{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TP - Diffusion thermique 1D\n",
    "On cherche à résoudre l'équation de diffusion à 1 dimension\n",
    "$$D \\frac{\\partial^2T}{\\partial x^2}= \\frac{\\partial T}{\\partial t}$$\n",
    "La température initiale est de 20°C. À t=0, on soumet le barreau à une température de 100°C en $x=0$ et de 10°C en $x=L$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "D[m^2/s]= 7.032348804500703e-06\n",
      "dx[m]= 0.00125\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "rho=7900.0 #kg/m^3\n",
    "lamda=25.0 #W/m/K\n",
    "cp=450.0 #J/kg/K\n",
    "L=0.1#m\n",
    "Ti=20.0#+273.15# K\n",
    "T0=100.0#+273.15#K\n",
    "TL=10.0#+273.15#K\n",
    "N=80\n",
    "tmax=400.0 #s\n",
    "idisplay=100 #frequence d'affichage des courbes\n",
    "D=lamda/(rho*cp)  #diffusivite\n",
    "print ('D[m^2/s]=',D)\n",
    "\n",
    "### creation maillage spatial \n",
    "x=np.linspace(0,L,N+1)\n",
    "###calcul dx, le pas spatial \n",
    "dx=x[1]-x[0]\n",
    "print (\"dx[m]=\",dx)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### On écrit ensuite :\n",
    "$$\\frac{\\partial^2T}{\\partial x^2}=(T(i+1,t_n)+T(i-1,t_n)-2T(i,t_n))/(\\Delta x)^2 $$\n",
    "Et \n",
    "$$\\frac{\\partial T}{\\partial t}=(T(x_i,n+1)-T(x_i,n))/\\Delta t $$\n",
    "On a alors :\n",
    "$$ T_{i}^{n+1}=F_o T_{i-1}^{n}+\\left(1-2F_o\\right) \\ T_{i}^{n}+F_oT_{i+1}^{n}$$\n",
    "avec $F_o$ coefficient de Fourier :\n",
    "$$F_o=\\frac{D \\Delta t}{(\\Delta x)^2} $$\n",
    "On doit avoir :\n",
    "$$\\Delta t < \\frac{(\\Delta x)^2}{2D} $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dtstab[s]= 0.11098265625\n",
      "nbfourier= 0.4995\n"
     ]
    }
   ],
   "source": [
    "###condition de stabilite\n",
    "beta=0.999  #coefficient de sécurité numérique\n",
    "dtstab=beta*dx**2/(2.0*D)\n",
    "print (\"dtstab[s]=\",dtstab)\n",
    "nbfourier=D*dtstab/dx**2   #nombre de fourier adimensionnel\n",
    "print (\"nbfourier=\",nbfourier)\n",
    "\n",
    " \n",
    "#calcul nb pas de temps bstep\n",
    "nbstep=int(tmax/dtstab)\n",
    "\n",
    "#condition initiale\n",
    "TA=Ti*np.ones(N+1)\n",
    "TB=Ti*np.ones(N+1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On détermine ensuite la température aux différents points à différents instants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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W0KXLXL797b+xe3dJWOpQQIiIRCgz44Ybclm0aAzr1hXxmc9cwn//90a6d5/H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\nCggREamTAkJEROqkgBARkTr9f4qSLjU68jy6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110542c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110ca8828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZBR9+WMGyZeXfCI1+/QKcdFIbTj451FMZNChIUpIGwxUQItLqZWb6yMtLIS/v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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1108b0828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f70e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110bf0be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FfJukONkg18YLGnOu0JgrZgd3b1LWQlldEIkys2nuXhw6R7rk2nhBY84VGnNq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\nEpcKQkRE4lJBiIhIXCoIERGJ6/8ANA//VCdUlD0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11119f7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SlwfNG4WlR+yivo0bYeHS0NOYvSiExoN/h7WxW3zXqgFt9/zf0Gi6c2rqVUCI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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1108d2cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WGl+H0Bj8Ptw7OrzeoA70KNyGZE/DrYAQEUkzZmEWvpabw9GxezPW/A7TFoRT\nUhPmQI3lK5NehwJCRCQD5FUP/RE7NYfT9oGxY+cBrcvdLx4ZdlWuiIikigJCRETKpIAQEZEyKSBE\nRKRMCggRESmTAkJERMqkgBARkTIpIEREpEzm7lHXUGVmtgiYG8dbNAYWJ6icTJBr7QW1OVeozZXT\nwt03L2+jjA6IeJnZRHcvirqOVMm19oLanCvU5uTQKSYRESmTAkJERMqU6wExKOoCUizX2gtqc65Q\nm5Mgp/sgRERkw3L9CEJERDYgKwPCzA40s6/MbKaZ9S/jdTOze2Kvf2Zmu1R033RV1Tab2VZmNsbM\nvjCzqWZ2Qeqrr5p4PufY69XN7BMzG5m6quMT57/tBmY2zMy+NLNpZrZ7aquvvDjbe1Hs3/QUM3vW\nzDZJbfVVU4E2tzWzD8xspZldWpl9K83ds2oBqgOzgFZATeBTYIf1tukJvAYY0AUYX9F903GJs81N\ngV1ij+sB07O9zaVevxh4BhgZdXtS0WZgCHB67HFNoEHUbUpWe4FmwBygduz588DJUbcpQW3eAtgV\nGAhcWpl9K7tk4xFEZ2Cmu89291XAUKDXetv0Ap7w4EOggZk1reC+6ajKbXb3Be7+MYC7/wJMI/zP\nle7i+Zwxs+bAQcAjqSw6TlVus5nVB/YBBgO4+yp3/ymVxVdBXJ8xYcbM2maWB9QBvktV4XEot83u\n/oO7fwSsruy+lZWNAdEM+LbU83n8+QtvQ9tUZN90FE+b/5+ZFQIdgfEJrzDx4m3zXcDlwNpkFZgE\n8bS5JbAIeCx2Wu0RM6ubzGIToMrtdff5wO3AN8AC4Gd3fzOJtSZKPN9BCf/+ysaAkCows3zgReBC\nd18WdT3JZGYHAz+4+6Soa0mhPGAX4EF37wgsBzKmj62yzKwh4a/nlsCWQF0zOzHaqjJPNgbEfGCr\nUs+bx9ZVZJuK7JuO4mkzZlaDEA5Pu/tLSawzkeJp857AoWb2NeEwfD8zeyp5pSZMPG2eB8xz93VH\nh8MIgZHO4mlvd2COuy9y99XAS8AeSaw1UeL5Dkr891fUnTKJXgh/Kc0m/OWwrqOm3XrbHMT/dmxN\nqOi+6bjE2WYDngDuirodqWrzetsUkzmd1HG1GXgf2C72+HrgtqjblKz2ArsBUwl9D0booO8XdZsS\n0eZS217P/3ZSJ/z7K/L/IEn6j9yTcDXOLOCq2LqzgLNijw24P/b650DRxvbNhKWqbQb2Ahz4DJgc\nW3pG3Z5IF7y7AAABsUlEQVRkf86l3iNjAiLeNgMdgImxz3o40DDq9iS5vTcAXwJTgCeBWlG3J0Ft\nbkI4IlwG/BR7vOmG9o1n0Z3UIiJSpmzsgxARkQRQQIiISJkUECIiUiYFhIiIlEkBISIiZVJAiIhI\nmRQQIglgZoVm9puZTa7kfsfEhmbOmCHHJXcoIEQSZ5a7d6jMDu7+HHB6kuoRiYsCQqQcZrZrbDKa\nTcysbmwSmh3L2acwNjHP42Y23cyeNrPuZjbOzGaYWedU1S9SVXlRFyCS7tz9IzMbAdwE1Aaecvcp\nFdi1NXAUcCrwEXA8YWiTQ4G/Ab2TU7FIYiggRCrmRsKX/Arg/AruM8fdPwcws6nAaHd3M/scKExK\nlSIJpFNMIhWzGZBPmJa1onMbryz1eG2p52vRH2eSARQQIhXzEHAN8DTw94hrEUkJ/RUjUg4zOwlY\n7e7PmFl14L9mtp+7vxN1bSLJpOG+RRIgNp/3SHff6NVNG9i3mDDxy8EJLkskLjrFJJIYvwP1q3Kj\nHPAAsDQpVYnEQUcQIiJSJh1BiIhImRQQIiJSJgWEiIiUSQEhIiJlUkCIiEiZ/g8Nft5HnL5yTwAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110410400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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48+mY/cJzd1ix4evAePkDuOn5sL43hFHfu84wji6BA5unpk4FhIhIxMygQ7Ow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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a22f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1111c4be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1106b9cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a12b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DzaUi2S4IC53FJCIyAf2BAIeHwhweCpNyjrvKJW4qDd0uLxWJAvv4Qeb7Qfbv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\nyIgUECIiMqL/B7NPY4Txm+QZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110be7a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DMM6kDw8xlCZ2MYUVPMGmsMsSSVmdrUH8Iy5ViHTDYfTmWYZzCHmcTx2/YDXbdIoOkajr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\nAOQKESoSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110fd4c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Zzj9CZXEX87iX+RxBQ04inx/QOCZ5VBAiInGoDdkMIZtLaM0cSvkH6/iYddzO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\nFYSIiFRIBSEiIhX6f1a6sm2aK81dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b88ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ms43ZbOAZVvA0K+hONiXkcwEdY+4MsyoIEZEoaUwaw+jEMDrxCQd5g03MZgP/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\nH4RW3dsNZ2LyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110fd04e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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W7CFgfnCjifx/7cjk/3E96dTgKWYxgSU6K6xIkJVVEHcBzYAdZjbFzKYA24EWwJ3BDidS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\nh77gp8sdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110623ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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spIDVFLCaNrSmB3m0oXVEXv1OBSEiEgaJJNKedrSnHUc5ykY2sYnNvMhs6lKH\nXHLIoTu1qe111AtUECIiYZZOOtcymEEMpISdFLGRZaxgBQW0oy09yKUlLT1fqlBBiIh4JJFEOtGR\nTnTkG76lmGI2sYUdlJBOOnm+pQqvTuuhghARiQD1qcf1XMdgBrGDEorYyHssYxkr6EB78silBdlh\nXapQQYiIRJAkkujMVXTmKr7mGzZSzGa2sI3t1CODXHLoTrcwZRERkYjUgPoM5XqGMIjt7GAjxbzL\nUpaxgsYtrySf/JB+vgpCRCTCVaMaXelCV7pwmK/ZSDHf/vhNyD838na8FRGRS2pIA4ZxA82+bBry\nz1JBiIhIuVQQIiJSLhWEiIiUSwUhIiLlUkGIiEi5VBAiIlIuFYSIiJRLBSEiIuUy55zXGfxmZl8D\nnwXwFvWB0B+OGDnibbygMccLjblqmjvnGlQ0UVQXRKDMrNg5l+t1jnCJt/GCxhwvNObQ0ComEREp\nlwpCRETKFe8FMcXrAGEWb+MFjTleaMwhENfbIERE5NLifQlCREQuISYLwsyuN7NdZvaJmT1ezutm\nZv/wvf6hmXWv7LyRyt8xm1lTM1tpZjvMbLuZ/Tb86f0TyPfZ93qimW0xswXhSx2YAP9t1zWz18xs\np5mVmFnv8KavugDH+zvfv+ltZjbHzKqHN71/KjHmdma23sx+MrM/VGXeKnPOxdQNSAQ+BVoAycBW\noMNF0wwFFgMG9AIKKztvJN4CHHMjoLvvfi3g41gfc5nX/wV4GVjg9XjCMWZgJjDRdz8ZqOv1mEI1\nXqAxsBeo4Xs8Dxjn9ZiCNOaGQB7wBPCHqsxb1VssLkH0AD5xzu1xzv0MzAVGXDTNCGCWK7UBqGtm\njSo5byTye8zOuQPOuc0AzrnvgRJK/3NFukC+z5hZE2AYMC2coQPk95jNrA5wNTAdwDn3s3PuWDjD\n+yGg7zGll1SuYWZJQCrwVbiCB6DCMTvnDjvnNgKnqzpvVcViQTQGvijzeD+//oF3qWkqM28kCmTM\nF5hZFtANKAx6wuALdMx/B/4InAtVwBAIZMzZwNfADN9qtWlmVjOUYYPA7/E6574E/h/wOXAA+M45\n914IswZLID+Dgv7zKxYLQvxgZmnA68B/c84d9zpPKJnZcOCwc26T11nCKAnoDjzrnOsGnASiZhtb\nVZlZOqW/PWcDVwI1zeweb1NFn1gsiC+BslfzbuJ7rjLTVGbeSBTImDGzapSWw2zn3BshzBlMgYy5\nL3CTme18etJ0AAACgUlEQVSjdDH8GjN7KXRRgyaQMe8H9jvnzi8dvkZpYUSyQMY7GNjrnPvaOXca\neAPoE8KswRLIz6Dg//zyeqNMsG+U/qa0h9LfHM5vqOl40TTD+OWGraLKzhuJtwDHbMAs4O9ejyNc\nY75omnyiZyN1QGMG1gBtfff/Hfir12MK1XiBnsB2Src9GKUb6B/zekzBGHOZaf+dX26kDvrPL8//\nQkL0lzyU0r1xPgX+h++5B4EHffcNeNr3+kdA7uXmjYabv2MG+gEO+BD4wHcb6vV4Qv19LvMeUVMQ\ngY4Z6AoU+77XbwHpXo8nxOP9X8BOYBvwIpDi9XiCNOYrKF0iPA4c892vfal5A7npSGoRESlXLG6D\nEBGRIFBBiIhIuVQQIiJSLhWEiIiUSwUhIiLlUkGIiEi5VBAiQWBmWWb2g5l9UMX57vCdmjlqTjku\n8UMFIRI8nzrnulZlBufcK8DEEOURCYgKQqQCZpbnuxhNdTOr6bsITacK5snyXZjnBTP72Mxmm9lg\nM1tnZrvNrEe48ov4K8nrACKRzjm30czmA/8bqAG85JzbVolZWwG3A+OBjcBdlJ7a5Cbg34CRoUks\nEhwqCJHK+TOlP+R/BH5TyXn2Ouc+AjCz7cBy55wzs4+ArJCkFAkirWISqZx6QBqll2Wt7LWNfypz\n/1yZx+fQL2cSBVQQIpUzGfifwGzgPzzOIhIW+i1GpAJmNgY47Zx72cwSgffN7Brn3Aqvs4mEkk73\nLRIEvut5L3DOXXbvpkvMm0/phV+GBzmWSEC0ikkkOM4Cdfw5UA54BjgaklQiAdAShIiIlEtLECIi\nUi4VhIiIlEsFISIi5VJBiIhIuVQQIiJSrv8PYwaf562UEaAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110efeba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lFyN5m7fYwDIWMZk3mMGF9KUT/SPy2k8qCBGRMEmkyrdnY+9hGxtYxjpeYx2v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\npIIQEZEiqSBERKRI/w8m+5iO4ERwggAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110be7908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NfM463mIsW5nvO5ZI3CivIGaZ2QQz++YwVytxDzA7vNFEKqYVOQxnErXI4D3uZwlPcZRD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\nmeniAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1110fc978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9/ioIEZEkkEMXuvAIbVnHGt5g1e6dMf+e2sUkIpJEsmhGe26HNSfH/HupIERE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\nLBWEiIiE9f8AlJV4w/0iovcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110d46dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pgoiWmS1x94NC50iUTBsvaMyZQmOOD33EJCIinVJBiIhIpzK9IO4IHSDBMm28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\n1P8DUpetrbtl0yoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f2b160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Mgf9tb2JmV5vZY2a2ysz2Lm/6kStwvJ+P/pt+2MyuNLPm8qYfnWGMeXszu9PM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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110e5ef98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b677b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Bvo0XNOZ8oTG3zVB379fSQlldEIkys7nuPjF0jnTJt/GCxpwvNObU0EdMIiLS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\nWSoIERFplgpCRESa9b+HCrPhMlV34QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110760ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KQkREyqSCEBGRMqkgRESkTCoIEREpkwpCRETKZJ5GN6eoLDPbCKyJ4yOaAJsS\nFCcTZNt4QWPOFhpz5Rzv7k3LWyijCyJeZlbk7r1C50iVbBsvaMzZQmNODu1iEhGRMqkgRESkTNle\nEI+EDpBi2TZe0JizhcacBFl9DEJERA4v27cgRETkMKplQZjZaWa2xMyWm9kNZXzdzOyB2Nfnm1nP\niq6brqo6ZjNrZWYTzWyRmS00s6tSn75q4vk5x76ea2bvm9mrqUsdnzj/225oZs+b2QdmttjM+qc2\nfeXFOd5rYv9Nl5jZs2ZWO7Xpq6YCY+5oZtPNbI+Z/bQy61aau1erB5ALrADaADWBeUDnQ5Y5HXgD\nMKAfMLOi66bjI84xNwd6xp7XB5ZW9zGX+vq1wDPAq6HHk4oxA08Al8ee1wQahh5TssYLtABWAXVi\nr58Dvh16TAka8zFAb+AO4KeVWbeyj+q4BdEHWO7uK919LzAWOPuQZc4G/uqRGUBDM2tewXXTUZXH\n7O7r3H0OgLt/ASwm+p8r3cXzc8bMWgJnAI+lMnScqjxmM2sADAEeB3D3ve6+NZXhqyCunzGQB9Qx\nszygLrA2VcHjUO6Y3X2Du88G9lV23cqqjgXRAvio1OuP+eovvMMtU5F101E8Y/4XM2sN9ABmJjxh\n4sU75vuAnwMHkxUwCeIZ8wnARuDPsd1qj5lZvWSGTYAqj9fdPwF+DXwIrAO2ufvbScyaKPH8Dkr4\n76/qWBBSBWaWD7wAXO3un4fOk0xmdiawwd2LQ2dJoTygJ/AHd+8B7AAy5hhbZZlZI6J/PZ8AHAvU\nM7NLw6bKPNWxID4BWpV63TL2XkWWqci66SieMWNmNYjK4Wl3fzGJORMpnjEPBM4ys9VEm+EjzOyp\n5EVNmHjG/DHwsbt/uXX4PFFhpLN4xjsKWOXuG919H/AiMCCJWRMlnt9Bif/9FfqgTKIfRP9SWkn0\nL4cvD9R0OWSZM/jPA1uzKrpuOj7iHLMBfwXuCz2OVI35kGWGkTkHqeMaMzAF6BB7fgvwq9BjStZ4\ngb7AQqJjD0Z0gP6K0GNKxJhLLXsL/3mQOuG/v4L/hSTpL/l0orNxVgA3x977IfDD2HMDHop9fQHQ\n60jrZsKjqmMGBgEOzAfmxh6nhx5Psn/OpT4jYwoi3jEDJwNFsZ/1S0Cj0ONJ8nhvBT4ASoAngVqh\nx5OgMTcj2iL8HNgae37U4daN56ErqUVEpEzV8RiEiIgkgApCRETKpIIQEZEyqSBERKRMKggRESmT\nCkJERMrBBZJuAAABT0lEQVSkghBJADNrbWa7zGxuJdf7Zmxq5oyZclyyhwpCJHFWuPvJlVnB3f8G\nXJ6kPCJxUUGIlMPMesduRlPbzOrFbkLTtZx1WsduzPMXM1tqZk+b2Sgze8/MlplZn1TlF6mqvNAB\nRNKdu882s3HA7UAd4Cl3L6nAqm2BbwDfBWYDFxNNbXIWcBNwTnISiySGCkKkYm4j+iW/G7iyguus\ncvcFAGa2EBjv7m5mC4DWSUkpkkDaxSRSMUcD+US3Za3ovY33lHp+sNTrg+gfZ5IBVBAiFfMw8Avg\naeCewFlEUkL/ihEph5ldBuxz92fMLBeYZmYj3H1C6GwiyaTpvkUSIHY/71fd/YhnNx1m3WFEN345\nM8GxROKiXUwiiXEAaFCVC+WA3wNbkpJKJA7aghARkTJpC0JERMqkghARkTKpIEREpEwqCBERKZMK\nQkREyvR/YcOy/PxtRwMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110fdbf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VcsKuTCQlFHQE8WeCUz9HWgr8NfbliMTWgaxq0Hk0XPI8bJ0bLG+64nkNrhMphIICopK7\nHzWfQeS5GvEpSSTGzOCs66HvIqiZC9NvgPHdYc+mgvcVSWMFBcTxprsoH8tCROKuUg50mwwXPAaf\nT4ahjWD1EB1NiBxDQQExycweNLPvL3O1wAPAlPiWJhIHlgFNboM+C6ByfZg8ACZdpZXrRPJRUED8\nCjgdWG1mw81sOLAKqA/cGe/iROKmSgPo8T6c+xCsHw1vNIJ1I8OuSiSpHPcqJnffAwwws9OBRpGn\nl7r72rhXJhJvGVnQ/G44tStMGwgTesGZP4Y2j0PZwkwiIFKyHfcIIjLqGXdf6+5vRW5r89tGJGVV\nbwI9P4Lce2Ht60HfxCdjwq5KJHQFnWIaW4j3KMw2IsktsxS0vA+unAVlawZXOU29FvYXepoxkRKn\noIBoZmY7j3PbhWZdlZKkRvNgHewWv4dVLwd9E5+8HXZVIqE4bkC4e6a7n3CcWyV3r52oYkUSIrM0\ntHogmEa8bDUY3y1yNLE97MpEEkprUoscS83cyNHE//73aGL9W2FXJZIwBXVSFzRXk0jJllkGWv1f\npG+iBrxzBUy5BvZ9FXZlInFX0BHErIRUIZLsaraIHE38AdYMgTcawrpRYVclElcFBcTxFgoSSS+Z\npaHV/XDlbChfCyZcCZP6axS2lFgFnUKqaWbHHDHt7v+IcT0iya/GOcEpp4V/hrkPBPM6tXkCzugX\nTAwoUkIUdASRCVQEKh3jJpKeMksFnde950OlusGcTu/0DJY6FSkhCjqC2OTuDySkEpFUVK0R9PwA\nFj8Ks38f9E2c/w9ocJ2OJiTlqQ9CJFoZWdDsrmC9ierNYPpP4e1LYee6sCsTiUpBAaElQEUKq3I9\n6D4VLnwStsyEoY1h8WNw+FDYlYkUS0EjqXWxt0hRWAY0+gX0XQont4UP7oDRbeCrpWFXJlJkGkkt\nEg+VToXLxkD7V2DnahjeHObcB4f2h12ZSKEpIETixQzq/QiuWg6n94W598PwFrD5w7ArEykUBYRI\nvJWrCR1egcvfhoO7glNO798KB3aFXZnIcSkgRBLl1C5B30TjW2DpP7UwkSQ9BYRIIpWuFCxp2vMD\nKHVCsDDRxH6wd3PYlYkcRQEhEobs1tB7XjBT7PpR8PrZsPw58MNhVybyPQWESFgySwfTdXw3wO7d\nn8Fb7WD7irArEwEUECLhq9IgGGB3yfPw1WIY1kyXxEpSUECIJAMzOOv6yCWxvYNLYoc1g43Tw65M\n0pgCQiSZlM+GDq/C5ePg0AF4qy1Mux72fRl2ZZKGFBAiyejUy6DvEjjnblj1H3j9LFg5GNzDrkzS\niAJCJFmVKg/nPQS95gUTAU67Fsa0hx0rw65M0oQCQiTZVW8CPd6Hi56GbQtgaFOYfS98uy/syqSE\nU0CIpALLgIaDoN8KOL0PzHsAhjaBzyaEXZmUYAoIkVRSPjuY16nrpODKp7GdYdIA2LMp7MqkBAot\nIMws08zmm9mYyONqZjbRzFZFflYNqzaRpFenA/RZBLn3wfqR8MZZsOQJLU4kMRXmEcTtwPI8j+8G\nJrt7PWBy5LGIHEtWWWh5L/RdDCe2hhm3wchWVPpmecH7ihRCKAFhZnWArsBzeZ7uAQyO3B8M9Ex0\nXSIpqXI96DIeOr4OezfT4tOb4d0bYZ8WhJTohHUE8SjwGyDvzGTZ7v7didTNQHbCqxJJVWZwxlXQ\nbwUbqvaGFc/B6w1gxQuaAFCKzTzBA2/MrBvQxd1vMrO2wF3u3s3Mdrh7lTzbbXf3o/ohzGwQMAgg\nOzs7d8iQIcWuZffu3VSsWLHY+6eadGsvpG+bs7M2U/+LR6m8bylfl23Equw72F32zLBLi5t0/T0X\nt83t2rWb6+4tC9zQ3RN6Ax4CNgDrCY4U9gIvAyuBWpFtagErC3qv3Nxcj8bUqVOj2j/VpFt73dO8\nzYcPuS//t/uLNdyfznB//zb3fTtCrS1e0vr3XAzAHC/E93XCTzG5+z3uXsfdc4D+wBR3vxp4ExgY\n2WwgMDrRtYmUKJYBZ10H/VbC2T8PrnJ6vQF8/LKm7JBCSaZxEA8DncxsFdAx8lhEolW2Glz0JPSa\nBZVOg6nXwJuXwJeLwq5MklyoAeHu09y9W+T+l+7ewd3ruXtHd9clGCKxVLMl9PwQLn4WdiyD4S1g\nxu2wf0fYlUmSSqYjCBGJN8uAs2+Afh/D2YP+e9pp5Yu62kmOooAQSUffn3aaA5VOh2nXwegLYeu8\nsCuTJKKAEElnNVtAzxnQ9kXYuQZGtIwMstMCRaKAEBHLgAYDg6udmtweDLIbUg+WPqm5ndKcAkJE\nAmWqwAWPQJ+FUL05vH8zjMiFje+GXZmERAEhIj9UrRF0mwSdhsL+7fDWJcGU4rs/C7sySTAFhIgc\nzSxYmOiq5ZB7L6wfFayLPe+PWskujSggROTYSpWHlvdBv+VwyuUw+/fwxtmwdoRGY6cBBYSIFKxS\nDlw6DLpNhlIVYWJvGNMRvloSdmUSRwoIESm82u2h93y48J/w5QIY1gzeu1mXxZZQCggRKZqMLGh0\nE/T/GBreBMufhtfOhMWPw6GDYVcnMaSAEJHiKVsdLnwiuCy2Zkv44PbgiOLT8WFXJjGigBCR6FRr\nBF0nQOfRcPggjLscxnaB7SvCrkyipIAQkeiZQc4VcNUSaP03+GIGDGsCM+7Q2tgpTAEhIrGTWQaa\n/Qr6r4IG18PSJ4JpO5Y8of6JFKSAEJHYK3ciXPx0cMVTjeYw4zYY1hQ+HavxEylEASEi8VO9KXSd\nGPRP+CEY1xXGdtb4iRShgBCR+Pquf6LvEjj/EdgyO7ja6d0bYe8XYVcnx6GAEJHEyCwNTe+AAauh\n0S2w8vmgf2L+w5rfKUkpIEQkscpWhzaPQd+lwcjsWfcEy56ufk39E0lGASEi4ahSHzqPgm5ToEw1\nmPwjGNUaNs8IuzKJUECISLhqtwvWxm77AuzeEKyNPaEPfL0m7MrSngJCRMKXkQkNrg3md2r5AHw2\nPphW/INfaiLAECkgRCR5lKoAub8PBtrVvxaWPB5MBLjwb3Bof9jVpR0FhIgknwq14JJngokAs8+H\nmb8OVrRbPUQd2QmkgBCR5FWtMXQZGwy2K10ZJg+AkefBxnfDriwtKCBEJPnV6Qi95kLbF2HvJnjr\nEhjfQzPGxpkCQkRSQ0YmNBgI/VbCuX+CjVNhaGN490ZKf6sZY+NBASEiqaVUeWh+DwxYE6xst/J5\nzlv7Y5hzHxzcHXZ1JYoCQkRSU7ma0OZxuGo5X1Y8D+beH1zxtOwpTS0eIwoIEUltlc9k2cn3Qc8P\noXJ9eO8XwamndSN1xVOUFBAiUjJkt4YrpgdTi1smTOgVjMrW1B3FpoAQkZLj+6nFF8HFz8Ku9UFI\nvNMTti8Lu7qUo4AQkZInIwvOviEYkd3qwcgVT01g+g2w5/Owq0sZCggRKblKlYcWv4X+a6DxbfDx\nS0FH9kd3w/4dYVeX9BIeEGZ2iplNNbNlZrbUzG6PPF/NzCaa2arIz6qJrk1ESqhyNeCCR4IxFHV7\nw4K/wGunB3M8abGiYwrjCOJb4Ffu3hBoDdxsZg2Bu4HJ7l4PmBx5LCISOyfUhQ4vQ+95cOJ5kTme\n6sOKF+DwobCrSzoJDwh33+Tu8yL3dwHLgdpAD2BwZLPBQM9E1yYiaaLGOdBlHHSbDOVOgunXw7Cm\nsH60Lo3NI9Q+CDPLAZoDHwHZ7r4p8tJmIDukskQkXdRuD1d+BJ2GwuFvg6udRl8Im94Lu7KkYB5S\nWppZRWA68KC7jzCzHe5eJc/r2939qH4IMxsEDALIzs7OHTJkSLFr2L17NxUrViz2/qkm3doLanO6\niEWbzb/lpK/HkbNtMGUOfcmXFVqztubP2FPm9BhVGVvRtLldu3Zz3b1lgRu6e8JvQCngHeDOPM+t\nBGpF7tcCVhb0Prm5uR6NqVOnRrV/qkm39rqrzekipm0+sMd93kPu/67s/pS5T77a/eu1sXv/GImm\nzcAcL8R3dRhXMRnwPLDc3f+R56U3gYGR+wOB0YmuTUQkmAzwbhiwFpr9GtYOg9cbwIzbYO8XYVeX\nUGH0QbQBrgHam9mCyK0L8DDQycxWAR0jj0VEwlG2GrT+MwxYDQ2ug6VPwmtnwOw/wIGdYVeXEFmJ\n/kB3fx+wY7zcIZG1iIgUqEJtuPhpaPormP2/MO//YNmT0Py30PAmyCobdoVxo5HUIiKFUaU+dHoD\nes2BGrnw4a8iYyieD66AKoEUECIiRVEzF7q+A92mQPmTg/mdhjYO+ipK2BgKBYSISHHUbhesQXHp\nyGB68Yl9YUQr+GxCiQkKBYSISHGZQd2e0GcRtH0R9m2DsZ1hTAf4YmbY1UVNASEiEq2MTGgwEPqv\nDJZB3b4URp0fjMz+aknY1RWbAkJEJFYyy0DjW2HAGmj1x8g6FE1hyjWwc23Y1RWZAkJEJNZKVYQW\nv4MB63442O69m2DPpoL3TxIKCBGRePl+sN0aOOsGWPEsDDkjWLBo31dhV1cgBYSISLxVOBku+hdc\ntSLPgkV1Yd4f4eDusKs7JgWEiEiiVD4D2v8H+iyEWm1h9u/h1dNh8WNwaH/Y1R1FASEikmjVm8Bl\no4NxFNUawwd3wJD6sOLfSTUqWwEhIhKW7NbQfQp0nQTlsmH6T+GNRrDmDfDDYVengBARCV2dDsHK\ndpeOhIxSMKkfDM+FT8eGOipbASEikgy+H5W9ENq9BAe+hnFd4c2LQ1sCVQEhIpJMMjKh/jXQbwVc\n+CTsXBOExNjLYeu8xJaS0E8TEZHCySwNjX4B/VfDeX+BLbNgRC5MvAq2r0hICQoIEZFkVqo8nPPr\nYAnUFn+Az8bB0EacseVfcf9oBYSISCooUxla3R8ERZM72FfqpLh/pAJCRCSVlKsJ5/+dz6teGfeP\nUkCIiEi+FBAiIpIvBYSIiORLASEiIvlSQIiISL4UECIiki8FhIiI5EsBISIi+TIPcSrZaJnZVuCT\nKN6iBrAtRuWkgnRrL6jN6UJtLprT3L1mQRuldEBEy8zmuHvLsOtIlHRrL6jN6UJtjg+dYhIRkXwp\nIEREJF/pHhDPhF1AgqVbe0FtThdqcxykdR+EiIgcW7ofQYiIyDGUyIAws8vMbKWZrTazu/N53czs\n8cjri8ysRWH3TVbFbbOZnWJmU81smZktNbPbE1998UTze468nmlm881sTOKqjk6U/21XMbNhZrbC\nzJab2fmJrb7oomzvLyP/TS8xs9fMrGxiqy+eQrT5LDP70Mz2m9ldRdm3yNy9RN2ATGANcDpQGlgI\nNDximy7AOMCA1sBHhd03GW9RtrkW0CJyvxLwcUlvc57X7wReBcaE3Z5EtBkYDNwQuV8aqBJ2m+LV\nXqA2sA4oF3n8BnBt2G2KUZtPBFoBDwJ3FWXfot5K4hHEucBqd1/r7geAIUCPI7bpAbzkgZlAFTOr\nVch9k1Gx2+zum9x9HoC77wKWE/zPleyi+T1jZnWArsBziSw6SsVus5lVBi4Gngdw9wPuviORxRdD\nVL9jIAsoZ2ZZQHlgY6IKj0KBbXb3Le4+GzhY1H2LqiQGRG3gszyPN3D0F96xtinMvskomjZ/z8xy\ngObARzGvMPaibfOjwG+Aw/EqMA6iaXNdYCvwQuS02nNmViGexcZAsdvr7p8DfwM+BTYBX7v7hDjW\nGivRfAfF/PurJAaEFIOZVQSGA3e4+86w64knM+sGbHH3uWHXkkBZQAvgX+7eHNgDpEwfW1GZWVWC\nv57rAicDFczs6nCrSj0lMSA+B07J87hO5LnCbFOYfZNRNG3GzEoRhMMr7j4ijnXGUjRtbgNcYWbr\nCQ7D25vZy/ErNWaiafMGYIO7f3d0OIwgMJJZNO3tCKxz963ufhAYAVwQx1pjJZrvoNh/f4XdKRPr\nG8FfSmsJ/nL4rqOm0RHbdOWHHVuzCrtvMt6ibLMBLwGPht2ORLX5iG3akjqd1FG1GXgPaBC5fx/w\n17DbFK/2AucBSwn6Hoygg/7WsNsUizbn2fY+fthJHfPvr9D/QeL0j9yF4GqcNcDvIs/dCNwYuW/A\nPyOvLwZaHm/fVLgVt83AhYADi4AFkVuXsNsT799znvdImYCIts3AOcCcyO96FFA17PbEub33AyuA\nJcB/gDLLKChAAAABjklEQVRhtydGbT6J4IhwJ7Ajcv+EY+0bzU0jqUVEJF8lsQ9CRERiQAEhIiL5\nUkCIiEi+FBAiIpIvBYSIiORLASEiIvlSQIjEgJnlmNk3ZragiPv1i0zNnDJTjkv6UECIxM4adz+n\nKDu4++vADXGqRyQqCgiRAphZq8hiNGXNrEJkEZrGBeyTE1mY50Uz+9jMXjGzjmY2w8xWmdm5iapf\npLiywi5AJNm5+2wzexP4I1AOeNndlxRi1zOBvsD1wGzgRwRTm1wB/BboGZ+KRWJDASFSOA8QfMnv\nA24r5D7r3H0xgJktBSa7u5vZYiAnLlWKxJBOMYkUTnWgIsGyrIVd23h/nvuH8zw+jP44kxSggBAp\nnKeB3wOvAH8OuRaRhNBfMSIFMLOfAAfd/VUzywQ+MLP27j4l7NpE4knTfYvEQGQ97zHuftyrm46x\nb1uChV+6xbgskajoFJNIbBwCKhdnoBzwJLA9LlWJREFHECIiki8dQYiISL4UECIiki8FhIiI5EsB\nISIi+VJAiIhIvv4/73ge8Vb9ZD4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1106b68d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1104a8c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SzvLy4cgLoqk7Tr0ZFrwLA5vScOp9yf/WSf8OIiISv+12gBOujc54OqYXP1Wt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1108eaac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RSf8EERGJ3w4V4G99olt3nN6Ln3aqlfSPVEGIiGSSqjXgkhF80eT0pH+UCkJE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\nRESkQCoIEREp0P8DlKldNsk0KwAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110dd3ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EiEi62Xt/uHsMjJwB+x4Ed1wGbRvA2y+l9EC2CkJEJF0dcSw89TbcNxE2boCe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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110944978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BEZ2jiQAH3wXLFkPbJuw1bkTSv7UKQkQkE1SsGE0A+NZKOO8SNuy0c9K/pQpC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b5bdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JSBSKSU4m7ZZbyF+9mqRTTmHbLbf4pu0oLIzaaTvMq4GbWQrwAXCHc+5lM6t0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\nEBGRRqkgRESkUSoIERFplApCREQa9f9MFxebHB2UagAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11045dbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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eoBjoBAwDZvhmmwEMD3Q2EQlPjU89lV5vvUXyRx8R0agRS4cPp/CnPw37a2N7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\nhVQQIiJSIRWEiIhU6P8AaK75jZH/Wa4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b29240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WrV5HCxperEGcBB5wzjUB2gF3m1kT4GFgnnOuATDPd19ExK8u7NmTpMxM4v7+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113077f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f43f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Boucle en temps\n",
    "for istep in range(1,nbstep):\n",
    "    #afficher pas de temps\n",
    "    #print (\"temps=\",istep*dtstab)\n",
    "    \n",
    "    #Boucle sur les noeuds internes du maillage\n",
    "    for i in  range(1,N):\n",
    "        TB[i]=nbfourier*TA[i+1]+(1-2*nbfourier)*TA[i]+nbfourier*TA[i-1]\n",
    "    #Traitement des conditions aux limites\n",
    "    #-------------------------------------    \n",
    "    TB[0]=T0\n",
    "    TB[N]=TL\n",
    "     \n",
    "    #Affichage du champ de temperature dans barre\n",
    "    if istep%idisplay==0:\n",
    "        plt.xlabel('x [m]')\n",
    "        plt.ylabel('T [C]')\n",
    "        plt.grid(True)\n",
    "        plt.plot(x,TB,color=plt.get_cmap('jet')(float(istep)/float(nbstep)))\n",
    "        plt.show()\n",
    "    #Copie pour le nouveau pas de temps\n",
    "    TA=TB.copy()\n",
    "    \n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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   "title_cell": "Table des Matières",
   "title_sidebar": "Sommaire",
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