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@germannp
Last active September 25, 2020 19:32
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"from scipy.integrate import odeint"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"variable_names = [\n",
" \"Free gluten\",\n",
" \"Gluten structure\",\n",
" \"Yeast\",\n",
" \"Starch\",\n",
" \"CO2\",\n",
" \"Bacteria\",\n",
" \"Hexose\",\n",
" \"Acid\",\n",
"]\n",
"\n",
"\n",
"def dXdt(X, t):\n",
" FG, G, Y, S, CO2, B, H, A = X\n",
"\n",
" dFGdt = -FG / 4\n",
" dGdt = FG / 4 - A * G / 10\n",
"\n",
" dYdt = Y * S / 2\n",
" dSdt = -Y * S / 2\n",
" dCO2dt = Y * S / 2 - (0.1 + (1 - G)) * CO2 / 2\n",
"\n",
" dBdt = B * H / 4\n",
" dHdt = -B * H / 4\n",
" dAdt = B * H / 4\n",
"\n",
" return [dFGdt, dGdt, dYdt, dSdt, dCO2dt, dBdt, dHdt, dAdt]"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"yeasted_dough = [1, 0, 0.2, 1, 0, 0, 1, 0] # Lots of yeast, no bacteria\n",
"time_points = np.linspace(0, 24, 50)\n",
"solution = odeint(dXdt, yeasted_dough, time_points)\n",
"solution = pd.DataFrame(solution, columns=variable_names, index=time_points)\n",
"solution[[\"Gluten structure\", \"CO2\"]].plot(color=[\"C1\", \"C0\"])\n",
"plt.title(\"Yeasted dough\")\n",
"plt.xlabel(\"Time\")\n",
"plt.ylabel(\"Concentration\")\n",
"plt.legend(frameon=False, loc=\"upper left\")\n",
"sns.despine()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sourdough = [1, 0, 0.05, 1, 0, 0.05, 1, 0] # Less yeast, some bacteria\n",
"solution = odeint(dXdt, sourdough, time_points)\n",
"solution = pd.DataFrame(solution, columns=variable_names, index=time_points)\n",
"solution[[\"Gluten structure\", \"CO2\", \"Acid\"]].plot(color=[\"C1\", \"C0\", \"C3\"])\n",
"plt.title(\"Sourdough\")\n",
"plt.xlabel(\"Time\")\n",
"plt.ylabel(\"Concentration\")\n",
"plt.legend(frameon=False, loc=\"upper left\")\n",
"sns.despine()\n",
"plt.show()"
]
},
{
"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": "3.7.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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