n",
    "        du = random.uniform(-dv,dv)\n",
    "        u[n] = u[n] + du\n",
    "        h_new = hamiltonian(u)\n",
    "        dh = 0.5*m*(u[n]**2-ov**2)\n",
    "        if dh < 0:         \n",
    "            h_stor[irun] = h_new        \n",
    "        else:                  \n",
    "            frac = math.exp(-dh/(Kb*T))\n",
    "            b = random.uniform(0.0,1.0)                  \n",
    "            if  b < frac:        \n",
    "                h_stor[irun] = h_new                             \n",
    "            else:            \n",
    "                u[n]  = u[n] - du\n",
    "                h_stor[irun] = h_old \n",
    "        if u[n] != ov :                                                  \n",
    "             irun = irun +1      \n",
    "    return h_stor,u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10\n",
    "u = starter(1)\n",
    "T = 300.0\n",
    "nrun = 100\n",
    "H,u = thermalize(u,T,nrun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000\n",
    "u = starter(1)\n",
    "T = 300.0\n",
    "nrun = 10000\n",
    "H,u = thermalize(u,T,nrun)\n",
    "\n",
    "X = np.arange(0,len(H),1)\n",
    "plt.figure(figsize = [15,4])\n",
    "plt.grid(True)\n",
    "plt.plot(X,H,\"-\")\n",
    "plt.show()           "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Speed Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_bins = 20\n",
    "plt.figure(figsize = [10,8])\n",
    "plt.hist(u,num_bins, density= 1.0, facecolor='green', alpha = 0.5)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_bins = 100\n",
    "plt.figure(figsize = [10,8])\n",
    "plt.hist(u,num_bins, density = 1.0, facecolor='green', alpha = 0.5)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}