ion-est-non-uni-fields.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import glob\n",
    "import re\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from utils import Graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below loads all simulation runs. At various fields, $2500$ electrons were spawned in GAr at $2$ PSI above a tip of radius $r = 1$ $\\mu$m and height $h = 3.5$ mm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_tree = {}\n",
    "\n",
    "for file in glob.glob('ion-est-non-uni-fields/*.txt'):\n",
    "    key = int(re.search(r'(\\d*)(?:V)', file).group(1))\n",
    "    if (key in file_tree):\n",
    "        file_tree[key].append(file)\n",
    "    else:\n",
    "        file_tree[key] = [file]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below plots total and estimated ionizations, where the first comes from the full, recursive algorithm and the second comes from raising $2$ to each simulation's primary ionizations. The printed values show different ways of estimating the total number of ionizations from the estimated number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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T+4fKC5Q0A5gB0NHRQa1WG1aAM3daOXCjCgw37qr19PRkH2O7cZ/kx31SrcoSlKT9gWURcaukrnpxg6bRRN0LBRGzgdkAnZ2d0dXV1bvJoEybdeWw5h+qRVO6WrLeZtVqNYb72trIcp/kx31SrSpHUG8GDpS0L7ABsAnFiGozSeumUdQEYElq3w1sC3RLWhfYFHikwvjMzCxjle2DiogTImJCREwEjgB+HhFTgOuAQ1KzqcDcNH15ekyq/3lEvGgEZWZm7aEV/4M6HjhG0kKKfUznpvJzgS1T+THArBbEZmZmmaj6IAkAIqIG1NL0fcBuDdo8DRw6GvGYmVn+fCYJMzPLkhOUmZllyQnKzMyy5ARlZmZZcoIyM7MsOUGZmVmWnKDMzCxLTlBmZpYlJygzM8uSE5SZmWXJCcrMzLLkBGVmZllygjIzsyw5QZmZWZaaSlCSviRpE0nrSbpW0kOS3lt1cGZm1r6aHUHtFRErgP0pLs3+KuDYyqIyM7O212yCWi/d7wtcGBGPVBSPmZkZ0PwVdX8s6R7gKeAjkrYCnq4uLDMza3dNjaAiYhbwJqAzIp4DngAOqjIwMzNrb82OoAB2ACZKKs9z/gjHY2ZmBjSZoCR9F3glcBvwfCoOnKDMzKwizY6gOoHXRkRUGYyZmVlds0fx3Qm8rMpAzMzMypodQY0DfifpJuCZemFEHFhJVGZm1vaaTVAnVRmEmZlZb00lqIi4XlIHsGsquikillUXlpmZtbtmz8V3GHATcChwGHCjpEOqDMzMzNpbs5v4Pg3sWh81pTNJ/Ay4pKrAzMysvTV7FN86vTbpPTyIec3MzAat2SRzlaSfSpomaRpwJTCvvxkkbSDpJkkLJN0l6XOpfDtJN0q6V9JFkl6SytdPjxem+olDf1pmZrama/ZcfMcCs4HXAzsDsyPi+AFmewZ4R0TsDEwG9pa0O3Aq8NWImAQ8CkxP7acDj0bE9sBXUzszM2tTTW+mi4hLI+KYiPi3iLisifYRET3p4XrpFsA7eGHf1Rzg4DR9UHpMqt9TkpqNz8zM1i79JihJv0z3j0taUbo9LmnFQAuXNEbSbcAy4Brgj8BjEbEyNekGxqfp8cBigFS/HNhyKE/KzMzWfP0exRcRb0n3Gw9l4RHxPDBZ0mbAZRRnRH9Rs3TfaLT0onP/SZoBzADo6OigVqsNJbRVZu60cuBGFRhu3FXr6enJPsZ24z7Jj/ukWk2fzTwi3jdQWV8i4jFJNWB3YDNJ66ZR0gRgSWrWDWwLdKdLemwKvOjKvRExm2J/GJ2dndHV1dVMCH2aNuvKYc0/VIumdLVkvc2q1WoM97W1keU+yY/7pFrN7oPasfwgJZB/6G8GSVulkROSNgTeCdwNXAfU/+Q7FZibpi9Pj0n1P/fZ083M2le/IyhJJwCfAjYs7XMS8CxpFNOPrYE5ksZQJMKLI+IKSb8D/kfSF4DfAuem9ucC35W0kGLkdMRQnpCZma0dBtoH9UXgi5K+GBEnDGbBEXE7sEuD8vuA3RqUP01xKiUzM7OmTxZ7gqTNgUnABqXy+VUFZmZm7a3ZgyQ+CBxNcVDDbRQHO/ya4j9NZmZmI67ZgySOprjUxp8iYg+KTXcPVhaVmZm1vWYT1NNpHxGS1o+Ie4BXVxeWmZm1u2Yvt9GdDhn/EXCNpEd54f9LZmZmI67ZgyT+KU2eJOk6ij/RXlVZVG1gYqv+IHzKfi1Zr5nZYA30P6gtGhTfke7H0uBMD2ZmZiNhoBHUrRTnw+vrPHmvGPGIzMzMGPiPutuNViBmZmZlzf4P6m2Nyv1HXTMzq0qzR/EdW5regOJURbfiP+qamVlFmj2K74DyY0nbAl+qJCIzMzMGccn3XrqB141kIGZmZmXN7oP6Gi9c3XYdYDKwoKqgzMzMmt0HdUtpeiVwYUT8qoJ4zMzMgOb3Qc2pOhAzM7OypvZBSdpf0m8lPSJphaTHS1fYNTMzG3HNbuI7Hfhn4I6IiIEam5mZDVezR/EtBu50cjIzs9HS7AjqOGCepOuBZ+qFEfGVSqIyM7O212yCOhnooTiLxEuqC8fMzKzQbILaIiL2qjQSMzOzkmb3Qf1MkhOUmZmNmmYT1EeBqyQ95cPMzcxsNDT7R92Nqw7EzMysbKBLvr8mIu6R9IZG9RHxm2rCMjOzdjfQCOoYYAZwWqms/F8oXw/KzMwqMdA+qHMkvSwi9oiIPYDzKA43vxM4pOrgzMysfQ2UoM4CnoVVl33/IjAHWA7MrjY0MzNrZwNt4hsTEY+k6cOB2RFxKXCppNuqDc3MzNrZQCOoMZLqSWxP4OeluoEOsNhW0nWS7pZ0l6SjU/kWkq6RdG+63zyVS9KZkhZKur2vAzPMzKw9DJSgLgSulzQXeAr4BYCk7Sk28/VnJTAzInYAdgc+Kum1wCzg2oiYBFybHgPsA0xKtxnAtwb/dMzMbG3R7ygoIk6WdC2wNXB16Wzm6wAfH2DepcDSNP24pLuB8cBBQFdqNgeoAcen8vPTOm6QtJmkrdNyzMyszQz4R92IuKFB2R8GsxJJE4FdgBuBjnrSiYilkl6amo2nuKxHXXcqWy1BSZpBMcKio6ODWq02mFBeZOZOK4c1/5qm2derp6dn2K+tjSz3SX7cJ9Vq9mSxQyZpLHAp8MmIWCGpz6YNyl50/amImE06grCzszO6urqGFd+0WVcOa/41zaIpXU21q9VqDPe1tZHlPsmP+6RazZ6Lb0gkrUeRnC6IiB+m4gckbZ3qtwaWpfJuYNvS7BOAJVXGZ2Zm+aosQakYKp0L3N3rwoaXA1PT9FRgbqn8/elovt2B5d7/ZGbWvqrcxPdm4H3AHaX/TH0KOAW4WNJ04M/AoaluHrAvsBB4EvhAhbGZmVnmKktQEfFLGu9XguI/Vb3bB8VlPczMzKrdB2VmZjZUTlBmZpYlJygzM8uSE5SZmWXJCcrMzLLkBGVmZllygjIzsyw5QZmZWZacoMzMLEtOUGZmliUnKDMzy5ITlJmZZckJyszMsuQEZWZmWXKCMjOzLDlBmZlZlpygzMwsS05QZmaWJScoMzPLkhOUmZllyQnKzMyy5ARlZmZZcoIyM7MsOUGZmVmWnKDMzCxLTlBmZpYlJygzM8uSE5SZmWXJCcrMzLJUWYKS9B1JyyTdWSrbQtI1ku5N95unckk6U9JCSbdLekNVcZmZ2Zph3QqXfR7wdeD8Utks4NqIOEXSrPT4eGAfYFK6vRH4Vrq3ETZx1pVNtZu500qmNdm2WYtO2W9El2dma7fKRlARMR94pFfxQcCcND0HOLhUfn4UbgA2k7R1VbGZmVn+RnsfVEdELAVI9y9N5eOBxaV23anMzMzaVJWb+AZDDcqiYUNpBjADoKOjg1qtNqwVz9xp5bDmX1t1bDjyr81w+6rd9fT0+DXMjPukWqOdoB6QtHVELE2b8Jal8m5g21K7CcCSRguIiNnAbIDOzs7o6uoaVkAjvZ9lbTFzp5WcdsfIvj0WTeka0eW1m1qtxnDf7zay3CfVGu1NfJcDU9P0VGBuqfz96Wi+3YHl9U2BZmbWniobQUm6EOgCxknqBj4LnAJcLGk68Gfg0NR8HrAvsBB4EvhAVXGZmdmaobIEFRFH9lG1Z4O2AXy0qljMzGzN4zNJmJlZlpygzMwsS05QZmaWJScoMzPLkhOUmZllyQnKzMyy5ARlZmZZcoIyM7MsOUGZmVmWnKDMzCxLTlBmZpYlJygzM8uSE5SZmWXJCcrMzLLkBGVmZllygjIzsyw5QZmZWZacoMzMLEtOUGZmliUnKDMzy5ITlJmZZckJyszMsuQEZWZmWXKCMjOzLDlBmZlZlpygzMwsS05QZmaWJScoMzPLkhOUmZllyQnKzMyytG6rAyiTtDdwBjAGOCciTmlxSDaCJs66siXrXXTKfi1Zr5kNTzYjKEljgG8A+wCvBY6U9NrWRmVmZq2STYICdgMWRsR9EfEs8D/AQS2OyczMWiSnTXzjgcWlx93AG3s3kjQDmJEe9kj6/TDXuymwfJjLGMpymm0/ULv+6hvV9dV+tfJPwDjgoSbiq8JI9MmqZejUEV/vUPtkMOWNylrVJ636jDQ7z0h/Rvoqd5+M3GdkUlNri4gsbsChFPud6o/fB3xtFNY7uxXLabb9QO36q29U11f73uXALS18Lwy7T4ayjKr7ZDDlfZS1pE9a9Rlpdp6R/oy4T4bffjh9Ur7ltImvG9i29HgCsGQU1vvjFi2n2fYDteuvvlFdX+1H6nUYCSMRy1CWUXWfDKZ8beuPoS6nmXlG+jPSV7n7ZHS+t1ZRymYtJ2ld4A/AnsBfgJuB90TEXS0NrE1JuiUiOlsdh73AfZIf90m1stkHFRErJX0M+CnFYebfcXJqqdmtDsBexH2SH/dJhbIZQZmZmZXltA/KzMxsFScoMzPLkhOUmZllyQnKzMyy5ARlTZH0CknnSrqk1bFYQdLBks6WNFfSXq2Op91J2kHSWZIukfThVsezNnCCamOSviNpmaQ7e5XvLen3khZKmgUQxTkSp7cm0vYxyD75UUQcBUwDDm9BuGu9QfbH3RHxIeAwwP+NGgFOUO3tPGDvcoHPKt9y5zH4PvlMqreRdx6D6A9JBwK/BK4d3TDXTk5QbSwi5gOP9Cr2WeVbaDB9osKpwE8i4jejHWs7GOxnJCIuj4h/BKaMbqRrJyco663RWeXHS9pS0lnALpJOaE1obathnwAfB94JHCLpQ60IrE319RnpknSmpG8D81oT2tolm1MdWTbUoCwi4mHAX4Kt0VefnAmcOdrBWJ/9UQNqoxvK2s0jKOutVWeVt765T/Li/hglTlDW283AJEnbSXoJcARweYtjanfuk7y4P0aJE1Qbk3Qh8Gvg1ZK6JU2PiJVA/azydwMX+6zyo8d9khf3R2v5bOZmZpYlj6DMzCxLTlBmZpYlJygzM8uSE5SZmWXJCcrMzLLkBGVmZllygjIbJEk9w5j3nKGcHV7SNEnbDHc5ZmsS/w/KbJAk9UTE2FFeZw3494i4ZTTXa9ZKHkGZDVG63MWXJd0p6Q5Jh6fyLkm1dGXVeyRdIEmpriapU9KBkm5Lt99Luj/Vnyjp5rTM2Wkdh1BcAO+C1H7D+nLSPEem9d+ZLr9Rj69H0smSFki6QVJHKj80tV0gaf5ov25mzXKCMhu6fwYmAztTXPbiy5K2TnW7AJ+kuKDdK4A3l2dM1w2aHBGTgQXAf6eqr0fErhHxOmBDYP+IuAS4BZiS5nmqvpy02e9U4B0pll0lHZyqNwJuiIidgfnAUan8ROBdqfzAEXotzEacE5TZ0L0FuDAino+IB4DrgV1T3U0R0R0RfwNuAyY2WoCk44CnIqJ+Rdw9JN0o6Q6KpLPjADHsCtQi4sF0jrgLgLelumeBK9L0raUYfgWcJ+koYEzTz9ZslPl6UGZD1+i6QHXPlKafp8FnTdKewKGkhCJpA+CbQGdELJZ0ErDBMGJ4Ll7Yybwqhoj4kKQ3AvsBt0manK73ZZYVj6DMhm4+cLikMZK2okg0NzUzo6SXUySjw0qb7OrJ6CFJY4FDSrM8DmzcYFE3Am+XNE7SGOBIipFcf+t+ZUTcGBEnAg+x+rWNzLLhEZTZ0F0GvIliH1IAx0XEXyW9pol5pwFbApel4yeWRMS+ks4G7gAWUVx3qO484CxJT6V1AhARSyWdAFxHMZqaFxFzB1j3lyVNSu2vTfGbZceHmZuZWZa8ic/MzLLkBGVmZllygjIzsyw5QZmZWZacoMzMLEtOUGZmliUnKDMzy9L/AYmPcOgiykSiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 2.7252 sum(2^k)/N: 3.792 Log-Normal Mean: 3.5806055919682502 2^(mean(N)): 2.9805942628205457\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 3.1808 sum(2^k)/N: 5.0728 Log-Normal Mean: 4.6631595643262065 2^(mean(N)): 3.5465099618299027\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 3.9524 sum(2^k)/N: 7.9608 Log-Normal Mean: 7.274131479538532 2^(mean(N)): 4.718734498696641\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 5.2084 sum(2^k)/N: 12.5072 Log-Normal Mean: 11.725262120455723 2^(mean(N)): 6.474640094455863\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 7.0176 sum(2^k)/N: 21.3504 Log-Normal Mean: 20.716996757020553 2^(mean(N)): 9.622421523109447\n"
     ]
    },
    {
     "data": {
      "image/png": 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V4EbgfcDwNOUHsBuwND1eAowCSOu3B1bVN2QzM6u3RiSop4CDJG2djiWNBx4B7gGOT3UmADenxzPTMmn93dGIeUkzM6uruieoiJhLdrLDA8CCFMNU4CvAWZIWASOAK9ImVwAjUvlZwJR6x2xmZvVX92NQABFxPnB+t+IngQNK1H0JOKEecZmZWXH4ShJmZlZITlBmZlZITlBmZlZITlBmZlZITlBmZlZITlBmZlZITlBmZlZITlBmZlZIFSUoSd+WtJ2kzSXNkrRS0idrHZyZmTWvSkdQh0XE88DRZBdv/V/Al2sWlZmZNb1KE9Tm6feRwLUR4auJm5lZTVV6Lb5bJD1GdoPBz0vaGXipdmGZmVmzq2gEFRFTgPcCrekeTi+S3XTQzMysJjbmaubvAkbnbioIcFWV4zEzMwMqTFCSrgbeBswHXkvFgROUmZnVSKUjqFZgD9/J1szM6qXSs/gWAm+sZSBmZmZ5lY6gdgIekXQf8HJnYUQcU5OozMys6VWaoL5eyyDMzMy6qyhBRcS9klqA/VPRfRGxonZhmZlZs6v0WnwfB+4DTgA+DsyVdHwtAzMzs+ZW6RTfvwD7d46a0pUk7gJm1CowMzNrbpWexbdZtym95zZiWzMzs41W6QjqF5J+CVyblk8Ebq9NSNZp9JTb6tre2WPXMzHX5uKLj6pr+2ZmeZWeJPFlSR8DDgYETI2Im2oamZmZNbWKr8UXETcAN9QwFjMzs9f1maAk/SYiDpH0Atm1915fBUREbFfT6MzMrGn1maAi4pD0e9v6hGNmZpap9HtQV1dSVilJwyXNkPSYpEclvVfSjpLulPR4+r1DqitJP5S0SNJDkvbtb7tmZjZwVHqq+J75hXRPqP02od0fAL+IiHcCewOPAlOAWRExBpiVlgGOAMakn8nAjzehXTMzGyD6TFCSzk3Hn94t6fn08wKwHLi5Pw1K2g54P3AFQES8EhFryO7QOy1VmwYclx4fC1wVmTnAcEm79qdtMzMbOFTJLZ4kfSsizq1Kg9I+wFTgEbLR0zzgTOCZiBieq7c6InaQdCtwcUT8JpXPAr4SEfd32+9kshEWLS0t+02fPr1sLB0dHQwbNqzkugXPrO3HsxvYWraC5es2LI8duX3jgimIvl4jzcj90ZX7o6dK+mTcuHHzIqK13L4q/R7UuemY0Bhgy1z57Eq2L9HmvsAZETFX0g/YMJ1XikqFVCLGqWSJj9bW1mhraysbSHt7O73Vm1jnL8kWwdlj1/PdBRteEotPbmtcMAXR12ukGbk/unJ/9FTNPqn0JInPALOBXwIXpN9f72ebS4AlETE3Lc8gS1jLO6fu0u8VufqjctvvBiztZ9tmZjZAVHqSxJlkt9r4S0SMA94D/LU/DUbEs8DTkt6RisaTTffNBCaksglsOMY1Ezglnc13ELA2Ipb1p20zMxs4Kr2SxEsR8ZIkJL0hIh7LJZj+OAO4RtIWwJPAqWTJ8npJk4CnyG7tAdk1/44EFgF/S3XNzGyQqzRBLZE0HPg5cKek1WzCNFtEzAdKHSAbX6JuAKf1ty0zMxuYKj1J4iPp4dcl3QNsD/yiZlGZmVnTK3ctvh1LFC9Iv4cBq6oekZmZGeVHUPPITunu7VTvt1Y9IjMzM8pfLHb3egViZmaWV9ExKEnvL1Xezy/qmpmZlVXpWXxfzj3eEjiAbPrv0KpHZGZmRuVn8X04vyxpFPDtmkRkZmZG5VeS6G4JsFc1AzEzM8ur9BjUf7DhAq2bAfsAD9YqKDMzs0qPQeVvbbEeuDYifluDeMzMzIDKj0FNK1/LzMyseiq93cbRkv4gaVXnXXUlPV/r4MzMrHlVOsX3feCjwIKo5Ba8ZmZmm6jSs/ieBhY6OZmZWb1UOoI6B7hd0r3Ay52FEfG9mkRlZmZNr9IEdRHQQXYViS1qF46ZmVmm0gS1Y0QcVtNIzMzMcio9BnWXJCcoMzOrm0oT1GnALySt82nmZmZWD5V+UXfbWgdiZmaWV+6W7++MiMck7VtqfUQ8UJuwzMys2ZUbQZ0FTAa+myvLfxfK94MyM7OaKHcM6nJJb4yIcRExDriS7HTzhcDxtQ7OzMyaV7kE9RPgFXj9tu/fAqYBa4GptQ3NzMyaWbkpviERsSo9PhGYGhE3ADdIml/b0MzMrJmVG0ENkdSZxMYDd+fWVfolXzMzs41WLslcC9wraSWwDvg1gKS3k03zmZmZ1USfCSoiLpI0C9gV+FXuauabAWfUOjgzM2teZafpImJOibI/1SYcMzOzTKWXOqo6SUPSXXpvTcu7S5or6XFJ10naIpW/IS0vSutHNypmMzOrn4YlKOBM4NHc8iXApRExBlgNTErlk4DVEfF24NJUz8zMBrmGJChJuwFHAZenZZFdlWJGqjINOC49PjYtk9aPT/XNzGwQUyPu4i5pBtmXfrcFvgRMBOakURKSRgF3RMRekhYCh0fEkrTuCeDAiFjZbZ+TyS7LREtLy37Tp08vG0dHRwfDhg0ruW7BM813kmLLVrB83YblsSO3b1wwBdHXa6QZuT+6cn/0VEmfjBs3bl5EtJbbV92/yyTpaGBFRMyT1NZZXKJqVLBuQ0HEVNLVLVpbW6Otra17lR7a29vprd7EKbeV3X6wOXvser67YMNLYvHJbY0LpiD6eo00I/dHV+6PnqrZJ434su3BwDGSjiS7hfx2wPeB4ZKGRsR6YDdgaaq/BBgFLElfGt4eWNVzt1ZtowuQpBdffFSjQzCzBqn7MaiIODcidouI0cAngLsj4mTgHjZcgHYCcHN6PDMtk9bfHY2YlzQzs7pq5Fl83X0FOEvSImAEcEUqvwIYkcrPAqY0KD4zM6ujhl5PLyLagfb0+EnggBJ1XgJOqGtgZmbWcEUaQZmZmb3OCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzArJCcrMzAqp7glK0ihJ90h6VNLDks5M5TtKulPS4+n3Dqlckn4oaZGkhyTtW++Yzcys/hoxgloPnB0R7wIOAk6TtAcwBZgVEWOAWWkZ4AhgTPqZDPy4/iGbmVm91T1BRcSyiHggPX4BeBQYCRwLTEvVpgHHpcfHAldFZg4wXNKudQ7bzMzqTBHRuMal0cBsYC/gqYgYnlu3OiJ2kHQrcHFE/CaVzwK+EhH3d9vXZLIRFi0tLftNnz69bPsdHR0MGzas5LoFz6ztz1Ma0Fq2guXrGh1FV2NHbt/Q9vt6jTQj90dX7o+eKumTcePGzYuI1nL7Glq1qDaSpGHADcAXIuJ5Sb1WLVHWI6tGxFRgKkBra2u0tbWVjaG9vZ3e6k2cclvZ7Qebs8eu57sLGvaSKGnxyW0Nbb+v10gzcn905f7oqZp90pCz+CRtTpacromIG1Px8s6pu/R7RSpfAozKbb4bsLResZqZWWPU/eOysqHSFcCjEfG93KqZwATg4vT75lz56ZKmAwcCayNiWR1DtgYa3eCR7Nlj19PW0AjMmlcj5nMOBj4FLJA0P5V9lSwxXS9pEvAUcEJadztwJLAI+Btwan3DNTOzRqh7gkonO/R2wGl8ifoBnFbToMzMrHB8JQkzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyskJygzMyukut/y3WygGT3ltkaHwOKLj2p0CGZ15xGUmZkVkhOUmZkVkhOUmZkVkhOUmZkVkk+SMBsAfKKGNSOPoMzMrJCcoMzMrJCcoMzMrJCcoMzMrJB8koSZVWT0lNs4e+x6JjbohA2fpNF8BkyCknQ48ANgCHB5RFzc4JDMrI58JmPzGRBTfJKGAJcBRwB7ACdJ2qOxUZmZWS0NlBHUAcCiiHgSQNJ04FjgkYZGZWZNpfsorpFTno1Ur5GkIqIuDW0KSccDh0fEZ9Lyp4ADI+L0XJ3JwOS0+A7gjxXseidgZZXDHcjcHz25T7pyf3Tl/uipkj55S0TsXG5HA2UEpRJlXTJrREwFpm7UTqX7I6J1UwIbTNwfPblPunJ/dOX+6KmafTIgjkEBS4BRueXdgKUNisXMzOpgoCSo3wNjJO0uaQvgE8DMBsdkZmY1NCCm+CJivaTTgV+SnWb+04h4uAq73qgpwSbg/ujJfdKV+6Mr90dPVeuTAXGShJmZNZ+BMsVnZmZNxgnKzMwKqSkTlKTDJf1R0iJJUxodTyNI+qmkFZIW5sp2lHSnpMfT7x0aGWM9SRol6R5Jj0p6WNKZqbwp+0TSlpLuk/Rg6o8LUvnukuam/rgunbTUNCQNkfQHSbem5Wbvj8WSFkiaL+n+VFa190zTJShfNul1VwKHdyubAsyKiDHArLTcLNYDZ0fEu4CDgNPS66JZ++Rl4NCI2BvYBzhc0kHAJcClqT9WA5MaGGMjnAk8mltu9v4AGBcR++S++1S190zTJShyl02KiFeAzssmNZWImA2s6lZ8LDAtPZ4GHFfXoBooIpZFxAPp8Qtk/4RG0qR9EpmOtLh5+gngUGBGKm+a/gCQtBtwFHB5WhZN3B99qNp7phkT1Ejg6dzyklRm0BIRyyD7hw3s0uB4GkLSaOA9wFyauE/SdNZ8YAVwJ/AEsCYi1qcqzfbe+T5wDvD3tDyC5u4PyD60/ErSvHS5Oajie2ZAfA+qyspeNsmal6RhwA3AFyLi+exDcnOKiNeAfSQNB24C3lWqWn2jagxJRwMrImKepLbO4hJVm6I/cg6OiKWSdgHulPRYNXfejCMoXzapd8sl7QqQfq9ocDx1JWlzsuR0TUTcmIqbuk8AImIN0E52bG64pM4Pts303jkYOEbSYrLDAoeSjaiatT8AiIil6fcKsg8xB1DF90wzJihfNql3M4EJ6fEE4OYGxlJX6XjCFcCjEfG93Kqm7BNJO6eRE5K2Aj5IdlzuHuD4VK1p+iMizo2I3SJiNNn/jLsj4mSatD8AJG0jadvOx8BhwEKq+J5pyitJSDqS7NNP52WTLmpwSHUn6VqgjezS+MuB84GfA9cDbwaeAk6IiO4nUgxKkg4Bfg0sYMMxhq+SHYdquj6R9G6yA9xDyD7IXh8RF0p6K9kIYkfgD8AnI+LlxkVaf2mK70sRcXQz90d67jelxaHA/0TERZJGUKX3TFMmKDMzK75mnOIzM7MBwAnKzMwKyQnKzMwKyQnKzMwKyQnKzMwKyQnKbBNI6ihfq9dtL+/PhYolTZT0pk3dj1nR+TRzs00gqSMihtW5zXay7+HcX892zerNIyizKlDmO5IWpvvjnJjK2yS1S5oh6TFJ16SrVpDKWyUdk+6nMz/dp+zPaf15kn6f9jk1tXE80Apck+pv1bmftM1Jqf2Fki7Jxdch6aJ0f6c5klpS+Qmp7oOSZte738z64gRlVh0fJbtv0t5klwX6Tuf1yMiujP4FsvuPvZXsum6vi4iZ6X46+wAPAv+eVv0oIvaPiL2ArYCjI2IGcD9wctpmXed+0rTfJWTXidsH2F9S560OtgHmpPs7zQY+m8rPAz6Uyo+pUl+YVYUTlFl1HAJcGxGvRcRy4F5g/7TuvohYEhF/B+YDo0vtQNI5wLqIuCwVjUt3a11AlnT2LBPD/kB7RPw13QLiGuD9ad0rwK3p8bxcDL8FrpT0WbLLGpkVRjPebsOsFvq6L0f+2myvUeJ9J2k8cAIpoUjaEvhPoDUinpb0dWDLTYjh1dhwwPn1GCLic5IOJLsR33xJ+0TEc2XaMasLj6DMqmM2cGK6yd/OZInmvko2lPQWsmT08dyUXWcyWpnuUXV8bpMXgG1L7Gou8AFJO0kaApxENpLrq+23RcTciDgPWEnXW9GYNZRHUGbVcRPwXrJjSAGcExHPSnpnBdtOJLs7603p/ImlEXGkpP8mu7r6YrLbxHS6EviJpHWpTSC7e6m3J4JNAAAAT0lEQVSkc8luASHg9ogod6uD70gak+rPSvGbFYJPMzczs0LyFJ+ZmRWSE5SZmRWSE5SZmRWSE5SZmRWSE5SZmRWSE5SZmRWSE5SZmRXS/wdsl59zD54H6wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 9.0996 sum(2^k)/N: 30.3968 Log-Normal Mean: 31.034579904148533 2^(mean(N)): 12.654687708081324\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 12.6356 sum(2^k)/N: 59.1208 Log-Normal Mean: 61.70760896564623 2^(mean(N)): 19.5568213890703\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 16.65 sum(2^k)/N: 85.036 Log-Normal Mean: 95.98605757478663 2^(mean(N)): 28.482423464079883\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 22.718 sum(2^k)/N: 141.0544 Log-Normal Mean: 163.39715616766293 2^(mean(N)): 39.83597553222944\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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G38tY2XZlN5b2kzJqyv2gIuJBSRXgkIj4cip+TNL3gQ+n173ALrnZJgMr6yxrLllio6urK7q7u4sKu61VKhXGymc7a4zcD6pnaj+nL21sl10+s7vYYAwYW/tJGRU5im/H1HJC0jjg1cCt1fNKkgQcDtyUZrkMeFsazbcvsDYiVhUVn5mZlVuRLaidgHmSNiVLhBdGxOWSfiNpR7IuvcXAe1L9K4DpwDLgH8DbC4zNzMxKrrAEFRE3Ai+tU37gAPUDeG9R8ZiZ2cbFV5IwM7NScoIyM7NScoIyM7NScoIyM7NScoIyM7NScoIyM7NSasqVJMysuTpbdPWM5acd1pL12tjkFpSZmZWSE5SZmZWSE5SZmZWSE5SZmZWSE5SZmZWSE5SZmZWSE5SZmZWSE5SZmZWSE5SZmZVSkbd831LSdZKWSLpZ0qdT+a6SrpX0V0kXSNo8lW+RXi9L0zuLis3MzMqvyBbUY8CBEbEnMA04RNK+wBeAMyJiCrAGOD7VPx5YExG7AWekemZm1qYKS1CR6UsvN0uPAA4ELkrl84DD0/MZ6TVp+kGSVFR8ZmZWboVeLFbSpsAiYDfgG8DfgAcjoj9V6QUmpeeTgBUAEdEvaS2wPXBfzTJnA7MBOjo6qFQqRb6FttXX1zdmPtueqf1DV9oIdIwr/3sZK/8zjRpL+0kZFZqgIuIJYJqkicAlwIvqVUt/67WWYr2CiLnAXICurq7o7u4enWDtGSqVCmPls53Voit7j7aeqf2cvrTcNyBYPrO71SE01VjaT8qoKaP4IuJBoALsC0yUVN3LJgMr0/NeYBeANH0b4IFmxGdmZuVT5Ci+HVPLCUnjgFcDtwBXA0ekascBl6bnl6XXpOm/iYj1WlBmZtYeiuwv2AmYl85DbQJcGBGXS/ozcL6kzwJ/As5O9c8GfiBpGVnL6ZgCYzMzs5IrLEFFxI3AS+uU3w7sXaf8UeDIouIxM7ONi68kYWZmpeQEZWZmpeQEZWZmpVTuH1XYmNI5Rn6PZGbN4RaUmZmVkhOUmZmVkhOUmZmVkhOUmZmVkhOUmZmVkhOUmZmVUkMJStIXJW0taTNJCyTdJ+ktRQdnZmbtq9EW1Gsi4iHgtWS3xXgB8JHCojIzs7bXaILaLP2dDpwXEb5Pk5mZFarRK0n8TNKtwCPAf0raEXi0uLDMzKzdNdSCioiTgFcAXRHxT+BhYEaRgZmZWXsbzrX4XgR05m7XDjB/lOMxMzMDGh/F9wPgy8D+wF7p0TXEPLtIulrSLZJulvSBVH6KpLslLU6P6bl5Tpa0TNJtkg7e4HdlZmYbvUZbUF3A7hERw1h2P9ATETdImgAsknRVmnZGRHw5X1nS7mS3ed8D2Bn4taQXRMQTw1inmZmNEY2O4rsJeM5wFhwRqyLihvR8HXALMGmQWWYA50fEYxFxB7CMOreGNzOz9tBoC2oH4M+SrgMeqxZGxOsbmVlSJ/BS4FpgP+AESW8DridrZa0hS17X5GbrpU5CkzQbmA3Q0dFBpVJp8C3YcPT19Y36Z9sztX9Ul9duOsaV/zNst/2xiP3EntZogjplQ1cgaTxwMfDBiHhI0reAU4FIf08H3gGozuzrdSlGxFxgLkBXV1d0d3dvaGg2iEqlwmh/trN8w8IR6Znaz+lLy32P0eUzu1sdQlMVsZ/Y0xr6b4+I30rqIBscAXBdRNw71HySNiNLTj+MiJ+kZa3OTf8ucHl62Qvskpt9MrCykfjMzGzsaXQU31HAdcCRwFHAtZKOGGIeAWcDt0TEV3LlO+WqvYHs/BbAZcAxkraQtCswJa3TzMzaUKP9BR8H9qq2mtKVJH4NXDTIPPsBbwWWSlqcyj4GHCtpGln33XLg3QARcbOkC4E/k40AfK9H8JmZta9GE9QmNV169zNE6ysifk/980pXDDLPHGBOgzGZWcl0tug84/LTDmvJeq1YjSaoX0r6FXBeen00gyQaMzOzkWp0kMRHJL2JrNtOwNyIuKTQyMzMrK01PGY1Ii4mG5FnZmZWuEETlKTfR8T+ktbxzN8kCYiI2LrQ6MzMrG0NmqAiYv/0d0JzwjEzM8sM52rmQ5aZmZmNlkYvFrtH/kW6J9TLRz8cMzOzzKAJKt2faR3wEkkPpcc6YDVwaVMiNDOztjTUj20/n84/fSkitk6PCRGxfUSc3KQYzcysDTX6O6iTJW1Ldn28LXPlC4sKzMzM2ltDCUrSO4EPkF1hfDGwL/C/wIHFhWZmZu2s0UESHyC71cadEXEA2c0H/15YVGZm1vYaTVCPRsSjAJK2iIhbgRcWF5aZmbW7Ri911CtpIvBT4CpJa/DNBM3MrECNDpJ4Q3p6iqSrgW2AXxYWlZmZtb2hrsW3XZ3ipenveOCBUY/IzMyMoVtQi8guElvvxoMBPH+gGSXtAswHngM8SXaLjjNT0rsA6CS7o+5REbEm3SL+TGA68A9gVkTcMKx3Y2ZmY8ZQF4vddQTL7gd6IuIGSROARZKuAmYBCyLiNEknAScBHwUOJfud1RRgH+Bb6a+ZmbWhRn8H9ap65YP9UDciVgGr0vN1km4BJgEzgO5UbR5QIUtQM4D5ERHANZImStopLcfMzNqMsnwwRCXpZ7mXWwJ7A4sioqEf6krqBBYCLwbuioiJuWlrImJbSZcDp0XE71P5AuCjEXF9zbJmA7MBOjo6Xn7++ec3EoLlLL177ZB1OsbB6keaEIw1zNtkYFMnbdOS9fb19TF+/PiWrHtjdsABByyKiK6h6jU6iu91+dfp/NIXG5lX0niyO/F+MCIeyk411a9ab9V1YpkLzAXo6uqK7u7uRsKwnFkn/XzIOj1T+zl9acM3XLYm8DYZ2PKZ3S1Zb6VSwceg4jT6Q91avWStoUFJ2owsOf0wIn6SildL2ilN3wm4N7fMXXKzT8a/tTIza1uNnoP6Gk+3ZjYBpgFLhphHwNnALRHxldyky4DjgNPS30tz5SdIOp9scMRan38yM2tfjfYX5M8D9QPnRcQfhphnP+CtwFJJi1PZx8gS04WSjgfuAo5M064gG2K+jGyY+dsbjM3MzMagRs9BzRvugtNgh4FOOB1Up34A7x3ueszMbGxq6ByUpNdK+pOkB6p31ZX0UNHBmZlZ+2q0i++rwBuBpdHIuHQzM7MRanQU3wrgJicnMzNrlkZbUCcCV0j6LfBYtbBmdJ6ZmdmoaTRBzQH6yK4isXlx4ZiZmWUaTVDbRcRrCo3EzMwsp9EE9WtJr4mIKwuNpo10NnC5ITOzdtboIIn3Ar+U9IiHmZuZWTM0+kPdCUUHYmZmljfULd//LSJulfSyetN9x1szMyvKUC2oD5Hde+n0XFn+t1AN3Q/KzMxsuIZKUN+T9JyIOABA0nHAm4DlwCnFhtYcHqxgZlZOQw2S+DbwODx12/fPk92mfS3ppoFmZmZFGKoFtWlEPJCeHw3MjYiLgYtzt9AwMzMbdUO1oDaVVE1iBwG/yU3zvafNzKwwQyWZ84DfSroPeAT4HYCk3ci6+czMzAoxaAsqIuYAPcC5wP65q5lvArxvsHklnSPpXkk35cpOkXS3pMXpMT037WRJyyTdJungDX1DZmY2NgzZTRcR19Qp+0sDyz4X+Dowv6b8jIj4cr5A0u7AMcAewM5kl1Z6QUQ80cB6zMxsDGr0UkfDFhELgQeGrJiZAZwfEY9FxB3AMmDvomIzM7Pya8VAhxMkvQ24HuiJiDXAJCDfUutNZeuRNJvsx8N0dHRQqVRGFEzP1P4RzT9WdYzzZ1M23iYDG+lxYEP19fW1bN3toNkJ6lvAqWRXoziV7AoV7wBUp27du/dGxFzSb7C6urqiu7t7RAHN8g916+qZ2s/pSz1Qs0y8TQa2fGZ3S9ZbqVQY6THIBlZYF189EbE6Ip6IiCeB7/J0N14vsEuu6mRgZTNjMzOzcmlqgpK0U+7lG4DqCL/LgGMkbSFpV2AKcF0zYzMzs3IprL9A0nlAN7CDpF7gU0C3pGlk3XfLgXcDRMTNki4E/gz0A+/1CD4zs/ZWWIKKiGPrFJ89SP05wJyi4jEzs41LU7v4zMzMGuUEZWZmpeQEZWZmpeQEZWZmpeQEZWZmpeQEZWZmpeQEZWZmpeQEZWZmpeQEZWZmpeQEZWZmpeRr95vZRq+zRbfN6ZnaT3dL1twe3IIyM7NScoIyM7NScoIyM7NScoIyM7NScoIyM7NSKixBSTpH0r2SbsqVbSfpKkl/TX+3TeWSdJakZZJulPSyouIyM7ONQ5EtqHOBQ2rKTgIWRMQUYEF6DXAoMCU9ZgPfKjAuMzPbCBSWoCJiIfBATfEMYF56Pg84PFc+PzLXABMl7VRUbGZmVn7N/qFuR0SsAoiIVZKenconASty9XpT2araBUiaTdbKoqOjg0qlMqKAeqb2j2j+sapjnD+bsvE2KZ+OcYz4GGQDK8uVJFSnLOpVjIi5wFyArq6u6O7uHtGKZ7XoF+hl1zO1n9OXluXfw8DbpIx6pvZz1AiPQTawZo/iW13tukt/703lvcAuuXqTgZVNjs3MzEqk2QnqMuC49Pw44NJc+dvSaL59gbXVrkAzM2tPhfUXSDoP6AZ2kNQLfAo4DbhQ0vHAXcCRqfoVwHRgGfAP4O1FxWVmZhuHwhJURBw7wKSD6tQN4L1FxWJmZhsfX0nCzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKyQnKzMxKqbAbFg5G0nJgHfAE0B8RXZK2Ay4AOoHlwFERsaYV8ZmZWeu1sgV1QERMi4iu9PokYEFETAEWpNdmZtamytTFNwOYl57PAw5vYSxmZtZiiojmr1S6A1gDBPCdiJgr6cGImJirsyYitq0z72xgNkBHR8fLzz///BHFsvTutSOaf6zqGAerH2l1FJbnbVI+HePg2dtt0+owNjoHHHDAolzv2YBacg4K2C8iVkp6NnCVpFsbnTEi5gJzAbq6uqK7u3tEgcw66ecjmn+s6pnaz+lLW/XvYfV4m5RPz9R+jhrhMcgG1pIuvohYmf7eC1wC7A2slrQTQPp7bytiMzOzcmh6gpK0laQJ1efAa4CbgMuA41K144BLmx2bmZmVRyv6CzqASyRV1/+jiPilpD8CF0o6HrgLOLIFsZmZWUk0PUFFxO3AnnXK7wcOanY8ZmZWTmUaZm5mZvYUDwkyMxuBzhaNBF5+2mEtWW8zuQVlZmal5ARlZmal5ARlZmal5ARlZmal5ARlZmal5ARlZmal5ARlZmal5ARlZmal5ARlZmal5ARlZmal5EsdmZlthNrhEktuQZmZWSk5QZmZWSk5QZmZWSmVLkFJOkTSbZKWSTqp1fGYmVlrlCpBSdoU+AZwKLA7cKyk3VsblZmZtUKpEhSwN7AsIm6PiMeB84EZLY7JzMxaQBHR6hieIukI4JCIeGd6/VZgn4g4IVdnNjA7vXwhcNsIV7sNsHaEy9iQ5TRaf6h6g00faFq98tqyHYD7GoivCKOxTTZkGUVvk5FsD2jdNmnVPtLoPK3aR6D9tslo7SNTImKbIZcSEaV5AEcC38u9fivwtYLXObcVy2m0/lD1Bps+0LR65bVlwPUt/D8Y8TbZkGUUvU1Gsj1auU1atY80Ok+r9pF23CbNOG7lH2Xr4usFdsm9ngysLHidP2vRchqtP1S9waYPNK1e+Wh9DqNhNGLZkGUUvU3aeXts6HIamcf7SPOW04zj1lPK1sX3LOAvwEHA3cAfgTdHxM0tDawNSbo+IrpaHYc9zdukfLxNilWqSx1FRL+kE4BfAZsC5zg5tczcVgdg6/E2KR9vkwKVqgVlZmZWVbZzUGZmZoATlJmZlZQTlJmZlZITlJmZlZITlDVE0vMlnS3polbHYhlJh0v6rqRLJb2m1fG0O0kvkvRtSRdJ+r+tjmcscIJqY5LOkXSvpJtqyte7onxk10c8vjWRto9hbpOfRsS7gFnA0S0Id8wb5va4JSLeAxwF+LdRo8AJqr2dCxySL/AV5VvuXIa/TT6RptvoO5dhbA9Jrwd+DyxobphjkxNUG4uIhcADNcW+onwLDWebKPMF4BfLUp3oAAADVUlEQVQRcUOzY20Hw91HIuKyiPh3YGZzIx2bnKCs1iRgRe51LzBJ0vaSvg28VNLJrQmtbdXdJsD7gFcDR0h6TysCa1MD7SPdks6S9B3gitaENraU6lJHVgqqUxYRcT/gg2BrDLRNzgLOanYwNuD2qACV5oYytrkFZbVacUV5G5y3Sbl4ezSJE5TV+iMwRdKukjYHjgEua3FM7c7bpFy8PZrECaqNSToP+F/ghZJ6JR0fEf1A9YrytwAX+oryzeNtUi7eHq3lq5mbmVkpuQVlZmal5ARlZmal5ARlZmal5ARlZmal5ARlZmal5ARlZmal5ARlNkyS+kYw7/c25OrwkmZJ2nmkyzHbmPh3UGbDJKkvIsY3eZ0V4MMRcX0z12vWSm5BmW2gdLuLL0m6SdJSSUen8m5JlXRn1Vsl/VCS0rSKpC5Jr5e0OD1uk3RHmv5JSX9My5yb1nEE2Q3wfpjqj6suJ81zbFr/Ten2G9X4+iTNkbRE0jWSOlL5kanuEkkLm/25mTXKCcpsw70RmAbsSXbbiy9J2ilNeynwQbIb2j0f2C8/Y7pv0LSImAYsAb6cJn09IvaKiBcD44DXRsRFwPXAzDTPI9XlpG6/LwAHplj2knR4mrwVcE1E7AksBN6Vyj8JHJzKXz9Kn4XZqHOCMttw+wPnRcQTEbEa+C2wV5p2XUT0RsSTwGKgs94CJJ0IPBIR1TviHiDpWklLyZLOHkPEsBdQiYi/p2vE/RB4VZr2OHB5er4oF8MfgHMlvQvYtOF3a9Zkvh+U2Yard1+gqsdyz5+gzr4m6SDgSFJCkbQl8E2gKyJWSDoF2HIEMfwznj7J/FQMEfEeSfsAhwGLJU1L9/syKxW3oMw23ELgaEmbStqRLNFc18iMkp5HloyOynXZVZPRfZLGA0fkZlkHTKizqGuB/5C0g6RNgWPJWnKDrftfI+LaiPgkcB/PvLeRWWm4BWW24S4BXkF2DimAEyPiHkn/1sC8s4DtgUvS+ImVETFd0neBpcBysvsOVZ0LfFvSI2mdAETEKkknA1eTtaauiIhLh1j3lyRNSfUXpPjNSsfDzM3MrJTcxWdmZqXkBGVmZqXkBGVmZqXkBGVmZqXkBGVmZqXkBGVmZqXkBGVmZqX0/wECyyEh9p1tBQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 31.95 sum(2^k)/N: 226.7312 Log-Normal Mean: 297.6573439341595 2^(mean(N)): 62.80467290671066\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wdtn0rlaH0FRjaTvJUVOO4ouIB4Fu4OCIWJmG8dYB3wb2Tc16gF1Lk+0CrGhGfGZmlp9GHsW3Y+o5IWkc8Erg9sp+JUkCDgduSZNcCbw1Hc23P7AmIlbWmLWZmbWBRo4X7ATMTfuhNgIuiYirJP1S0o4UQ3qLgHen9lcD04ClwD+BtzUwNjMzy1zDElRE3AzsXaP8wH7aB3BCo+IxM7MNi88kYWZmWXKCMjOzLDlBmZlZlpygzMwsS05QZmaWJScoMzPLkhOUmZllyQnKzMyy5ARlZmZZcoIyM7MsOUGZmVmWnKDMzCxLTlBmZpYlJygzM8uSE5SZmWXJCcrMzLLkBGVmZllqWIKStLmkGyUtlnSrpI+n8t0k3SDpL5IulvS0VL5Zer401U9sVGxmZpa/Rvag1gEHRsRewBTgYEn7A58GzomIScBq4PjU/nhgdUTsDpyT2pmZWZtqWIKKQm96umm6BXAgcGkqnwscnh4flp6T6g+SpEbFZ2ZmedukkTOXtDGwENgd+ArwV+DBiOhLTXqACenxBGA5QET0SVoDbA/cVzXPmcBMgI6ODrq7uxv5EtpWb2/vmHlvZ03uG7zRBqBjXP6vZax8Zuo1lraTHDU0QUXE48AUSdsAlwMvrNUs3dfqLcVTCiLmAHMAOjs7o6ura3SCtfV0d3czVt7bGbN/0uoQRsWsyX2cvaShm+yILZve1eoQmmosbSc5aspRfBHxINAN7A9sI6myle0CrEiPe4BdAVL91sADzYjPzMzy08ij+HZMPSckjQNeCdwGXAcckZodB1yRHl+ZnpPqfxkRT+lBmZlZe2jkeMFOwNy0H2oj4JKIuErSn4B5kj4J/BE4L7U/D/iOpKUUPadjGhibmZllrmEJKiJuBvauUX4nsG+N8keBIxsVj5mZbVh8JgkzM8tS3ocEmdkGZWKLjphcdtahLVmuNZZ7UGZmliUnKDMzy5ITlJmZZckJyszMsuQEZWZmWXKCMjOzLDlBmZlZlpygzMwsS05QZmaWJScoMzPLkhOUmZllyQnKzMyy5ARlZmZZcoIyM7Ms1ZWgJH1G0laSNpU0X9J9kt7c6ODMzKx91duDelVEPAS8BugBngecPNAEknaVdJ2k2yTdKumkVH66pHskLUq3aaVpTpG0VNIdkl49zNdkZmZjQL0XLNw03U8DLoqIByQNNk0fMCsi/iBpS2ChpGtT3TkR8blyY0l7AMcAewI7A7+Q9LyIeLzOGM3MbAyptwf1Y0m3A53AfEk7Ao8ONEFErIyIP6THa4HbgAkDTHIYMC8i1kXEXcBSYN864zMzszFGEVFfQ2lb4KGIeFzS04GtIuLvdU47EVgAvAh4PzADeAi4iaKXtVrSl4HrI+K7aZrzgJ9GxKVV85oJzATo6Oh46bx58+qK34amt7eX8ePHtzqMUbHknjWtDmFUdIyDVY+0Ooo8TZ6wdUuWO5a2k2aaOnXqwojoHKxdvUN8AC8EJkoqT3PhYBNJGg9cBrwvIh6S9DXgDCDS/dnA24FaY4ZPyZ4RMQeYA9DZ2RldXV1DeAlWr+7ubsbKeztj9k9aHcKomDW5j7OXDGWTbR/Lpne1ZLljaTvJUV2fdknfAZ4LLAIq+4SCQRKUpE0pktP3IuKHABGxqlT/TeCq9LQH2LU0+S7AinriMzOzsafen2OdwB5R73ggoOIoivOA2yLi86XynSJiZXr6euCW9PhK4PuSPk9xkMQk4MZ6l2dmZmNLvQnqFuCZwMrBGpYcALwFWCJpUSr7MHCspCkUPbBlwLsAIuJWSZcAf6I4AvAEH8FnZta+6k1QOwB/knQjsK5SGBGv62+CiPgNtfcrXT3ANGcCZ9YZk5mZjWH1JqjTGxmEmZlZtboSVET8SlIHsE8qujEi7m1cWGZm1u7qPRffURQHLBwJHAXcIOmIRgZmZmbtrd4hvo8A+1R6TelMEr8ALh1wKjMzs2Gq91RHG1UN6d0/hGnNzMyGrN4e1M8k/Ry4KD0/mgGOxjMzMxupeg+SOFnSGyn+2yRgTkRc3tDIzMysrdV9Yq+IuIzitEVmZmYNN2CCkvSbiHiZpLWsf+JWARERWzU0OjMza1sDJqiIeFm637I54ZiZmRXq/R/Ud+opMzMzGy31Hiq+Z/lJuibUS0c/HDMzs8KACUrSKWn/04slPZRua4FVwBVNidDMzNrSgAkqIj6V9j99NiK2SrctI2L7iDilSTGamVkbqvd/UKdI2pbiIoKbl8oXNCowMzNrb/Ve8v0dwEkUl2FfBOwP/A44sHGh2VgzcfZPWh2CmW1A6j1I4iSKS23cHRFTgb2BfzQsKjMza3v1JqhHI+JRAEmbRcTtwPMHmkDSrpKuk3SbpFslnZTKt5N0raS/pPttU7kknStpqaSbJb1kJC/MzMw2bPUmqB5J2wA/Aq6VdAWwYpBp+oBZEfFCiiHBEyTtAcwG5kfEJGB+eg5wCMU+rknATOBrQ3olZmY2ptR7kMTr08PTJV0HbA38bJBpVgIr0+O1km4DJgCHAV2p2VygG/hQKr8wIgK4XtI2knZK8zEzszYz2Ln4tqtRvCTdjwceqGchkiZS7Le6AeioJJ2IWCnpGanZBGB5abKeVLZegpI0k6KHRUdHB93d3fWEYEPU29s76u/trMl9ozq/dtMxzu9hf1r1PdCI7cSeNFgPaiHFSWJVoy6A5wy2AEnjKc6C/r6IeEiqNauiaT/LWL8gYg4wB6CzszO6uroGC8GGobu7m9F+b2f4KL4RmTW5j7OX1H0BgraybHpXS5bbiO3EnjTYyWJ3G8nMJW1KkZy+FxE/TMWrKkN3knYCKlfq7QF2LU2+C4Pv5zIzszGq3v9BvaJW+UB/1FXRVToPuC0iPl+quhI4Djgr3V9RKj9R0jxgP2CN9z+ZmbWvescLTi493hzYl2L4b6A/6h4AvAVYImlRKvswRWK6RNLxwN+AI1Pd1cA0YCnwT+BtdcZmZmZjUL1H8b22/FzSrsBnBpnmN9TerwRwUI32AZxQTzxmZjb21fs/qGo9wItGMxAzM7OyevdBfYknj6jbCJgCLG5UUGZmQ9Gq8zzOmtz3xJ86bfTVuw/qptLjPuCiiPhtA+IxMzMD6t8HNbfRgZiZmZXVtQ9K0msk/VHSA5Wr6kp6qNHBmZlZ+6p3iO8LwBuAJeloOzMzs4aq9yi+5cAtTk5mZtYs9fagPghcLelXwLpKYdUZIszMzEZNvQnqTKCX4iwST2tcOGZmZoV6E9R2EfGqhkZiZmZWUu8+qF9IcoIyM7OmqbcHdQLwQUnrgH9RnGMvImKrhkVmDVPPv+5nTe7z9ZvMrKXq/aPulo0OxMzMrGywS76/ICJul/SSWvUR8YfGhGVmZu1usB7U+4GZwNmlsvJ/oQa6HpSZmdmwDXaQxLckPTMipkbEVOACisPNbwGOaHRwZmbWvgZLUF8HHoMnLvv+KWAusAaY09jQzMysnQ2WoDaOiAfS46OBORFxWUR8DNh9oAklnS/pXkm3lMpOl3SPpEXpNq1Ud4qkpZLukPTq4b4gMzMbGwZNUJIq+6kOAn5Zqhts/9UFwME1ys+JiCnpdjWApD2AY4A90zRflbTxYMGbmdnYNViCugj4laQrgEeAXwNI2p1imK9fEbEAeGCgNiWHAfMiYl1E3AUsBfatc1ozMxuDBuwFRcSZkuYDOwHXlM5mvhHwnmEu80RJb6W4Su+siFgNTACuL7XpSWVPIWkmxZGFdHR00N3dPcww2tesyX2DtukYV187ax6vk/x0jMPfQQ006B91I+L6GmV/HubyvgacQXGo+hkUh6+/neLMFE9ZTD/xzCEdoNHZ2RldXV3DDKV91XOGiFmT+zh7Sb0nGrFm8DrJz6zJfRzl76CGqfdcfKMiIlZFxOMR8W/gmzw5jNcD7FpquguwopmxmZlZXpqaoCTtVHr6eor/UwFcCRwjaTNJuwGTgBubGZuZmeWlYeMFki4CuoAdJPUApwFdkqZQDN8tA94FEBG3SroE+BPQB5wQEY83KjYzM8tfwxJURBxbo/i8AdqfSXFhRDMzs+YO8ZmZmdXLhwS1SD3XZDIza2dtn6CcKMzM8uQhPjMzy5ITlJmZZckJyszMsuQEZWZmWXKCMjOzLDlBmZlZlpygzMwsS05QZmaWJScoMzPLkhOUmZllyQnKzMyy5ARlZmZZcoIyM7MsOUGZmVmWGpagJJ0v6V5Jt5TKtpN0raS/pPttU7kknStpqaSbJb2kUXGZmdmGoZE9qAuAg6vKZgPzI2ISMD89BzgEmJRuM4GvNTAuMzPbADQsQUXEAuCBquLDgLnp8Vzg8FL5hVG4HthG0k6Nis3MzPLX7CvqdkTESoCIWCnpGal8ArC81K4nla2snoGkmRS9LDo6Ouju7h5RQLMm941o+rGqY5zfm9x4neSnYxwj/g6y/uVyyXfVKItaDSNiDjAHoLOzM7q6uka04Bm+5HtNsyb3cfaSXD4eBl4nOZo1uY+jRvgdZP1r9lF8qypDd+n+3lTeA+xaarcLsKLJsZmZWUaanaCuBI5Lj48DriiVvzUdzbc/sKYyFGhmZu2pYeMFki4CuoAdJPUApwFnAZdIOh74G3Bkan41MA1YCvwTeFuj4jIzsw1DwxJURBzbT9VBNdoGcEKjYjEzsw2PzyRhZmZZ8iFBZmYjMLFFRwIvO+vQliy3mdyDMjOzLDlBmZlZlpygzMwsS05QZmaWJScoMzPLkhOUmZllyQnKzMyy5ARlZmZZcoIyM7MsOUGZmVmWnKDMzCxLTlBmZpYlJygzM8uSE5SZmWXJCcrMzLLUkutBSVoGrAUeB/oiolPSdsDFwERgGXBURKxuRXxmZtZ6rexBTY2IKRHRmZ7PBuZHxCRgfnpuZmZtKqchvsOAuenxXODwFsZiZmYtpoho/kKlu4DVQADfiIg5kh6MiG1KbVZHxLY1pp0JzATo6Oh46bx580YUy5J71oxo+rGqYxyseqTVUViZ10l+WrlOJk/YujULHgVTp05dWBo961dL9kEBB0TECknPAK6VdHu9E0bEHGAOQGdnZ3R1dY0okBmzfzKi6ceqWZP7OHtJqz4eVovXSX5auU6WTe9qyXKbqSVDfBGxIt3fC1wO7AuskrQTQLq/txWxmZlZHpqeoCRtIWnLymPgVcAtwJXAcanZccAVzY7NzMzy0Yq+aQdwuaTK8r8fET+T9HvgEknHA38DjmxBbGZmlommJ6iIuBPYq0b5/cBBzY7HzMzylNNh5mZmZk9wgjIzsyw5QZmZWZb8pwozsw3QxBb9h3PZWYc2bVnuQZmZWZacoMzMLEtOUGZmliUnKDMzy5ITlJmZZckJyszMsuQEZWZmWXKCMjOzLDlBmZlZlpygzMwsS05QZmaWJScoMzPLkhOUmZllKbsEJelgSXdIWippdqvjMTOz1sgqQUnaGPgKcAiwB3CspD1aG5WZmbVCVgkK2BdYGhF3RsRjwDzgsBbHZGZmLaCIaHUMT5B0BHBwRLwjPX8LsF9EnFhqMxOYmZ4+H7hjhIvdGlgzwnkMZz71th+s3UD1/dXVKq8u2wG4r474GmE01slw5tHodTKS9QGtWyet2kbqnaZV2wi03zoZrW1kUkRsPehcIiKbG3Ak8K3S87cAX2rwMue0Yj71th+s3UD1/dXVKq8uA25q4edgxOtkOPNo9DoZyfpo5Tpp1TZS7zSt2kbacZ0043urfMttiK8H2LX0fBdgRYOX+eMWzafe9oO1G6i+v7pa5aP1PoyG0YhlOPNo9Dpp5/Ux3PnUM423kebNpxnfW0/IbYhvE+DPwEHAPcDvgTdFxK0tDawNSbopIjpbHYc9yeskP14njbVJqwMoi4g+SScCPwc2Bs53cmqZOa0OwJ7C6yQ/XicNlFUPyszMrCK3fVBmZmaAE5SZmWXKCcrMzLLkBGVmZllygrK6SHqOpPMkXdrqWKwg6XBJ35R0haRXtTqedifphZK+LulSSf/d6njGAieoNibpfEn3SrqlqvwpZ5SP4vyIx7cm0vYxxHXyo4h4JzADOLoF4Y55Q1wft0XEu4GjAP83ahQ4QbW3C4CDywU+o3zLXcDQ18lHU72NvgsYwvqQ9DrgN8D85oY5NjlBtbGIWAB1B07pAAADYUlEQVQ8UFXsM8q30FDWiQqfBn4aEX9odqztYKjbSERcGRH/CUxvbqRjkxOUVZsALC897wEmSNpe0teBvSWd0prQ2lbNdQK8B3glcISkd7cisDbV3zbSJelcSd8Arm5NaGNLVqc6siyoRllExP2AvwRbo791ci5wbrODsX7XRzfQ3dxQxjb3oKxaK84obwPzOsmL10eTOEFZtd8DkyTtJulpwDHAlS2Oqd15neTF66NJnKDamKSLgN8Bz5fUI+n4iOgDKmeUvw24xGeUbx6vk7x4fbSWz2ZuZmZZcg/KzMyy5ARlZmZZcoIyM7MsOUGZmVmWnKDMzCxLTlBmZpYlJyizIZLUO4JpvzWcs8NLmiFp55HOx2xD4v9BmQ2RpN6IGN/kZXYDH4iIm5q5XLNWcg/KbJjS5S4+K+kWSUskHZ3KuyR1pyur3i7pe5KU6roldUp6naRF6XaHpLtS/amSfp/mOSct4wiKC+B9L7UfV5lPmubYtPxb0uU3KvH1SjpT0mJJ10vqSOVHpraLJS1o9vtmVi8nKLPhewMwBdiL4rIXn5W0U6rbG3gfxQXtngMcUJ4wXTdoSkRMARYDn0tVX46IfSLiRcA44DURcSlwEzA9TfNIZT5p2O/TwIEpln0kHZ6qtwCuj4i9gAXAO1P5qcCrU/nrRum9MBt1TlBmw/cy4KKIeDwiVgG/AvZJdTdGRE9E/BtYBEysNQNJHwQeiYjKFXGnSrpB0hKKpLPnIDHsA3RHxD/SOeK+B7wi1T0GXJUeLyzF8FvgAknvBDau+9WaNZmvB2U2fLWuC1SxrvT4cWpsa5IOAo4kJRRJmwNfBTojYrmk04HNRxDDv+LJncxPxBAR75a0H3AosEjSlHS9L7OsuAdlNnwLgKMlbSxpR4pEc2M9E0p6NkUyOqo0ZFdJRvdJGg8cUZpkLbBljVndAPyXpB0kbQwcS9GTG2jZz42IGyLiVOA+1r+2kVk23IMyG77Lgf+g2IcUwAcj4u+SXlDHtDOA7YHL0/ETKyJimqRvAkuAZRTXHaq4APi6pEfSMgGIiJWSTgGuo+hNXR0RVwyy7M9KmpTaz0/xm2XHh5mbmVmWPMRnZmZZcoIyM7MsOUGZmVmWnKDMzCxLTlBmZpYlJygzM8uSE5SZmWXp/wMHRDDqfk+/LwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual M: 42.6532 sum(2^k)/N: 348.1872 Log-Normal Mean: 495.0375194838228 2^(mean(N)): 92.84806893372316\n"
     ]
    }
   ],
   "source": [
    "total_means = []\n",
    "child_means = []\n",
    "\n",
    "for key, value in sorted(file_tree.items()):\n",
    "    child_ion_list = []\n",
    "    total_ion_list = []\n",
    "    \n",
    "    for file in value:\n",
    "        _t, _x, _y, _z, _ke, _drift, _ionized, _child_ions = np.loadtxt(file, delimiter=',', unpack=True, ndmin=1)\n",
    "        child_ion_list.append(_child_ions[-1])\n",
    "        total_ion_list.append(_ionized[-1])\n",
    "        \n",
    "    child_ion_list = np.array([k + 1 for k in child_ion_list])\n",
    "    total_ion_list = np.array([k + 1 for k in total_ion_list])\n",
    "    \n",
    "    child_means.append(np.mean(child_ion_list))\n",
    "    total_means.append(np.mean(total_ion_list))\n",
    "\n",
    "    mu = np.mean(np.log(2) * child_ion_list)\n",
    "    var = np.var(np.log(2) * child_ion_list)\n",
    "    \n",
    "    # plt.rcParams['font.size'] = 14\n",
    "    # plt.rcParams['font.family'] = 'serif'\n",
    "    # fig = plt.figure(figsize=(6, 6))\n",
    "    \n",
    "    plt.hist(total_ion_list, rwidth=1.0, histtype='stepfilled')\n",
    "    \n",
    "    plt.title(f'Total Ionizations at {key} V/cm Bulk Field')\n",
    "    plt.xlabel('Ionizations')\n",
    "    plt.ylabel('Simulations')\n",
    "    \n",
    "    plt.grid()\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    \n",
    "    # plt.savefig(f'total_ion_dist_{key}.pdf', bbox_inches='tight')\n",
    "    \n",
    "    # plt.rcParams['font.size'] = 14\n",
    "    # plt.rcParams['font.family'] = 'serif'\n",
    "    # fig = plt.figure(figsize=(6, 6))\n",
    "    \n",
    "    plt.hist(2**np.array([k - 1 for k in child_ion_list]), bins=[2**k for k in np.arange(1, 13, 1)], rwidth=1.0, histtype='stepfilled')\n",
    "\n",
    "    plt.title(f'Estimated Ionizations at {key} V/cm Bulk Field')\n",
    "    plt.xlabel('Ionizations')\n",
    "    plt.ylabel('Simulations')\n",
    "    \n",
    "    plt.xscale('log')\n",
    "    \n",
    "    plt.grid()\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    \n",
    "    # plt.savefig(f'est_ion_dist_{key}.pdf', bbox_inches='tight')\n",
    "    \n",
    "    print('Actual M:', sum([k + 1 for k in total_ion_list]) / 2500, 'sum(2^k)/N:', sum(2**child_ion_list) / 2500, 'Log-Normal Mean:', np.exp(mu + 0.5 * var), '2^(mean(N)):', 2**np.mean(child_ion_list))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below shows an example of altering the $2^\\bar{N}$ estimation. Whether the fit of this modification is specific to this particular configuration is unknown."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.rcParams['font.size'] = 14\n",
    "# plt.rcParams['font.family'] = 'serif'\n",
    "# fig = plt.figure(figsize=(12, 6))\n",
    "\n",
    "volt_vals = np.arange(500, 1600, 100)\n",
    "\n",
    "plt.plot(volt_vals, total_means, label='Total Ionizations')\n",
    "\n",
    "plt.title('Estimated Ionizations')\n",
    "plt.xlabel('Bulk Field [V/cm]')\n",
    "plt.ylabel('Ionizations')\n",
    "\n",
    "plt.plot(volt_vals, 2**(np.array(child_means) * 0.82), label='Estimated Ionizations (using $2^{0.82N}$)')\n",
    "\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# plt.savefig(f'fitted_ion_est.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}