particle_testing-for_basili.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from particles import Particles as par\n",
    "from moments import Moments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# This is the data in the x direction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The columns are the time steps. Each row represents a particle and its position at each time step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The media has a length of 100 mm, start_time = 0, step = 10, end_time = 15000. time is in minutes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>1491</th>\n",
       "      <th>1492</th>\n",
       "      <th>1493</th>\n",
       "      <th>1494</th>\n",
       "      <th>1495</th>\n",
       "      <th>1496</th>\n",
       "      <th>1497</th>\n",
       "      <th>1498</th>\n",
       "      <th>1499</th>\n",
       "      <th>1500</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 1501 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   0     1     2     3     4     5     6     7     8     9     ...   1491  \\\n",
       "0     0     0     0     0     0     0     0     0     0     0  ...    100   \n",
       "1     0     0     0     0     0     0     0     0     0     0  ...    100   \n",
       "2     0     0     0     0     0     0     0     0     0     0  ...    100   \n",
       "3     0     0     0     0     0     0     0     0     0     0  ...    100   \n",
       "4     0     0     0     0     0     0     0     0     0     0  ...    100   \n",
       "\n",
       "   1492  1493  1494  1495  1496  1497  1498  1499  1500  \n",
       "0   100   100   100   100   100   100   100   100   100  \n",
       "1   100   100   100   100   100   100   100   100   100  \n",
       "2   100   100   100   100   100   100   100   100   100  \n",
       "3   100   100   100   100   100   100   100   100   100  \n",
       "4   100   100   100   100   100   100   100   100   100  \n",
       "\n",
       "[5 rows x 1501 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "part = par('./data/position_data_a.txt', dimension=1,time_end=15000,time_step=10)\n",
    "part.qx.head()\n",
    "# particle_distribution_df = part.particle_distribution(90,part.time,part.qx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### shape of the dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 1501)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "part.qx.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# cumulative distribution of particles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "At slice L=  0\n",
      "At slice L=  20\n",
      "At slice L=  40\n",
      "At slice L=  60\n",
      "At slice L=  80\n",
      "At slice L=  100\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x108881940>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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KKcvU3z8O3Ap4gN9JKRer68cAs4FOwAIp5f1+jtWuY2Brstdw5/w72f7b7UZL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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108ae4898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for l in range(0, 120, 20):\n",
    "    print('At slice L= ',l)\n",
    "    plt.plot(range(0,15010,10),part.particle_distribution(l,part.time,part.qx).cumulative)\n",
    "plt.grid(1)\n",
    "plt.xlabel('time [min]')\n",
    "plt.ylabel('number of particles')\n",
    "plt.title('cumulative distribution of particles at various lengths of the media')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# discrete distribution of particles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "At slice L=  0\n",
      "At slice L=  20\n",
      "At slice L=  40\n",
      "At slice L=  60\n",
      "At slice L=  80\n",
      "At slice L=  100\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 200)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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N9uVskBG0nEGj5cwd/CiaOqVUhcO8k9mjENOEcz6ayOBNoj2akY+PpDCvMGY/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\n+axadU8TJDQI8v3MVbSiCQh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oAsJpOksFXmNqTn/l9KgcYR8D+errjYb+vvtgZ3wCxQhe\nTv9eveLr7rMP9O3rfhx7uRXy3LlzcjkT8NyePfy9TRvW7NnDa1u8e3EhEZ4ZMSKu3GrQr+jTh/WH\nHBIp71VURL+iIjYeeiibDz2U4xwBAF7Ncicf+ePKbcEQNUoxf9eumPE+dkVT+VnykfZ2RdPYAZyh\nVsazTaRoivp5N6CJqK5ezOzr72XplUshz5CrZnXzAhiCwE8vqXEYHyWxkXBRlFIoVc/Gjc+xdeub\n7N69nMWLL3Ctm+toRRMQTtNZc3w0Xk5/rx7Nl+ujaTzu/OTOyHJCH01+PuTnU+KV3wyivhqngnvo\nIVi7NrZs4UL44gv347z0UnTZUl4nnOBed794n0GJS7XyggJ+fsMN3FJW5rI1SoNSdLNlQrA4vFMn\nlh10ECGRGCXx9YQJzD3wQPYpLKRbYWGccvdqltvm5SX10TgHkdbft4E8mxXzpDfhnW/L8Ys93Niv\nojlw/oGUUkqotaloCrwVTeshrT23JaP65FuNBQ8fjR+S+WgAeve+giFDjIzL7dpNSFh3yZKfN1kW\nN6wezdy5xv/4zM/WeBvjIW/d+ibl5dMClSFb0IomIILM3jyy20g+u+CzuHI/x59WOi3Sq/E0nTU0\n+Mvg7KVoWrWKHR8D0LWrdy+lXbvo8nXXGck7vcJ8n33WvdyD5zZuTLg9rFScH8bCMpu1tvXYuhQU\n0MVFMVl4Ncs9Cws9tnjT+neb6VkO/zYDKEYuhr7/5/+ru8fPosEA9uSXXox+azRFfY1eSl4b45ol\nz1vRWL2eZhFK7ViTvLx2FBX1A6BNm+EpPZcTK+rMmgunsvITams3UVn5ubndGm/ThOwdOYZWNAHh\nNJ01x0cjIhzW77C4ckvRXH/w9XHb7Ly3/L3EJ7B6NLRwnialjDlsJiT48uzfP05hFTfjlOPatYsZ\nK9PK7FE5VfAEuzJMgJePpigU4klHcIR1rgcGDeKp4e6NYCgMF3y+ILLeyz2C25XCnlHl1vc6D7Ol\njXbj2yF5wjjGkdfOVDQJTGehovQqGj8+mlCoIGK62rbtnSafqylYCmT8+OjvfunSq5k79zB27Pgq\nst2a1mBvRiuagGgIp26GTQtL0Zw07KSE9U54wTBLJTWd+eHyy41BnC1BcbGhZKyouJtvbvKhfmgq\njvxQKKZHY73wxziUWbKccpF65v9f7bsvjw8dyu8GD45su8jhu7Lu/wHt2jHCY5K4UBju/G10/fhG\ntJWdj45eQ0HX+F5Y3+vjlY81j01eW1PRJDCdJVM0vgIJUtyjEcmPBB9YIciNZZ99zmrSfps2vQBA\nXZ09oajxzOfMmWjr0WhFoxVNQDhn2ExF/iMxmzm/jaInlZURRZNUzscfT55qJiiefNI4l+XLuPde\nwGOsjwftTDNY3ptvRsrskWRWjySReSwR1p1/cPBgLu/Th/G2npDzXlpnrXcx37Uyxyjm10O7KpLy\npcvcd/kdoh8Lkifs++t96X15bzoc1gGAIb93JDsNA3nGOBpnj6b/1P6RaoV9jJ6SFCV+z7r/pHti\nofuvbJaPZuHCXlCb+DmJFCBiyBsKNS14oWPHQ21r/t/1sjLDD2X3JVkh24Du0djQiiYgnCloUoEV\nJJBsjhoLVx/Npk3wt781fpbNVHDllXDDDdF166vfnqrmlFNidknUbN3Urx+3DxgAQMjWm6uyjY1p\n7hNyKvm6BNMR3LjvvoAxksRZ620zFqLzdhicJOp2zLtjuC3J1D4SEgbfP5hhjw9jwG0DXOuosIr4\nZEJtzWAAc73/Lf3p+0ujBzT69dEx++1z1j6R5QO+OCCynHTSs1Z7mtWj6d37MtfygQPvpUsX4wZu\n3foW7dtPIC+vXUy2ATe6d/+pa3lR0b6R5T59Lm+itJjyvBFZtno0jRlYmqtoRRMQTtNZKnwfeaE8\n1FRFv479mn4QK7zY/MpP61wajz1mRLBZqWUsReMYy1JsWw597J2t+r5BgzjInOYgZDvGAFuiTC8f\ni98+ojPpZq3tPM57efegQYDRo/EyYz50Y/Jzdi38hrDjl9r9dKM3Me5TF0eG42IO+NJUDoqIjyaU\nH4qUgVE+5HdGD6hgH6MXEZni2fY4rJ4QH3+Puo7m4NPj3oEPjnKRQ0V7NB9/L377bXfSOj8+ynDy\nZCPFzpQpUaXWpk00RF2pevbf/zUAamvXUVDQhSlTdsZMIeBG167Hx5V163ZqxJlvHLvxitHblxRr\nOlu27NpGHztX0IomIFpiHI3FkC5DUFOTmyTumH4Ht310Gxe9bsvwbCmaysbPiJgyikyTh5sfw1QM\nt11wAZJAyQDw+utM7tQJVVxMnk0BjG/fPpKl2Uuh+FU0Q9u0QdkUip9os56FhZG2ev/58JL7h3VC\nGhyv1qh/mRkK3NpF28UUq2I6HGiY0vLa5CEhoVgVR7ZHQqRD0fqt9jWUqZvfJ79rtCdcMMaM+Bu2\nBDIP/M0AAB/dSURBVPJcBHnicuizzvOa+GyKa8NuKQzLJAZwwAHREH77vDSdOhXb9nN/FoMH/w6A\nnj3Pi9tmKKxoM2if8rlbtx96y+4DbTqLohVNQDhn2GyJOSrqb0seNnn3p3fzdOnT0QIrjb6paDJi\nLo3WraFDh+jMn/YBoiKUAHefe27y45x6Kjz6KBx5JAPKY8ejWL2a/dq0aVIoshcTO3Sg7vDDAfd7\nWXf44RzUoUMkp9rYedDD/2SUnGVmPlE25dFgF9+nC+TwusMjisMupxR6+/3a7NeGw2sPJ6+jIXun\nufdQ334ZYzYYyqb7GZ2h8zY4zehdcO4z8SfuliwlUqyiadNmv4gS+fzzBbByAEWhQTGDIpWqR0SY\nMmU3w4c/FSl3ms46dz7GLHcPZunTx5i+QGI+EG1m1pB7AIcTr/E+Orw5SgYY6nODlog6c9KU89Xs\n2E4RpKdH4+XPaNUqdjroUCiaYTpZan6TqVbutGuuAeD26dO5vlMnI5INeHDQIH7bvz9FoZDrNM/d\nmxgcAEZkW7Jto82ggYuf8qzqSmVH47+ynaK8J7y+ZQundOvmapKzIsvsRExlNg7deGjCqDOAUEGI\n1gONhrqi4gO2b/8oMqeLUnXQ3zaO6YJp8Qdok3hckFP+CRNmU7veauwL4JpH2O+L8Q5FY/QQ8vKc\ncwfFXosVHOClaKLHjO5nVwoFBc3LXrFkyS8AY74dN7ZufYe6uo0o1UBhYS9X016uoHs0ARHkOJpU\nsKt2F0/OeZL1m8xU76YJLWPk3CfqcI6JcnvkEZa+8krS3fs7Bm7mh8N0qa42poEGCkIhOhcU0CYv\nj/YugRDP77cfqw4+uGmymzjv5c45O6n4tILqpdUsOn8RiweMT3qMHbYI3Qufguq2sdv/+nO4/FE4\n9dtvqW5oYF6lkUIoRnkmsQNachbuU5iwrtXL6Xt9XyYummiWFRAOG+lkwuFa4pxHTtp7pDg640UA\nasvN1DQP/gqA8r9WsPWNrXDtw4xffyLsaU2etHP0Orww7sGkSUtMWY3n7KVoot3B+DluDjxwPoWF\nPX2c09tHs23b2+Yx3RXN0qVXsHjx+Xz33UUsXdq8IIRMRyuagKgP13umjskE3ljyBpe8cQk1O7ez\nrj3wR2e6jAzCZjpbnZfHzx2zYNo55z1jcGort0nVPvsMrroqtuzDD13nxemYn0+/gGfXnHf0PEoP\nL2XJz5ew8ZmN7Ll0ZdJ9NtsihssGxW679mF49Ueww+zl/HvzZn65zAhZW2WbNntHg39TTX7HfMa8\n6zHPjqmEQgUh2o4wNF4oVBhJt6+UD0XTb417+UajEVe1Zu/l3ePgl79j6RVLjbl45o1j6aUrjW0q\nqvTGjHmP/v1vixxGhRXbPthGpCLQpo2VYNQMdc9LPA4s1k9kLLdrtz95ef4G8SbDTdEopWKSfOb6\nbJ1a0QSEU9Gk0/dxxv5nxJX9YeYfANi6dS0z9gW6Gy1ai8k5bZoxcZofpk+HTz8F4D9btiRMenWK\nmf24sm3b+I3W7J72r/2jjwZbxuQgse5lx7w8/rP//tEPZrPB3v5e8lkYLUXzpyvit80bB3U2N8TW\n+vpIUJfdAPVnc1rslbt3s8tlkrsYH40IXY71Z5406kd7NFVV8+h/+wDf+0ZYahvfY11AOA/mGBkj\nVt62EojOm6MaFPWV9fTv+iCdOx9Nfn6HyO47Zu/gm2OMeYrsZrhRo/7NoEH3A/57NEOGPBoT3dat\n22n063crI0c+x5gx70dS3ThJlpPNqWiqq7+junqxo07jkqJmG1rRBERdQx0FeU238zeVx45/LDKQ\n0+KSAy6Jq2cl3nz1/UepzYNNuxrhkQ6C887z7W/hwANhsjG3/Mo97pO63f3kk1y2eTNHlJZy67PP\n8v3Zs72P5zxGcwe8JmFw69acYu+FefzK2oyIdzZ/bo4dfPXHyc8TViqqaGyNrLU0cNYsrrL7vppB\nQ4NxD0OhQmpqjISqGzb8nbrRbzX+YHW234mPAZ2qQbHw7IWsGjMxPmgh7L7SvfsPad3ayNrQvv1E\nevY0PnJ69zY0uEghvXpdbBzfvHd9+14FtjlQW7Xal0GD7qZHj7Pp0uVoRo16NXKcxuD00cyePYJ1\n6x5z1qKubhvhcG4GDmhFExB14ToKQtEfUEv5Pq6cdCVHDDDmS3n4uId54OgHaJ3vbSr4w3vws/nQ\n43dGQsbi4mLqM/jlrgmH44zgBy9YwK3PP8+fR46k244d3P300wxIlFxz167Y6atTlOnA/syVUoTr\nzIbP42N1gKM3UPtoH/r/rCe7BvgzwVaHw5F2ugHzXgE7Buez3DS7bXOZ5trPu9lxSkc6HdEpsr54\n8TnGOauXUlERDTOvrfW+7+3n/iq+8NXTKPjYNoHf82fDc+4T+o3DeO7hmjC1601zXVihwl7+qFil\nJSIUFvYkP78TI0YYkZfDhv2Jzp2PYcKE2bRta01iF1VQXbseT+fOx7rK06HDgZHjxMiZJCebm+nM\nmosnWqeBGTO6smrVndTWbs45U5pWNAFRF05PjwbgjFFncMygY7j24Gu58bAb6dQq2kCcPPxkz/2U\nUqyuXE3BXemR2w81Dn/KCyNHMtOajmD//eHtt5Mf5NJLoYdt2uMUp9QRjEm/wrsM2StKKlzr5bWP\nfj13Pq4zx141lMcOGMHsj/q41ndy18qVkYH3J3zzDa0++YTH163jr/WbGx3d5mT8J+NpMzza46qq\nmgfAypW3xdTbsuU172Ncc0984Z+u4rBXbo2uv3UiPHVxQllKp5RSNdfI01N6ZCnzjp0X2WaPsHOL\nwDv00A1xvaCxY9+jXbuxtv2i71i7dmMZO/bdhPLYsXo4oZC3f8+elsaioqLEWQuAmpq1lJZ+L3K/\ncwWtaAIinT6aSw+8lPfOiWZsHtIlagN3mtUAKszxkfXhej748IOUy9dU7l+1iqfKy2OM4M4ZMWPG\n3Iwc6X6gf/8btm6FF1+M3ydASkpKGNmmDUd17uxrKmZrThjaheh4WMdI+cT2yZNDXtizJzVKsdHU\nnytM8+CVDlOZ2/iYxr6by5Zdx+7d/k1wkydXUlysCIUKKC5WFBc3Ld+Z5aOxUzm9kooPDcVd9U0V\ncw6eE9nWufORtG7dlKkCmiZfv343I5JPaSkJsxL4GbBpKbvy8n+we/cS2raNz5iQzWhFExB1DbGm\ns3RSkFcQyRxgVzoAn+0LPzCT1daF6wi1VMLMJvD2tm1xZZM6dIgtsJTGihXw5Zdx9WO4/37zIJPg\n6XgTSBAsnDSJBwYPZv0T65PWDRWa+cYWjYrJT3ZSt24x2Qfc6GqO+1k5EL6XJGHCsupqBnpNSufC\n55/3orT0KNatexyALVveSLJHLG6NbnGxov9H8UndBt47kMk7Jjfq+ADzjpnH3ClzI+slUkLvvN9y\n0EGLPffZMWsHX452e0cab6bq3v10Bg261zYnjfGRecQRTTN51ddH33Wl6pqcIDRTydxWJstwms4y\nYXzKrlt2cdWk2PDegjDUmm1zXUMdBx12EOA/UWdLUm+ZQpxGcPtXuqUoi4qgbVuoqoLtHtFd33wT\nXbYGeAZIY595ZFR+YeODE7o0Iinq+9u3xwRVPN69Oyt2x5pztm37gOXLbwKgtracioqPWLr0SpYu\nvZY9e5Y3SjavqY3tnespu6YwZdcU+v26n+egUctH48b2D7bTsCPW+VX1TWwa7C1vbGHVvaui+3y8\nnV3f7oo7VtOmFzB+L4WFPRg3zp42x/1a9t331004R+6gFU1AZFKPxqJNQRsK84x42LE9xnLid3DQ\nOqgzn/pPXvkJE/5mhJTe80nUnr5823L++EX6x9l8vmNH8kpWj8bKl9a2LXTqBL9ycUTb8erJPfqo\nsa8VGt0ENr+6Oa5s7Idj48qsFP2FRY035TVmmoO3zJ7h2QsXUl5Tw/9t3swHDmW8fv2fWbPmgbh9\n1617xPO4kyYZvYdx4z6JlA0Z8kdCPn4HeW3yIrnXrPuw37/2Y8LcCRy8xhg4W9S/cV/1q+5exfKb\nlrP2T2v56oCvWPvIWspuLWPxxYuNwAxTLy29dmlMQEHdB2MZWDab9X9N3gu1sHoyAwZM5ZBD1scp\n1zFjjImFLFNeXl47Cgtj5yvam8jcEYZZhpuPJhN6NVb+tY/P+5jOlxnhxXVmu/b+ivehDBgIvy35\nLQrF6H1GM33VdB6Z9QjXHpy+bLPLqm0+jtJSGDeO0gPNSVnsSsKpaCw6dSIh06fDsmVQVgarV8PO\nnVBYGElhw9q1UZ+OD+q21fH2k28zNjyWspvL4rZbUyiPfns084+fT7+b+0W+8A9ymgMTMLR1a5bu\n3s0hHTrwp6FDWbVnDw+t8RgUiTkOyeSFTZsY164dlJYytbCQmoZ6js/7lA75+eTnGz6iqir/CrZ1\n62GAMYXyxImLqK3dQKdOh3vW95o22irP75JP+3HR3sXchrnsh39fxc7ZO9k5O5qJoNtpRoh5+VPl\n9Lm8D5teMkL61z2yjkH3DopMZ73op1YE2BJ6X9rb59kMRRUKFTJz5ncUFcUq16KivkyatJSCgs7U\n1KyndeshlJdP830tuYZWNAHx3dbv0hZ15ofOrTuzJw9aNURNZ06mlkwF4OC+xhfl8m3LGdxlsHvl\nFHOczcz1+NChHDFxIqOsQZkPPQQXmRmpLaXjHNXvJ5fb0KHe2xo5X8/K21ey4rEVdMBdabQa2Ioh\njw2hyzGGsm89pHU0Rb+HueV/o0fzcUUFvzMVyW39+3Nhz54MnDWLPBGu6NOHx9YaY1qmjRjB+Yu9\n/RMWL24yGtvy2lruXT6D0fwMgPxetwDw1VejPfctLOxNba3x1T9q1GuICKNGvUpBQXcKC/ehbdsR\nnvuCMd10h0Pj74/b9U+YM4GaxTXQtMkvAaj8LPoOrH5gdYzZbMNTG+hwcAc6TPSv5C3Gj59Bq1ax\naRvsPZpRo16jTZuRkZk/Cwq6AjB27PvMmuVI97CXoE1nAbG6cjXDu0YjXjKhNwPQrU03bp1ihJPu\nMkeV19mf+sD4fb5YaziOhzwWG0iwfNty7+mhA8aaUOzdMWO4/MQTo0oGjKwGU6YYyzVmriynYrAU\nzZ//bExH3VgamWRz14JdcT6FgfcNpOspRiMTKgjR98q+0a96H26ZE7p25e6BAyOTuY1v144BrVtz\n+4ABkeg7KyjgvJ6J83L1NXt8c6uqTJ+XojdRU9G7GxIHC4gUxowh6d79VPP/ab5nfM1vn0+Xo90H\n7fa/rT/tRkdTvrQf357jzjyOkc+PpOPkaEReJFLPB3WbotFem1+ONWcuu3oZcybNoWFP/CCn+qp6\naqwcbC507HgoRUXR+11cXMx++z3P0G4vocKK7t1PjSgZO61b239sxvYBA+6gZ88L6dLl+34vKyvR\niiYA6hrqyJM8+nTwN/6hJckL5XH3kXcDEDbbA68ejRtl28vYvMv4kQ55bAgfrDDCoWvqa9hT7z5q\nPwjWmgrk8I4dE1fcHT9GAYALL4Qbb4TLLoMTzOksH/H2N8RRXQ2bN8OWLYYZrbLSs5dU9U0VFR/F\njpXpfUVv+t/Un/xO3o7x1kNa0+WExNkSikIhpg4YwI+7d+cQ08Q2dcAAisye3NGdO3N699gplXsV\nFvLU8OH8pHt3SsxAis4ORTyKBfye6OymR/GR6/l79f0lAH37XkOXLscxfvznMbnGgmLgnQMp7BE/\nfUOPs3rQ+bhoFuWDlh0UWe55odHY977Cr7krnu8u+C6ubNGZi5jZaybhGv8BMh06HMTS0T3Y9K/E\nGTd69bqUgw5agdWdHTDgt4wY8RQFBfsk3C/byThFIyLfF5HFIrJURLIiVKO6rpo2BbHpRDJinhcH\nVl+kffuu0cJ4d0IMgx4dxD6/24et1VsB41oBvvfM9zjkqUNSICVsr6uLyFoUCiW+l//f3rlHV1Xl\nd/zzDTehQCIP5Q0aRKMxgspblgr4aHV0sOp0OT6YQbtsO7ahS60KzKo67XQJskZbVGrH2hkHtT5G\nRez4nCkxY0dwJhiFAVSiqAFxGJTIIxCS/PrH3vfm3OQGAtxLTnR/1ror++yzz9nfe2/O/e3Hb/92\ne4ZmwgSYPz+9zKxZbcu1Nz/yxBMuonT//jB8uJvz6dPHBeQ0g8bGVAy15A9SdN1HyX0lYEaiqK2h\n6VnakyMmHUGiKMHoX7QT0LIVT5WVMaj1PBQwoKCAJ8rcCvcZAwfyaGkpmyZP5trBg3myrCy1/UGf\nlKExqK6mL/uPuwZwYu1FAOzd6xwKevc+nREj/qlD1x4qye/9yAuOpGhCEXl/kkd+//zU5msnPnQi\nU20qJfeVpDkO7G/rgyjJeZskzXub2bHKea9tvH8fm7Zl0AnQWLfvKBsnnPAAPXqMoLj4Do455vZU\n/oABl9Ot2xEkEv0oKhrXQfVdh1gZGrlY4PcB5wMnAVdIamcVXnyob6ynR376QsLq/UXaO9wsX84A\nP7++q6f78bm87HLYvI9rImxvcJOsSeeCqk+rqN5czdota/d12UHRzwe9TEhI2vdnedxx7Z9LEp2L\nKS93cdcWLoTx49120gfC+PEuZlt+PhV5r1GnMlZOcIsG17MegGOHvQDf/Cbk5XHUpUe1bH/smbBm\nQioacjb5WWkpV0YjIAAlfoitTyLBmVSyjLO5dNs2/pnb0so10P5Q4QaO4cbN/VAHGk+qqOCXGdY/\nHQzJ771obBFjV4zlrPqzyMvPY9CMQamtrJMMvGJgaphyyPUH38OpLKhkz0euN11zUw2NXzZSoQoq\nVNESUqgdnQC1d9dSWViZsVyU4uLb2P2Dy1l5uvvfOfLIb3DmmXWcccZWxo7dz3qwLkjcnAEmAOvN\nbAOApMeBi4Hs/5plkUw9mm3bMocd6TRWrEglp5Scx+J3FlO3p47bJ93OzXNupvDOQqYVT2PZhsyr\n/y541G3KNP3x6QwpGpIyOCctOonFlyzm6tFXc8urt/Dsumep213HH24+9KCde6e4GG77/CxHjWp/\nQ7Ukp5zSUmbhwpb88nJ48MEDE7VyZdrhTlqcJXawg17UcHTtAnBz9PR9ci5nnvMpcGbLRWYtTgwH\nO+clQU0NHHssjBzphgUvuqhNsUReHjZ1Kv++/FKG46JHDP38lTbl/oO/ppz7eI7pTGQFg2iJYXYN\nP22pNoOxGdWrFzubmpjiPf3Oe+cdlp58MlXbt/ODj1rWsfxF//48WVaWdu3e5mYKKitpnjKlzVxP\ne9/7cfe0bVwce2f6JPvGf9t3b2TorKFsXLj/HsvrvV9PpSsLKuk+vDt7PnGGqPC0Qna8tcP1ZL2D\nZv37mXvYTTub+HXhr5nS3PI+P3/pc/Z+9vXY5jlWPRpgKBD11az1ebFl0n9OYu2WtW0MTezYsCGV\nfPjP3Za7Qwpdy69XgWtdzz93Pk23ZY4Aue6PLR5Nm7ZvSpufmfHsDPQDseA3C1j/+Xq27NrCrBdn\n8frHr1NybwkXPnbhPqVdt/Q6/qH6JVRR0aFWc1bJFI4mGWV60aJ2L/sS59r7HjcCMI5r/d9Wcbse\neACeew4mT3bGYdSodPdsyQ3JSVBS0hLdYMqUll1HZ86El9PjbzXnw/L1E7BpU11UhGUZGggzZ2L/\ns5SKClG6+1kKcV5XX375RpuiE49063yssZ4aRlLHEUxrZ96mNat27uSD3bv5SWT77OmrV6cZGYCn\ntmzhxa1bOX7FCtbv2sXC2lpurHGLQfNee40TKiooWbKE41es4Io1a7i3tpb7N6Ybg4ovvuDKNWva\naJhQVUWtX5S6zK8ROnru0altqJOUPuIGSIrGFKU84Pr847A29ztrT2Y37aSRAVLx18BFJkjTqQqq\np1Xz8YKPAVLx2dZds44KVbDmqpb3sPuT3VRNrAKganwVFYkKrOnwON0cLnS4vIg6gqTLgPPN7Dp/\nfDUw0czKI2Vs6cI4jWEaSReiaFyxex75gBuujo8ro8xoUgJTXlpkp4WL32fWjHQ33+a89j1uDrBW\nkjNDsvbbNKZmUOuJYCNvjxvrW/jYx8y6MvNeINlA/pVoaqb3nr00S+SZsb0gn6IG1+Lc2qMAAf3q\nXRThRoowP9zUg1p68glznhZ3Xnboz9OWngX039XAjoJu1Ce60X9XQyo/Sb/mBraNgb6/hby90NBN\n1LVay9F/VwPN+fDF+PT7z5sHs2en5+26bjA9H/yUnUu7ccn0Fxi3eiV/87NHwOD7N81l04BB/PTW\ncr6z4P5Dem+DP9vMpwMHcfyGGt4v3o/rvBc6sboqlbWybDR78/PT8gBWnDqWkg9r6Fu3jaqTT6H7\n7gSj362iW2Me435zGhcvdeV+fP27fDq0nvoeTSQaxbvFYziifgNHf7KN8rtL6fd5dxrym7ntrreY\nd8PYDr2necxjNrMznmsoaKLmuO2Urml/XVftsJ0Mq+3F2pO2pcptXdTEZd87p0P1dxRJmFlu98ho\nr+6YGZpJwB1mdr4/ngM0m9n8SJn4CA4EAoEuRDA0gNyqp3eBc4BNwJvAFWYW6zmaQCAQCLRPrJwB\nzKxR0t8BL+O2unsoGJlAIBDo2sSqRxMIBAKBrx5x8zprl85eyClpuKRlkn4vabWkWT6/n6RXJb0n\n6RVJfSLXzPF610n600j+WEmr/LkDWK7eYa3dJL0l6fkYa+wj6eeS1kpaI2liTHXe4L/vVZIek9Q9\nDjol/ZekzyStiuRlTZd/n0/4/OWSjsmizgX+e39b0jOSekfOxUZn5NxNkpol9YvkxUqnpHL/ma6W\nFJ3T7hSdbTCz2L9ww2jrgWIgH6gGSg+zhkHAqT5diJtLKgXuAm7x+bcC83z6JK8z3+teT0sP8k1g\ngk+/gPO0y6bWG4FHgaX+OI4aHwau9ekE0DtuOnGu9R8A3f3xE8B346ATtzDnNGBVJC9ruoDrgUU+\nfTnweBZ1ngfk+fS8uOr0+cOBl3AxNPrFUScwDXgVyPfH/TtbZxvd2Xooc/kCTgdeihzPBmZ3sqYl\nwLnAOmCgzxsErPPpOcCtkfIvAZOAwcDaSP63gQeyqGsY8Ev/z/e8z4ubxt7ABxny46ZzKPAx0Bdn\nDJ/H/UjGQqf/8Yj+4GRNly8z0acTwJZs6Wx17hLgkbjqBJ4CRpNuaGKlE3gSODtDuU7VGX11laGz\nWC3klFSMa1WswD3YyWXUnwHJGCBDSK0PB1o0t87fSHbfyz3AzaTvTxs3jSOALZJ+ImmlpAcl9Yqb\nTjPbCPwIZ2w2AdvM7NW46YyQTV2pZ87MGoG66NBRFrkW16KOnU5JFwO1ZvZOq1Ox0gkcD5zlh7oq\nJCUXGsZGZ1cxNLHxWJBUCDwN/L2ZbY+eM9cM6DStki4C/mBmb9FOIPrO1uhJAGNwXfQxwE5IX/EW\nB52S+gLTcS3IIUCh3CLiFHHQmYm46ooi6ftAg5k91tlaWiOpJzAXuD2a3Uly9kcC6Gtmk3CNzCc7\nWU8buoqh2YgbK00ynHSLfFiQ2xj8aWCxmS3x2Z9JGuTPDwaSQb5aax6G07zRp6P5HQsTu38mA9Ml\nfQj8N3C2pMUx04ivo9bMktEDf44zPJtjpvNc4EMz2+pbd8/ghnHjpjNJNr7n2sg1R/t7JYDeZpad\naJnunjOBbwBXRbLjpHMkroHxtn+ehgFVkgbGTCe+jmcA/DPVLOmoOOnsKobmd8DxkoolFeAmqZYe\nTgGSBDwErDGzf42cWoqbIMb/XRLJ/7akAkkjcN3bN81sM/ClnJeVgBmRaw4JM5trZsPNbARu3PV/\nzWxGnDR6nZuBTySV+Kxzgd/j5kBioxP4CJgkqYe//7nAmhjqTJKN7/m5DPf6FvCrbImUdD6u5X2x\nmUU3NYqNTjNbZWYDzWyEf55qgTF+aDI2Oj1LgLMB/DNVYGZ/jJXObEz0HI4XcAHO02s9MKcT6j8D\nN+9RDbzlX+cD/XCT7+8BrwB9ItfM9XrXAX8WyR8LrPLnFuZI7xRavM5ipxE4Bfgt8DauNdY7pjrv\nwEUPX4XzlMuPg05cj3UT0IAbU78mm7qA7rghmPeB5UBxlnRe6+/5UeQ5WhQjnXuSn2er8x/gnQHi\nptP/Ty729VYBUztbZ+tXWLAZCAQCgZzSVYbOAoFAINBFCYYmEAgEAjklGJpAIBAI5JRgaAKBQCCQ\nU4KhCQQCgUBOCYYmEAgEAjklGJpAIBAI5JRgaAJfeST1lvS9yPEQSU/loJ47JNVKuuMAr3tQUul+\nytwg6SNJ9x6SyECgEwgLNgNfeXy07efNbFSO67kd2G5md+fo/t8FxplZeS7uHwjkitCjCXwdmAeM\nlNt1dL6kY5I7FEqaKWmJ3I6UH0r6W0k3+u0L3vARnJE0UtKLkn4nqVLSCe3UlYrw63s4D/vyGyRd\nIukuSe/4eyV8uQpJY3x6h6QfSqr29Q/IdO9AoCsRDE3g68CtQI2ZnWZmt9L2B7sMtwHXeOBfgB3m\nti94A/iOL/NjoNzMxuECQi7qYN0jcJvQTQceAX5lZqOBeuBCXyY6rNATeMPMTgUqgesi58LwQ6BL\nkuhsAYHAYWB/PYFlZrYT2CmpDhedGVzQwdFym7JNBp5ywW4BKOhAvQa8aGZNklYD3czs5ci9izNc\n02Bmv/DpKtyOnoFAlyYYmkDARcJN0hw5bsY9I3nAF2Z22kHcuwHAzJol7W1VT7cM5VuXCc9ooMsT\nhs4CXwe2A0UHcZ0AzO2k+qGkb4Hbm0jS6CzoCnMuga8FwdAEvvKY2Vbg/yStkjQfN6SVnO9oveVx\n63Ty+CrgLyVVA6txcy4dqr6ddKbjfdUfCHRZgntzIJAlvHvzDjP7UY7uPxMYG9ybA12N0KMJBLLH\nDuCvDnTBZkeQdAMwG6jL9r0DgVwTejSBQCAQyCmhRxMIBAKBnBIMTSAQCARySjA0gUAgEMgpwdAE\nAoFAIKcEQxMIBAKBnPL/x9E4IzSzdocAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108ae4080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for l in range(0, 120, 20):\n",
    "    print('At slice L= ',l)\n",
    "    plt.plot(range(0,15010,10),part.particle_distribution(l,part.time,part.qx).discrete)\n",
    "plt.grid(1)\n",
    "plt.xlabel('time [min]')\n",
    "plt.ylabel('number of particles')\n",
    "plt.title('discrete distribution of particles at various lengths of the media')\n",
    "plt.ylim(0,200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Temporal Moment Calculation (order = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "moment for slice L=  0 0.0\n",
      "moment for slice L=  20 259926500.0\n",
      "moment for slice L=  40 517744200.0\n",
      "moment for slice L=  60 775593400.0\n",
      "moment for slice L=  80 1031306900.0\n",
      "moment for slice L=  100 1170428300.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1088d7320>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WME/THfCawQXMrA4wCbjT3XeXfc/DLHfeHyczuxLY5u4r+PKFcUDhHAtCx9oO\nGOLu7Qhnn31hCKJQjoWZ1SN0rM0IAVbHzPqU3aZQjsXRJPHdKz0u6Q74LUDTMs+b8sXfQHnPzGoT\nwn2suz8ff/kjM/t6/P2GwLao6sug7wBXm9kG4Gngu2Y2lsI8FpuBze6+LP58IiHwPyzAY9Ed2ODu\n2939IDAZuJDCPBaHVfR3onyeNom/VqF0B/znF0qZ2XGECYKpaf7MrGFmBowA1rj7oDJvTQVujD++\nEXi+/J/NN+5+v7s3dffmhEm0Oe7+EwrzWHwIbDKzb8Zf6g78HzCNAjsWwF+ATmZ2QvzvS3fCJHwh\nHovDKvo7MRX4sZkdZ2bNgRbA0kr35O5p/QGuAN4mTAjcl+7Py6Yf4CLCePNKYEX8pxg4BZgFvAPM\nAE6OutYMH5cuwNT444I8FsB5wDJgFaFrPamAj0UJ4QSE1YRJxdqFciwI/5rdCuwnzFf2rey7A/fH\ns3QdcHmi/etCJxGRPJUV92QVEZHUU8CLiOQpBbyISJ5SwIuI5CkFvIhInlLAi4jkKQW8iEieUsCL\niOSp/wcBPRgEnyii0QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108833240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = []\n",
    "for i, l in enumerate(range(0,120,20)):\n",
    "    particle_distribution_df = part.particle_distribution(l,part.time,part.qx)\n",
    "    dis = particle_distribution_df['discrete'].values\n",
    "#     dis = dis[dis!=0]\n",
    "#     plt.scatter(range(dis.shape[0]),dis,color=colors[i])\n",
    "    mom = Moments.temporal_moment(1,range(0,15010,10),dis)\n",
    "    m.append(mom)\n",
    "    print('moment for slice L= ',l,mom)\n",
    "plt.plot(range(0,120,20),m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normalized Temporal Moment Calculation (order = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "moment for slice L=  0 nan\n",
      "moment for slice L=  20 2599.265\n",
      "moment for slice L=  40 5177.442\n",
      "moment for slice L=  60 7755.934\n",
      "moment for slice L=  80 10324.4258685\n",
      "moment for slice L=  100 12657.3840164\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x108935748>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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N0ofT2G4BhkZEDVAjqX/ZnyZndXV1eYewThxny6qEOCshRnCcRVJWcoiIxREx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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10881c8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = []\n",
    "for i, l in enumerate(range(0,120,20)):\n",
    "    particle_distribution_df = part.particle_distribution(l,part.time,part.qx)\n",
    "    dis = particle_distribution_df['discrete'].values\n",
    "#     dis = dis[dis!=0]\n",
    "#     plt.scatter(range(dis.shape[0]),dis,color=colors[i])\n",
    "    mom = Moments.normalized_temporal_moment(1,range(0,15010,10),dis)\n",
    "    m.append(mom)\n",
    "    print('moment for slice L= ',l,mom)\n",
    "plt.plot(range(0,120,20),m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question: on the above graoh we can see that for L=100mm, the mean residence time is 12657 min ?\n",
    "i know that the simulation time was 15000 mi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Temporal Moment Calculation (order = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "moment for slice L=  0 0.0\n",
      "moment for slice L=  20 709603965000.0\n",
      "moment for slice L=  40 2.75541792e+12\n",
      "moment for slice L=  60 6.129797126e+12\n",
      "moment for slice L=  80 1.0798623625e+13\n",
      "moment for slice L=  100 1.4932950839e+13\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10899c2b0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fPjGzjmY2zczeM7N3zewPidfbmtkUM5tnZs+YWZuoa20uZlZmZm+b2aTE85K8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\n+v81UvuKIByUWAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108944320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = []\n",
    "for i, l in enumerate(range(0,120,20)):\n",
    "    particle_distribution_df = part.particle_distribution(l,part.time,part.qx)\n",
    "    dis = particle_distribution_df['discrete'].values\n",
    "#     dis = dis[dis!=0]\n",
    "#     plt.scatter(range(dis.shape[0]),dis,color=colors[i])\n",
    "    mom = Moments.temporal_moment(2,range(0,15010,10),dis)\n",
    "    m.append(mom)\n",
    "    print('moment for slice L= ',l,mom)\n",
    "plt.plot(range(0,120,20),m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normalized Temporal Moment Calculation (order = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "moment for slice L=  0 nan\n",
      "moment for slice L=  20 7096039.65\n",
      "moment for slice L=  40 27554179.2\n",
      "moment for slice L=  60 61297971.26\n",
      "moment for slice L=  80 108105151.917\n",
      "moment for slice L=  100 161489681.399\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x107e20e80>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wP/4x1NUp3KV5msGLlIlly+DCC+GLL2D69HCnjEhLNIMXSTj3sAnHEUfAwIEwZYrCXfKj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\ngSs+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10882fd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = []\n",
    "for i, l in enumerate(range(0,120,20)):\n",
    "    particle_distribution_df = part.particle_distribution(l,part.time,part.qx)\n",
    "    dis = particle_distribution_df['discrete'].values\n",
    "#     dis = dis[dis!=0]\n",
    "#     plt.scatter(range(dis.shape[0]),dis,color=colors[i])\n",
    "    mom = Moments.normalized_temporal_moment(2,range(0,15010,10),dis)\n",
    "    m.append(mom)\n",
    "    print('moment for slice L= ',l,mom)\n",
    "plt.plot(range(0,120,20),m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": [
    ""
   ]
  }
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