Diffusie-Week3-Group32.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*pas dit blok aan (dubbelklik om te wijzigen)*\n",
    "\n",
    "# 2020 Diffusie werkcollege opdracht\n",
    "***\n",
    "\n",
    "## Datum: 20-feb-2020\n",
    "## Hoofdstuk: 3\n",
    "## Groep nummer: 32\n",
    "***\n",
    "## Student 1\n",
    "    naam: Julian van Doorn\n",
    "    Studentnr: s2518074\n",
    "\n",
    "## Student 2\n",
    "    naam: Bálint Bosman\n",
    "    Studentnr: s2593149\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# Dit blok moet altijd als eerste worden uitgevoerd. Verwijder het dus niet!\n",
    "# voer blokken uit met shift-enter, of met de ▶-knop in de knoppenbalk\n",
    "\n",
    "from __future__ import division\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "outputs": [
    {
     "name": "stdout",
     "text": [
      "Shape of richtingen: (10000, 2000)\n",
      "Shape of eind_posities: (10000,)\n"
     ],
     "output_type": "stream"
    },
    {
     "data": {
      "text/plain": "Text(0, 0.5, 'Frequency')"
     },
     "metadata": {},
     "output_type": "execute_result",
     "execution_count": 20
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.4 a\n",
    "\n",
    "moleculen = 10000\n",
    "step_size = 0.05\n",
    "bin_size = 0.2\n",
    "steps = 2000\n",
    "\n",
    "bins = np.arange(- steps * step_size - bin_size / 2, steps * step_size + bin_size / 2, bin_size)\n",
    "centers = np.arange(-steps * step_size, steps * step_size, bin_size)\n",
    "\n",
    "richtingen = np.random.choice([-step_size, step_size], (moleculen, steps))\n",
    "print(f'Shape of richtingen: {np.shape(richtingen)}')\n",
    "\n",
    "eind_posities = np.sum(richtingen, axis=1)\n",
    "print(f'Shape of eind_posities: {np.shape(eind_posities)}')\n",
    "\n",
    "frequencies, grenzen = np.histogram(eind_posities, bins)\n",
    "\n",
    "plt.bar(centers, frequencies, width=bin_size)\n",
    "plt.title('Distrubution of the molecules with v = 0')\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Frequency')\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0, 0.5, 'Propability')"
     },
     "metadata": {},
     "output_type": "execute_result",
     "execution_count": 21
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.4 b\n",
    "\n",
    "# De kans dat een molecuul zich bevind op positie X is de frequentie geddeld door het aantal.\n",
    "normalized = frequencies / moleculen\n",
    "\n",
    "plt.bar(centers, normalized, width=bin_size)\n",
    "plt.title('Propability distrubution of the molecules with v = 0')\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Propability')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "outputs": [
    {
     "name": "stdout",
     "text": [
      "Shape of posities: (10000, 2000)\n"
     ],
     "output_type": "stream"
    },
    {
     "data": {
      "text/plain": "<matplotlib.legend.Legend at 0x133c04550>"
     },
     "metadata": {},
     "output_type": "execute_result",
     "execution_count": 22
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.4 c\n",
    "\n",
    "posities = np.cumsum(richtingen, axis=1)\n",
    "print(f'Shape of posities: {np.shape(posities)}')\n",
    "\n",
    "timestamps = range(1, steps, steps // 11)\n",
    "for t in timestamps:\n",
    "    frequencies, grenzen = np.histogram(posities[:,t], bins)\n",
    "\n",
    "    plt.bar(centers, frequencies, label=f't={t}', width=bin_size)\n",
    "\n",
    "plt.title('Distrubution of the molecules with v = 0')\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.4 d\n",
    "mean_x = []\n",
    "mean_x_squared = []\n",
    "\n",
    "for t in timestamps:\n",
    "    mean_x.append(np.average(posities[:,t]))\n",
    "    mean_x_squared.append(np.average(np.square(posities[:,t])))\n",
    "    \n",
    "mean_x = np.array(mean_x)\n",
    "mean_x_squared = np.array(mean_x_squared)\n",
    "variance = mean_x_squared - np.square(mean_x)\n",
    "\n",
    "plt.scatter(timestamps, mean_x)\n",
    "plt.title('Average position over time v = 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position')\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(timestamps, mean_x_squared)\n",
    "plt.title('Average position over time squared v = 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position squared')\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(timestamps, variance)\n",
    "plt.title('Variance over time v = 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Variance')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "outputs": [
    {
     "name": "stdout",
     "text": [
      "De diffusieconstante is: [0.002513   0.00127498 0.00126226 0.00125312 0.00125234 0.00126153\n",
      " 0.00125745 0.00125804 0.0012509  0.00125856 0.00125436 0.00124565]\n",
      "Excluding the first point the average is D=0.0013618502031500753\n"
     ],
     "output_type": "stream"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.4 e\n",
    "\n",
    "# <x^2> = 2Dt where D is the Diffusion constant and t the time\n",
    "plt.scatter(timestamps,0.5 * mean_x_squared / timestamps)\n",
    "plt.axis(ymin=0, ymax=0.005)\n",
    "plt.grid()\n",
    "print(f'De diffusieconstante is: {0.5 * mean_x_squared / (timestamps)}')\n",
    "print(f'Excluding the first point the average is D={np.mean(0.5 * mean_x_squared / (timestamps))}')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "outputs": [
    {
     "name": "stdout",
     "text": [
      "De diffusieconstante is: [0.009984   0.00496905 0.00496858 0.00494807 0.00491483 0.00495057\n",
      " 0.0049364  0.004962   0.00495077 0.00496413 0.00499673 0.00501771]\n",
      "Excluding the first point the average is D=0.004961713964043183\n"
     ],
     "output_type": "stream"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD4CAYAAADlwTGnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAZ9UlEQVR4nO3dcYyc9X3n8fenu5g6ONgEqlWy9t06xaVaglpgZdNLGq3PEV7nerGPMyejljg9Uqs6nEvahMo+FBqhIuKjLW0EpHJrq4TksqYupauec05aM42QDoMNtMbAhsVwhzeEHGBDltoYO9/7Y34mw2R2d2b8zOywv89LWu0zv+f3PL/v88zM89l5nplZRQRmZpafn5npAszMbGY4AMzMMuUAMDPLlAPAzCxTDgAzs0x1z3QBjbjggguir6+vqWXfeOMNzjnnnGILKoDrakyn1gWdW5vrakyn1gXN17Z///6XI+LnfmpGRLxrfi6//PJo1gMPPND0sq3kuhrTqXVFdG5trqsxnVpXRPO1AfuixjHVp4DMzDLlADAzy5QDwMwsUw4AM7NMOQDMzDLlADAzy5QDwMwsUw4AM7NMOQDMzDLlADAzy1RdASBpSNKopDFJm2rMP1vSjjR/r6S+1H6+pAckTUi6Y5J1j0h64kw2wszMGjdtAEjqAu4EVgH9wDWS+qu6XQcciYgLgduBLan9OPBF4AuTrPsqYKK50s3M7EzU8wpgKTAWEYci4gQwDKyu6rMauDtN7wRWSFJEvBERD1IOgneQNA/4XeAPmq7ezMyappjmn8JLWgsMRcSn0+1rgWURsbGizxOpz+F0+9nU5+V0+1PAQNUytwPfBR4D/i4iPjTJ+BuADQA9PT2XDw8PN7WhExMTzJs3r6llW8l1NaZT64LOrc11NaZT64Lma1u+fPn+iBiobp+R/wcg6ZeBn4+I3zl9vWAyEbEV2AowMDAQg4ODTY1ZKpVodtlWcl2N6dS6oHNrc12N6dS6oPja6jkFNA4sqri9MLXV7COpG5gPvDLFOn8FGJD0PPAg8AuSSvWVbGZmRagnAB4BlkhaLGkOsA4YqeozAqxP02uBPTHFuaWI+GpEfCAi+oCPAN+LiMFGizczs+ZNewooIk5K2gjsBrqA7RFxUNLNlP/LzAiwDbhH0hjwKuWQACD9lX8uMEfSGuDKiHiy+E0xM7NG1HUNICJ2Abuq2m6qmD4OXD3Jsn3TrPt5oOYFYDMzax1/EtjMLFMOADOzTDkAzMwy5QAwM8uUA8DMLFMOADOzTDkAzMwy5QAwM8uUA8DMLFMOADOzTDkAzMwy5QAwM8uUA8DMLFMOADOzTDkAzMwy5QAwM8uUA8DMLFMOADOzTDkAzMwy5QAwM8tUXQEgaUjSqKQxSZtqzD9b0o40f6+kvtR+vqQHJE1IuqOi/3sk/U9JT0s6KOnLRW2QmZnVZ9oAkNQF3AmsAvqBayT1V3W7DjgSERcCtwNbUvtx4IvAF2qs+g8j4heBS4EPS1rV3CaYmVkz6nkFsBQYi4hDEXECGAZWV/VZDdydpncCKyQpIt6IiAcpB8HbIuJfIuKBNH0CeBRYeAbbYWZmDVJETN1BWgsMRcSn0+1rgWURsbGizxOpz+F0+9nU5+V0+1PAQOUyFcsuoBwAH4uIQzXmbwA2APT09Fw+PDzczHYyMTHBvHnzmlq2lVxXYzq1Lujc2lxXYzq1Lmi+tuXLl++PiIHq9u5CqmqSpG7gm8BXah38ASJiK7AVYGBgIAYHB5saq1Qq0eyyreS6GtOpdUHn1ua6GtOpdUHxtdVzCmgcWFRxe2Fqq9knHdTnA6/Use6twDMR8Sd19DUzswLVEwCPAEskLZY0B1gHjFT1GQHWp+m1wJ6Y5tySpD+gHBSfa6xkMzMrwrSngCLipKSNwG6gC9geEQcl3Qzsi4gRYBtwj6Qx4FXKIQGApOeBc4E5ktYAVwKvAzcCTwOPSgK4IyL+osiNMzOzydV1DSAidgG7qtpuqpg+Dlw9ybJ9k6xW9ZVoZmat4E8Cm5llygFgZpYpB4CZWaYcAGZmmXIAmJllygFgZpYpB4CZWaYcAGZmmXIAmJllygFgZpYpB4CZWaYcAGZmmXIAmJllygFgZpYpB4CZWaYcAGZmmXIAmJllygFgZpYpB4CZWaYcAGZmmaorACQNSRqVNCZpU435Z0vakebvldSX2s+X9ICkCUl3VC1zuaQDaZmvSGrJP4m//7FxPvzlPRwYf40Pf3kP9z823ophzMzedaYNAEldwJ3AKqAfuEZSf1W364AjEXEhcDuwJbUfB74IfKHGqr8K/BawJP0MNbMBU7n/sXE233eA8aPHABg/eozN9x1wCJiZUd8rgKXAWEQciogTwDCwuqrPauDuNL0TWCFJEfFGRDxIOQjeJun9wLkR8VBEBPA1YM2ZbEgtt+0e5dhbp97RduytU9y2e7TooczM3nW66+jTC7xQcfswsGyyPhFxUtJrwPnAy1Os83DVOntrdZS0AdgA0NPTQ6lUqqPksnWLfgSLytM9c+Hzl5xMc37U0HpaaWJiomNqqeS6GteptbmuxnRqXVB8bfUEwIyKiK3AVoCBgYEYHByse9kbv7zn7dM/n7/kJH90oLy5vQvm8plfr389rVQqlWhkm9rFdTWuU2tzXY3p1Lqg+NrqOQU0ztt/RwOwMLXV7COpG5gPvDLNOhdOs84zdsPKi5h7Vtc72uae1cUNKy8qeigzs3edegLgEWCJpMWS5gDrgJGqPiPA+jS9FtiTzu3XFBEvAq9LuiK9++eTwN82XP001lzay61XXULvgrlA+S//W6+6hDWX1jzbZGaWlWlPAaVz+huB3UAXsD0iDkq6GdgXESPANuAeSWPAq5RDAgBJzwPnAnMkrQGujIgngf8C/CUwF/hW+incmkt7WXNpL6VSqWNO+5iZdYK6rgFExC5gV1XbTRXTx4GrJ1m2b5L2fcCH6i3UzMyK5U8Cm5llygFgZpYpB4CZWaYcAGZmmXIAmJllygFgZpYpB4CZWaYcAGZmmXIAmJllygFgZpYpB4CZWaYcAGZmmXIAmJllygFgZpYpB4CZWaYcAGZmmXIAmJllygFgZpYpB4CZWaYcAGZmmaorACQNSRqVNCZpU435Z0vakebvldRXMW9zah+VtLKi/XckHZT0hKRvSvrZIjbIzMzqM20ASOoC7gRWAf3ANZL6q7pdBxyJiAuB24Etadl+YB1wMTAE3CWpS1Iv8F+BgYj4ENCV+pmZWZvU8wpgKTAWEYci4gQwDKyu6rMauDtN7wRWSFJqH46INyPiOWAsrQ+gG5grqRt4D/D9M9sUMzNrRHcdfXqBFypuHwaWTdYnIk5Keg04P7U/VLVsb0T8b0l/CPxf4Bjw7Yj4dq3BJW0ANgD09PRQKpXqKPmnTUxMNL1sK7muxnRqXdC5tbmuxnRqXVB8bfUEQOEknUf51cFi4CjwV5J+IyK+Xt03IrYCWwEGBgZicHCwqTFLpRLNLttKrqsxnVoXdG5trqsxnVoXFF9bPaeAxoFFFbcXpraafdIpnfnAK1Ms+zHguYj4fxHxFnAf8G+a2QAzM2tOPQHwCLBE0mJJcyhfrB2p6jMCrE/Ta4E9ERGpfV16l9BiYAnwMOVTP1dIek+6VrACeOrMN8fMzOo17SmgdE5/I7Cb8rt1tkfEQUk3A/siYgTYBtwjaQx4lfSOntTvXuBJ4CRwfUScAvZK2gk8mtofI53mMTOz9qjrGkBE7AJ2VbXdVDF9HLh6kmVvAW6p0f77wO83UqyZmRXHnwQ2M8uUA8DMLFMOADOzTDkAzMwy5QAwM8uUA8DMLFMOADOzTDkAzMwy5QAwM8uUA8DMLFMOADOzTDkAzMwy5QAwM8uUA8DMLFMOADOzTDkAzMwy5QAwM8uUA8DMLFMOADOzTDkAzMwyVVcASBqSNCppTNKmGvPPlrQjzd8rqa9i3ubUPippZUX7Akk7JT0t6SlJv1LEBpmZWX2mDQBJXcCdwCqgH7hGUn9Vt+uAIxFxIXA7sCUt2w+sAy4GhoC70voA/hT4XxHxi8AvAU+d+eaYmVm96nkFsBQYi4hDEXECGAZWV/VZDdydpncCKyQptQ9HxJsR8RwwBiyVNB/4KLANICJORMTRM98cMzOrlyJi6g7SWmAoIj6dbl8LLIuIjRV9nkh9DqfbzwLLgC8BD0XE11P7NuBblINgK/Ak5b/+9wOfjYg3aoy/AdgA0NPTc/nw8HBTGzoxMcG8efOaWraVXFdjOrUu6NzaXFdjOrUuaL625cuX74+Iger27kKqalw3cBnwmYjYK+lPgU3AF6s7RsRWymHBwMBADA4ONjVgqVSi2WVbyXU1plPrgs6tzXU1plPrguJrq+cU0DiwqOL2wtRWs4+kbmA+8MoUyx4GDkfE3tS+k3IgmJlZm9QTAI8ASyQtljSH8kXdkao+I8D6NL0W2BPlc0sjwLr0LqHFwBLg4Yj4AfCCpIvSMisonw4yM7M2mfYUUESclLQR2A10Adsj4qCkm4F9ETFC+WLuPZLGgFcphwSp372UD+4ngesj4lRa9WeAb6RQOQT8ZsHbZmZmU6jrGkBE7AJ2VbXdVDF9HLh6kmVvAW6p0f448FMXJczMrD38SWAzs0w5AMzMMuUAMDPLlAPAzCxTDgAzs0zN1CeBzczele5/bJzbdo/y/aPH+MCCudyw8iLWXNrbnrF+6dT0CzXAAVCwGX1wtHCsmRivnWb7vvTjsrixNt93gGNvlQ/E40ePsfm+AwCFj1lrrPEjp7j/sfHCxnIAFGimHxytGmsmxjs9ZvUTe0GLxpnN+/LosbfY/A9+XBbhtt2jb4912rG3TnHb7tHCx6s11o8jCh3L1wAKNNWD49081kyMd/qJPX70GMFPnthHj71V+FizfV++9NpxPy4L8v2jxxpq7/SxHAAFmm0Pjpkcb7In9kuvHS98rNm+L0+c+nHbxpvt+/IDC+Y21N7pYzkACjTbHhwzOd5kT+DJDmZnYrbvyzldtZ/mflw27oaVFzH3rK53tM09q4sbVl40yRLFjvUzUqFjOQAKNNMPjlaNNRPjTfYEnuxgdiZm+77smf+zflwWZM2lvdx61SX0LpiLgN4Fc7n1qktacr2h1li9580tdCxfBC7Q6TumHe9IaOdYMzHeDSsvesfFPSg/sXvmzyl8rNm+LxfMPYtbr+r347LAMdv17rfqsUqlUqHrdwAUbCYfHLNpvMme2Atee6Zl483Wfdnu8Wbzts02DgDrWLWe2KVSawLALEe+BmBmlikHgJlZphwAZmaZcgCYmWXKAWBmlqm6AkDSkKRRSWOSNtWYf7akHWn+Xkl9FfM2p/ZRSSurluuS9JikvzvTDTEzs8ZMGwCSuoA7gVVAP3CNpP6qbtcBRyLiQuB2YEtath9YB1wMDAF3pfWd9lngqTPdCDMza1w9rwCWAmMRcSgiTgDDwOqqPquBu9P0TmCFJKX24Yh4MyKeA8bS+pC0EPh3wF+c+WaYmVmj6vkgWC/wQsXtw8CyyfpExElJrwHnp/aHqpY9/cmePwF+D3jvVINL2gBsAOjp6Wn6o9ATExOFf4y6CK6rMZ1aF3Ruba6rMZ1aFxRf24x8EljSrwE/jIj9kgan6hsRW4GtAAMDAzE4OGX3SZVKJZpdtpVcV2M6tS7o3NpcV2M6tS4ovrZ6TgGNA4sqbi9MbTX7SOoG5gOvTLHsh4FPSHqe8imlfyvp603Ub2ZmTaonAB4BlkhaLGkO5Yu6I1V9RoD1aXotsCciIrWvS+8SWgwsAR6OiM0RsTAi+tL69kTEbxSwPWZmVqdpTwGlc/obgd1AF7A9Ig5KuhnYFxEjwDbgHkljwKuUD+qkfvcCTwIngesjoth/a29mZk2p6xpAROwCdlW13VQxfRy4epJlbwFumWLdJaBUTx1mZlYcfxLYzCxTDgAzs0w5AMzMMuUAMDPLlAPAzCxTDgAzs0w5AMzMMuUAMDPLlAPAzCxTDgAzs0w5AMzMMuUAMDPLlAPAzCxTDgAzs0w5AMzMMuUAMDPLlAPAzCxTDgAzs0w5AMzMMuUAMDPLVF0BIGlI0qikMUmbasw/W9KONH+vpL6KeZtT+6iklaltkaQHJD0p6aCkzxa1QWZmVp9pA0BSF3AnsAroB66R1F/V7TrgSERcCNwObEnL9gPrgIuBIeCutL6TwOcjoh+4Ari+xjrNzKyF6nkFsBQYi4hDEXECGAZWV/VZDdydpncCKyQptQ9HxJsR8RwwBiyNiBcj4lGAiPgR8BTQe+abY2Zm9VJETN1BWgsMRcSn0+1rgWURsbGizxOpz+F0+1lgGfAl4KGI+Hpq3wZ8KyJ2VizbB3wX+FBEvF5j/A3ABoCenp7Lh4eHm9rQiYkJ5s2b19SyreS6GtOpdUHn1ua6GtOpdUHztS1fvnx/RAxUt3cXUlWTJM0D/hr4XK2DP0BEbAW2AgwMDMTg4GBTY5VKJZpdtpVcV2M6tS7o3NpcV2M6tS4ovrZ6TgGNA4sqbi9MbTX7SOoG5gOvTLWspLMoH/y/ERH3NVO8mZk1r54AeARYImmxpDmUL+qOVPUZAdan6bXAniifWxoB1qV3CS0GlgAPp+sD24CnIuKPi9gQMzNrzLSngCLipKSNwG6gC9geEQcl3Qzsi4gRygfzeySNAa9SDglSv3uBJym/8+f6iDgl6SPAtcABSY+nof5bROwqegPNzKy2uq4BpAPzrqq2myqmjwNXT7LsLcAtVW0PAmq0WDMzK44/CWxmlikHgJlZphwAZmaZcgCYmWXKAWBmlikHgJlZphwAZmaZcgCYmWXKAWBmlikHgJlZphwAZmaZcgCYmWXKAWBmlikHgJlZphwAZmaZcgCYmWXKAWBmlikHgJlZphwAZmaZcgCYmWWqrgCQNCRpVNKYpE015p8taUeav1dSX8W8zal9VNLKetdpZmatNW0ASOoC7gRWAf3ANZL6q7pdBxyJiAuB24Etadl+YB1wMTAE3CWpq851mplZC9XzCmApMBYRhyLiBDAMrK7qsxq4O03vBFZIUmofjog3I+I5YCytr551mplZC3XX0acXeKHi9mFg2WR9IuKkpNeA81P7Q1XL9qbp6dYJgKQNwIZ0c0LSaB0113IB8HKTy7aS62pMp9YFnVub62pMp9YFzdf2r2s11hMAMyoitgJbz3Q9kvZFxEABJRXKdTWmU+uCzq3NdTWmU+uC4mur5xTQOLCo4vbC1Fazj6RuYD7wyhTL1rNOMzNroXoC4BFgiaTFkuZQvqg7UtVnBFifptcCeyIiUvu69C6hxcAS4OE612lmZi007SmgdE5/I7Ab6AK2R8RBSTcD+yJiBNgG3CNpDHiV8gGd1O9e4EngJHB9RJwCqLXO4jfvHc74NFKLuK7GdGpd0Lm1ua7GdGpdUHBtKv+hbmZmufEngc3MMuUAMDPL1KwPgJn8yglJiyQ9IOlJSQclfTa1f0nSuKTH08/HK5ap+dUZLarveUkHUg37Utv7JH1H0jPp93mpXZK+kmr7Z0mXtaimiyr2y+OSXpf0uZnYZ5K2S/qhpCcq2hreP5LWp/7PSFpfa6wC6rpN0tNp7L+RtCC190k6VrHf/qximcvT/T+WaleLamv4viv6eTtJXTsqanpe0uOpvW37bIpjRHseZxExa38oX2B+FvggMAf4J6C/jeO/H7gsTb8X+B7lr774EvCFGv37U41nA4tT7V0trO954IKqtv8ObErTm4AtafrjwLcAAVcAe9t0//2A8odY2r7PgI8ClwFPNLt/gPcBh9Lv89L0eS2o60qgO01vqairr7Jf1XoeTrUq1b6qRfusofuuFc/bWnVVzf8j4KZ277MpjhFteZzN9lcAM/qVExHxYkQ8mqZ/BDzFTz4JXctkX53RTpVf63E3sKai/WtR9hCwQNL7W1zLCuDZiPg/U/Rp2T6LiO9Sfldb9XiN7J+VwHci4tWIOAJ8h/L3YhVaV0R8OyJOppsPUf5szaRSbedGxENRPoJ8rWJbCq1tCm37qpip6kp/xf8n4JtTraMV+2yKY0RbHmezPQBqfY3FVAfgllH5G1IvBfampo3pJdz20y/vaH+9AXxb0n6Vv3IDoCciXkzTPwB6Zqg2KL+duPJJ2Qn7rNH9MxP77T9T/ivxtMWSHpP0j5J+NbX1plraVVcj912799mvAi9FxDMVbW3fZ1XHiLY8zmZ7AHQESfOAvwY+FxGvA18Ffh74ZeBFyi8/Z8JHIuIyyt/Ker2kj1bOTH/lzMj7hFX+gOAngL9KTZ2yz942k/tnMpJupPyZm2+kpheBfxURlwK/C/wPSee2uayOu++qXMM7/9Bo+z6rcYx4WysfZ7M9AGb8KycknUX5jv1GRNwHEBEvRcSpiPgx8Of85JRFW+uNiPH0+4fA36Q6Xjp9aif9/uFM1EY5lB6NiJdSjR2xz2h8/7StPkmfAn4N+PV00CCdXnklTe+nfG79F1INlaeJWlZXE/ddO/dZN3AVsKOi3rbus1rHCNr0OJvtATCjXzmRzi1uA56KiD+uaK88d/4fgNPvTJjsqzNaUds5kt57epryRcQneOfXeqwH/raitk+mdyFcAbxW8RK1Fd7xV1kn7LOK8RrZP7uBKyWdl059XJnaCiVpCPg94BMR8S8V7T+n8v/fQNIHKe+fQ6m21yVdkR6nn6zYlqJra/S+a+fz9mPA0xHx9qmddu6zyY4RtOtxdiZXsN8NP5Svmn+Pcorf2OaxP0L5pds/A4+nn48D9wAHUvsI8P6KZW5MtY5SwLsypqjtg5TfXfFPwMHT+4by13j/A/AM8PfA+1K7KP8Tn2dT7QMtrO0cyl8mOL+ire37jHIAvQi8Rfmc6nXN7B/K5+TH0s9vtqiuMcrngE8/zv4s9f2P6f59HHgU+PcV6xmgfDB+FriD9M0ALait4fuu6OdtrbpS+18Cv13Vt237jMmPEW15nPmrIMzMMjXbTwGZmdkkHABmZplyAJiZZcoBYGaWKQeAmVmmHABmZplyAJiZZer/A9X21nCcri3aAAAAAElFTkSuQmCC\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.3 f\n",
    "step_size = 0.1\n",
    "\n",
    "bins = np.arange(- steps * step_size - bin_size / 2, steps * step_size + bin_size / 2, bin_size)\n",
    "centers = np.arange(-steps * step_size, steps * step_size, bin_size)\n",
    "\n",
    "richtingen = np.random.choice([-step_size, step_size], (moleculen, steps))\n",
    "eind_posities = np.sum(richtingen, axis=1)\n",
    "frequencies, grenzen = np.histogram(eind_posities, bins)\n",
    "posities = np.cumsum(richtingen, axis=1)\n",
    "timestamps = range(1, steps, steps // 11)\n",
    "\n",
    "mean_x = []\n",
    "mean_x_squared = []\n",
    "\n",
    "for t in timestamps:\n",
    "    mean_x.append(np.average(posities[:,t]))\n",
    "    mean_x_squared.append(np.average(np.square(posities[:,t])))\n",
    "    \n",
    "mean_x = np.array(mean_x)\n",
    "mean_x_squared = np.array(mean_x_squared)\n",
    "variance = mean_x_squared - np.square(mean_x)\n",
    "\n",
    "plt.scatter(timestamps,0.5 * mean_x_squared / timestamps)\n",
    "plt.axis(ymin=0, ymax=0.015)\n",
    "plt.grid()\n",
    "print(f'De diffusieconstante is: {0.5 * mean_x_squared / (timestamps)}')\n",
    "print(f'Excluding the first point the average is D={np.mean((0.5 * mean_x_squared / (timestamps))[1:])}')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Onze berekeningen laten zien dat bij step_size = 0.05 we een D=0.0013 en met step_size = 0.1 we een D=0.0054. Dit is dus ongeveer 4 keer zo groot. Onze step_size is verdubbeld dus wellicht zit hier een kwadratisch verband tussen."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "outputs": [
    {
     "data": {
      "text/plain": "(-10, 109.790000000003, -419.05, 8800.05)"
     },
     "metadata": {},
     "output_type": "execute_result",
     "execution_count": 26
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.5 a\n",
    "step_size = 0.05\n",
    "\n",
    "bins = np.arange(- steps * step_size - bin_size / 2, steps * step_size + bin_size / 2, bin_size)\n",
    "centers = np.arange(-steps * step_size, steps * step_size, bin_size)\n",
    "\n",
    "# We hebben 2 * links en 3 * rechts -> 40% / 60%\n",
    "richtingen = np.random.choice([-step_size, -step_size, step_size, step_size, step_size], (moleculen, steps))\n",
    "eind_posities = np.sum(richtingen, axis=1)\n",
    "frequencies, grenzen = np.histogram(eind_posities, bins)\n",
    "posities = np.cumsum(richtingen, axis=1)\n",
    "timestamps = range(1, steps, steps // 11)\n",
    "\n",
    "for t in timestamps:\n",
    "    frequencies, grenzen = np.histogram(posities[:,t], bins)\n",
    "\n",
    "    plt.plot(centers, frequencies, label=f't={t}')\n",
    "\n",
    "plt.title('Distrubution of the molecules with v > 0')\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.axis(xmin=-10)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We zien dat de toppen zich naar rechts verplaatsen, dit is ook waar de stikstof naartoe stroomt. Dit is dus verwacht."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.5 b\n",
    "mean_x = []\n",
    "mean_x_squared = []\n",
    "\n",
    "for t in timestamps:\n",
    "    mean_x.append(np.average(posities[:,t]))\n",
    "    mean_x_squared.append(np.average(np.square(posities[:,t])))\n",
    "    \n",
    "mean_x = np.array(mean_x)\n",
    "mean_x_squared = np.array(mean_x_squared)\n",
    "variance = mean_x_squared - np.square(mean_x)\n",
    "\n",
    "plt.scatter(timestamps, mean_x)\n",
    "plt.title('Average position over time v > 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position')\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(timestamps, mean_x_squared)\n",
    "plt.title('Average position over time squared v > 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position squared')\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(timestamps, variance)\n",
    "plt.title('Variance over time v > 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Variance')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "outputs": [
    {
     "name": "stdout",
     "text": [
      "De diffusieconstante is: [0.0025955  0.01039398 0.01939583 0.02842582 0.03755498 0.04665451\n",
      " 0.05566665 0.06473383 0.07378628 0.08288692 0.09200901 0.10105767]\n",
      "Excluding the first point the average is D=0.05568777008157007\n",
      "De drifsnelheid is: [0.01953    0.01005643 0.0100157  0.01000526 0.01001537 0.01001646\n",
      " 0.01001147 0.01001146 0.0100103  0.01001241 0.01001473 0.01001342]\n",
      "Uitgezonderd van het eerste punt is de driftsnelheid gemiddeld 0.01001663698836527\n"
     ],
     "output_type": "stream"
    }
   ],
   "source": [
    "# Opgave 3.5 c\n",
    "# <x^2> = 2Dt where D is the Diffusion constant and t the time\n",
    "print(f'De diffusieconstante is: {0.5 * mean_x_squared / (timestamps)}')\n",
    "print(f'Excluding the first point the average is D={np.mean((0.5 * mean_x_squared / (timestamps))[1:])}')\n",
    "\n",
    "# De driftsnelheid is de afgeleide van de gemiddelde x waarde.\n",
    "print(f'De drifsnelheid is: {mean_x / (timestamps)}')\n",
    "print(f'Uitgezonderd van het eerste punt is de driftsnelheid gemiddeld {np.mean((mean_x / (timestamps))[1:])}')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Opgave 3.5 d\n",
    "De gemiddelde verplaatsing is (60 - 40) * 0.05 / deeltjes = 1 / 10000 = 0.00001 (waarin deeltjes het aantal deeltjes is).\n",
    "\n",
    "Het tweede moment is D * t = 0.01 * 1 = 0.01 waarin D de hiervoor berekende diffusie constante is en t = 1 (tijdstap).\n",
    "\n",
    "De variantie is dan 0.01 - 0.00001^2 ~= 0.01. "
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "outputs": [
    {
     "name": "stdout",
     "text": [
      "Numerieke variantie op t=1 is 0.004809579100000001.\n"
     ],
     "output_type": "stream"
    }
   ],
   "source": [
    "# Opgave 3.5 e\n",
    "print(f'Numerieke variantie op t=1 is {variance[0]}.')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Door de verplaatsing van de stikstof kan je niet zomaar normale variantie gebruiken, maar moet je gebruik maken van centrale variantie. Hierin zit een factor 2 verwerkt die we terug zijn in het verschil tussen de voorspelde en gemeten waarden."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "outputs": [
    {
     "data": {
      "text/plain": "(-10, 108.95, -500.0, 10500.0)"
     },
     "metadata": {},
     "output_type": "execute_result",
     "execution_count": 30
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.5 f\n",
    "bin_size = 1\n",
    "bins = np.arange(- steps * step_size - bin_size / 2, steps * step_size + bin_size / 2, bin_size)\n",
    "centers = np.arange(-steps * step_size, steps * step_size, bin_size)\n",
    "\n",
    "for t in timestamps:\n",
    "    frequencies, grenzen = np.histogram(posities[:,t], bins)\n",
    "\n",
    "    plt.plot(centers, frequencies, label=f't={t}')\n",
    "\n",
    "plt.title('Distrubution of the molecules with v > 0')\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.axis(xmin=-10)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "outputs": [],
   "source": [
    "# Opgave 3.6 a\n",
    "\n",
    "def diffuse(n_molecules=10, n_t=25, dx=0.05):\n",
    "    time = np.linspace(0, n_t, n_t)\n",
    "    \n",
    "    richtingen = np.random.choice([-dx, -dx, dx, dx, dx], (n_molecules, n_t))\n",
    "    posities = np.cumsum(richtingen, axis=1)\n",
    "    \n",
    "    M1 = np.average(posities, axis=0)\n",
    "    M2 = np.average(np.square(posities), axis=0)\n",
    "    variance = M1 - np.square(M2)\n",
    "    \n",
    "    return time, M1, M2, variance"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.6 b\n",
    "time, M1, M2, variance = diffuse()\n",
    "\n",
    "plt.scatter(time, M1)\n",
    "plt.title('Average position over time v > 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position')\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(time, M2)\n",
    "plt.title('Average position over time squared v > 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position squared')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "outputs": [],
   "source": [
    "# Opgave 3.6 c\n",
    "from scipy.stats import linregress\n",
    "\n",
    "def linear_fit(x, y):\n",
    "    # linregress uses least square method.\n",
    "    slope, intercept, r_value, p_value, std_err = linregress(x,y)\n",
    "    \n",
    "    return f'f(x)={slope:.2f}x + {intercept:.2f}', slope, intercept"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.6 d\n",
    "f_x, a, b = linear_fit(time, M1)\n",
    "\n",
    "plt.scatter(time, M1)\n",
    "plt.plot(time, a * time + b)\n",
    "plt.title('Average position over time v > 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "outputs": [
    {
     "name": "stdout",
     "text": [
      "STD: 0.0004608836010963429, AVG: 0.001801087627652929.\n"
     ],
     "output_type": "stream"
    }
   ],
   "source": [
    "# Opgave 3.6 e\n",
    "\n",
    "diffusion_constants = []\n",
    "for i in range(0, 10):\n",
    "    time, M1, M2, variance = diffuse()\n",
    "    \n",
    "    diffusion_constants.append(np.mean(M2[1:] / (2 * time[1:])))\n",
    "    \n",
    "diffusion_constants = np.array(diffusion_constants)\n",
    "print(f'STD: {np.std(diffusion_constants)}, AVG: {np.mean(diffusion_constants)}.')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "outputs": [
    {
     "name": "stdout",
     "text": [
      "Using 108 atoms gives an error <5%.\n"
     ],
     "output_type": "stream"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Opgave 3.6 f\n",
    "\n",
    "result = 1\n",
    "n = 0\n",
    "while result >= 0.05:\n",
    "    n += 1\n",
    "    diffusion_constants = []\n",
    "    for i in range(0, 10):\n",
    "        time, M1, M2, variance = diffuse(n_molecules=n)\n",
    "        \n",
    "        diffusion_constants.append(np.mean(M2[1:] / (2 * time[1:])))\n",
    "        \n",
    "    diffusion_constants = np.array(diffusion_constants)\n",
    "    result = np.std(diffusion_constants) / np.mean(diffusion_constants)\n",
    "\n",
    "print(f'Using {n} atoms gives an error <5%.')\n",
    "time, M1, M2, variance = diffuse(n_molecules=n)\n",
    "f_x, a, b = linear_fit(time, M1)\n",
    "\n",
    "plt.scatter(time, M1)\n",
    "plt.plot(time, a * time + b)\n",
    "plt.title('Average position over time v > 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   }
  },
  {
   "cell_type": "code",
   "source": [
    "# Opgave 3.6 g\n",
    "diffusion_constants = []\n",
    "for i in range(0, 10):\n",
    "    time, M1, M2, variance = diffuse(n_t=10000)\n",
    "    \n",
    "    diffusion_constants.append(np.mean(M2[1:] / (2 * time[1:])))\n",
    "    \n",
    "diffusion_constants = np.array(diffusion_constants)\n",
    "print(f'STD: {np.std(diffusion_constants)}, AVG: {np.mean(diffusion_constants)}.')\n",
    "print(f'STD/AVG: {np.std(diffusion_constants)  / np.mean(diffusion_constants)}')\n",
    "\n",
    "time, M1, M2, variance = diffuse(n_t=10000)\n",
    "f_x, a, b = linear_fit(time, M1)\n",
    "\n",
    "plt.scatter(time, M1)\n",
    "plt.plot(time, a * time + b)\n",
    "plt.title('Average position over time v > 0')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Position')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n",
     "is_executing": false
    }
   },
   "execution_count": 41,
   "outputs": [
    {
     "name": "stdout",
     "text": [
      "STD: 0.0067178561552430115, AVG: 0.2531044603728124.\n",
      "STD/AVG: 0.026541832353913823\n"
     ],
     "output_type": "stream"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Dus ja, met heel veel tijdstappen kan in ieder geval een STD van 3% worden bereikt.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "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"
  },
  "pycharm": {
   "stem_cell": {
    "cell_type": "raw",
    "source": [],
    "metadata": {
     "collapsed": false
    }
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}