Modeling Heat(1).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Heat Transfer in Materials - Modeling Heat Pulse in ceramics, metals and polymers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### In this notebook you will use the heat equations you learned in your background readings and apply them to modeling the expected heat impulses.  Thinking back to the reading, you will notice these two equations related to conductivity and diffusivity. ![Diffusion Equation](attachment:Heat.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### You will also need to use this equation to model the flow over the length of the material. ![Partial Derv](attachment:Heat2.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### This first block of code will explain how to write a program to model the heat flow over some length of material."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the libraries you need\n",
    "import numpy as np\n",
    "from numpy import pi\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This program is based on a git https://gist.github.com/mick001/53c26a1022137657afbd\n",
    "\n",
    "#This is for 1010 Steel\n",
    "#Setting up the figure you want to plot\n",
    "fig = plt.figure()\n",
    "fig.set_dpi(100)\n",
    "ax1 = fig.add_subplot(1,1,1)\n",
    "\n",
    "# Setting up the Diffusion constant\n",
    "k = 2\n",
    "\n",
    "#Setting a visualization scaling factor so you can see the pulse\n",
    "scale =7\n",
    "\n",
    "#Length of the rod (0,L) on the x axis\n",
    "L = 8\n",
    "\n",
    "#Initial contitions u(0,t) = u(L,t) = 0. Temperature at x=0 and x=L is fixed\n",
    "x0 = np.linspace(0,L+1,10000)\n",
    "t0 = 0\n",
    "temp0 = 25  #Temperature of the rod at rest (before heating)\n",
    "\n",
    "#Increment\n",
    "dt = 0.01\n",
    "\n",
    "#Heat function (see the diffusion equation)\n",
    "def u(x,t):\n",
    "    return temp0 + scale*np.exp(-k*t)*np.sin(x)\n",
    "\n",
    "#Gradient of u\n",
    "def grad_u(x,t):\n",
    "                               #du/dx              #du/dt\n",
    "    return scale*np.array([np.exp(-k*t)*np.cos(x),-k*np.exp(-k*t)*np.sin(x)])\n",
    "\n",
    "a = []\n",
    "t = []\n",
    "\n",
    "for i in range(500):\n",
    "    value = u(x0,t0) + grad_u(x0,t0)[1]*dt\n",
    "    t.append(t0)\n",
    "    t0 = t0 + dt\n",
    "    a.append(value)\n",
    "\n",
    "#This sets up the animation feature for the program\n",
    "\n",
    "k = 0\n",
    "def animate(i):         #The plot shows the temperature evolving with time\n",
    "    global k            #at each point x in the rod\n",
    "    x = a[k]            #The ends of the rod are kept at temperature temp0\n",
    "    k += 1              #The rod is heated in one spot, then it cools down\n",
    "    ax1.clear()\n",
    "    plt.plot(x0,x,color='red',label='Temperature at each x')\n",
    "    plt.plot(0,0,color='red',label='Elapsed time '+str(round(t[k],2)))\n",
    "    plt.grid(True)\n",
    "    plt.ylim([temp0-2,2.5*scale])\n",
    "    plt.xlim([0,L])\n",
    "    plt.title('Heat equation')\n",
    "    plt.legend()\n",
    "    \n",
    "anim = animation.FuncAnimation(fig,animate,frames=360,interval=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### So one can see, over the length of the material (bar, rod) that heat will travel as a pulse. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now you will take the equation and make it more specific to the materials in your table and model the heat pulse in these materials. This code is adapted from  https://scipython.com/resources/examples/the-one-dimensional-diffusion-equation/¶\n",
    "#### This is different from the time evolving plot in the first code block. This one takes a snapshot of the heat pulse at three different times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(296.1217173008038, 381.44393668311983) (291.6198730442708, 475.9826660703137)\n",
      "(298.7729564260953, 325.76791505199964) (297.3434691800467, 355.787147219019)\n",
      "(299.6411798769103, 308.14755232319357) (299.1597253051225, 317.6457685930114)\n"
     ]
    },
    {
     "data": {
      "image/png": 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0De8Bzxs2bNj2dWaWTfkeeJ574OlyAbeiW7x48Q7nvyGX6LvttpsLuFmGbd68efstZOACnjYXcCu6pnrgkLsqPX+Bm5llT+Mh9Pz7/O1lVl4u4FZUa9euZd26dc0WcPfAzbKr8RC6JGpqati4cWOKUXVdLuBWVE3dA57nAm6WbY2H0AFqamrYtGlTShF1bS7gVlRN3QOeN2LECJYsWUJ9fX25wzKzImjcAwfo1auXe+ApcQG3omqtB15fX09tbW25wzKzImh8DhzcA0+TC7gVVb6AN9cDb7iNmWVLcz1wF/B0uIBbUS1atIjevXvTr1+/nda5gJtlW3PnwD2Eng4XcCuqhQsX7jQLW16+V+4CbpZNTQ2huweeHhdwK6pFixZtnza1saFDhyLJBdwsozZs2ECvXr12WOYeeHpcwK2o8j3wpvTo0YMhQ4a4gJtl1MaNG9lll112WOYeeHpcwK1oIqLZWdjyfC+4WXZt3LixyR64C3g6XMCtaFauXEldXV2zQ+jg6VTNsqy5Au4h9HS4gFvR5J/17R64WefU1DlwD6GnxwXciqalSVzyRowYwTvvvMPWrVvLFZaZFcGWLVuor693D7yCuIBb0eR74K0NoUcE77zzTrnCMrMiyBdpX8RWOVzArWhamoUtz5O5mGVTvoA3dxFbRKQRVpfmAm5Fs2DBAgYNGkRNTU2z23gyF7Nsaq6A5z/7meDl5wJuRTNv3jze8573tLiNe+Bm2bRhwwag6R444GH0FLiAW9HMnz+fUaNGtbjNkCFD6NGjB2+99VZ5gjKzomjpHHjD9VY+LuBWFNu2bWP+/Pmt9sCrqqoYNWoUb7zxRpkiM7NiaK4Hnv+cX2/l4wJuRbF48WI2b97cagEH2GeffVzAzTJmzZo1APTv33+H5fknD65du7bsMXV1LuBWFPPnzwdodQgdYO+99+aNN97wVatmGZIv4I0fFZz/nF9v5eMCbkUxb948gIJ74KtXr2blypWlDsvMimT16tVA8wU8v97KxwXciuL111+nW7duBfXA99lnHwAPo5tlSGtD6O6Bl58LuBXFK6+8wj777NPiPeB5o0ePBmDOnDmlDsvMimTNmjVUVVXtdBV6vqC7gJefC7gVxSuvvML+++9f0Lbvfe97qa6u5qWXXipxVGZWLKtXr6Zfv35I2mG5h9DT4wJuHbZlyxbmzJlTcAGvrq7mgAMOYMaMGSWOzMyKZc2aNTud/4bcRC7du3d3DzwFLuDWYbNmzWLr1q0cdNBBBe8zZswYXnzxRV+JbpYRK1asYNddd91puSR23XVXli9fnkJUXZsLuHXYc889B8ARRxxR8D6HHHIItbW1nlLVLCMWL17MsGHDmlw3bNgwlixZUuaIzAXcOuzZZ59l6NCh7LXXXgXvM3bsWAD+8pe/lCosMyuiJUuWNPukweHDh7uAp8AF3Dpk27ZtPP744xx11FE7XdzSksMOO4x+/frx2GOPlTA6MyuGbdu28c4777TYA1+8eHGZozIXcOuQ6dOns3jxYk499dQ27de9e3eOPfZYJk+eTH19fYmiM7NiqK2tZevWra32wJ3L5eUCbh1yxx130LNnT0466aQ273vOOeewcOFCpkyZUoLIzKxYXn75ZQD23XffJtfvu+++bNmyhblz55YzrC4vEwVcUo2kFyTNlPSypOuT5e+R9Lyk1yXdK6k6Wd4z+Tw3WT8qzfg7qzfffJM777yTc889l0GDBrV5/1NPPZXhw4dz/fXXs23bthJEaJXOuZ0NM2fOBGj2TpODDz54h+2sPDJRwIE64JiIOBgYA5wg6QjgB8BPIuK9wErgc8n2nwNWRsRo4CfJdlZEs2bNYvz48VRXV/Ptb3+7XW1UV1fzwx/+kOeff57Pfe5zrFixoshRWgY4tytcRPDAAw8wevRohg4d2uQ2BxxwAAMGDGDChAlljq5r6552AIWI3M3C65KPPZJXAMcA5yTL7wKuA24FTkveA/we+JkkRQs3Hc+ePZsPfehD+e9r+N2NY2nzumK0UUntr1+/niVLltCvXz/uv/9+9txzT9rr3HPPZc6cOXznO9/hN7/5DXvttRcDBw6ke/fu9OjRg27dsnKMae1R7txOvrNxDP7cwue6ujreeustbrrpJppTXV3NhRdeyI9//GNeeeUVBgwY4NwtA2VlIg1JVcB0YDRwM/Aj4LnkSBxJewCPRMSBkmYBJ0TEgmTdG8AHI2JZozYvAi5KPh4IzCrLjymO3YBlrW5VGRxrabw/IvqmHURHObd3kKV/f1mKFbIVb0G5nYkeOEBE1ANjJA0AHgD2a2qz5H+bup9ppyOViLgNuA1A0rSIGFukcEsuS/E61tKQNC3tGIrBuf0ux1o6WYq30NzO3BhHRKwCngSOAAZIyh+EjATy03otAPYASNb3B3yC1ayCObfN2iYTBVzS4OToHEm9gOOAV4EngE8mm/0z8GDy/qHkM8n6/23pHJmZpcO5bdZ+WRlCHw7clZwr6wbcFxGTJL0C3CPpRuBF4FfJ9r8CfiNpLrmj87MK+I7bShB3KWUpXsdaGlmKtTnO7R051tLJUrwFxZqZi9jMzMzsXZkYQjczM7MduYCbmZllkAt4EyRdJSkk7ZZ2LM2R9CNJsyW9JOmB/IVAlUTSCZJeS6a9/Hra8bRE0h6SnpD0ajKl5+Vpx9QaSVWSXpQ0Ke1YssK5XRxZye3Ontcu4I0kk0YcD7yVdiyteAw4MCIOAuYA30g5nh0kFyXdDJwI7A+cLWn/dKNq0VbgyojYj9xtTJdUeLwAl5O7YtsK4NwujozldqfOaxfwnf0E+BpNTA5RSSJiSkRsTT4+R+5e2UpyODA3It6MiM3APeSmwaxIEbE4Iv6WvF9LLoF2Tzeq5kkaCXwCuD3tWDLEuV0cmcntzp7XLuANSDoVWBgRWXukzmeBR9IOopHdgbcbfF5ABSdOQ8kTrg4Bnk83khb9lFwx8mPcCuDcLqpM5nZnzOus3AdeNJIeB4Y1seqbwNXAx8sbUfNaijUiHky2+Sa5YaK7yxlbAQqa8rLSSOoD3A98OSLWpB1PUySdDCyNiOmSPpZ2PJXCuV02mcvtzprXXa6AR8RxTS2X9AHgPcBMSZAbtvqbpMMjYkkZQ9yuuVjzJP0zcDJwbAXORrV9ystEw+kwK5KkHuSS/O6IqOTnIh4JnCrpJKAG6CfptxFxXspxpcq5XTaZyu3OnNeeyKUZkuYDYxs/5ahSSDoBuAk4OiJq046nsWSe6jnAscBC4K/AORHxcqqBNUO5v+x3ASsi4stpx1Oo5Ej9qog4Oe1YssK53TFZyu3Ontc+B55dPwP6Ao9JmiHp52kH1FByEc6lwB/JXThyXyUmeANHAp8Gjkn+e85IjoTNys25XTydOq/dAzczM8sg98DNzMwyyAXczMwsg1zAzczMMsgF3MzMLINcwM3MzDLIBdzMzCyDXMDNzMwyyAXcSkLSLyQdmXYcZlY8zuvK4olcrCQkzQAOjYj6tGMxs+JwXlcW98CtzSQ9Ien45P2Nkv6z0fr9gDn5JJd0vqSXJM2U9BtJoyTNlnS7pFmS7pZ0nKRnJL0u6fAUfpZZl+a8zh73wK3NJH0UuAH4JXAOcGrDI3JJVwCrIuIOSQcAE4AjI2KZpIFAP2AuuWfzvkzuYQgzgc8BpwIXRMT4cv4ms67OeZ097oFbm0XEn8g9E/gK4KwmhtPGAY8m748Bfp9/8lNErEiWz4uI/4uIbeSSfWry2MT/A0aV+CeYWSPO6+xxAbc2S56vPByoi4i1jdbtAgyIiPzzgQU0NcxT1+D9tgaft9EFn1Nvljbndfa4gFubSBoO3A2cBqyXNK7RJv8APNHg81TgHyUNSvYfWJZAzaxgzutscgG3giVH4ROAKyPiVeA7wHWNNjuRd4fZSJ4T/F3gKUkzgZvKE62ZFcJ5nV2+iM2KStLfgA9GxJa0YzGz4nBeVyYXcDMzswzyELqZmVkGuYCbmZllkAu4mZlZBrmAm5mZZZALuJmZWQa5gJuZmWWQC7iZmVkGuYCbmZllkAu4mZlZBrmAm5mZZZALuJmZWQa5gJuZmWWQC7iZmVkGuYCbmZllkAt4JybpHEnTJK2TtFjSI5I+UqS2F0oaU6S2Bkp6QNJ6SX+XdE4L216a/KY6SXcW4/vNskTSfEkbk7zOv0YUoV3ndMZ0TzsAKw1JVwBfB74A/BHYDJwAnAY83cG2dwOGAK92MMy8m8nFNxQYA/xB0syIeLmJbRcBNwLjgF5F+n6zrDklIh4vVmPO6WxyD7wTktQfuAG4JCImRMT6iNgSEQ9HxFeTbULS6Ab73CnpxgLaHg28Te7fznJJyyW1+0BQUm/gTODaiFgXEU8DDwGfbmr75PdMBJYX0Pa/Jr2KtZJek3Rse+M0q3SSRki6X1KtpHmSvlTgfpnJ6aR953XCBbxz+hBQAzxQ7IYjYi5wFfD7iOgTEYMiYmt+vaRJklY185rURJPvA+ojYk6DZTOBAzoSp6T3A5cCh0VEX3JH9/M70qZZpZLUDXiYXO7sDhwLfFnSuNb2zUpOJ7E4rxvwEHrnNAhY1jAJi+xgYEZTKyLi5Da21QdY3WjZaqBvO+JqqB7oCewvqTYi5newPbNKMlFSPr+fBL4HDI6IG5Jlb0r6JXAWuVNorclCToPzegfugXdOy4HdOjIM1oox5I6oi2Ed0K/Rsn7A2o40mvQqvgxcByyVdE8xLvQxqxDjI2JA8hoP7AWMaNg7Bq4mdw66EBWf0+C8bswFvHN6FtgEjG9hmw3ALg0+Dyuk4WSo7kCaOVpPrnRf18zrkSZ2mQN0l/TeBssOBpq62KVNIuJ/IuIj5P64BfCDjrZpVqHeBuY1KOoDIqJvRJzU2o5ZymlwXjfkIfROKCJWS/oWcHMyzDYF2AIcB/xDRHyNXLKeI+ll4HjgaGAa5C5oS9r5TBPN90peTR78RcSJbYx1vaQJwA2SLiTXEzgN+HBT2yejCt2BKqBKUg2wtfHpguRc2e7AM+QOZjY2F7NZJ/ACsEbSvwL/Se4K8P2AXhHxV2gxrzOR08m2zusGuuwP7+wi4ibgCuAaoJbcEfqlwMRkk8uBU4BVwLkNlgPsQS5Bmmp3PfBz4BVJC4oU7hfJ/QFZCvwOuDh/u0ly9H91g22vIZe0XwfOS95f00SbPYHvA8uAJeRukbm6ie3MMi8i6snl8xhgHrl/97cD/Rts1mReZyinwXm9A0VE2jFYBZFUTe5c2EERsSXteMys45zXnZMLuJmZWQaVZQhdUo2kFyTNlPSypOuT5XcmEw7MSF5jkuUfk7S6wfJvNdPunxtss0jSxGT5rspN4/dS8r0HluN3mnU1zm2z9JTrIrY64JiIWCepB/B0g6sXvxoRv29inz+3dv9hRByVfy/pfuDB5OPVwIyIOF3SvuSm9euys/WYlZBz2ywlZemBR8665GOP5FW0sXtJfYFjePdCrP2Bqcl3zwZGSSr0fkgzK5Bz2yw9ZbuNTFIVMB0YDdwcEc9Luhj4bjKMNhX4ekTUJbt8SNJMchPdX9XMJPh5pwNTI2JN8nkmcAa53sDh5O4XHAm80yimi4CLAHr37n3ovvvuW4yfalYW06dPXxYRg9OOw7ltVlyF5nbZL2KTNIDcHN2XkZsxbAlQDdwGvBERN0jqB2xLhuVOAv4jIt7bQpuPALdHxP3J537AfwCHAP8H7AtcGBHNzjQ0duzYmDZtWlF+o1k5SJoeEWPTjiPPuW1WHIXmdtnvA4+IVeTm7j0hIhYnQ3B1wH8DhyfbrMkPy0XEZKCHco+724mkQcl+f2jwHWsi4oKIGAOcDwwmd2+kmZWIc9usvMp1Ffrg5OgcSb3IzQg2W9LwZJnITfs5K/k8LFlGMkzWjeYfNfcpYFJEbGrwfQOS+x4BLgT+1GAIzsyKxLltlp5ynQMfDtyVnCvrBtwXEZMk/a+kwYDITe35hWT7TwIXKzcN6EbgrEjG+iVNJjdktijZ9ixyM/M0tB/wa0n1wCvA50r428y6Mue2WUo8kUvC58ksayrtHHilcm4X34QJE/j617/OL3/5S44++ui0w+l0KvYcuJmZZduNN97I66+/zo9+9KO0Q+nSXMDNzKxgS5cu5cXjPz9UAAAgAElEQVQXXwTgscceY8sWT62eFhdwMzMr2KxZswD47Gc/y+bNm5k9e3bKEXVdLuBmZlawfAE/77zzAJgxY0aa4XRpLuBmZlawWbNmMXDgQD784Q8jiTfffDPtkLosF3AzMyvY66+/zr777kvPnj0ZMWIE8+fPTzukLssF3MzMCvb222+z5557AjBq1CgX8BS5gJuZWUEiggULFjBy5EjABTxtLuBmZlaQ5cuXU1dXxx577AHkCvjbb7/N1q1bU46sa3IBNzOzgrz99tsA23vgu+++O/X19dTW1qYZVpflAm5mZgVZsGAB8G4BHzJkCADvvPNOs/tY6biAm5lZQRYvXgzAiBEjABg6dCiQm53Nys8F3MzMCpIv1IMHDwbeLeDugafDBdzMzApSW1tLv3796NmzJ+ACnjYXcDMzK0htbe323jdA3759qamp8RB6SlzAzcysIEuXLt1+4RqAJIYMGeIeeEpcwM3MrCCNe+CQG0Z3AU+HC7iZmRXEBbyyuICbmVmrIoLa2todhtDBBTxNLuBmZtaqVatWsXXr1p164IMGDWLFihVEREqRdV0u4GZm1qr8dKlNFfC6ujo2btyYRlhdmgu4mZm1qrkCPnDgQABWrFhR9pi6OhdwMzNrVb5A5wt2ngt4elzAzcysVStXrgRg11133WG5C3h6XMDNzKxVLuCVxwXczMxalS/gAwYM2GG5C3h6XMDNzKxVK1eupF+/flRVVe2wPF/Aly9fnkZYXZoLuJmZtWrlypU7DZ8D9OrVi549e7oHngIXcDMza1VzBVwSAwcOdAFPgQu4mZm1qrkCDriAp8QF3MzMWrVq1SoX8ArjAm5mZq1yD7zyuICbmVmrXMArjwu4mZm1KP+wkpYKuG8jKz8XcDMza1Fzs7DlDRw4kI0bN7Jp06ZyhtXluYCbmVmLWivg+eX57aw8XMDNzKxFLuCVyQXczMxa1Nw86Hn56VRdwMvLBdzMzFrkHnhlcgE3M7MWFVrAfStZebmAm5lZi1obQncPPB0u4GZm1qKVK1fSp08fevTo0eT6fGF3AS8vF3AzM2tRS7OwAVRVVdG/f38PoZeZC7iZmbWotQIOuWF098DLywXczMxaVEgBHzhwoAt4mbmAm5lZi9wDr0wu4GZm1qJCC7jPgZeXC7iZmbXIPfDK5AJuZmbN2rx5Mxs2bCj4HHhElCkya7WASxrZwrpTihuOmZWLc9sK0dosbHm77rrr9mJv5VFID3yqpFGNF0r6LPDTYgdkZmXj3LZWtaWAN9zeSq+QAv4V4DFJ780vkPSNZPnRpQrMzErOuW2tcgGvXN1b2yAiJkuqAx6RNB64EDgM+GhE+P8ps4xyblshCi3gfqRo+RV0EVtETAU+AzwJ7A0c6wQ3yz7ntrWmrT1w30pWPoVcxLZW0hrgEaAfcCywtMHyVkmqkfSCpJmSXpZ0fbL8bkmvSZol6Q5JPZLlX5U0I3nNklQvaWAT7R4r6W/Jdk9LGp0s30vSVEkvSXqypYt1zLoq57YVIl/A8z3s5ngIvfwK6YGPAwZERN+IqI6I3hHRL/ncr8DvqQOOiYiDgTHACZKOAO4G9gU+APQiN4RHRPwoIsZExBjgG8BTEdHUYd2twLnJdv8DXJMs/zHw64g4CLgB+F6BcZp1Jc5ta1VrjxLN8xB6+RVSwM8Hpkm6R9JnJA1r65dEzrrkY4/kFRExOVkXwAtAU0fTZwO/a65pcj0HgP7AouT9/sDU5P0TwGltjdmsC3BuW6tae5RoXt++fenWrZsLeBkVchHbFwAk7QucCNwpqT+55HkUeCYi6ltrR1IVMB0YDdwcEc83WNcD+DRweaN9dgFOAC5tptkLgcmSNgJrgCOS5TOBM4H/AE4H+koaFBHLG7V/EXARwJ577tnaTzDrVJzbVohCZmED6NatGwMGDPA58DIqeCa2iJgdET+JiBOAY4CngU8Bz7e85/b965PhsJHA4ZIObLD6FuBPEfHnRrudQu6PSHP/Ir4CnBQRI4H/Bm5Kll8FHC3pRXK3wywEtjYR020RMTYixg4ePLiQn2HW6Ti3rSUrVqwoqICDp1Mtt1Z74E2JiI3A5OTV1n1XSXqS3NH3LEnfBgYDn29i87NoZohN0mDg4AZH+/eS6zUQEYuAM5Lt+gBnRsTqtsZq1tU4t62xQnvg4EeKlltZ5kKXNFjSgOR9L+A4YLakC8ldSHN2RGxrtE9/ckfYDzbT7Eqgv6T3JZ+PB15N9t1NUv63fQO4o5i/x8xynNudX1sKuJ9IVl4F98Al1ZA7xxXAGxGxqQ3fMxy4KzlX1g24LyImSdoK/B14VhLAhIi4IdnndGBKRKxvFMdk4MKIWCTpX4D7JW0jl/SfTTb7GPA9SQH8CbikDbGadSnObWtJWwv4vHnzShyR5bVawCV1B/6NXAL9nVySjpT0K+CaiNjp/FNjEfEScEgTy5v9/oi4E7izieUnNXj/APBAE9v8Hvh9a3GZdWXObStEWwu4h9DLp5Ah9B8BuwLvASZFxCHAPsBu5O7JNGtWfX29Hy9YuZzb1qJCHyWa50eKllchBfxk4KKIWEvuylEiYg25C1NOLmFslmHLly/n7LPPpqamhkGDBnHjjTdSX9/qHUlWXs5ta1Ghs7Dl7brrrtTX17N27dpShmWJQs6B5ydjAFCDhfXJ+SmzHaxevZqPfvSjzJ07ly984Qu8/fbbXHvttSxatIibb76Z5Jyopc+5bS0qdB70vIbTqfbrV+hkftZehfTAX5V0fvI+PxsSks4juTLUrKHPf/7zzJkzh8mTJ/Nf//VfTJw4ka9+9avceuut3HPPPWmHZ+9ybluL2lrAPZ1qeRVSwC8BLkvu75wt6ceSngIuAy4uZXCWPY8//jj33nsv1157Lccee+z25d/73vc44ogjuOyyy1i92rftVgjntrUof0tYe3rgVnqtFvCIWBARhwHfAeYDbwHXR8QHk0kVzACICL761a+y995787WvfW2HdVVVVfzsZz9j+fLl/PSnP00pQmvIuW2tae8Quu8FL4+C7wOP3HODp7a6oXVZjz32GDNmzOBXv/oVNTU1O60/9NBDOf300/n3f/93vvKVr/gcWYVwbltzOnIO3EqvLDOxWdfwwx/+kBEjRnDuuec2u803vvEN1q5dy69//esyRmZm7VHoo0TzfA68vFzArShmz57N1KlTueyyy+jZs2ez2x122GEcdthh3HLLLb5X1KzCFfoo0bzevXvTvXt3D6GXiQu4FcVdd91FVVUVn/nMZ1rd9otf/CKvvvoqTz75ZMnjMrP2a8ssbACSPBtbGbmAW4fV19fz61//mhNPPJFhw4a1uv0//dM/0bdvX37729+WIToza6+2FnDwdKrl5AJuHTZlyhQWLVrEBRdcUND2vXr14owzzuD+++9n06a2PDfDzMpp2bJl7Lbbbm3ax48ULR8XcOuwe+65h1133ZWTTy589s1zzjmH1atXM3lymx87bWZlsmzZMgYPHtymffxI0fJxAbcO2bp1Kw8//DCnnHIK1dXVBe93zDHHMHToUO6+++4SRmdmHdGeHriH0MvHBdw65M9//jMrV65k/Pjxbdqve/fufOpTn2Ly5MmsX7++9R3MrKy2bt3KypUrXcArmAu4dcjEiROpqanh4x//eJv3PeOMM9i0aRNTpkwpQWRm1hH5x4K25xz4qlWr2LbNz8MpNRdwa7eIYOLEiXz84x+nd+/ebd7/qKOOYuDAgTzwwAMliM7MOmLZsmUA7eqBR4SfeVAGLuDWbjNmzOCtt95q8/B5Xvfu3TnllFN4+OGH2bJlS5GjM7OOqK2tBWjXRWzg2djKwQXc2m3ixIl069atTVefNzZ+/HhWrVrFn/70pyJGZmYd1d4euKdTLR8XcGu3iRMn8pGPfKTNR+gNffzjH6dXr14eRjerMO0t4IMGDdphfysdF3BrlzfffJOXXnqp3cPnebvssgvjxo1j4sSJnhvdrILkC3C+IBdqyJAhALzzzjtFj8l25AJu7fLggw8CcNppp3W4rdNPP52FCxcyffr0DrdlZsWxbNky+vTp0+SjgVsydOhQAJYuXVqKsKwBF3Brl4kTJ3LQQQex9957d7itT3ziE1RVVTFx4sQiRGZmxdCeSVwA+vbtS01NjXvgZeACbm1WW1vL008/3eHh87xBgwZx1FFHuYCbVZDa2tp2Xd8iiaFDh7qAl4ELuLXZpEmT2LZtW9EKOOSuRn/55ZeZO3du0do0s/arra1tVw8ccAEvExdwa7OJEyey5557MmbMmKK1mT+Xnj+3bmbpWrJkSUGPB26KC3h5uIBbm6xfv54pU6Ywfvx4JBWt3VGjRjFmzBgPo5tVgG3btvHOO+8wfPjwdu3vAl4eLuDWJlOmTGHTpk1FHT7PO+2003jmmWd89apZypYtW8bWrVvbXcCHDBlCbW2t50MvMRdwa5MHHniAXXfdlaOOOqrobY8fP56I4OGHHy5622ZWuMWLFwN0aAi9vr6e5cuXFzMsa8QF3Aq2efNmHn74YU477TS6d+9e9PYPPvhg9tprL58HN0vZkiVLADo0hA6ezKXUXMCtYE8++SSrVq3ijDPOKEn7khg/fjxTpkxh3bp1JfkOM2tdvgfuAl7ZXMCtYBMmTKB3794cf/zxJfuO8ePHU1dX52eEm6Woo0Po+cKfb8dKwwXcClJfX8/EiRP5xCc+0eapFdviIx/5CAMHDvTV6GYpWrx4Mf369WOXXXZp1/4jR44EYMGCBcUMyxpxAbeCPPvss7zzzjslGz7P6969OyeffDKTJk3yM8LNUrJo0aJ2D58D9O7dm4EDB/LWW28VMSprzAXcCjJhwgSqq6s56aSTSv5d48ePZ+XKlfz5z38u+XeZ2c7+/ve/s9dee3WojT322IO33367SBFZU1zArVX19fXce++9nHDCCfTt27fk3zdu3Dj69OnDPffcU/LvMrOduYBngwu4terJJ59k0aJFnHfeeWX5vl122YUzzjiD++67j02bNpXlO80sZ8OGDdTW1rqAZ4ALuLXqt7/9Lf369ePkk08u23eed955rF69mj/84Q9l+04zY/t5644W8D333JMVK1awfv36YoRlTXABtxZt3LiR+++/nzPPPJNevXqV7XuPOeYYhg0bxm9/+9uyfaeZ5YbPoeMFfI899gBwL7yEXMCtRQ899BBr164t2/B5XlVVFeeccw5/+MMfWLFiRVm/26wryxfwUaNGdaidvffeG4A333yzoyFZM1zArUW/+MUv2GuvvTj66KPL/t2f/vSn2bJli3vhZmU0b948unfvzogRIzrUzvve9z4AXnvttWKEZU1wAbdmzZ49myeeeILPf/7zVFVVlf37x4wZwwc/+EFuueUWIqLs32/WFc2ePZvRo0d3OOcHDRrEwIEDmTNnTpEis8ZcwK1ZP//5z+nRowef+9znUovhkksu4bXXXmPq1KmpxWDWlbz66qvst99+RWnrfe97nwt4CbmAW5NWr17NnXfeyZlnnsmQIUNSi+NTn/oUu+22Gz/72c9Si8Gsq9i8eTNz5851Ac8IF3Br0q233srq1au56qqrUo2jpqaGiy++mAcffJBZs2alGotZZzd37lzq6+uLWsAXLFjgpwuWiAu47WTDhg3cdNNNjBs3jkMPPTTtcLj88svp06cP3/3ud9MOxaxTe/XVVwGKVsAPOuggAGbOnFmU9mxHLuC2k1tvvZXa2lq++c1vph0KkLsY5pJLLuHee+/d/gfGzIrvxRdfpKqqqmgFPN8BmDZtWlHasx25gNsOli1bxne+8x3GjRvHUUcdlXY421155ZX06dOHK664wlekm5XICy+8wEEHHdTux4g2NmLECEaMGOECXiIu4LaDa665hnXr1nHTTTelHcoOBg8ezPXXX8+jjz7KQw89lHY4Zp3Otm3b+Otf/8rhhx9e1HYPPfRQ/vrXvxa1TctxAbftHn/8cX7xi1/wpS99if333z/tcHZy6aWXcsABB3DZZZexatWqtMMx61RmzpzJqlWr+PCHP1zUdo888khee+01Fi1aVNR2zQXcErW1tVxwwQW8//3vr9iLxXr06MEdd9zB4sWL+Zd/+RcPpZsV0ZQpUwA4/vjji9ruiSeeCMCjjz5a1HbNBdyAuro6Tj/9dJYtW8bdd99d1oeWtNXhhx/Ov/3bv/H73/+eG2+8Me1wzDqNhx56iIMPPpjhw4cXtd0PfOAD7L777kyePLmo7ZoLeJe3ceNGxo8fzzPPPMNdd91VEbeNteaqq67i/PPP51vf+lbFnas3y6I33niDv/zlL5x99tlFb1sSp59+OpMmTaK2trbo7XdlLuBd2Pz58/nYxz7GH//4R26//Xb+8R//Me2QCiKJ22+/nTPPPJMrr7ySSy65hI0bN6Ydlllm/eQnP6F79+4le+rgF7/4Rerq6rjttttK0n5XVZYCLqlG0guSZkp6WdL1yfL3SHpe0uuS7pVUnSzvmXyem6wf1Uy7J0h6Ldnu6w2WN9mu5WzYsIHvf//7HHTQQbz22mtMmDAh1fnO26NHjx7ce++9XHnlldxyyy0ccsghPPjggz4vXmbO7ex76aWXuO2227jgggvYfffdS/Id++23H5/4xCf4wQ9+4OeDF1NElPwFCOiTvO8BPA8cAdwHnJUs/zlwcfL+i8DPk/dnAfc20WYV8AawN1ANzAT2T9Y12W5Lr0MPPTQ6s1WrVsVDDz0UX/jCF6J///4BxKmnnhpvvvlm2qF12OOPPx6jR48OIN7//vfH9ddfH88//3zU1dWlHVpJAdOiDPnb0su5nW0vvvhi7LnnnjF06NCora0t6Xe9/vrr0bdv39h///3j9ddfL+l3ZV2hua0oc49F0i7A08DFwB+AYRGxVdKHgOsiYpykPybvn5XUHVgCDI4GwTbcPvn8jWTV94HaptptKa5Ro0bFtddeu0MPrqn3WVi/du1aVqxYwYoVK1i6dCmvvfYaCxcuBKBXr16MHz+eSy65hCOPPLLZ/x5Zs3XrVn73u99xxx138NRTTxERVFdXs88++7DXXnsxcuRI+vXrR9++fenTpw81NTVUVVXRrVu3nf63W7dsnFk677zzpkfE2LTjyKvk3P72t78NNJ8/5V6X9ncvXbqUadOm8dRTTzFkyBAmT57M//t//49Se+qppzjttNNYv349xx13HIcccgiDBw+md+/e9OzZE0kAO/1vc8s6q3PPPbeg3C5bAZdUBUwHRgM3Az8CnouI0cn6PYBHIuJASbOAEyJiQbLuDeCDEbGsQXufTLa5MPn8aeCDwHXNtdtETBcBFyUfDwSy9LSM3YBlrW5VGRxrabw/IvqmHYRzu6iy9O8vS7FCtuItKLe7lyMSgIioB8ZIGgA8ADQ12W7+aKKpQ6zGRxrNbVPIvvmYbgNuA5A0rZJ6M63JUryOtTQkVcT8lM7t4nGspZOleAvN7bKPFUbEKuBJcufJBiTDaAAjgfxUPQuAPQCS9f2BFY2a2r5No/2XtdCumZWIc9usvMp1Ffrg5OgcSb2A44BXgSeATyab/TPwYPL+oeQzyfr/jZ3H+v8KvDe5KrWa3AUxDyXbNdeumRWRc9ssPeXqgQ8HnpD0ErnkfCwiJgH/ClwhaS4wCPhVsv2vgEHJ8iuArwNIGiFpMkBEbAUuBf5I7g/GfRHxcrJ/c+22JGs3KGYpXsdaGpUQq3O7uBxr6WQp3oJiLftV6GZmZtZx2bhfxszMzHbgAm5mZpZBLuBNkHSVpJC0W9qxNEfSjyTNlvSSpAfyFxJVkuamw6xEkvaQ9ISkV5MpQS9PO6bWSKqS9KKkSWnHkhXO7eLISm539rx2AW8kmRzieOCttGNpxWPAgRFxEDAH+EYr25dVMrnHzcCJwP7A2ZL2TzeqFm0FroyI/cjdBnVJhccLcDm5i7ysAM7t4shYbnfqvHYB39lPgK/RzAQRlSIipiRX6wI8R+6e2EpyODA3It6MiM3APcBpKcfUrIhYHBF/S96vJZdApXmyQxFIGgl8Arg97VgyxLldHJnJ7c6e1y7gDUg6FVgYETPTjqWNPgs8knYQjewONHzs0AIqOHEaUu4JWYeQezBHpfopuWK0Le1AssC5XVSZzO3OmNdlm0q1Ukh6HBjWxKpvAlcDHy9vRM1rKdaIeDDZ5pvkhonuLmdsBSh42stKIqkPcD/w5YhYk3Y8TZF0MrA0IqZL+lja8VQK53bZZC63O2ted7kCHhHHNbVc0geA9wAzk6fdjAT+JunwiFhSxhC3ay7WPEn/DJwMHNvEbFZpa246zIolqQe5JL87IiakHU8LjgROlXQSUAP0k/TbiDgv5bhS5dwum0zldmfOa0/k0gxJ84GxDZ+SVEkknQDcBBwdEbVpx9NYMl/1HOBYYCG5WbrOaTCjVkVR7i/7XcCKiPhy2vEUKjlSvyoiTk47lqxwbndMlnK7s+e1z4Fn18+AvsBjkmZI+nnaATXUynSYlehI4NPAMcl/zxnJkbBZuTm3i6dT57V74GZmZhnkHriZmVkGuYCbmZllkAu4mZlZBrmAm5mZZZALuJmZWQa5gJuZmWWQC7iZmVkGuYBbSUj6haQj047DzIrHeV1ZPJGLlYSkGcChEVGfdixmVhzO68riHri1maQnJB2fvL9R0n82Wr8fMCef5JLOl/SSpJmSfiNplKTZkm6XNEvS3ZKOk/SMpNclHZ7CzzLr0pzX2eMeuLWZpI8CNwC/BM4BTm14RC7pCmBVRNwh6QBgAnBkRCyTNBDoB8wl92zel8k9DGEm8DngVOCCiBhfzt9k1tU5r7PHPXBrs4j4E7lnAl8BnNXEcNo44NHk/THA7/NPfoqIFcnyeRHxfxGxjVyyT00em/h/wKgS/wQza8R5nT0u4NZmyfOVhwN1EbG20bpdgAERkX8+sICmhnnqGrzf1uDzNrrgc+rN0ua8zh4XcGsTScOBu4HTgPWSxjXa5B+AJxp8ngr8o6RByf4DyxKomRXMeZ1NLuBWsOQofAJwZUS8CnwHuK7RZify7jAbyXOCvws8JWkmcFN5ojWzQjivs8sXsVlRSfob8MGI2JJ2LGZWHM7ryuQCbmZmlkEeQjczM8sgF3AzM7MMcgE3MzPLIBdwMzOzDHIBNzMzyyAXcDMzswxyATczM8sgF3AzM7MMcgE3MzPLIBdwMzOzDHIBNzMzyyAXcDMzswxyATczM8sgF3AzM7MMcgHvgiSdI2mapHWSFkt6RNJHitT2QkljitTWpUmcdZLuLEabZp2VpPmSNiZ5nX+NKEK7zukK5QLexUi6Avgp8G/AUGBP4BbgtCK0vRswBHi1o20lFgE3AncUqT2zzu6UiOjT4LWoI405pyubC3gXIqk/cANwSURMiIj1EbElIh6OiK8m24Sk0Q32uVPSjQW0PRp4m9y/qeWSlkvq3pF4kxgnAssL+P5/TXoKayW9JunYjny3WWchaYSk+yXVSpon6UsF7uecrnAu4F3Lh4Aa4IFiNxwRc4GrgN8nR/6DImJrfr2kSZJWNfOa1JHvlvR+4FLgsIjoC4wD5nekTbPOQFI34GFgJrA7cCzwZUnjWtvXOV35OnQ0ZZkzCFjWMAmL7GBgRlMrIuLkEn0nQD3QE9hfUm1EzC/hd5lVsomS8vn9JPA9YHBE3JAse1PSL4GzgD8W0J5zuoK5B961LAd26+gwWAvGkDvSL6ukp/Bl4DpgqaR7inHxjlkGjY+IAclrPLAXMKJh7xi4mtz1L4VwTlcwF/Cu5VlgEzC+hW02ALs0+DyskIaToboDaeZoPbnSfV0zr0cKjL9ZEfE/EfERcn+wAvhBR9s06wTeBuY1KOoDIqJvRJzU2o7O6crnIfQuJCJWS/oWcHMyzDYF2AIcB/xDRHyNXLKeI+ll4HjgaGAa5C5oS9r5TBPN90peTR4URsSJbY03GSnoDlQBVZJqgK2NTwEk58t2B54hd4Cysbk4zLqYF4A1kv4V+E9gM7Af0Csi/got5rVzusL5P0gXExE3AVcA1wC15I7QLwUmJptcDpwCrALObbAcYA9yCdVUu+uBnwOvSFpQpHCvIZe4XwfOS95f08R2PYHvA8uAJeRue7m6SDGYZVZE1JPL5zHAPHI5cjvQv8FmTea1c7ryKSLSjsEyQFI1uXNhB0XElrTjMbOOc15nmwu4mZlZBpVlCF1SjaQXJM2U9LKk65Pll0qam0wesluD7b8qaUbymiWpXtLAJtqVpO9KmiPp1fwEBZI+Jml1gza+VY7fadbVOLfN0lOWHrgkAb0jYp2kHsDT5M611gEryd2vODYiljWx7ynAVyLimCbWXQD8A/CZiNgmaUhELJX0MeCqEt+naNblObfN0lOWq9Ajd5SwLvnYI3lFRLwIkPsb0Kyzgd81s+5i4JyI2JZ8z9KiBGxmBXFum6WnbLeRSaoCpgOjgZsj4vkC9tkFOIHcVdJN2Qf4J0mnk7ui+ksR8Xqy7kOSZpKbPP+qiHi5ifYvAi4C6N2796H77rtvG3+VWXqmT5++LCIGpx2Hc9usuArN7bIV8OR2hjGSBgAPSDowIma1stspwDMRsaKZ9T2BTRExVtIZ5J5wcxTwN2CvZFjvJHK3Qr23iZhuA24DGDt2bEybNq1dv80sDZL+nnYM4Nw2K7ZCc7vs94FHxCpy58VOKGDzs2h+iA1gAXB/8v4B4KDkO9ZExLrk/WSgR8MLacys+JzbZuVVrqvQBydH50jqRW7mr9mt7NOf3CxgD7aw2UQgfwHM0cCcZN9hycU1SDqc5HF4HfkNZrYz57ZZesrVAx8OPCHpJeCvwGMRMUnSl5IZfkYCL0m6vcE+pwNTktmAtpM0We9Oav994ExJ/0fuqTsXJss/CcxKzpP9J3BW+IZ3s1JwbpulxBO5JHyezLJG0vSIGJt2HJXOuV1c27Zt46GHHuKll17iiCOO4Pjjj2/tbg5dsOMAACAASURBVANro0Jz2w8zMTOzgtTV1fHJT36SSZMmbV92/vnnc8cdd1BVVZViZF2TH2ZiZmYFufjii5k0aRI//elPWbduHddeey2//vWvue6669IOrUtyATczs1Y9+uij/Pd//zdXX301l19+Ob179/7/7d15fFT19f/x1wkJS9gRUFARKIKIQSQLu192EDC4ICggiwvaKi0u1S9SBazaH79a3P0pihQRlFUtChiMUSAsmUAIFUEW0YSohKgEMCwmOb8/ZpJiGmAiM3NnMuf5eOTB5M6de9+TcHLmbp/L9OnTGTduHE899RSZmZlORww71sCNMcackaoyefJkWrVqxdSpU0uniwgzZ86kfv36PPjggw4mDE/WwI0xxpzRv/71L7Zu3cqjjz5K1apVf/Vc/fr1eeihh/j444/JyMhwKGF4sgZujDHmjJ577jmaN2/OyJEjy33+rrvuonbt2jz99NMBThberIEbY4w5rd27d5OSksIdd9xBZGT5Fy7VrVuX8ePHs2TJEn788XSj4xpfswZujDHmtEouERs/fvwZ5xs3bhwnT55k0aJFAUpmrIEbY4wpl6qycOFC+vbtS9OmTc84b4cOHWjXrh1vvvlmgNIZa+DGGGPKtXXrVvbt28ewYcPOOq+IMGrUKDZs2EBOTk4A0hlr4MYYY8q1ZMkSqlSpwnXXXefV/EOHDgXcZ60b/7MGbowxplzLli2jZ8+eNGzo3R1b27ZtS6tWrXj//TPdaM74ijVwY4wx/2Xfvn3s3LmTa6+91uvXiAhDhw7lk08+4fDhw35MZ8AauDHGmHIkJSUBMGDAgAq9LjExkV9++YWPP/7YH7HMKayBG2OM+S9JSUk0a9aMNm3aVOh1Xbp0oVatWiQnJ/spmSlhDdwYY8yvFBYWkpycTP/+/St8r++oqCiuvvpq2wIPAGvgxhhjfiUtLY38/PwK7z4v0bdvX3bt2kV2draPk5lTWQM3xhjzK8nJyYgIffr0+U2v79u3b+lyjP9YAzfGGPMra9asoX379tSvX/83vf6KK66gcePGthvdz6yBG2OMKVVYWMiGDRvo0aPHb16GiNCrVy/WrFnjw2SmLGvgxhhjSmVkZPDzzz+fUwMH6NatG9nZ2WRlZfkomSnLGrgxxphSa9euBTjnBt69e3cAUlNTzzmTKZ81cGOMMaXWrFnD7373O5o0aXJOy4mJiaFWrVqsW7fOR8lMWdbAjTHGAFBcXMy6devOeesbIDIyki5dutgWuB9ZAzfGGAPAzp07+eGHH7j66qt9srxu3bqxbds28vPzfbI882vWwI0xxgD/OV5dcvz6XHXr1g1VZePGjT5Znvk1a+DGGGMA9whsDRo0oFWrVj5ZXqdOnahSpYrtRvcTa+DGGGMAcLlcxMXFVXj889OpXbs2V155pTVwP7EGbowxhoKCAj7//HPi4+N9utxOnTqRnp5OcXGxT5drrIEbY4wBMjMzKSoqIi4uzqfLTUhI4PDhw+zatcunyzXWwI0xxuDefQ74fAu8ZHlpaWk+Xa6xBm6MMQZ3A2/SpAkXXnihT5d72WWXUatWLWvgfmAN3BhjDC6Xy+db3wBVqlQhLi7OGrgfWAM3xpgwl5+fz5dffumXBg7u4+CZmZmcOHHCL8sPV9bAjTEmzG3evBnw/fHvEgkJCZw8eZJt27b5Zfnhyhq4McaEufT0dABiY2P9snw7kc0/rIEbY0yYc7lctGjRgoYNG/pl+RdffDHnn3++NXAfswZujDFhzl8nsJUQERISEkovVTO+YQ3cGGPC2MGDB/nmm2/82sDBfRx8586ddmcyH7IGbowxYcxfA7iUFR8fj6qWHm83584auDHGhDGXy4WI0LFjR7+up+QDgjVw37EGbowxYSw9PZ3LLruM2rVr+3U9DRo0oGXLlnYc3IesgRtjTJhSVb+fwHaq+Ph4a+A+ZA3cGGPC1P79+zlw4EBAG3hWVha5ubkBWV9lZw3cGGPCVKBOYCtRsh7bCvcNa+DGGBOmXC4XkZGRXHnllQFZX8eOHRERa+A+Yg3cGGPClMvlon379lSvXj0g66tVqxZt27a1M9F9xBq4McaEoZJrsuPi4gK63pIT2VQ1oOutjKyBG2NMGNqzZw/5+fkBO/5dIj4+ntzcXLKzswO63srIGrgxxoShQJ/AVsJOZPOdszZwEbnoDM9d69s4xphAsdoOby6Xixo1atCuXbuArvfKK68kKirKGrgPeLMFniwizctOFJHbgGd9HcgYEzBW22HM5XJx1VVXERkZGdD1VqtWjZiYGGvgPuBNA78PWC0il5ZMEJHJnun/469gxhi/s9oOU4WFhWRkZAR893mJ+Ph40tPTKS4udmT9lcVZG7iqrgDuBlaKyBUi8iwwBLhaVff7O6Axxj+stsPXjh07KCgoCPgZ6CXi4+M5fPgwe/bscWT9lYVXJ7GpajIwDvgUaAn0UdWfvF2JiFQXkTQRyRSR7SIy3TO9hYhsEpHdIrJQRKp6pjcTkRQRyRCRbSIy6DTLvc+zvM9F5G0Rqe6ZPl9EvvRMf0NEorzNakw4sdoOT06dwFbCTmTzDW9OYjsiIoeBlUAdoA+Qe8p0b5wAeqvqlUAHYKCIdAZmAM+o6qXAT8Dtnvn/AixS1auAm4GXy8l1IfBHIE5VrwCqeOYFmA9cBsQANYA7vMxpTNiw2g5fLpeLOnXqcOmll559Zj+4/PLLqVGjhjXwc+TNFvgAoJ6q1lbVqqpaU1XreL6v481K1O2o59soz5cCvYElnulzgetKXoL7DwpAXeDb0yw6EqghIpFAdMl8qrrCs04F0oDTnm1rTBiz2g5TLpeLuLg4IiKcuZI4MjKSq666yhr4OfLmtzcGSBeRd0RknIhc8FtWJCJVRGQrkAusBvYCh1S10DPLfuBCz+NpwGgR2Q+sACaWXZ6q5gBPA1nAd0C+qiaVWWcUcCuw6rdkNqaSs9oOQ8ePHyczM5OEhARHc8THx5ORkUFhYeHZZzbl8uYktrtVtSPuwqsP/FNENojIUyJytYhU8WZFqlqkqh1wf2JOANqWN5vn31uAf6rqRcAgYJ6I/CqriNQHhgItgKZATREZXWZ5LwNrVHVteZlEZIKIpItI+sGDB715G8ZUGlbb4Wnr1q0UFhYGRQM/duwY27dvdzRHKPN6/4mq7lTVZ1R1IO7dY+uAm4BNFVmhqh7CfcJMZ6CeZxcZuIu/ZHfa7cAiz/wbgOpAwzKL6gvsU9WDqvoLsAzoWvKkiEwFGgH3nyHLLFWNU9W4Ro0aVeRtGFNpWG2Hl5Ld1sHQwAG7sck5+E0HQFT1mOdY1ERVPet1CCLSSETqeR7XwF2gO4AUYJhntrHA+57HWbhPqEFE2uIu8rIfo7OAziISLSLimX+H5zV34D6+d4uq2oWGxnjJarvyS0tLo0mTJlx44YVnn9mPWrVqRd26de04+DkI1BkMTYAUEdkGuIDVqvoB8DBwv4jsAc4DZnvmfwC4U0QygbeBcaqqItJURFYAqOom3CfJbAH+7XkvszyvfwU4H9ggIltF5LGAvEtjwo/VdohJS0tzfOsbICIigri4OGvg58DrMfQ812G2wn0sa6+qHvf2taq6DbiqnOlf4T5mVnb6F0C3cqZ/i/u4Wcn3U4Gp5cwX2LEBjQlhVtvh49ChQ+zatYuxY8c6HQWAuLg4/vGPf3D8+PGA3ZO8MvHmOvBIEfm/uM8knQu8BWSLyP855RiXMSbEWG2Hn5LjzcGwBQ7u4+CFhYVkZmY6HSUkeVOkfwdq4T4j9EFVnSoidYCZuC/1mOTHfCaEqCpZWVmkpaWxb98+srOzOXbsGKrKeeedR5MmTYiJiSE2Npb69es7HddYbYedtLQ0AMeGUC3r1BHZOnXq5HCa0ONNAx8CtPYcp7oWmKqqh0XkLuBLrMjDWnFxMevXr+ftt99m+fLlZGdnlz5Xt25datasCcAPP/zAiRMnSp+LjY3l+uuv5+abb+Z3v/tdwHMbwGo77KSlpdG6dWvq1avndBQALr74Yho3bmzHwX8jb05iKxn1CEBOmVgE2FmgYer48eO89tprXH755fTo0YM5c+YQHx/PCy+8QHp6Ovn5+Rw6dIicnBxycnI4duwYubm5JCUl8de//pWoqCj+8pe/0KpVKwYNGsTq1av5z38zEyBW22HG5XIFze5zABEpvTOZqThvGvgOERnjeVw67KFnYIUdfkllglZxcTFz5syhZcuWTJgwgejoaObOncuBAwdYunQp9957L7GxsdSp8+uROEWERo0a0a9fP/7yl7+wYcMGsrOzmTZtGhkZGfTv359evXqxYcMGh95ZWLLaDiM5OTl8++23jt3A5HTi4uLYsWMHR44ccTpKyPGmgd8DTBSRT4GdIvK0iHyGewjE3/sznAkuLpeL+Ph4brvtNpo1a8bHH3/M5s2bGTNmDLVr167w8i666CKmTp3K119/zQsvvMDOnTvp2rUr48aNIy8vzw/vwJRhtR1GSo5/B9MWOLiPg6sqW7ZscTpKyPFmKNX9qhoP/BX4GvcgC9NVtZPn0g9TyZ04cYIpU6bQpUsXDhw4wPz589mwYQN9+vTBPc7GualWrRr33nsve/fuZfLkycyfP5+2bduyePFiH6Q3p2O1HV42bdpEVFQUHTp0cDrKr9itRX+7igylmqyqL6jq86r6iT9DmeCxa9cuEhISeOqppxg7dizbt29n5MiRPmncZdWsWZOnnnqKLVu20LJlS4YPH86dd97Jzz//7PN1mf+w2g4P69evp2PHjkF3vXXjxo1p1qyZNfDfwJl7yZmQsHTpUuLi4sjJyeGDDz5g9uzZ1K1b1+/rjYmJYd26dUyePJnZs2cTHx/Pzp07/b5eYyqrkydP4nK56Nbtv8bQCQoJCQls2lShofcN1sBNOYqLi3nooYcYNmwYbdu2JSMjg8GDBwc0Q1RUFE899RRJSUnk5eXRuXNnPvroo4BmMKay2LJlC8ePH6dr165nn9kB3bp145tvvmH//v1ORwkp1sDNrxQUFHDTTTfx97//nbvvvps1a9Zw8cUXO5anb9++uFwuLrnkEgYNGsSzzz5rl5sZU0Hr168HCOoGDpCamupwktBiDdyUys3NpXfv3rz77rs888wzvPzyy1SrVs3pWFxyySWkpqaSmJjIfffdx3333UdxsV2mbIy3UlNTadGiBU2aNHE6Srk6dOhAdHQ069atczpKSLHxjg0AWVlZ9O7dm5ycHJYsWcINN9zgdKRfqVWrFkuXLuWBBx7g2WefJS8vjzlz5hAVFeV0NGOCmqqSmppKv379nI5yWlFRUXTu3Nm2wCvItsAN+/fvp1evXuTl5ZGSkhJ0zbtEREQEM2fO5Mknn2T+/PkMHTrUzlA35iz27dvHgQMHgvYEthLdu3cnMzOTw4cPOx0lZFgDD3M5OTmlzTspKYnOnTs7HemMRIRHHnmEWbNm8dFHHzFw4EAbwcmYMyjZqg3W498lunfvTnFxMRs3bnQ6SsiwBh7GvvvuO3r37s3333/PqlWrgm6EpjO58847eeedd9iwYQMDBw60T+3GnEZqaip16tShXbt2Tkc5o86dOxMREWHHwSvAGniY+v7770uPea9atYouXbo4HanCbrrpJhYuXEhaWpo1cWNO47PPPqNbt25UqVLF6ShnVLt2bTp06GANvAKsgYeh3Nxc+vTpQ1ZWFitXrgz6Y2NncuONN7Jw4UJcLhcDBgwgPz/f6UjGBI1vv/2WnTt30rt3b6ejeKV79+5s3LiRkydPOh0lJFgDDzMHDx6kT58+7Nu3jw8//JAePXo4Hemc3XDDDSxevJj09HT69+9vTdwYj08//RSAXr16ORvESz179uTYsWM2KpuXrIGHkby8PPr27cuePXv44IMP6Nmzp9ORfOa6665j6dKlZGRk2O50YzxSUlKoV69e0N3A5HR69uxJREQEycnJTkcJCdbAw8SPP/5Iv3792LVrF8uXLw+ZXWoVkZiYyMKFC0lPT+eaa66xs9NN2EtJSeHqq68O+uPfJerXr0/Hjh2tgXvJGngY+Omnn+jXrx87duzgvffeo2/fvk5H8pvrr7+ed955h02bNjF48GCOHj3qdCRjHJGVlcXevXtD7sN679692bhxo9WuF6yBV3KHDh2if//+fP755yxbtowBAwY4HcnvbrzxRhYsWEBqaipDhgyxwV5MWEpJSQFC5/h3iT59+lBYWGhno3vBGngllp+fz4ABA8jMzGTp0qUMGjTI6UgBM3z4cObNm8fatWtJTEykoKDA6UjGBFRycjLnnXceV1xxhdNRKqR79+5UrVrVdqN7wRp4JXX48GEGDhzIli1bWLx4MUOGDHE6UsCNHDmSuXPnkpKSwtChQzl27JjTkYwJiOLiYlatWsWAAQOIiAitP/PR0dF06dLFGrgXQus3a7xy5MgRBg0ahMvlYtGiRQwdOtTpSI4ZPXo0c+bMITk5mRtuuIHjx487HckYv9uyZQsHDx7kmmuucTrKb9KvXz8yMjL4/vvvnY4S1KyBVzJHjx5l8ODBbNy4kXfeeYfrr7/e6UiOGzt2LK+//jqrVq3ixhtv5MSJE05HMsavVqxYgYiE7DkvJXsMV6xY4XCS4GYNvBL5+eefGTJkCKmpqcyfP59hw4Y5HSlo3Hbbbbz66qusWLGCm266yUZ6MpXaypUriY+Pp1GjRk5H+U3at2/PRRddxIcffuh0lKBmDbySKCgoIDExkbVr1zJv3jxGjBjhdKSgM2HCBF5++WWWL1/OiBEj+OWXX5yOZIzP5eXlsWnTppDdfQ7uuw4OHjyYpKQk22N2BtbAK4GCggKuvfZaUlJSmDt3LiNHjnQ6UtD6/e9/zwsvvMB7773HLbfcYk3cVDqrVq1CVUO6gYN7N/rRo0dZs2aN01GCljXwEFey27ykeY8ePdrpSEHv3nvv5ZlnnmHp0qWMHj2awsJCpyMZ4zNLly6ladOmxMfHOx3lnPTu3Zvq1avzwQcfOB0laFkDD2Elzfuzzz7jzTff5NZbb3U6UsiYNGkSTz/9NIsWLWLMmDHWxE2lcPTo0dKTNUPt8rGyoqOj6d+/P8uWLaO4uNjpOEEptH/DYezo0aMMGjSINWvWMG/ePNvy/g0eeOABZsyYwdtvv8348eMpKipyOpIx52TFihUcP3680pzAOnz4cPbv38+GDRucjhKUIp0OYCru8OHDpWebv/XWW9xyyy1ORwpZDz30EIWFhUyZMoUqVaowe/bskLnxgzFlLVmyhMaNG9OtWzeno/hEYmIi1atXZ+HChZXmPfmSbYGHmIMHD9K7d2/Wr1/P/PnzrXn7wCOPPML06dOZO3cuEyZMsN11JiQVFBTw4YcfcsMNN1SaD6G1a9dm0KBBLF682PaQlcMaeAjJysqiR48ebN++nffff5+bb77Z6UiVxmOPPcZjjz3GG2+8wR133GHHxE3IWbZsGQUFBZXu78KIESP4/vvvWbt2rdNRgo7tQg8RO3fupF+/fhw+fJikpCR69OjhdKRKZ9q0aYgI06dPJzc3l4ULF1KzZk2nYxnjlTlz5tCyZctK97dh8ODB1K5dm3/+85/07NnT6ThBxbbAQ8C6devo3r07J0+e5LPPPqt0BRosRIRp06bxyiuvsHLlSnr16kVubq7TsYw5q2+++YZPPvmEsWPHhvzZ52XVrFmTkSNHsmjRIg4dOuR0nKBSuX7TldBbb71Fnz59aNCgAampqXTo0MHpSJXeXXfdxbvvvsvnn39O165d2b17t9ORjDmjuXPnAjBmzBiHk/jHnXfeybFjx1iwYIHTUYKKNfAgpapMnTqVW2+9la5du7Jx40ZatWrldKywkZiYyCeffMKhQ4fo1KkTq1evdjqSMeU6efIkr7zyCv3796d58+ZOx/GL2NhYOnbsyKxZs1BVp+MEDWvgQejIkSOMGDGCxx9/nPHjx/PRRx/RoEEDp2OFnc6dO5OWlsaFF17IwIEDefrpp+2Phwk6S5Ys4bvvvmPSpElOR/GrCRMmkJmZyfr1652OEjSsgQeZ7du3Ex8fz9KlS5kxYwazZ8+matWqTscKWy1btmTDhg1cf/31/PnPf+bWW2+loKDA6VjGAO49dc8++yytW7cO2VuHemv06NGcd955zJgxw+koQcMaeBBZsGABCQkJHDp0iOTkZB566CFExOlYYa9WrVosXryYJ554ggULFhAXF0dmZqbTsYzhs88+w+Vy8ac//anSnbxWVs2aNZk4cSLLly9n+/btTscJCpX7Nx4i8vPzGTNmDKNGjSI2NpYtW7bY5RJBRkSYMmUKSUlJ/PTTTyQkJPDCCy/YLnXjGFXl0UcfpWnTptx2221OxwmIe+65hxo1avC3v/3N6ShBwRq4wz755BNiYmJYsGABjz32GMnJyTRt2tTpWOY0+vbty7Zt2+jXrx9//OMfGTRoEFlZWU7HMmHo448/Zt26dUyZMoXq1as7HScgGjZsyMSJE1mwYAEZGRlOx3GcNXCH/PTTT9x999306dOHGjVqsH79eqZPn05UVJTT0cxZNGrUiOXLl/P888+zZs0a2rVrx4svvmhDsJqAKSws5M9//jPNmjXj9ttvdzpOQE2ePJn69evz8MMPOx3FcdbAA0xVefPNN2nTpg2vvfYakyZNIiMjg4SEBKejmQoQESZOnFh6rfjEiRPp3r27bRWYgHjppZfIzMxk5syZVKtWzek4AVWvXj0effRRVq9ezbvvvut0HGepqn2pEhsbq/62bt067datmwLaqVMnzcjI8Ps6jf8VFxfrm2++qQ0bNlQR0XHjxmlOTo7f1wukaxDUTrB/BaK2AykrK0tr166tAwYM0OLiYqfjOOLkyZPaoUMHveCCC/SHH35wOo7PeVvbtgUeANu3b2fo0KF0796dr776itdee43169fbqGqVhIhw6623snv3bh588EEWLFjApZdeyiOPPEJeXp7T8UwlUlhYyKhRo1BVXnrppbC9SiUqKoo33niDgwcPcs899+DueWHImy4fDl/++JSempqqiYmJCmidOnX0ySef1KNHj/p8PSa47N27V0eMGKEiotHR0frAAw/ot99+6/P1YFvgjtW2U6ZMmaKAzps3z+koQeGJJ55QQJ977jmno/iUt7XteHEFy5evivzYsWP69ttvl+4qb9CggU6dOlXz8vJ8snwTOr744gsdNWqURkREaFRUlN588826du1an+32tAYe2Np22uuvv66A3n777U5HCRpFRUWamJioVapU0Q8//NDpOD5jDTyARV5cXKxbt27VSZMmaYMGDRTQ5s2b63PPPWdb3EZ3796tkyZN0rp16yqg7du313/84x+6f//+c1quNXD/13awmDdvnlapUkUHDBigJ0+edDpOUMnPz9eOHTtqtWrV9KOPPnI6jk9YA/dzkRcVFWlaWpo+/PDD2qpVKwW0atWqOnz4cE1KStKioqIKLc9UfkePHtVXX31VY2NjFVAR0Z49e+qLL76oe/furfDyrIH7p7aDSVFRkf7tb39TQHv16qWHDx92OlJQysvL0/bt22tkZKTOmjXL6TjnzBq4j4u8uLhY9+zZo7NmzdIRI0Zoo0aNFNDIyEjt37+/vvrqq3rw4MEzLsOYEl9++aVOmzZN27Rpo4AC2qZNG500aZK+9957mpube9ZlWAP3TW0Hq6+//loHDBiggI4YMUKPHTvmdKSgdujQIR04cKACOnz4cD1w4IDTkX4zb2tb3POauLg4TU9PB6C4uJjs7GwyMzNJT09n8+bNpKenk5ubC0CTJk3o06cP/fr1Y8iQIXanMHNOdu/ezYoVK1i5ciWffvopJ06cAODSSy+la9eudOjQgZiYGGJiYmjcuHHp60Rks6rGOZU7VJxa26EgJyeH559/nueee46IiAhmzpzJXXfdFbZnnFdEYWEhM2bM4PHHH6dGjRrcd999TJw4MeT+Rntd2950+XP9AqoDaUAmsB2Y7pneAtgE7AYWAlU906t5vt/jeb75aZY7EPjSM9//njK93OWe6euCCy7QG2+8UWNiYrR69eqlW0UREREaExOj48eP15dffll37NgRttdeGv87duyYrlu3TmfMmKGJiYnauHHj0v+LgDZu3Fh79OihY8aMCYot8FCo7VDYAt+/f7++/vrreu2112pkZKSKiI4aNUqzs7OdjhaSvvjiC73uuusU0GrVqumwYcN0wYIF+t133zkdzSve1nZAtsDF/dGxpqoeFZEoYB3wJ+B+YJmqviMirwCZqvr/ROQPQHtVvVtEbgauV9URZZZZBdgF9AP2Ay7gFlX9QkQWlbfcs2TU1q1b07p1a9q0aUPr1q1p164dV111FdHR0T7+iRjjvQMHDvDvf/+79GvPnj3s27eP/fv3O74FHgq1HRcXpy6XC6DkQ0DA/i0qKuLo0aMcOXKk9OvHH38kKyuL7OxsvvrqK7Zs2cJ3330HQLNmzRg+fDh/+MMfaNGixVl++uZstm3bxuzZs3n77bc5ePAgAC1atODyyy+nbdu2XHTRRZx//vmcf/751KtXj+joaKKjo6lRowbR0dFERkYSERFBREQEIhKwvSDeboEHfBe6iETjLvLfAx8CF6hqoYh0Aaap6gAR+cjzeIOIRALfA430lLCnzu/5frLnqf8DHCxvuWfKFRsbq5s3b/bxuzXGf4JtF3qw1raIBOVxwrp163LJJZdw5ZVXEhsbS8+ePWnfvr3tKveDwsJCMjIySElJYfPmzezYsYNdu3aVHq7yloiUNvRTG7uvFRQUeFXbkT5f82l4PlVvBloBLwF7gUOqWuiZZT9woefxhUA2gKdQ84HzgFOHtSqd55TXd/LMd7rlls00AZjg+faEiHz+m99g4DXk1z+PYGZZ/aON0wEgNGobCLrazs/PZ9u2bWzbto158+aVTA6l/3+hlBV8kFdVKSoqoqioyEeR2ti+dgAABX1JREFUTsur2g5YA1fVIqCDiNQD3gXaljeb59/yPtKU/RR9unm8eW1JplnALAARSQ+mrZmzCaW8ltU/RCQozsyy2vYdy+o/oZTX29oO+FjoqnoI+BToDNTz7EYDuAj41vN4P3AxgOf5usCPZRZVOk+Z1+edYbnGGD+x2jYmsALSwEWkkefTOSJSA+gL7ABSgGGe2cYC73se/8vzPZ7nPzn1GJmHC7hURFqISFXgZuBfnvlOt1xjjA9ZbRvjnEBtgTcBUkRkG+7iXK2qHwAPA/eLyB7cx7dme+afDZznmX4/8L8AItJURFaA+/gZcC/wEe4/GItUdbvn9adb7pnMOve3GVChlNey+kcwZLXa9i3L6j+hlNerrDaQizHGGBOC7H7gxhhjTAiyBm6MMcaEIGvg5RCRB0VERaSh01lOR0T+LiI7RWSbiLxbciJRMBGRgSLypYjsEZH/dTrPmYjIxSKSIiI7RGS7iPzJ6UxnIyJVRCRDRD5wOkuosNr2jVCp7cpe19bAyxCRi3EP4ZjldJazWA1coartcQ87Ofks8weUZ3CPl4BrgMuBW0TkcmdTnVEh8ICqtsV9GdQ9QZ4X3EOW7nA6RKiw2vaNEKvtSl3X1sD/2zPAQ5xmgIhgoapJp4xItRH3NbHBJAHYo6pfqepJ4B1gqMOZTktVv1PVLZ7HR3AXULmjfAUDEbkIGAy87nSWEGK17RshU9uVva6tgZ9CRBKBHFXNdDpLBd0GrHQ6RBnlDYcZtIVzKhFpDlyF+65XwepZ3M2o2OkgocBq26dCsrYrY10HbCjVYCEiHwMXlPPUFOARoH9gE53embKq6vueeabg3k00P5DZvOD1sJfBRERqAUuBSap62Ok85RGRIUCuqm4WkZ5O5wkWVtsBE3K1XVnrOuwauKr2LW+6iMTgvtdwpufuMhcBW0QkQVW/D2DEUqfLWkJExgJDgD7ljGbltNMNhxm0xH07zKXAfFVd5nSeM+gGJIrIINz3464jIm+p6miHcznKajtgQqq2K3Nd20AupyEiXwNxqhqUd9sRkYHATOB/VPWg03nK8oxXvQvoA+TgHqVr5CkjagUVcf9lnwv8qKqTnM7jLc8n9QdVdYjTWUKF1fa5CaXarux1bcfAQ9eLQG1gtYhsFZFXnA50qrMMhxmMugG3Ar09P8+tnk/CxgSa1bbvVOq6ti1wY4wxJgTZFrgxxhgTgqyBG2OMMSHIGrgxxhgTgqyBG2OMMSHIGrgxxhgTgqyBG2OMMSHIGrgxxhgTgqyBG78QkVdFpJvTOYwxvmN1HVxsIBfjFyKyFYhV1SKnsxhjfMPqOrjYFripMBFJEZF+nsdPiMjzZZ5vC+wqKXIRGSMi20QkU0TmiUhzEdkpIq+LyOciMl9E+opIqojsFpEEB96WMWHN6jr02Ba4qTARuRp4HHgNGAkknvqJXETuBw6p6hsi0g5YBnRT1TwRaQDUAfbgvjfvdtw3Q8gEbgcSgfGqel0g35Mx4c7qOvTYFripMFVdg/uewPcDN5ezO20AsMrzuDewpOTOT6r6o2f6PlX9t6oW4y72ZM9tE/8NNPfzWzDGlGF1HXqsgZsK89xfuQlwQlWPlHkuGqinqiX3BxagvN08J055XHzK98WE4X3qjXGa1XXosQZuKkREmgDzgaHAzyIyoMwsvYCUU75PBoaLyHme1zcISFBjjNesrkOTNXDjNc+n8GXAA6q6A/grMK3MbNfwn91seO4T/CTwmYhkAjMDk9YY4w2r69BlJ7EZnxKRLUAnVf3F6SzGGN+wug5O1sCNMcaYEGS70I0xxpgQZA3cGGOMCUHWwI0xxpgQZA3cGGOMCUHWwI0xxpgQZA3cGGOMCUHWwI0xxpgQ9P8BiVJ2NGNPL0AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x576 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Modeling the difference between copper and iron\n",
    "\n",
    "# Cross sectional area of bar in m3, heat added at x=0 in J\n",
    "A, H = 1.e-4, 1.e3\n",
    "\n",
    "# Temperature in K at t=0\n",
    "theta0 = 300\n",
    "\n",
    "# Metal element symbol, specific heat capacities per unit volume (J.m-3.K-1),\n",
    "# Thermal diffusivities (m2.s-1) for Cu and Fe\n",
    "metals = np.array([('Cu', 3.45e7, 1.11e-4), ('Fe', 3.50e7, 2.3e-5)],\n",
    "                  dtype=[('symbol', '|S2'), ('cp', 'f8'), ('D', 'f8')])\n",
    "\n",
    "# The metal bar extends from -xlim to xlim (m)\n",
    "xlim, nx = 0.05, 1000\n",
    "x = np.linspace(-xlim, xlim, nx)\n",
    "\n",
    "# Calculate the temperature distribution at these three times (to show heat evolution)\n",
    "times = (1e-2, 0.1, 1)\n",
    "\n",
    "# Create our subplots: three rows of times, one column for each metal\n",
    "fig, axes = plt.subplots(nrows=3, ncols=2, figsize=(7, 8))\n",
    "for j, t in enumerate(times):\n",
    "    for i, metal in enumerate(metals):\n",
    "        symbol, cp, D = metal\n",
    "        ax = axes[j, i]\n",
    "        # The solution to the diffusion equation\n",
    "        theta = theta0 + H/cp/A/np.sqrt(D*t * 4*np.pi) * np.exp(-x**2/4/D/t)\n",
    "        # Plot, converting distances to cm and add some labelling\n",
    "        ax.plot(x*100, theta, 'k')\n",
    "        ax.set_title('{}, $t={}$ s'.format(symbol.decode('utf8'), t))\n",
    "        ax.set_xlim(-4, 4)\n",
    "        ax.set_xlabel('$x\\;/\\mathrm{cm}$')\n",
    "        ax.set_ylabel('$\\Theta\\;/\\mathrm{K}$')\n",
    "\n",
    "# Set up the y axis so that each metal has the same scale at the same t\n",
    "for j in (0,1,2):\n",
    "    ymax = max(axes[j,0].get_ylim()[1], axes[j,1].get_ylim()[1])\n",
    "    print(axes[j,0].get_ylim(), axes[j,1].get_ylim())\n",
    "    for i in (0,1):\n",
    "        ax = axes[j,i]\n",
    "        ax.set_ylim(theta0, ymax)\n",
    "        # Ensure there are only three y-tick marks\n",
    "        ax.set_yticks([theta0, (ymax + theta0)/2, ymax])\n",
    "        \n",
    "# We don't want the subplots to bash into each other: tight_layout() fixes this\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
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    "## Your Code Requirement - Rename this notebook with the name_your initials. \n",
    "#### 1.  Make a new code block and plot each of the materials in your table for the time evolution peak by changing the diffusion constant. You may need to change the scale.\n",
    "#### 2. Make a new code block and plot each of the materials (either alone or in an array) for the three time snapshots.  \n",
    "#### 3. Make sure to save all figures (add the code) so that you can create your assignment for the class."
   ]
  },
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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