mol_dyn_mc_ising.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "initialize 2 dim matrix 100X100 - with zeros\n",
      "set one corner of this array 10X10 with particles, which we want to see evolving - with one\n",
      "particle positions shown with value 1 in the 2dim matrix to visualize easier!\n",
      "define function which will measure the interaction energy - lennard jones potential\n",
      "\n",
      "md monte carlo - ising\n",
      "> one random number generator to choose a position in the matrix\n",
      "    then we check if its filled by a particle already, otherwise restart\n",
      "        another random number generator to move it somewhere in the matrix\n",
      "            check if this new position is filled\n",
      "                if free, what is the energy difference?\n",
      "                    if -ve, flip\n",
      "                    else flip with probability\n",
      "\n",
      "arena = np.zeros([12,12])\n",
      "for i in xrange(3):\n",
      "    for j in range(3):\n",
      "        arena[i,j] = 1\n",
      "\n",
      "move_posn = np.arange(144)\n",
      "for i in xrange(10):\n",
      "    site = np.random.choice(move_posn)\n",
      "    if arena[site%12,site/12] = 1\n",
      "        tmp = np.random.random()\n",
      "        if arena[tmp%12,tmp/12] != 1\n",
      "            arena[site%12,site/12] = 0\n",
      "            arena[tmp%12,tmp/12] = 1\n",
      "\n",
      "md monte carlo - taught\n",
      "> initial positions defined - [particle no., x, y] for n particles, boundary conditions defined\n",
      "> random number generator to choose a particle!\n",
      "> 2 random number generators to choose move in x and move in y,\n",
      "> if already filled, dont move\n",
      "> if not move! - hard balls\n",
      "\"\"\"\n",
      "> if moved, change in energy?\n",
      "> if energy (final-energy)< 0; flip!\n",
      "> else: flip with probability exp(energy) - lennard jones potential.\n",
      "\"\"\"\n",
      "np.zeros([n,2]) n - no. of particles, 2 x & y coordinates\n",
      "np.zeros([n,2,2])"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\"\"\"\n",
      "import time, time.time()\n",
      "arena = np.zeros([100,100])\n",
      "for i in xrange(10):\n",
      "    for j in range(10):\n",
      "        arena[i,j] = 1\n",
      "plt.imshow(arena)\n",
      "\"\"\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "'\\narena = np.zeros([100,100])\\nfor i in xrange(10):\\n    for j in range(10):\\n        arena[i,j] = 1\\nplt.imshow(arena)\\n'"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "arena = np.zeros([12,12])\n",
      "for i in xrange(3):\n",
      "    for j in range(3):\n",
      "        arena[i,j] = 1\n",
      "plt.imshow(arena)\n",
      "        \n",
      "move_posn = np.arange(144)\n",
      "for i in xrange(10):\n",
      "    site = np.random.choice(move_posn)\n",
      "    if arena[site%12,site/12] == 1 :\n",
      "        tmp = np.random.choice(move_posn)\n",
      "        if arena[tmp%12,tmp/12] != 1:\n",
      "            arena[site%12,site/12] = 0\n",
      "            arena[tmp%12,tmp/12] = 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Nm2cOHjzo1RhxFy9eND6fzyxatMiUlJSYkpIS8/3333s9Vlxzc3PanKX/+eefTVlZmVm4\ncKF544030uIsvTHG1NbWmnA4bIqKikxVVZXp7e0d9xk2b95sXnjhBeP3+00wGDRffvml+eOPP8zq\n1avNggULTHl5ufnzzz/Hfa5BvLUWsEh6nPoFMC4IHrAIwQMWIXjAIgQPWITgAYsQPGARggcs8h8c\nOs8lfZmcKAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb151172c>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "arena = np.zeros([12,12])\n",
      "for i in xrange(3):\n",
      "    for j in xrange(3):\n",
      "        arena[i,j] = 1\n",
      "        \n",
      "#plt.imshow(arena)\n",
      "\n",
      "move_posn = np.arange(144)\n",
      "for i in xrange(100000):\n",
      "    site = np.random.choice(move_posn)\n",
      "    if (arena[site%12,site/12] == 1) :\n",
      "        #print \"yes! there's a ball at\", site\n",
      "        tmp = np.random.choice(move_posn)\n",
      "        if (arena[tmp%12,tmp/12] != 1):\n",
      "            #print \"yes, you can move\", site, \"to\", tmp\n",
      "            arena[tmp%12, tmp/12] =1\n",
      "            arena[site%12, site/12] =0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print arena"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  1.]\n",
        " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  1.]\n",
        " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.  1.  0.  0.  0.  0.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.  0.  0.  0.  0.  1.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.  0.  0.  0.  1.  0.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.  0.  0.  0.  0.  1.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
        " [ 1.  0.  0.  0.  0.  1.  0.  0.  0.  1.  0.  0.]]\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.imshow(arena)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.image.AxesImage at 0xb133ac2c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nP/tZrFmzBmvXrsX3v//9uLNUpVQqYXx8HJs3b447KwCACxcuYGJiAqtXr8bY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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb14d30cc>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "arena = np.zeros([9,2])\n",
      "for i in xrange(9):\n",
      "    arena[i][1] = i%3\n",
      "    arena[i][0] = i/3\n",
      "print arena"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.  0.]\n",
        " [ 0.  1.]\n",
        " [ 0.  2.]\n",
        " [ 1.  0.]\n",
        " [ 1.  1.]\n",
        " [ 1.  2.]\n",
        " [ 2.  0.]\n",
        " [ 2.  1.]\n",
        " [ 2.  2.]]\n"
       ]
      }
     ],
     "prompt_number": 93
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = []\n",
      "y = []\n",
      "for i in xrange(len(arena)):\n",
      "    x.append(arena[i][0])\n",
      "    y.append(arena[i][1])\n",
      "plt.scatter(x,y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 94,
       "text": [
        "<matplotlib.collections.PathCollection at 0xb00a20cc>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UHDp0SGfPntWZM2f04x//WGvWrHHVcLS5fPmyGhsb1dvb63UriEBbW5va29u9bgMR6O3t\nVWNjoy5fvux1K2OOq+CvqqrSjBkzlJaWptjYWC1btkwHDhwYUFNeXq6VK1dKkgoKCnTx4kW1tra6\nGTZq/Ou/lmnKlCRlZd2r6dPvVHV1tdctIUyXL1/WokWPKTk5Q3/1V3dqyZLH1d3d7XVbCNNvf/tb\nJSWlKSvrXiUmTtO+ff/mdUtjiqvgb2pqUmpqav/rlJQUNTU1XbemsbHRzbBRob6+Xt/+9jO6fPmY\nLl1qUVvbD/W1rz2qvr4+r1tDGL73vc06cqRP3d0fqbu7Vf/5n53atOklr9tCGHp6evS1rz2qCxd2\n6tKlFl26FNSqVd9RQ0OD162NGa6C33GcsOqMMRGdF81+//vfKzb2fkmzP3/nm+rouKTz58972RbC\ndOzYO7p06duS/lLS/9KlS6t17Bh/YosGLS0tunzZSPrG5+/kKibmHv3hD3/wsq0xJcbNycnJyQqF\nQv2vQ6GQUlJSrlnT2Nio5OTkIa9XWlra/3MgEFAgEHDTnqfuuOMO9faeknRBUqKkU3KcHiUmJnrc\nGcKRlZWm6uq31NPzdUlGf/EXv1ZW1h1et4UwTJ06VVeudEiq1Z9uvNrU21ur22+/3ePO3AsGgwoG\ng+4vZFzo6ekxd955p3n//ffNH//4R+P3+01dXd2AmoMHD5pFixYZY4w5efKkKSgoGPJaLlsZk/7u\n754zPl+KmTRpsfH5bjVvvPFvXreEMLW2tpo77sg2Eyd+yUyceL9JT59lzp8/73VbCNPPfva6ufnm\nW01CwiPG50s2//APL3jd0qiINDedz0+O2OHDh7Vhwwb19fVp9erVeu655/Tqq69KkkpKSiSp/5s/\ncXFx2r17t/Lz8wddx3GcQVtC48GpU6d07tw5zZ49W+np6V63g2Ho6urS0aNH5TiO5s+fr5tvvtnr\nljAM7733nmpra5WWlia/3+91O6Mi0tx0HfwjZbwGPwCMlkhzkyd3AcAyBD8AWIbgBwDLEPwAYBmC\nHwAsQ/ADgGUIfgCwDMEPAJYh+AHAMgQ/AFiG4AcAyxD8AGAZgh8ALEPwA4BlCH4AsAzBDwCWIfgB\nwDIEPwBYhuAHAMsQ/ABgGYIfACxD8AOAZQh+ALAMwQ8AliH4AcAyBD8AWIbgBwDLEPwAYJmYSE+8\ncOGCHn/8cX3wwQdKS0vTG2+8ocmTJw+qS0tL06RJk3TTTTcpNjZWVVVVrhoGALgT8R3/1q1bVVhY\nqNOnT+vBBx/U1q1bh6xzHEfBYFA1NTXWhn4wGPS6hVHF/KIb87NPxMFfXl6ulStXSpJWrlypn//8\n51etNcZEOsy4MN7/wWN+0Y352Sfi4G9tbVVSUpIkKSkpSa2trUPWOY6jhx56SHPnztVrr70W6XAA\ngBFyzT3+wsJCffjhh4Pef/HFFwe8dhxHjuMMeY3jx49r+vTpOn/+vAoLCzVz5kzNnz/fRcsAAFdM\nhO666y7T0tJijDGmubnZ3HXXXdc9p7S01Pzwhz8c8rOMjAwjiYODg4MjzCMjIyOi/I74Wz1FRUXa\ns2ePNm7cqD179qi4uHhQTVdXl/r6+jRx4kR1dnbql7/8pV544YUhr3f27NlIWwEADINjTGR/83rh\nwgV985vf1Llz5wZ8nbO5uVlPP/20Dh48qPfee0/f+MY3JEm9vb361re+peeee25EJwAAGJ6Igx8A\nEJ08eXL3woULKiwsVFZWlh5++GFdvHhxyLq0tDTNmTNHeXl5mjdv3g3ucvgqKio0c+ZMZWZmatu2\nbUPWrF+/XpmZmfL7/aqpqbnBHbpzvfkFg0ElJCQoLy9PeXl52rx5swddRmbVqlVKSkrS7Nmzr1oT\nzWt3vflF89qFQiEtXLhQOTk5mjVrlnbu3DlkXbSuXzjzG/b6RfQ3Ay49++yzZtu2bcYYY7Zu3Wo2\nbtw4ZF1aWpppb2+/ka1FrLe312RkZJj333/fdHd3G7/fb+rq6gbUHDx40CxatMgYY0xlZaUpKCjw\notWIhDO/X//612bJkiUedejOb37zG/O73/3OzJo1a8jPo3ntjLn+/KJ57VpaWkxNTY0xxpjPPvvM\nZGVljat/98KZ33DXz5M7/vH48FdVVZVmzJihtLQ0xcbGatmyZTpw4MCAmv8574KCAl28ePGqzz+M\nNeHMT4qe9fqi+fPna8qUKVf9PJrXTrr+/KToXbtp06YpNzdXkhQfH6/s7Gw1NzcPqInm9QtnftLw\n1s+T4B+PD381NTUpNTW1/3VKSoqampquW9PY2HjDenQjnPk5jqMTJ07I7/dr8eLFqquru9Ftjppo\nXrtwjJe1a2hoUE1NjQoKCga8P17W72rzG+76Rfx1zuux7eGvq83hi774u3K453ktnD7z8/MVCoXk\n8/l0+PBhFRcX6/Tp0zeguxsjWtcuHONh7To6OrR06VLt2LFD8fHxgz6P9vW71vyGu36jdsf/q1/9\nSrW1tYOOoqIiJSUl9f+m0NLSottuu23Ia0yfPl2SNHXqVD366KNj+j/ylpycrFAo1P86FAopJSXl\nmjWNjY1KTk6+YT26Ec78Jk6cKJ/PJ0latGiRenp6dOHChRva52iJ5rULR7SvXU9Pjx577DE98cQT\nQz5TFO3rd735DXf9PNnq+fPDX5Ku+fDXZ599Jkn9D39d6xsXXps7d67OnDmjhoYGdXd3a9++fSoq\nKhpQU1RUpL1790qSKisrNXny5P4tr7EunPm1trb231VVVVXJGKPExEQv2h1x0bx24YjmtTPGaPXq\n1br77ru1YcOGIWuief3Cmd+w18/d3zdHpr293Tz44IMmMzPTFBYWmo8//tgYY0xTU5NZvHixMcaY\n+vp64/f7jd/vNzk5OWbLli1etDoshw4dMllZWSYjI6O/31deecW88sor/TVr1641GRkZZs6cOaa6\nutqrViNyvfm9/PLLJicnx/j9fnP//febkydPetnusCxbtsxMnz7dxMbGmpSUFPOTn/xkXK3d9eYX\nzWt39OhR4ziO8fv9Jjc31+Tm5ppDhw6Nm/ULZ37DXT8e4AIAy/C/XgQAyxD8AGAZgh8ALEPwA4Bl\nCH4AsAzBDwCWIfgBwDIEPwBY5r8Ay41BxHnjCL4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0153eac>"
       ]
      }
     ],
     "prompt_number": 94
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "atom_list = np.arange(9)\n",
      "disp = np.arange(99)\n",
      "for iterations in xrange(10):\n",
      "    atom = np.random.choice(atom_list)\n",
      "    x = np.random.choice(disp)\n",
      "    y = np.random.choice(disp)\n",
      "    if arena[:].all() != np.array([x, y]).all():\n",
      "        arena[atom] = np.array([x, y])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 96
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print arena[:]\n",
      "print len(arena)\n",
      "x = []\n",
      "y = []\n",
      "for i in xrange(len(arena)):\n",
      "    x.append(arena[i][0])\n",
      "    y.append(arena[i][1])\n",
      "print x,y\n",
      "#plt.scatter(arena[:][0],arena[:][1])\n",
      "plt.scatter(x,y);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 27.  46.]\n",
        " [ 86.   8.]\n",
        " [ 29.  76.]\n",
        " [ 13.  82.]\n",
        " [  1.   1.]\n",
        " [ 81.  86.]\n",
        " [ 37.  22.]\n",
        " [  2.   1.]\n",
        " [  2.   2.]]\n",
        "9\n",
        "[27.0, 86.0, 29.0, 13.0, 1.0, 81.0, 37.0, 2.0, 2.0] [46.0, 8.0, 76.0, 82.0, 1.0, 86.0, 22.0, 1.0, 2.0]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xb006d64c>"
       ]
      }
     ],
     "prompt_number": 97
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "if arena[0].all() == np.array([1., 1.]).all():\n",
      "    print \"ohhyeah!!!\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ohhyeah!!!\n"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "if arena[:].all() != np.array([5.,5.]).all():\n",
      "    print \"ohhyeah!!!\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ohhyeah!!!\n"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "from scipy.constants import N_A, nano, pico, m_p, k\n",
      "#import scipy.spatial.distance as spd\n",
      "\n",
      "atom_list = np.arange(900)\n",
      "disp = np.arange(125)\n",
      "\n",
      "a = 0.3405*nano\n",
      "e = 119.8*k\n",
      "beta = 1./np.power(10,3)\n",
      "J = 0.5\n",
      "\n",
      "def potential_e(site):\n",
      "    #dist= np.zeros(len(atoms)-1)\n",
      "    dist = []\n",
      "    for i in xrange(len(arena)):\n",
      "        #j = 0\n",
      "        if i != site:\n",
      "            temp = np.sqrt((arena[site][0]-arena[i][0])**2+(arena[site][0] - arena[i][1])**2)\n",
      "            dist.append(temp)\n",
      "            # temp = spd.euclidean(arena[i],arena[j])\n",
      "            #j += 1\n",
      "            #dist[j] = temp\n",
      "    sum_u = 0\n",
      "    for i in xrange(len(dist)):\n",
      "        sum_u += ((a/dist[i])**12 - (a/dist[i])**6)*4*e\n",
      "    \n",
      "    return sum_u\n",
      "\n",
      "arena = np.zeros([900,2])\n",
      "for i in xrange(len(arena)):\n",
      "    arena[i][1] = i%30\n",
      "    arena[i][0] = i/30\n",
      "\n",
      "sys_energy = []\n",
      "accepted_moves = 0\n",
      "\n",
      "for i in xrange(9000):\n",
      "    to_move = np.random.choice(atom_list)\n",
      "    pre_move_e = potential_e(to_move)\n",
      "    new_x = np.random.choice(disp)\n",
      "    new_y = np.random.choice(disp)\n",
      "    old_posn = arena[to_move]\n",
      "    arena[to_move] = np.array([new_x, new_y])\n",
      "    post_move_e = potential_e(to_move)\n",
      "    if post_move_e - pre_move_e < 0 :\n",
      "        sys_energy.append(potential_e(to_move))\n",
      "        accepted_moves += 1\n",
      "    else :\n",
      "        temp = np.random.random()\n",
      "        if temp < np.exp(-beta*J*(post_move_e-pre_move_e)):\n",
      "            sys_energy.append(potential_e(to_move))\n",
      "            accepted_moves += 1\n",
      "        else :\n",
      "            sys_energy.append(potential_e(to_move))\n",
      "            arena[to_move] = old_posn"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "-c:40: RuntimeWarning: divide by zero encountered in double_scalars\n",
        "-c:40: RuntimeWarning: invalid value encountered in double_scalars\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.spatial.distance as spd\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "# used to compare energy before and after a move\n",
      "# we assumed that epsilon and alpha are 1\n",
      "def local_energy(site):\n",
      "    local_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        if site != i:\n",
      "            dist = spd.euclidean(system[site],system[i])\n",
      "            local_sum += -((1/dist)**12-(1/dist)**6)\n",
      "    return local_sum\n",
      "\n",
      "# total energy of the system\n",
      "def system_energy():\n",
      "    total_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        total_sum += local_energy(i)\n",
      "    return total_sum\n",
      "\n",
      "def radial_number_density():\n",
      "    rad_dist = []\n",
      "    for i in xrange(len(system)):\n",
      "        for j in xrange(len(system)):\n",
      "            if i != j:\n",
      "                temp = spd.euclidean(system[i],system[j])\n",
      "                rad_dist.append(temp)\n",
      "    return rad_dist\n",
      "\n",
      "n = 100 # number of particles\n",
      "# initializing the system\n",
      "# the atoms occupy a square of size 10X10\n",
      "system = np.zeros([n,2])\n",
      "for i in xrange(len(system)):\n",
      "    system[i][0] = i%10 # np.sqrt(n) wont work as it will return a float\n",
      "    system[i][1] = i/10 # we need an integer denominator for this to work!\n",
      "\n",
      "global_energy = []\n",
      "accepted_moves = 0\n",
      "\n",
      "plt.subplot(131)\n",
      "alist = radial_number_density()\n",
      "anarray = np.asarray(alist)\n",
      "plt.hist(anarray,10);\n",
      "\n",
      "T = 1.\n",
      "# T = np.array([5.,5./2,1./1./2,1./10])\n",
      "beta = 1./T\n",
      "# B = 1./T\n",
      "#for beta in B:\n",
      "for time in xrange(5000):\n",
      "    site = np.random.choice(np.arange(n)) # atom to be moved\n",
      "    # this atom can now move in the range (-alpha,alpha) in x & y\n",
      "    #xmove = np.random.choice(np.array([-2.,-5./3,-4./3,-1,-2./3,-1./3,0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #ymove = np.random.choice(np.array([-2.,-5./3,-4./3,-1,-2./3,-1./3,0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #xmove = np.random.choice(np.array([0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #ymove = np.random.choice(np.array([0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    xmove = np.random.choice(np.array([0.,1.,2.,3.,4.]))\n",
      "    ymove = np.random.choice(np.array([0.,1.,2.,3.,4.]))\n",
      "    pre_move_e = local_energy(site)\n",
      "    system[site] = system[site] + np.array([xmove,ymove])\n",
      "    if system[site][0] > 100 :\n",
      "        system[site][0] = system[site][0]%100\n",
      "    #if system[site][0] < 0 :\n",
      "    #    system[site][0] = system[site][0]%100\n",
      "    if system[site][1] > 100 :\n",
      "        system[site][1] = system[site][1]%100\n",
      "    #if system[site][1] < 0 :\n",
      "    #    system[site][1] = system[site][1]%100\n",
      "    post_move_e = local_energy(site)\n",
      "    if post_move_e - pre_move_e < 0:\n",
      "        global_energy.append(system_energy())\n",
      "        accepted_moves += 1\n",
      "    else :\n",
      "        temp = np.random.random()\n",
      "        if temp < np.exp(-beta*(post_move_e - pre_move_e)):\n",
      "            global_energy.append(system_energy())\n",
      "            accepted_moves += 1\n",
      "        else :\n",
      "            system[site] = system[site] - np.array([xmove,ymove])\n",
      "            global_energy.append(system_energy())\n",
      "# we get global_energy, accepted moves as the outputs here.\n",
      "plt.subplot(132)\n",
      "alist = radial_number_density()\n",
      "anarray = np.asarray(alist)\n",
      "plt.hist(anarray,10);\n",
      "plt.subplot(133)\n",
      "plt.plot(global_energy)\n",
      "print \"accepted_moves\", accepted_moves"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "accepted_moves 4425\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lV3EFIHlcgSoX312JyBh5t594wp12dbW2d9wOqevr14/ozh1Jq2UekCq2To8QJk+ejGHD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\n++kn4fOxY0L7ZLL26x6nTgn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       "text": [
        "<matplotlib.figure.Figure at 0xaf9a3f6c>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.spatial.distance as spd\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import time\n",
      "# used to compare energy before and after a move\n",
      "# we assumed that epsilon and alpha are 1\n",
      "def local_energy(site):\n",
      "    local_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        if site != i:\n",
      "            dist = spd.euclidean(system[site],system[i])\n",
      "            local_sum += -((1/dist)**12-(1/dist)**6)\n",
      "    return local_sum\n",
      "\n",
      "# total energy of the system\n",
      "def system_energy():\n",
      "    total_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        total_sum += local_energy(i)\n",
      "    return total_sum\n",
      "\n",
      "def radial_number_density():\n",
      "    rad_dist = []\n",
      "    for i in xrange(len(system)):\n",
      "        for j in xrange(len(system)):\n",
      "            if i != j:\n",
      "                temp = spd.euclidean(system[i],system[j])\n",
      "                rad_dist.append(temp)\n",
      "    return rad_dist\n",
      "\n",
      "n = 900 # number of particles\n",
      "# initializing the system\n",
      "# the atoms occupy a square of size 10X10\n",
      "system = np.zeros([n,2])\n",
      "for i in xrange(len(system)):\n",
      "    system[i][0] = i%30 # np.sqrt(n) wont work as it will return a float\n",
      "    system[i][1] = i/30 # we need an integer denominator for this to work!\n",
      "\n",
      "global_energy = []\n",
      "accepted_moves = 0\n",
      "\n",
      "#plt.subplot(131)\n",
      "radial_dist_before = radial_number_density()\n",
      "#anarray = np.asarray(alist)\n",
      "#plt.hist(anarray,10);\n",
      "\n",
      "T = 1.\n",
      "# T = np.array([5.,5./2,1./1./2,1./10])\n",
      "beta = 1./T\n",
      "# B = 1./T\n",
      "#for beta in B:\n",
      "time_per_loop = []\n",
      "for looptime in xrange(100):\n",
      "    start_time = time.time()\n",
      "    site = np.random.choice(np.arange(n)) # atom to be moved\n",
      "    # this atom can now move in the range (-alpha,alpha) in x & y\n",
      "    #xmove = np.random.choice(np.array([-2.,-5./3,-4./3,-1,-2./3,-1./3,0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #ymove = np.random.choice(np.array([-2.,-5./3,-4./3,-1,-2./3,-1./3,0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    xmove = np.random.choice(np.array([0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    ymove = np.random.choice(np.array([0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #xmove = np.random.choice(np.array([0.,1.,2.,3.,4.]))\n",
      "    #ymove = np.random.choice(np.array([0.,1.,2.,3.,4.]))\n",
      "    pre_move_e = local_energy(site)\n",
      "    system[site] = system[site] + np.array([xmove,ymove])\n",
      "    if system[site][0] > 100 :\n",
      "        system[site][0] = system[site][0]%100\n",
      "    #if system[site][0] < 0 :\n",
      "    #    system[site][0] = system[site][0]%100\n",
      "    if system[site][1] > 100 :\n",
      "        system[site][1] = system[site][1]%100\n",
      "    #if system[site][1] < 0 :\n",
      "    #    system[site][1] = system[site][1]%100\n",
      "    post_move_e = local_energy(site)\n",
      "    if post_move_e - pre_move_e < 0:\n",
      "        global_energy.append(system_energy())\n",
      "        accepted_moves += 1\n",
      "        #print \"yes\"\n",
      "    else :\n",
      "        temp = np.random.random()\n",
      "        if temp < np.exp(-beta*(post_move_e - pre_move_e)):\n",
      "            global_energy.append(system_energy())\n",
      "            accepted_moves += 1\n",
      "            #print \"barely yes\"\n",
      "        else :\n",
      "            system[site] = system[site] - np.array([xmove,ymove])\n",
      "            global_energy.append(system_energy())\n",
      "            #print \"nyooo!!!!\"\n",
      "    print \"we're done with the mc loop %f\" % (time.time()-start_time)\n",
      "    time_per_loop.append(time.time()-start_time)\n",
      "# we get global_energy, accepted moves as the outputs here.\n",
      "#plt.subplot(132)\n",
      "radial_dist_after = radial_number_density()\n",
      "#anarray = np.asarray(alist)\n",
      "#plt.hist(anarray,10);\n",
      "#plt.subplot(133)\n",
      "#plt.plot(global_energy)\n",
      "#print \"we're done with plotting routine %f\" % (time.time()-start_time)\n",
      "print \"accepted_moves\", accepted_moves"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "accepted_moves 353\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hQ4ewZs0aREREYNasWTAajaiurkZTUxM6OzuRkZEBAFi3bh3efPNNAMDhw4exfv16AMCq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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xafdffbec>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.subplot(121)\n",
      "anarray = np.asarray(radial_dist_before)\n",
      "plt.hist(anarray,10);\n",
      "plt.subplot(122)\n",
      "anotherarray = np.asarray(radial_dist_after)\n",
      "plt.hist(anotherarray,10);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 'radial_dist_before' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-31-f0c3674573dd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m121\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0manarray\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mradial_dist_before\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0manarray\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m122\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0manotherarray\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mradial_dist_after\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mNameError\u001b[0m: name 'radial_dist_before' is not defined"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0qj///DOhuf+anp6O6SY41nMr6f9Gubu7W7311lvKYrGo5uZmpZRSly5dUpcuXQqv+fjj\nj5XFYlHFxcVqcHAwLXPr6upUVlaWKikpUSUlJerAgQNpmfu8ZAYQ6+xvvvlGFRUVKafTqS5cuJCW\nuXNzc+r9999XxcXFyul0qs7OzqTM9Xg8Kjc3VxkMBmUymVRHR0fC5xbfCCPR+F8iSTQGQKIxABKN\nAZBoDIBEYwAkGgMg0RgAifY/PixH4rctnVcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xaf5e252c>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(global_energy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = []\n",
      "y = []\n",
      "for i in xrange(len(system)):\n",
      "    x.append(system[i][0])\n",
      "    y.append(system[i][1])\n",
      "plt.scatter(x,y);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mc0/q9eWpVgfRZOpNSYrk2LGTFDy+++47qlSSvIJsQJ0uQOEZ4XA42KFDEk2m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KfYhr7yQqK6vncNZFY2Hz5s3YvHnzlQ9wNZ8cFRUVDA8P59GjR1lWVnbTHYCKP0Ob\nEXiZGs00+vo2cUl1WhdDh46iIKQReI0m023s1KmnWz+5CwsL2bRpK+nn8qsUhGj+859zZX0yMmZK\n2xOvUa//GyMjY2VbOXv27JG+mc4lsIiCYJUlGSovL2d8fIq0VfMaBaELx4y5TzbHkiVLKQjhBF6h\nVvswrdZmspzn2dnZ0iHjPwi8REFowhUr6l8+jCQ/++wzqcDFC1SpHqeHR4DL4ePVsmPHDukn+QIC\n8ykI/ty5c6ejvbS0lG3aJElZ+l6jIHTg/fdPlY2xYMGzFIRWBJZSp7ufwcER1/yn+vvvfyD9qnuJ\navWj9PIKktUtzcvLo79/U2o0Uwi8QkFo4ZImd+TI8dI24Ws0GocxMTFVdvAtZv20EniGKtVcms3+\nsuyPxcXFDA9vJ2XLfJVmcxynT58lm+Pxx5+iILQj8Cp1ur+zefM2sjOG/fv302z2p0o1m8BzFIQA\nfvXVV472iooKJif3oNE4RNJ3N9555xi3dHX8+HH6+IRQo5lOYAkFoSnffnu5W2PcjLhrO686nH/9\n+vWYMmUKbDYbxo0bh5kzZ8raG3o4/5dffomPPloDHx8PZGQ8hKZNm7p1vc1mw9Klr2Hnzn2Ijo5E\nRsYUt7/FnTt3Ds8++wJycvJw6609MGLE3bKwbJJYvvxdbNy4DWFhIZgx4xFZkiwA+Omnn7B06Ruo\nrLRhwoTR6Nixo6y9pKQEixe/iIMHs5GS0h4TJ05wqRb/+eef49NP18Pf3xvTp0+RJfMCgKNHj+L5\n519BYWEJ7rnndqSnp7t1nwCwadMmvPvux7BYTHj44UmIiopye4y62L17N15//W2oVCpMnHgvEhMT\nZe1FRUV49tnncfjwcaSldcL48WNdwuBXrvwIa9Z8g+Bgf8yYMfWKwuDr4quvvsKHH34GT08zMjIe\nRFhYmKz95MmTeO65l3D2bAGGDr3VJbWB3W7Ha68tw/btu9G6dQtMmzYVgiDI+uzcuROZme9Bq9Xg\ngQf+jpiYGFl7QUEBnnnmefzxRy7S01MxevQol7X3wQcfYv36zWjWLAjTp091SXmRlZWFJUuWoaKi\nEmPHjpC5cQJiaovFi19EVtZhdO6cgPvvn+j49l9fjh07hueeW4ILF4oxfPhg9OvXz63rb0bctZ1/\n+dwsCgoKCg0Rd23nXzoCVEFBQaGxoBhzBQUFhUaAYswVFBQUGgGKMVdQUFBoBCjGXEFBQaERoBhz\nBQUFhUaAYswVFBQUGgGKMVdQUFBoBCjGXEFBQaERoBhzBQUFhUaAYswVFBQUGgGKMVdQUFBoBCjG\nXEFBQaERoBhzBQUFhUaAYswVFBQUGgGKMVdQUFBoBCjGXEFBQaERoBhzBQUFhUaAYswVFBQUGgFX\nbMxnz56N0NBQJCQkICEhARs2bLiWcikoKCgouMEVG3OVSoVHHnkEe/fuxd69e9G3b99rKdd1Z/Pm\nzTdahHqhyHntuBlkBBQ5rzU3i5zuclXbLO5Ujm7o3Cx/YEXOa8fNICOgyHmtuVnkdJerMuYvv/wy\n4uLiMG7cOBQUFFwrmRQUFBQU3ORPjXnv3r0RExPj8u+LL77ApEmTcPToUezbtw/BwcHIyMi4XjIr\nKCgoKFyGitdgryQ7OxsDBw7E/v37XdoiIyNx+PDhq51CQUFB4S9FREQEDh06VO/+2iudKDc3F8HB\nwQCAzz77DDExMTX2c0cYBQUFBYUr44q/mY8ePRr79u2DSqVCixYtsGzZMgQGBl5r+RQUFBQU6sE1\n2WZRUFBQULixXJcI0IYcYLRhwwa0bt0aUVFRWLRo0Y0Wp1bCwsIQGxuLhIQEJCcn32hxHIwdOxaB\ngYGybbbz58+jd+/eaNmyJdLT0xuEp1NNcjbEdZmTk4MePXogOjoa7dq1w5IlSwA0PJ3WJmdD0uml\nS5fQsWNHxMfHo23btpg5cyaAhqfL2uR0W5e8DsyePZuLFy++HlO5RWVlJSMiInj06FGWl5czLi6O\nWVlZN1qsGgkLC+O5c+dutBgufP/999yzZw/btWvneG/69OlctGgRSXLhwoV89NFHb5R4DmqSsyGu\ny9zcXO7du5ckWVRUxJYtWzIrK6vB6bQ2ORuaTktKSkiSFRUV7NixI7du3drgdEnWLKe7urxuuVnY\nAHdzdu3ahcjISISFhUGn02H48OFYvXr1jRarVhqiDlNTU+Hj4yN774svvsCYMWMAAGPGjMHnn39+\nI0STUZOcQMPTaVBQEOLj4wEAFosFbdq0wYkTJxqcTmuTE2hYOhUEAQBQXl4Om80GHx+fBqdLoGY5\nAfd0ed2MeUMMMDpx4gSaNm3qeB0aGupYkA0NlUqFXr16ISkpCZmZmTdanD8lLy/PcRgeGBiIvLy8\nGyxR7TTEdVlFdnY29u7di44dOzZonVbJ2alTJwANS6d2ux3x8fEIDAx0bAs1RF3WJCfgni6vmTG/\nGQOMVCrVjRah3mzfvh179+7F+vXrsXTpUmzduvVGi1QvVCpVg9VzQ12XAFBcXIyhQ4fipZdegoeH\nh6ytIem0uLgYw4YNw0svvQSLxdLgdKpWq7Fv3z4cP34c33//Pb777jtZe0PR5eVybt682W1dXrGf\n+eVs3LixXv3Gjx+PgQMHXqtpr4omTZogJyfH8TonJwehoaE3UKLaqfLpt1qtGDJkCHbt2oXU1NQb\nLFXNBAYG4tSpUwgKCkJubi4CAgJutEg14ixXQ1qXFRUVGDp0KEaNGoXbbrsNQMPUaZWcI0eOdMjZ\nUHXq5eWF/v37Y/fu3Q1Sl1VUyfnf//4XaWlpjvfro8vrss2Sm5vr+P+fBRhdb5KSkvD7778jOzsb\n5eXlWLlyJQYNGnSjxXLh4sWLKCoqAgCUlJTg66+/bjA6rIlBgwZh+fLlAIDly5c7HvSGRkNclyQx\nbtw4tG3bFlOmTHG839B0WpucDUmnZ8+edWxNlJaWYuPGjUhISGhwuqxNzlOnTjn61EuX1/xYtgZG\njRrFmJgYxsbGcvDgwTx16tT1mLZerFu3ji1btmRERATnz59/o8WpkSNHjjAuLo5xcXGMjo5uUHIO\nHz6cwcHB1Ol0DA0N5VtvvcVz586xZ8+ejIqKYu/evZmfn3+jxXSR880332yQ63Lr1q1UqVSMi4tj\nfHw84+PjuX79+gan05rkXLduXYPS6U8//cSEhATGxcUxJiaGzzzzDEk2OF3WJqe7ulSChhQUFBQa\nAUrZOAUFBYVGgGLMFRQUFBoBijFXUFBQaAQoxlxBQUGhEaAYcwUFBYVGgGLMFRQUFBoBijFXUFBQ\naAQoxlxBQUGhEfD/zw04+EEL068AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xafe30c8c>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}