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@germannp
Last active January 5, 2019 16:29
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Cell-cell Interaction Potentials"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from scipy.integrate import cumtrapz\n",
"sns.set_palette('viridis')\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Polynomial Potentials"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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0WB0+4MhOMAAk+8uJ96pIjHdlyVfl76J7ThpZyS5gqJ6tAjD+bJc8urewlPfn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\npKvYhJo7AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8adb3f5d30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(0, 1, 0.01)\n",
"f, axarr = plt.subplots(2, sharex=True, figsize=(6, 8))\n",
"f.suptitle('$U(r) = -(x - 0.5)(x - 1)^{2n}$', fontsize=18)\n",
"\n",
"for n in np.arange(1, 7):\n",
" y = -(x - 0.5)*(x - 1)**(2*n)\n",
" axarr[0].plot(x, y)\n",
" axarr[1].plot(x, -y/y.min())\n",
" \n",
"axarr[1].set_ylim([-1, 2])\n",
"axarr[1].set_xlim([0, 1])\n",
"sns.despine()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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dYBZ8Tpy1AL0/wzKucWQMTx6xwdu4ZdbFpnWCY4/qQvrO1smWcarWNSSGmatb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MAAAg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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad8605e48>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(0, 1, 0.01)\n",
"f, axarr = plt.subplots(2, sharex=True, figsize=(6, 8))\n",
"f.suptitle('$U(r) = -(x - m)(x - 1)^{2}$', fontsize=18)\n",
"\n",
"for m in np.linspace(0.5, 0.75, 6):\n",
" y = -(x - m)*(x - 1)**2\n",
" axarr[0].plot(x, y)\n",
" axarr[1].plot(x, -y/y.min())\n",
" \n",
"axarr[1].set_ylim([-1, 2])\n",
"axarr[1].set_xlim([0, 1])\n",
"sns.despine()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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FJiulmvm4TUIIIYSoYP7I4bCUZyGt9VhMkHHIm0qpGzAByNDybEMplQQklfLyx0CR1rpr\nebYlhBBCCP/xdcCRgunlOFIcZvRJeUaebAPqnMT+7qaM4CS6lpWP9AUe65bnubPPxSexWSGEEKLG\nK1cHQnn5+pbKEqC+Uir2iOc6A2u11nlHLqiUGqKUuuiY9VsCW05ifx8CHUv52Q0QZHUxz/MdTofr\npA5ECCGEEL7j0x4OrfUKpdRiYIRS6jGgLvAIMApAKbUeuENrPR/T8/GeUuoqYDvwANAE+Pwk9rcX\n2FvSa0qpIrc3OGubvJ1n3v6ZEY9dc8rHJoQQQohT549Ko9diAo19wBzgM631GO9rzYBw77+fAqYB\nszGJpdcDPbXWe3zWEk8QAInBOSyJ/5vdO1N9tmkhhBBClJ/F4/FUdBv8Qim1pU7dpEb/GuPAZvGw\nJiOJbZ/24vv37sFi8eltKSGEEKI6qtQ5HJWK1WIjx9EYgGaRB9jY/CAzpq6s4FYJIYQQNU+1DjgA\netczRU7tVhdtz97MiC9nkpOdX8GtEkIIIWqWah9wNI88n3xXBABt43az/ywPb702tYJbJYQQQtQs\n1T7gsFgsNI+6AoD4oFyS2+1h0vqN/LN0W8U2TAghhKhBqn3AAdAt8WbcHpP70rHOdjJb2Xhl+ESK\nCh0V3DIhhBCiZqgRAUewLZqwwA4ANAo7SFjzTDaHFPH1/82r4JYJIYQQNUONCDgAzq/1b8Akj3Zs\nsI3sJha+mLCQrRv3V2zDhBBCiBqgxgQcSSEdgAQAWkbvw9owj6wGQYwa9jMul7tiGyeEEEJUczUm\n4LBYLLSPuwGA2MA8VP295NaDVQdT+eWHRRXcOiGEEKJ6qzEBB0DLqMvxeAIBaBe3C3e9InKTg/j4\nwzns25Newa0TQgghqq8aFXDYbeEkh5tp6uuHpFG7Thp5dSA9ysabL02iupZ5F0IIISpajQo4AM6O\nuxEAm8VDh1o7cdVykF8nkEWrdzBj0vIKbp0QQghRPdW4gCM2qBnhgc0AaBp2gIja2eQleshLCmbM\n6OmkpmRVcAuFEEKI6qfGBRwA7WNNL0dEQCFtEvfgjHdSkGAjLcjN28Mny60VIYQQwsdqZMDRMLwn\nVks4AC0i9xNaO4+CeA/5icHM/2sD82asruAWCiGEENVLjQw4bFY7LaOuBCApKIMGsak44twUxlrI\nTwzm/ZFTyUjPreBWCiGEENVHjQw4AFpEXw1YsFqgdcxe7PH5FMR5KIyzk1pYyPsjZUZZIYQQwldq\nbMARHphEUkhnABqHppAYnYUzxk1hDOTXDmHujNX8MXttBbdSCCGEqB5qbMAB0CpmIADBNiet4vZi\niyukMMZDUYSNomg77wyfLLdWhBBCCB+o0QFH3dBzCQuoA0CzsAPERefgjHZTGAsFiUGkZ+XJrRUh\nhBDCB2p0wGGxWGkVfR0AcfZcGsekQEwRRVHgCLNSkBjMPLm1IoQQQpy2Gh1wADSN7IfVEgxA87AD\nxEXl4ox2URAHhTF2nCE2ubUihBBCnKYaH3DYbeE0i+wDQHJIGrWjMnBHOXCGgTPUJJBmpOfy3qtT\nKrilQgghRNVV4wMOgBZR1wJmfpXmEQeIiczDGWV6OZwhNopi7Pw+c40UBBNCCCFOkQQcQHRQI2qH\ndAKgSWgK8ZHZuKKcuILBEQGFtUJw2yy8M2IyaQezK7i1QgghRNUjAYdXy2jTyxFqc9AoIpXIiAKT\nyxELLhvk1womOzNfprEXQgghToEEHF71ws4jLCAJMENk4yNzcEU6cQdBYTQ4ou04Q20s/GODTGMv\nhBBCnCQJOLysFpu33Dkk2HNICsskLLQQZ5SLomgLbhs46ofjAca8/iv792ZUbIOFEEKIKkQCjiM0\ni7wcmyXI/DtsPwlRObgiXbgDPRTEQqEViuKDyMst5PXnf8btdldwi4UQQoiqQQKOIwTZImkc0RuA\n+iFpxIblEhJShDPahSPSgisQimqF4Aq0sHLJViZ9v6iCWyyEEEJUDRJwHKNltJlfxWbxmBEr3l4O\nj81DYYIFl8eDpUk0HmDsOzPZsTWlYhsshBBCVAEScBwjJqgxSaHnAGaIbHRoHkF2B85oJ44QcIRC\nltWNJ8ZOUaGTV58Zh8PhrOBWCyGEEJWbBBwlaBV9PQAhNgfJIeneXg43HpsHZ6IND+BuGInHCpvW\n7+Xrj+dVbIOFEEKISk4CjhLUDe1CZGB9AJqH7ScqLI/AACfOGCdFNjdFkZBT6CCsdSIA33/6B2tW\n7qjIJgshhBCVmgQcJbBYrMW5HDGBeSTYc4iLysUV4cYd6MadaMNjhb3uQgJignG7PYx6djx5uYUV\n3HIhhBCicpKAoxRNIvtgt0YA0Dx8PzHhedhsLpwxLoo8blwJNjweCGgZhwfYuzudMa9Pq9hGCyGE\nEJWUzwMOpVR9pdRkpdRBpdRWpdSIcqxTVymVpZR6ztftOVWB1hCaR10BQN2gDCICC4iLzMUd7sZt\nd1MQ4cEVCPsycqjTJRmA6ROX89ecdRXZbCGEEKJS8kcPx3hgJ9AQ6AUMUEo9fIJ13gYq3VAPFXUN\nFmxYLNA09ABxkblYrW5csS5cHg9B9YMB2JyfS2TtSADefGkSqSlZFdlsIYQQotLxacChlOoEtAUG\naa1ztNabgdHAXWWs0xdoAUz2ZVt8ITywNg3CewDQODQFu81JXEQurlA37iA3qRTiDrNQ5HAR2jYR\nLBayMvMY+dwEqUIqhBBCHMHXPRwdgG1a6yO/4i8DlFIq7NiFlVLBwDvAfYDLx23xiUPJo4FWN41C\nDhIXlYvV4oYEM2NsYIMQPMD6XSm069MSgBWLtjD+6wUV1WQhhBCi0vF1wBEHpB/zXJr3Mb6E5YcC\nf2mtK20hi8SQs0gIbg2YIbIBVhcxEXkU2Z24gt2kFeYTnhwKwPKUVBq0qA3Ap+/OZtP6vRXWbiGE\nEKIyCfDDNi3lWUgp1Qq4A2hzqjtSSiUBSaW8bHe5fNNp0jr6JubuG0JYQBH1gtNxRgWQlh1GYG0L\nrm0eMsKc2KyQlVtAeLuGBG1NpbDQwYghP/HuV3cTHGL3STuEEEKIqsrXPRwpmF6OI8UBHu9rR3of\neF5rfTqTkdwNLC3lp25ubu5pbPqw5PALCQ+sA4AK24fN5iQmPI88axHuMDd5DgdJbWIB+GvVNnre\nbEqj79x2kI/emO6TNgghhBBVma8DjiVAfaVU7BHPdQbWaq3zDj2hlKoPXAC8oJRKUUqlADcAg5RS\nS05ifx8CHUv52R0WdlzayCmxWmy0ir4BgFi7KQRWKzoXCx6Catvw4GFjbjqR8SEAzNLb6dxdATBl\n3BIZKiuEEKLG8+ktFa31CqXUYmCEUuoxoC7wCDAKQCm1HnMbZQGQfMzqb2CG0448if3tBUpMlFBK\nFdlstpM+htI0jezHitSPKXJn0zxsHylFEUSF55GRYyE0Ogh3BgQ3CiXzYD4p6TkEnpdM/LpIDh7I\nYvSLE2nWMonEpGiftUcIIYSoSvxRh+NaTKCxD5gDfKa1HuN9rRkQrrX2aK33HPkD5AFZWusDfmjT\naQu0hqCiBgBQNziTCFs+dWLyAQ/WBA8ei4eNaWm0bG9uvUz5ax1X3HUBFouFnKx8RjwzDpezUg7E\nEUIIIfzO4vF4KroNfqGU2lKvXr1Gs2fP9tk285wHGbf1atw42Zwbz9Kshuw+GE1GTihx+WHk7nWS\nEB5G0BYH2dmF1E2Mom+jBvz46R8A3Pzf7tx6T0+ftUcIIYTwo3INAikvmUvlJIQGxNMo4lIAGoWm\nEWR1UC/W9HLkhRfhsXpIyclFda4LwO4DmWRH22jd3sw8++3Y31m5ZGtFNV8IIYSoMBJwnKTWMTcC\nYLW4aRp6AI+1kKiwfPJdDpIahQPw+47ttGtbD4AfZqzgqv9eQHhkCG63h1efGUdmum9GzwghhBBV\nhQQcJykmqAl1Qs8FoHnYQWy4aBBfAHjYY8nEZrfgcLvJi4XQkEDcHg/vjv+LB57uD0BqSjavv/Az\n1fVWlhBCCFESCThOQZuYmwEItDpoFJqKy1JATHgBRW4X9ZubSdyW7NxNr0taAbB9bzqrU9Pof62p\nz7Hwjw1S+lwIIUSNIgHHKagd0pG4oBYAtApPwYKHhvGFgIf1eQeIizWlzmft2krns0z+xjfTlnL+\nle1o3NyUPh/79kzWrdpZIe0XQgghzjQJOE6BxWKhTcwtAATb8kkOTqOIPBIji/AAkfUD8eBhb2Y2\ntVvHERZix+3xMPyzWTz+4gBCQu24XG6GP/0TWZl5Ze9MCCGEqAYk4DhF9cO7ExFoEkPPijwIeGjg\n7eVYl3WAlo0TAPhu2SpuHmBupWzfm87UxRv435ArANi/N0PyOYQQQtQIEnCcIqvFRuuYmwAIs2VT\nOyiLPHcOyTFuADLD8wmwWXG4XPyZsosuZzUAzK2V+KZx9L26IwB/z9NM+PbvijkIIYQQ4gyRgOM0\nNI3oQ7DNTBvTLjIVgDqxeYCHrTlpdG1vekAWbNnBuRc2Kb61MuzD6fz7gV40alYLgLFvzWT96l0V\ncgxCCCHEmSABx2mwWYNoFT0QgKiANGIDc8hxZaMSzRwuKwr2UDfGjFr54M+F3HPDeQDs2JfO2F8W\nMmTEQIJD7DidLl4e9ANZGZLPIYQQonqSgOM0qagBBFrNqJQOURkAxERmYsFDSn4u7dqaXoyUnDw2\nFGRwfvvGAHw/fTn7c/N4+BmTz3FgXyYjnxuP2+2ugKMQQggh/EsCjtNkt0XQPPIqAGID9xNhKyDb\nmU3HusEA/LpXc2ELb/7G4pVc3b89UeHmtRc/ns45Fzbn8utMUunivzbynXfeFSGEEKI6kYDDB1rG\nXI+VAMDDOTFZAASEpGC1eMhzOgiqbSPUbqqOvjFvPk/8+2IA9qVmM/qrudz16GU0b2Vmmf1yzG+s\nWLSlog5FCCGE8AsJOHwgLCCBJpF9AIgP3E2otZBsZw49Gpr8jck71nFd1zYArN6znxRLAb27msJh\nU/5Yw9+rtzPk1YHF860MH/ITqSlZFXMwQgghhB9IwOEjbWL+hQUr4KJLjEn+zLftIizQhgdYUbSb\n5rXiABg9+09uu+ZcEmLCAHhl7EyCwoN4ctjVAGSk5fLyUz/idLgq4lCEEEIIn5OAw0ci7fVoGG5u\nlSTYdxBkdZDlzOXSJjEALNy/k77nKixATmERb89bwJA7zVT36Vl5DP9kJp3Pb8YNd1wAwJoVO/i/\nt2dUyLEIIYQQviYBhw+dFXsrAB4cnBdbCMAe50bqhpuejG+3L2dgp7MAmL52I/lBbq7u2RaAeUs3\n88u81dx690W0P6cRABO++Zu501ed6cMQQgghfE4CDh+KCWpCcpjpoUi0byPQ4iTHmU/PxiaXY3t2\nBgnJoSRGmADkxSm/cec1Xalf2/SCjP5qLntTs3l6+HUk1Ioyzw2byLZN+yvgaIQQQgjfkYDDx9rG\n3gaA21NA9zgzR8ranFW0TzBzq3y4diEPX2IKgO3Nyuaj+YsZdm8fbDYr+YUOho6ZRnhkCM+MHEhg\noI3CAgfDnvie3OyCijkgIYQQwgck4PCx+OBWJIWauhqJ9s0EWFwUuIvoVC8AgGxHIUvzdtGrRRMA\nvly4AmcQ/HdAVwBWb9rLZ5MW0qJNPe57si8Au3ekMmroBCkKJoQQosqSgMMP2saYXg6nJ4deCXYA\nFmesoF9DU2X0240ruL7bWYTZzdwqz/0yi5v6daRtc1OL45Of/2b1pr30GdCR3leeDcCCeeulKJgQ\nQogqSwIOP6gVcjYJwSY5ND5wAwGA0+OiTlwuIQGmANg76+bzcM9uAKzbl8JXC1fwwt19CA0OxOX2\nMHTMNPILHTwwqB/NWppA5IsPfmPRnxsq6rCEEEKIUyYBhx9YLJbiXI4idzp9apsk0b9TV3Bbq1YA\nLNq/k8hEO+3q1gbg7d/m47B5eOxfPQHYtT+D17/8DXtQIM+Nup6o6FA8Hg8jhoxj947UCjgqIYQQ\n4tRJwOEndUO7EhdkqonGBKwm2GrDjYfCgJ3UD48G4NVl8xjctweBViuFThfPTJpJn/Nb0uvc5gBM\n/n0NM//WJCZFM+TVgVhtVnJzCnj+0W/Jyy2ssGMTQgghTpYEHH5iejluB6DAlUq/2mZo7KK01dx5\nlunl2JN1jjODAAAgAElEQVSXxeyUjdx9YWcAFm/fxU/LVvPU7b2oHRcBwIhPZ7EnJZN2nRpx9yO9\nAdixNYVRMrOsEEKIKkQCDj9KDjuf2KBmAIRbVxBuMwmk6/JWcn5SQwDGrF5In/bNaZZoyp6PmvkH\nuU4HL9zbF6vFQk5eIUPHTMPpcnPlDedySf/2AMyfu55vx/5+5g9KCCGEOAUScPiR6eW4A4B8VwpX\n1DEFvv7J3MhA1YAAi5Uit4uRK+bx8hWXmgCjsIjnp8ymXfM63HHVuWb5DXv4dOLfWCwWHhrcv3hm\n2S/G/Mb8uesr5uCEEEKIkyABh5/VD7uAGHtTAOwsIc4eDsCvB+Zyq+oAwPQdG8i05nNrFzMEdu6G\nrUxdvYHbr+xyxFDZhSzXu7AHBfLsqBuIjjWJqCOfHcfWjVKJVAghROUmAYefWSxW2nlzOfKc+7mq\njqk4uj1vL+3rBBEfHArA0EUzuefCc0mOMSXNX5r2G1kFBQy7ty/hoUG4PR6GfjCNzJx8EmtH8dyo\nGwgIsJGfV8Tzj31LZnpuxRygEEIIUQ4ScJwB9cO7E203Rb/crj+pH2qCjp92zeDxDmbulS1ZaXyz\naTkvXt4LgPS8fIZNmUNSfCRP32Ge25+azYsfz8Dj8dC6fX0eGtwfgH2703lp0A8ynb0QQohKSwKO\nM+DIXo5c597iXo7Uokws9hQ6JdQD4J1V80lOjOL6jqZo2K9rN/Lrmg30OlcxwDur7B/LNvP9jOUA\n9L6yA1fd2AWAf5Zu44PXpp3R4xJCCCHKSwKOM6RB+EVE2c208zmFs2gTZf79085ZDOp4HlaLhXyn\ng5eWzOGJSy+kTpQZRvvClDmk5uTx8M3daZocD8A73/7Oui37ALjr4UvpcK6Zl2XyT4v55cdFZ/rQ\nhBBCiBOSgOMMMb0c/wYgx7mHfrVM8a88VwHLs5dzW4uOAEzboVl6cBcvX3kJ4L21MnUOwfZAXrq/\nH8H2AJwuN8+8N4Wc/EJsATYGj7iOuvXNsNr3R01j2cLNZ/4AhRBCiDJIwHEGNQy/uDiX40D+JM6P\nN7dOpuz5g5tUSxJCzMiToYtm0qFBHW7oZG6jTF+7kWmrNY3qxvHEbRcDsOtAJsPHzsLj8RARGcLz\no28kLDwYt8vNS0/+wI6tKRVwhEIIIUTJJOA4gywWK+3j7gQg17mfngl2bBYrTo+LcbtnMKSjmUdl\nW3Y6H69ZxOOXXFB8a2XY1N9Izcmj3wWt6HNeSwBmLdRM+G0VAPUbJRxV/vy5h78hKyOvAo5SCCGE\nOJ4EHGdY/bDuxAaZuVK2Z4+jX22T9PlHynKax4XQuVYyYBJI04ryjrq18sKU2QA8+e+LaZBkioi9\n8dVvrN9m6nB07NKE+5/sC8DeXWkMe+I7HA7nmTs4IYQQohQ+DziUUvWVUpOVUgeVUluVUiPKWHao\nUmqbUipLKbVKKXWLr9tT2VgsFtrH/heAfNdBzol1EBYQAsDHWybwwjmXEGCxUuhy8tyiGXRplMyN\n3lsrM9ZtYvKq9YQG23nlwf4E2QMocrgY/M5kcvLMZG79rz2neOTKqmXbeWf4ZDweTwUcqRBCCHGY\nP3o4xgM7gYZAL2CAUurhYxdSSv0PuMW7TBTwPPCZUqqdH9pUqdQL60Z8cGsANmZ+zw3J5lbKhuzt\n7Hfu5M5WZjK3ubu3MHW75vFLLiguCDZsym/sy8ymaXICT3rzOXYfyOTFj6cXBxZ3PdKbc84zc7hM\nn7icHz7/84wenxBCCHEsnwYcSqlOQFtgkNY6R2u9GRgN3FXC4iuAm7TWm7TWHq31OCATaOXLNlVG\nppfD5HIUuNJoEnqAOsGmNsdnWydxT5vO1As3AcYLi2fhsrh5dUBvLEB2YSGDJ87A7fbQ/8LW9L/Q\nBC5zl2ziu1+XAWCzWXn6lWtp0CQRgE/emcXvM9ec4aMUQgghDvN1D0cHYJvWOuuI55YBSikVduSC\nWut5WuvFmBeDlVIPAE5gto/bVCnVCe1MYrDpzFmX8Q23NboUgJTCdGbs/5NhnU3uxoH8HF5f/jsd\n6tflzvM6ATB/yw6+XbISgCdu7Xm4Psf3f/DPhj0AhIUH8+JbNxMTZ+ZuGfnceNas3HHmDlAIIYQ4\ngq8Djjgg/Zjn0ryP8SWtoJT6CMgFHgGu0lof8HGbKiWLxVI8YqXQnUmEdS1tokwBrx92zuTsxET6\n1FcAfKGXsfLgXh68qCvNE81pHDXjD7YeTCc4KJDhD15OaHAgLpebIe9NJj3LjE6plRTNsDdvIig4\nEEeRkxce/ZbdO1Mr4GiFEELUdP7I4bCczMJa67uAUOBFYMrJ5HAopZKUUh1K+gHsLlflnlskKbQj\ntUNMwa81Gd9wW0MzZ0q+q5Cvtk1laOdehAfa8QCD//4Vq9XKyKsvI9BqpcDp5Kmfp+N0uamfFMOQ\nO00PyYG0HJ55bwpOlxuA5q3q8tTL12KxWMjMyOPZh76W4bJCCCHOOF8HHCmYXo4jxQEe72sl0loX\naq0/AxYB/zmJ/d0NLC3lp25ubuWfQbVD/D0AONy55DnmcnGiSRidsW8Bee4sHmt/IQBr0vbz+fql\ntKidwAMXdQVg5a69fPSnKWXe61zFDb3NdPdL1u7kw5/+Kt5Htx4tuOexywDYvSOV5x/7lqJCx5k5\nQCGEEALfBxxLgPpKqdgjnusMrNVaH/W1Wik1SSl13zHru4GT+Uv4IdCxlJ/dYWFhZaxaOSQEtyY5\nzAQV6zN+ZGDyuQRZ7bjx8NHmcfyr+dmcFVcbgNdX/M6unEz+060TZycnAfDe3L/5Z5eZV+XBGy6g\nXfO6AHwxeTFzl2ws3s9VN3bhqhvOBWDNih2MGjoBt9t9xo5TCCFEzebTgENrvQJYDIxQSkUopVpg\ncjPeB1BKrVdKdfMu/icwSCnVXillU0pdDlwMTDqJ/e3VWi8r6Qcostlsvjw8vzk77i7AgstTxM6c\nCQxMNgmjqzI3sSDtH4Z3uQybxUKe08EzC6djs1oYOeAywux2XB4PT4yfRm5hEQEBNl55sB9xUSbQ\neuHD6Wzfm1a8n7sevYyu3VsA8PvMNXz85owzfqxCCCFqJn/kcFwL1AX2AXOAz7TWY7yvNQPCvf9+\nDfgImIIZDvsK8B+t9Tw/tKlSiwlqTJMIc8tjY9Yv9KrVjFpBppNo7JafaRode1Rtjklb15IcG80z\nfXsAsD0tg+G/mtMWHx3OKw/2x2azkldQxKC3fiGvoAgww2WfevkaWp5VD4DxXy9g/Nfzz+ShCiGE\nqKEs1bUKpVJqS7169RrNnl01RtnmOPYyYdv1uHHSKPwSbIFX88rasQDc3KAPA+r2oveksezIySA2\nKIRZV/6XmKAQHvlxCr+uNbdO3rn+ci5p2RSA76Yv442v5gJwcefmvPxAPywWk8+bmZ7LI3eMZfcO\nM2Jl8PDr6H5pmzN8xEIIISq5kxoEciIyl0olER6YRPOoqwDYmjOTFuEhtI0y1UJ/2jmLbGc2w7ua\nXpC0wnxeWjIbi8XC8/17USvCdBo9M2km+7NyALj+0rO5tKsZVjt70Qa+nLK4eF9RMWG8/M4tRMea\nWy+jnhvPP0u3nZHjFEIIUTNJwFGJtI39NwGWYABWpH7E3U2vwYqFQreDT7dO4rykhlzXxExpP37L\nGubt3kJ0aHBxFdLM/AKe/nk6brcHi8XC4DsupVl9U8H0/R/+ZME/W4v3lVQvlpfevoXgEDsOh4vn\nH/2WrRv3n/FjFkIIUTNIwFGJhATE0jL6egB25c0n2LqfvnXOB+D3lGWsztjEkE49iQ8OBUxtjlxH\nEV0a1+f2bqaex/wtO/h0wVKzveBARj58BVHhwXg88Ox7U9m5/3BdtmYt6/DMyIHYvFPaD37gS/bt\nObZumxBCCHH6JOCoZNrE3EyQNRKApSnvcXP9PkQEmABjzOafiLDbed5b9nx3bhajlptk0Yd7dqNV\nkpk75Y3Zf7FqtxkqWychipcf6I/VYiE7r5An35hEbn5R8f7O6daMR4eaWzlpB7MZ8sCXZKRX/vol\nQgghqhYJOCoZuy2ctrG3A3CwcC1phYu4pWE/ALbm7mHKnj/p16AFveqZ5NDP1y9l8f6d2AMCeP2a\nvoQGBuJ0u3nsp6nkFJgp689pXZ+HbjS1PrbsTmXYR78eNWV9r37t+O/DplLpru2pPPvQV+TlFp6x\nYxZCCFH9ScBRCamoAYQH1AFgWeoHXFq7M03CzVDWr7ZNJcORzStdLiPSHoQHeHL+VPKdDhrFx/Bs\nv4sA2JGeybCpc4q3ecNlHbjsvJaAmVl27M9/H7XPa/91Htf+y5RI2bB2D8Oe+A6Hw+nvQxVCCFFD\nSMBRCdmsds6OvwuAbMduNmf9wr1NrwMg15XPp1snkRgaznPnmLlXtmanM3rFHwBc1a4Vl59lintN\n+mc9P69YC5jJ4p6+oxctGtUC4OPxC5izeMNR+/3PQ5fQq5+Zymb5wi2MfHY8LpdUIxVCCHH6JOCo\npBqF9yIuyAQOK9M+oUlYIpfU6gLA7P2LWJu5hWsat6FH3cYAjF23mGUpu7FYLAzt15P6MVEADJsy\nh60HTSJosN0kkRZXIh3zK3rb4cl5rVYrjzx7JZ3Pbw6YaqTvjphMda3VIoQQ4syRgKOSslisdIy/\nH4BCVwar07/i9kaXExYQAsD7m37EjZvhXS4jIjAIt8fDE/OnUuByEh4cxOvX9iXAaiXP4eCxn6ZS\n6L09Uis2gpEPX4E90EZBkZMn3pxIaubhJNGAQBtDRlxHm7MbADB1/FI+eWfWGT56IYQQ1Y0EHJVY\nUmhH6oaamWHXZnxHgLWAWxv2B2Br7m6m7vmLpLBIhnTqCcDmzFTeWvknAGfVrc0jF59n1t13gFdn\n/F683TZNkxj8HzPSZX9qNoPenETREfkawSF2hr1xE02VmSDuh8//5PvP/vDz0QohhKjOJOCo5DrG\n34eZ2K2Qlan/R5+k84oTSL/cNoX0oiyub9qWC5IaAvDhmoUsT9kDwO1dO9K9WSMAvlm8kmmrdfF2\n+5zXilv7nwPAqk17Gf7JrKNunYRFBPPyu7dQr0EcAJ+8M4sp4w5XKxVCCCFOhgQclVxMUBOaRvYF\nYGPWZDKLNh+VQPrJlolYLBaGd+1DeKAdt8fDY39NJt/pwGq1MGJAb5IiIwB4ZtIstqUeLux1z3Xn\nccHZJgdk6p9r+fyXowOK6Nhwhr93Kwm1TD7IO8OnMGfaP34/ZiGEENWPBBxVQPu4u7wlzz0sTnmb\nFhENubS2SSCdc2AxK9M3UC88iuc6XQzAlqw0RnoLgsWEhjD6OpPPkVtUxCM/TinO57BZrbxwb1+a\nJscD8MGPfzJ74dEjVxKTohnxwa1Ex4bh8XgYNXQCf81Zd4aOXAghRHUhAUcVEBaQQOuYmwHYl7+U\nXbnzub3RlUQGmtEm7236AYfbwXVN29KzbhMAPl23hPn7tgNwdnKd4nyOdftSGDF93uFth9h5/dGr\niI0y1Uxf+HAaazbvPWr/9RrEM/z9WwmPDMHtcvPK0z+y+K+N/j1oIYQQ1YoEHFVE65ibCA0wE7Et\nOfgO4QFB/KeRKUm+O/8AP+6chcViYUTXPkTbzQRwT/w1hewiUzH09q4d6dHc5HN8u+QfJq9aX7zt\n2vGRvPbIlQQF2ih0uHj8jYnsPZh11P4bN6vNK+/+i9CwIJxOF8Oe+I4Vi7b4/biFEEJUDxJwVBGB\n1hA6xN0DQJZjBzpzAhfX6sxZUabE+fc7ZrA7/wCJoeG81KU3YOZaeWnJbACsVgvDr+pNnSiTz/Hs\npJlsPHCwePutmyQx9J4+AKRl5vHY6xPIyT+6vLlqXZcX37qZoOBAigqdDH30W9as2OHfAxdCCFEt\nSMBRhTSO6H24GFjqWIrc2dzf7HoCLDacHhfvbfwBj8dD/4Yt6d/QlDH/ftM/zNm1CTD5HG9e159A\nq5V8h5OHvp9MTuHhidwu7tyc+waa2Wk370pl8DuTcTpdR7WhzdkNeH70jQTaAyjIL+KZh75i/epd\nZ+LwhRBCVGEScFQhFouVTgkPAlDozuKftE9JDq3FtcmmxPnKjA3MPbAEgBc7X0pCiMnxeHL+NFIL\n8gBoW682g/v0AGBrajrPTJxx1HDYW/ufQ/8LWwOwcNV2Xv1s9nGVRjuc24RnR15PQICNvNxCBt//\nJRvX7fHfgQshhKjyJOCoYmqHnE39sB4ArM8YR1bRTgYmX0JSsBlp8n9bfibbkUtMcAgju5nhtAcL\nchk0f2px4HBDp7Zc0db0lPy6diNf/L28ePsWi4Wnbu9F59b1AZg0bzWfTFx4XDvOvaA5g4dfh81m\nJTengKfu+4JN6/cet5wQQggBEnBUSR3j78NKAG6cLD74DkE2O/c3GwhAhiObsVt+BuCiuk24VXUA\nYNauTXy3cSVggorn+/eiWaIp6jVq5h8s3b67ePuBATaGP3R58XDZj8bNZ8ofa45rx3k9W/L0K9di\ntVnJycrnqfs+Z/OGff47cCGEEFWWBBxVUKS9Hi1jrgdgV+6f7M79m7NjWtAz0VQOnbl/IcvTTVXR\npzteRJMoE1gMWzKbrVlpAITaA3l74OWEB9lxut08/OMUDmTnFO8jPDSI0Y8PICEmHICXx85k8Zrj\nE0Qv6NWaQS9dg9VqITszn6fv/ZytG/f77+CFEEJUSRJwVFFtY/5NiM0EEotS3sTlcXBnkwHFtTne\n3fgdBa4iQgICeev8ywmwWMl3Onj4z19wuE0iaKP4GIZfZUa0pOTk8r8fJlN0RJJordgI3nh8AKHB\ndlwuN4PemsTGHSnHtaXHpW14YtjVWK0WMjPyGHTPZ2zZKD0dQgghDrM9//zzFd0Gv3j33Xf/FxkZ\nGXPbbbdVdFP8wma1E2yLYUfu7xS6M7Fbw0kO60h8UDTzD64kx5mPy+Pi7JgWJIaGE2C18te+7ezP\ny8ECdK1tZoNtkhBLkdPF0h172JeVQ3pePj2aNy7eT1xUGC0b1WLG35rCIie/L9tMz87NiQgNOqo9\njZrVonbdGBbMXU9BgYM/Zq6lY5cmxMZHnMnTIoQQwnde8OXGpIejCmsc0Zv4YDOiZGXaJ+Q7U+me\n0JFOMa0AmLBrDpuydwJwd+tz6VwrGYB3Vy1gyYHDQ1n/17MbFzRtCMB3S/7hx6WrjtrPuWc14Jk7\nLwXgYEYu/xs5jozs/OPa06tfO5709nRkZebx5D2fy+gVIYQQgAQcVZrFYuXchEcAcLjzWJY6BovF\nwv3NBhJstePGw1sbvsHpdmGzWhl9Xn8iAoNwezz8749JZBYWAGZOldeu6UNyjJmkbdjU31ix8+gR\nJ33Pb8UDN1wAwPa96Tz6+gTyCxzHtaln37Y8+aLJ6cjJyuepez9nw9rdxy0nhBCiZpGAo4qLD25F\n08h+AGzKmkJKwVoSg2O5rdHlAGzJ3c2E3XMAqBcexStdLgNMFdKnFkwrHiobFRLMuzdcQWhgIA6X\ni4d++IWU7Nyj9nVL307ceJkZ9bJm8z4Gv3t8YTCAiy47i6de9o5eyS7gqXu/YN2qnf45AUIIIaoE\nCTiqgQ5x9xJoNcmii1LewONx06/OBbSIaAjA19umsTPPjBy5vFFLrm/aFoBpO3TxUFkAVSueV64y\nt04OZOfy4Pe/UOR0Fr9usVh46Mbu9O5qanjMX7mVV8bOxO0+ujAYQPdL2zDYO2Q2N6eAp+/7glXL\ntvn82IUQQlQNEnBUAyEBsbSLvR2AgwVr2JQ1FZvFyv+a30iAxYbD4+RN/TUujxuAoef0onFkLAAv\nLJ7FxozDc6pc1ro5/z3fDK9dsWsvQycfXWnUarXw7F296dzGJJ1O+XMtb38777hqpGCGzD776kAC\nA23k5xUx5IGvWPr3Zv+cBCGEEJWaBBzVRMvogUTZzWywS1Pfp9CVRf2wJG5uYKqNrs/exqTdcwEI\nDbTzzoVXYrfaKHA5efD3iRQ4D+djPNyzW/HMshNWrOWzBcuO2ldggI0RD11Oq8a1APj212V8NmlR\nie3qdlFLho6+EXtQAIWFDoY+/DV//659euxCCCEqPwk4qgmrJYAuCY8BUOjKYNnBMQBck9yTZuGm\nTPkX26awO+8AAK1jazG440UArM9I4eWlvxVvy2a18trVfWiWcLgS6e8btx61v7AQO288fjUN65ie\nkjE//cW4WSspyTndmvHS27cQHGLH4XAx7PHv+H3m8ZVLhRBCVF8ScFQjtUM70CjC5GBsyJrIwYK1\n2Cw2HlY3EWCxUeR28OaGb4pvrdzWoiMX12sCwJd6GVO3ry/eVnhwEO/feAVRIcG4PR4e/WkqW1LS\njtpfdEQIbw+6hqT4SABGfTGb6QvWU5J2nRox/P1bCQ0LwuVyM3zwj0yfuKzEZYUQQlQ/EnBUM53i\nH/AmkHr4+8BruD0uGobV4cYGZnTK2qwt/LJ7HmCSQEd160ftUFOca9D8aWzPTi/eVnJsNG8N7E+A\n1UpOYRH3fjuRjLyCo/ZXKzaCtwddQ0xkKB4PvPDhr/y5YkuJbWvVNpmRH/6byKhQ3G4Po4dNZPzX\n8/1wFoQQQlQ2EnBUM6EB8bSPvROA1ML1bMicCMC19XrRJLweAF9sm8zufHNrJTY4lHcvvBKbxUK2\no5D75v1MgevwyJQujZIZ4p3OfntaxnHlzwHq147h7SevJizElEB/+u1fSpx3BaBZyzq89n+3E5dg\ngpwPR0/nizFzSkw6FUIIUX1IwFENtYi+hhh7UwCWp35IgTOdAKuNR5rfTIDFRqHbwWj9FS6PCRw6\nJdbjibO7A7AmbT8vL5lz1PZuPKcdN53TDoCF23bywpTZxwUIzRsk8sbjAwi2B1DkcPH46J9ZuaHk\ngl8NGicyeux/SKpn8j++/ngeH4yahtvt9t1JEEIIUalIwFENWS0BdEl8HIAidzZLDr4HQKPwusW3\nVtZnbWPcztnF69zV+lx61j2czzF527qjtjn4sh7F5c/HLV/D//215Lj9tmtel9cevQp7oI2CIieP\nvDaBdVtKnsStdt0YXv+/O2jYJBGAid8v5LWhE3A6ji8kJoQQouqTgKOaSgxpW1yBdHP2VPblmQTN\n65J7oSJMDY2vt09jS47phbBaLLx+Xn/qhJoE0KcWTCueyh4gwGbljWv70izRjFx5fdafTF+78bj9\nntO6PsMfupwAm5Xc/CIeGjWeTTuPn2EWIC4hglEf306LNuZWz+yp/zD00W8oyC/yxSkQQghRifg8\n4FBK1VdKTVZKHVRKbVVKjShj2XuUUuuVUllKqWVKqSt83Z6arGP8/QRZzfwoCw6MxOUuwmax8Zj6\nF0HWQJweF6/rL3G4TQ2OmOAQ3ul+JQEWKzmOIu6dN4H8I+pzhAcHMeamq4gPCwVg0PhfWbX7+B6M\n89s3Zth9fbFaLGTlFPDgq+PYtiftuOUAIqNCeXXMbXTsam4BLZm/iSfv/ozM9NwSlxdCCFE1+aOH\nYzywE2gI9AIGKKUePnYhpdTVwCvAv4EY4F3gB6VUQz+0qUYKtkXTKeFBALIcO1iV/gUAdUMTuaPx\nlQBsy93DV9unFa/TMaEugzqYfI716SkM+fvXo/I16kZH8v6NVxIUYKPA6eTebyayKz3zuH1f3Lk5\nz97VG4sF0jLzuH/4j+zYm37ccgDBIXZeeONGevYxJdf1mt08+p9P2L83wwdnQQghRGXg04BDKdUJ\naAsM0lrnaK03A6OBu0pYPAR4Wmv9t9bapbX+BMgGuviyTTVdk4g+1A4xE66tSv+SzKJtAPRNOp+z\noxUA43bOZk3m4ZLjd7bqTN8G5rXxW9bw1YblR22zbb3avDrA5IIczM3jv19NOG64LJgZZp++4xKz\nXEYu9w3/gR37Sg46AgMDeGLYAK6+uSsAu7Yf5NE7xrJ14/5TPXQhhBCViK97ODoA27TWWUc8twxQ\nSqmwIxfUWn+ttf7w0P+VUtFABCBzmfuQxWKhS+KTWC2BuD0OFhwYhcfjwWqx8rC6iTBbCB48jNZf\nkecsKF5nZLe+xfOtDFs8i+Upe47a7mWtm/PkpRcCsDU1nfu/m0ihw8mxruxxFoNu7wVASnou973y\nI7v2l9xzYbVaueuR3tzxoFn+4IEsHv3PWFYsKrmuhxBCiKrD1wFHHHDsV9hDN+/jT7Dux8ACrfUf\nPm5TjRdlr0/bmNsA2J+/nE1ZUwCID4rh3qbXArCvIJUPN48rXic8MIgPe1xNaEAgDreb++ZNILUg\n76jt3t61A7d0bg/A0h17eOrn6SXOHHt1z7Y8cVtPAFLSc7hv+I/sPlBy0GGxWPh/9u4zOq7qetj4\nc6dpRr333kbFkm25997onRAgIYRAQgIJSUhISPKHJEDKmwoECDUFCIQWcC+4yJarLFt91HvvI00v\n74exZMuS7JEtg4HzW8vLa91758ydWZbv1jn77H3rXUv44WPXI5fLMAyZefSBf/PxlsKL/BYEQRCE\nT9OlyOGQJnOxVqtVaLXa14F04JZJvjZCq9XmjPcHUNntYovlsGkBd+CndO1Oye96BpPNFRcuD53N\n0hDXksvO9sPkdp4uN57iH8zvFrqav7Ua9Dy473/Yz6iVIUkSP1m/jDVproTPLSUV/H7H+PHiTatn\n8IM7Xb1b2rv155zpAFhz9Qx+9Zfb0XiqsNns/PZn7/LWa7miQJggCMJn1FQHHJ24ZjnOFAQ4T50b\nRavVqoHNQAywRKfTjb9/cmL3AfkT/IkaGhI7HYbJZSrmh/0IALNjgCOdfwZcQcO3U24hxCMAgKcr\n36LTdHqS6qr4dO5Onw3AgbZ6flew96xxZfz+xg1Mj44A4NWD+fzz0Pg9Um5ZO5Pv3b4cgLZuPd98\nYuKcDoBZC5L5w0t3Exjsqkr6ytM7efa3m7DbRCApCILwWTPVAccxIFar1QaecWwuUKrT6QzjXP8f\nwASs0ul0Ez95JvYCMGuCP81eXl7neOkXT7hmJim+rp3HtYM7aBzcD4C3wpMfau9EQmLIZuQPun+N\nNFGKYFAAACAASURBVHgD+MmsFcwNiwHghZLD/K+2dNS4aqWC5267hrhAfwCe3LqXjUXjN3G7bX0O\nD92xHHAtr3zribcn3DILkKSN4M+v3UNsQggAH/33KI99/00MQ+YL+AYEQRCET4s01VPUWq02DygG\nfgBEAZuA3+t0uue1Wm05cLdOp8vTarW3A48BWTqdbuwWh4u/j5ro6OiEXbt2nf/iLxCLXc8H9bdj\ntHfhqQjh2tjXUcm9AfhH7UbebtwOwF0JV3NzzJqR13UZh7h602u0GvSo5QreWX8H04LCR43d2NPH\nbS+/RdeQAaVMxnNfvo7FyXHj3sc7O0/w+3+4SqgH+nny7E9uJjHq7Mmx0/QDRn75w/9QmF8HQGJq\nOL/885cJCfO74O9CEARBOKdJpUicz6XI4bgJV6DRBnwMvKbT6Z4/dS4FGJ52+BoQB/RotVqDVqs1\nnvr7hTEjClNGJfdhfujDABhsneSfKnsOcHvcBlJ9YgH4V90mKvWnG7AFa7z4+4ob8ZArMNlt3Lfn\nvTFJpDGB/rx4x/V4qVRYHQ4efOujcQuDgSun45FTu1d6+g3c/8TbVDZMvKLm46vhyWfvZM1VriTV\nmoo2vvvVF6kqb72Ab0EQBEH4pE35DMflQsxwnNve1l9QN7gTgLVRTxPhOQuAZmMHD+b/DpPDQqQ6\nhL/kPIynQj3yuveqi/n+gY0AzA+L5V9rbkUpk48a+1BtI9/49/tY7XYCPDW8fvctJAYHMp6P9hXz\nxEvbcTrB18uDv/zoRjISw8e9FsDpdPLmy/v4x3Ou2RG1RsUjT9zIgmVpF/5lCIIgCOOZ0hkO+WOP\nPTaV4102nnnmme/6+voGfPWrX/20b+WyFKaZTtXAJuxOMx2mQlJ8r0EmKfBVehGo8uVQdxF6m4FO\nUw8Lg6cjSa5/d+mBoegtZgq6Wmga6kdvMbP8VNO3YdEBfiSFBLKtpAKj1cZuXS3rMlLwVnuMuQ9t\nXChRoX7sy6/GZLGx45CO6amRRAT7jnvfkiSRlRNPVGwQR3IrsJht7N1egspDQcb0mJH7FARBEC7a\n41M5mAg4vqCUMg2eihAahvZiceixO81Eec0DINErihZjJ3WGVuoMrYSqA0nyjh557aKIeI51NNE4\n2M+JrlZCNd5knZXPkRwSRLC3F3sqatGbzeyrqmNDZioalXLMvaTEhpAUHcyeY1WYrTZ2HNaRnhBG\ndJj/hPefkBLG9NkJHNqnw2SyUnC4hrbmXuYsSkEuFz0JBUEQpsCUBhzif+YvsASftUR7LgSgtO8t\nOoxFwPBW2VuJVLt2hjxX9Q4NhtO5GAqZjGeXXkestysg+MXh7eS11Y8Z/0uzs/neStf4NV093PPv\n99Gbxt9dsmJOCv/v+9fioZRjttj4wR8/YM+xsd1oz5Q5I5a//uvekRb3Ozed5MfffI2+nsHJfA2C\nIAjCJ0AEHF9gw2XPlTJvwMmB9l9jc7g2DHkq1Pw4/S4Ukhyzw8JvSl/FbD/dNj5AreHllTfho/TA\n5nTwrT3vUzcwdmfzfUvmcvdCV35IaWsH33zjA4wW65jrABZkJ/Dnh2/AU63EZnfw06c3snFfyTk/\nQ3hkAH969R7mL3X1fik92cgDd/6dap1IJhUEQbiciCWVLziV3AuNIpDGoVzMjgFsTiNRXq7+eYEe\nfngpNOT3ltFvHURvG2Ju0LSR1wapPckIDOPDulJMdhu5rXVcl5iJWq4YuUaSJBYmxtI5OERJawet\n/XpKWztYn5GKXDY23o0I8WNOZiy7j1ZistjYd7waT7WS7JTICT+DUqVg6ZpMLBYbpScbGRo0s3Pj\nSSJiAkdmPwRBEIRJEzkc7hABh/sCVCl0m3UMWBvpMpUQrsnBW+mqHJrqE0f1UBPNxg4qBxuJ0YQR\n5xUx8tp43wB8VB7sbaml12ykpLudaxIykJ2RvClJEktT4qnr7qOyo5uGnj6qO7tZk56CTDY2yTM0\n0IdF0xPZd7wKg8nK4eJ6LFYbczJjJ0wKlckkcuYlEREdyNEDlVgsNvbvKsVqtZM9K37c9xEEQRDO\nSeRwCFNLkiQWhP4YlcxVQvxA+xNYHYaRcw+l3j5S+vyvlW/SaBjdMv5rabO5LcVVHyO3tZbHj+4c\n0/NELpPx2+vXsSwlAYDtZVX8+P2to3qznCkpJpi///xLI4mj/9x4lKde2YHNPv71w1ZfOZ0/vHQ3\nwaGuXS5vvZrLYw+9wZB+ymvLCYIgCJMgAg4BAE9FMPNCfgDAoK1lVEEwH6UXj5zK5zDazTxV+gom\n++nkT0mS+OW8NSwIP1U0THecl8uOjnkPpVzOX265igUJrjLpm4p1/OzDHeN2mAWIDPHj7z+/FW2c\na1nkf3uKefSZjZgmyAEZps2M4ul/3UvGdNf7HDlQyQNf+Tt1Ve3nfJ0gCIJw6YglFWGEvyqRXnMN\n/dY6us3lhGqy8VFGAa5W9mfmc3Sae1kQlD2yxCGXZKyJTmFHUyW9ZiO5LbWk+YeQ7B886j0Uchnr\nMlLIb2impV9PeVsnnYNDLE9NGHe5xFOtYs18LcVVrbR2DVDX0sPx8iaWzUpCPc4W22EaTw9Wbsim\nr2eIqvJW9P1Gdmw8IfI6BEEQ3CdyONwhAo7JkySJcM1MqvSbsTtNtBmPk+x7BQqZq2BXqk8cDYY2\nGgxt1A21EOjhR8qpUugAaoWClVFJfFRXisFmZUdTFYsj4onw8hn1Pkq5nLUZKRypa6JtYJCS1g76\njCaWJsePG3SolArWzNdS19pDXUsP7d16cgtqWDwzER/PscXEhsnlMuYtSSUoxIfjh6pH8joMQ2Zm\nzE5AJup1CIIgnIvI4RAuHY0ikAWhPwbAYOvgUMf/GzknSRLfTb2NKI1rhuD5qndG9VsBiPHx58UV\nN+EhV2C227hn9zs06PvGvI+3h4oX77ierMgwAF4/coKntu4dk/sxzEOl4InvXMnNa1y5InUtPdzz\n+JtU1E/cf2X4nq+4YTb/76W7CQ5z5XW89/pBfvLtf9LTpXfnKxEEQRCmgAg4hDHivJeR7HslAHWD\nO6kZ2D5yzlOh4acZd+MhU2Jz2nmq9BX01qFRr58ZEslfFl+NBHSbDNy16236zMYx7+Oj9uClO28g\nI9wVwPzzcAFPbt0zYdAhl8n4wZ0r+M6tSwDo6hvivl+/xeGisUXHzpY2LZpnX/8mM+a4klYL8+v4\n9pef5+Sx2vN/IYIgCMJFE0sqwrgiPGdRq9+FxaGn1XiMBJ81I23s/VU+BKn8OdRdxJDdSM1QM8tC\nZ43aCpvsH4y3UsW+U9tlj3Y0cW1CBoqzGr2plQrWZqRwsLqBzsEhCpvbzrm8IkkS01OjiAnzZ39B\nDWarje2HdIT4e6GNDzvnZ1JrVKxcn4XF6qrXYTRa2LX5JAqFTPRhEQRBGEvkcLhDBBwXRy6pCFan\nUT2wGbvTTI+5gkSf9UiSa1Is0TuafoueysEGWk1d2J12ZgRoR40xMziSfouJE12ttBr0lPd2ckVc\n2qjABECjVLIuI5W8GlfQUdTcRs+QgaXJ4yeSAiTHhpCdEsm+49WYLTZyC2qw2uzMSj934CCTyciZ\nl0RyWgTH8qowm22cOFpLZWkLsxck46GeOBFVEAThC0YEHO4QAcfF81KGYXda6TCdZMjWhlLmSagm\ne+T8jAAthX2VdJp7KRmoId4zgliv003cJEliaWQiVf3dVPZ3UTPQQ6dxiFXRSWOCArVSwfrMVA6e\nCjqKW9rpGhxiWcrEQUdUqB9LcpLIO1HLoMHMyYpm6lt7WTwjEcV5EkJj4oNZtmYaJSca6OnS09zY\nw55txWinRREa7ncR35ogCMLnhgg43CECjqkRpplB89BBjPYu2g0FRHstxFPh2uoql2TMDkhnb2c+\nRruZoz0lzA/Kwl91eleKJEmsiknmWEcTTUP9FPe0uXq4hMeOeS+1UsGGzFQO1TbSoXeVQm/pH2BF\nauKYWZFhAb6erFmgpaC8ic7eIWqau8kva2TxjEQ055mt8PbVsPqqGQwOGKkobcEwZGbHxpMo5GKJ\nRRAEARFwuEcEHFNDkmSEaaZTObARB1bajAUk+16BXHI9zDUKNem+CXzcfhSL00ZBn46VYXNQyU4/\n7BUyGWtjU9jdVE2XycCh9oZxW9oDeCgVrD+1ZbZdP0h5Wyd1Xb2sTEsat/cKuGp1rF+YTl3LqW2z\nPXo+PlLBrIwYgvy8zvn55HIZcxenEpMQ4to6e2qJpaywiVnzk9B4qi7i2xMEQfhMEwGHO0TAMXXU\ncn/U8gCahg5gdvRjtHcT67105HyIRwD+Sh+O9JSgtxmoG2xhaWjOqFkJD7mC1TEpbKnXobea2d1c\nTYp/MClnFQYDV9CxYZqWgsZWWvoHqOzsprytkzVpyRMulSgUclbOTcFksVJU2cqgwcyWA2UkRgcT\nFxF43s8YnxTKsjWZlBY20t2pp7W5l12bC0lICScy+vyvFwRB+BwSAYc7RMAxtQI9tPRZ6ui31NJj\nrsRXFUOAR9LI+WTvGLot/VQPNtFi6sTssJATkDZqDG+lB8uiEvmorgyjzcr2xgpmBEcS5xMw5v1U\nCjkbMlMpaWmnobefuu5eCpvbWJueglIuH3M9gEySmJcVT0SwL3kna7FY7ew8rEOllJOdEnneJRIf\nXw1rrp6ByWilrKgJ06ldLEaDhaxZ8chFoTBBEL5YRMDhDhFwTC1Jkoj0nEOtfidWxyCthiPE+6zC\nQ+47cj4nII2ivio6zb2UDdQS5hFIonf0qHEC1Z4sDI/jo7oyTHYbWxsqWBAWS6SX75j3VMrlrM9M\nobKjm5quXhp7+zlW38SatGQ8lIoJ7zU1LpRZ6THsL6jBZLZxtKSBpo5+FmTHo5ggWBkml8uYvSCZ\n1Iwojh+qxmyyUlbYyNH9lWTlxOEXcO4lGkEQhM8RUWlU+HSo5D4sDX8cCTlWh4F9rf+Hw2kbOa+U\nKflpxtdHOss+XfkfSvtrxoyTHRzBiytuRCWTY7RZ+drH/6Wst2P891Qo+NPNV3JVlmu2JL+hha+8\n9g6d+qFxrx82QxvFq49/maToIAC2Hijjvl+/TVvXgFufdd6SVJ77z/3kzHPN4lTpWvnO7S+w6d2j\nExYmEwRBECYmZjiESfFShiFJMtqM+RjsnTicViI954ycV8s9yPZPZfepJNKjPSUsCZmJl0IzapwY\nb3/SA0LZVF+OyW5jW0MFa2NS8ffQnP2WyGUyVqUl0TNkdG2XHTKwq7yKFdpEfDXqCe/Vx0vN+kUZ\n1J/qwdLVN8S2vDIykyKICB47o3I2Ty8PVm7IwstbTWF+HRaLjcO5FVSWtTBjTqJIKBUE4fNOLKm4\nQwQcl06IOosO40kGba10mAoJVmfgq4oZOR+g8iXGM4zczgJMDgtFfZWsDJuDQjZ6GSTRL4g4nwC2\nNlS4mr01VrIuNhVf1dggQiZJLEtJwOl0crS+mX6TmS0lFSxKiiPY23PCe1Up5ayam4pCLiO/rBGT\nxcaWvDJ8vTzISAw/b16HJElkZMcwb0kqRcfr6e8z0NzQzY6PThAZE0RsQsgkvz1BEITPDBFwuEME\nHJeOJMmI9JxDjX4rNqeJlqFDo0qfA8R4hiNHRmF/Jb1WPfWGVhaHzBxTTyMtIJQgtSe7m6vRW83s\nbKxifWwqPqqxXWAlSWJeQgy+ag9yq+oxWKxsLtaRExNJpP/EMxaSJDEzLZq0+FAOnKzFbLGRd7KO\nls4B5mfFoVCcO68DIDDYh3XXzMRoMFNe3IzZZGXvjmLaW/qYPjsBlcfEOSWCIAifUSLgcIcIOC4t\npcyLQFUKNfpt2J1mOk0lJPluGCl9DpDpl0SLsZM6QyvNxg6MdhOzAtPHjDU9OGKk70q/xcTu5mo2\nxGrxUo6/ZDE9OoLYAH8+1lVjstnYVFxOckgQSSHn3r4aFxHI8tnJHCmup3/QRGVDJ/sLapg7LRY/\n77FLOWdTKOTMWZRC5oxYTh6rxTBkpqaijY+3FBGXFCq2zwqC8HkjAg53iIDj0vNRRQFO2o0FGGwd\n2BwmorzmjZyXJIk5QZkUn9q5Uq6vw0/pRapP3JixckKiUMpk5LXV02s2sqe5hivj0/BUjF8tVBse\nQmZkKLvKqzHZ7GwtqcBfoyE7emwxsTP5+2jYsDiDxrY+6lp66BkwsCm3lPjIQOIj3QsYIqIDWXfN\nTLraB6itascwZGbX5pP0dA+SnROPUiVmOwRB+FwQAYc7RMDxyQjVTKfTWMSgrYVOUzGBHin4qU4H\nFHJJztygaeR1nWTQZuB4TxkpPrFEaULHjDU3LAaH08Hh9kZ6zAZyW2q5Mi4NzQRBR3xQAAsT49hZ\nXo3RamNfVR1mq435CbHnzM1QKRWsmpuKp1rFsdIGzFY7Ow7psFht5KTHIJOdv6S5ykPJ4pUZxCeH\ncfJYHWaTlcqyFvZsLSI+OYyIqLG1RQRBED5jRMDhDhFwfDJc+RzzqNFvx+Y00Gw4RLzPypH6HABq\nuYpZAens7jiG2WHlcHcxswMzCVCNzbuYHxaL0WYlv7OZLtMQ+1pquSJOO2HQEebrzZq0ZPZV1tJv\nMnO8sYWGnj6WpyZMWArddd8S2SmR5KTHcLCwDqPZysmKFo6XNTJvWhxemrE5JOOJSwxhzdUzaG/p\no6Gmk6FBEzs3uWY7smbGoRKzHYIgfHaJgMMdIuD45ChlGoLUadQMbMXuNNNuPEGSzwZk0umHra/S\ni3SfePZ0HMPisHKku5jFwWO3y0qSxOKIeAasZk50tdBlGmJvSw1XnGOmw99TzRXTtBypa6JDP0RF\nRxdH65tZoU1Eozx3A7eIYF/WLUyjrKaNtm49bd16thwoIzkmmJgw92Yp1BoVS9dkEpsQ4prtMLtm\nO3ZtKSQ6NpjouCC3xhEEQbjMiIDDHSLg+GR5KyOQSUpajccw2nsYsrUT67V01NJGqDqQMHUQB7sL\nMdrNHO8tZ1lIDh7y0cmhkiSxLDKBQauFgq4WukwG9jbXsCFu4pwOT5WSq7LS0LV3UtfdR0u/np1l\nVSxJjsff89wJoZ5qFesXZeB0ODlZ0YzJbGNrXvmklljA1Y9l7dUz6Gjrp76mE8OQmd1bi2hu6GZa\nThxqjajbIQjCZ4oIONwhAo5PXqg6mz5LDf2WOnotVajlAQSrM0Zdk+AdhVKSc7Kvgn7rIGUDtSwN\nyUEhG701VZIklkYmYLBZOd7ZfDroiNXiOcHuFaXc1X9FbzJT2NxGv9HER0XlzIyJOOe2WQCZTGJ2\nZizTkiM4XFiHyWLjZEULx0oamJ0Rg4/XxAXGzqTWqFi6OpOk1HCKjtdjNFioq+pgx4cF+Ad5k5gS\nJtreC4LwWSECDneIgOOTJ0kSUV7zaRjch9nRT4vhCBGes/FSho26LsM3kQHbEBX6BjrNvTQa21kU\nPGNMjQ5JklgSEY/JbiO/s5luk4HdzTWsj02dcMusTJJYmpKAv0bD/up6TFYbHxWWE+nnS1r4+Yt0\nRYf5s25hOuW17bR2DdDeo2dTbimRIX4kRY/tbDuRmIQQ1l83E32/karyVswmK3l7yikuqCcjOwZf\nv4mLlQmCIFwmRMDhDhFwfDrkkooIz9lU67dgd1poHjpIgs8alLLTTc9cjd7SaTC00mhop9HQjt42\nxOyAjDG//Q/ndJjtdo51NtFjNrC9sYI1MSnjViQdlh0dTmZkKB/rajDb7K6dLBYr8xNixgQ2Z/PS\nqFi/KB25JHFC14zZauPjo5W0dg0wJzMWpRuFwsC1k2X+Ui1ZOfGUFTai7zfS1tLH5vfzcTqdpGVF\niw60giBczkTA4Q4RcHx61HJ/fFVx1A3uwuY00mkqIdF3PTLp9INaJknMC8qiuK+aTnMvFfoG5JKc\naf7JY8aTJIlFEXFIksSh9gb6LSa21lewMjqJgHF6rwyLDwpgWUoCeytqGTRbKGhspaSlg+WpCXgo\nzr17RCaTyEmPYXZGLMdKGhg0Wqhs6OTjoxVkJoUTGujj9vcRHhXAhutzkMkkygqbsFntnDxWx/5d\npcQmhBAuttAKgnB5EgGHO0TA8enyV8XjcFrpMJ3EYOvAaOsh2mvRqBkMuSRnflA2R3tK6LcOUthf\niZ/Se9zCYJIkMT88Fk+FktzWOvRWM5vqylkWmUiwZuKW8cHeXlyVpaWgsYW2gUHqe/r4uLyaxUnx\n+HuePy8jPNiXK5dk0tLRT21zNwODJjbuK8EJZKdGuZ1QKlfImT47gSWrM6iraqejtZ+BPgM7N52k\nqb6LjOwYPL3c24orCILwCREBhztEwPHpC9PMpNtUht7aRI9Zh4fcjxB15qhrPORK5gVlkdd1kiG7\nkfyeMiI1IcR7RY475qzQ6JHeKwablY11ZSwMjyPMc+IZB0+Vimuy0+jQD1HW1kmvwchHhWWkh4cS\nG+h/3s/hoVKwcm4KYUG+5Jc2YLHaOV7WxOHCOmamRePnc/6y6MP8ArxYc/UMwiL8KS1sxGyyUlfd\nweb38lGqFKSmRyITyyyCIFwepjTgkJxO51SOh1arjQX+BswH9MBbOp3ukQmu9QJeAL4MpOl0uoop\nvI+a6OjohF27dk3VkMIFsNj1bGr8BgPWBiTkrI7646h29sNajJ08fOLP9Fn1yJDx88x7mBs0bcJx\n36ku4kd5m3E4nXgpVPx9xQ0siog/5704nU7+dbiA32zbh8PpRAK+t2oR9y6e4/bOkeaOPh57YSuF\nFS2AKxh58Lal3LByutuzHcP0A0Zee3YXm949xvDPYWxiCN/64QZy5iVNaixBEIRLYEq31F2KX6Xe\nAxqBeGA1cL1Wq/3e2RdptdoIIB+wAlMb9QiXDZXch5WRv0Ml88GJnb2tP2PA0jjmukhNCL/Ouh8v\nhQYHDp4qe5WivsoJx70pKYtnl16LSiZnyGbha7v+y6a68nPeiyRJfGV+Di/ecT1+GjVO4E+7DvDg\nWxsZNJnd+jxRof48/+gt3H/LYhRyGWaLjd//42Me/N27tHYNuDXGMB9fDQ/85Cr++s9vkJoZBUBD\nTSc/uf+f/PKH/6GtuXdS4wmCIFzOpnSGQ6vVzgbygGCdTjdw6th9wHd1Ol3GWddmA3FAIVCLmOH4\nXGseOsyulh/gxIGfMo4rYl4c1c5+WGl/DT8rehazw4pG7sETWd9B6zs2p2NYXmsd39j9HkM2CxLw\nq3nruEM787z309Tbz4NvbaS0rQOAxOBAnrn1ahLP03H2TBX1HTz2/Baqm7oB8FQreeC2ZVy/ImvS\ntTYcDgfbPyzglWd20d87BIBSpeDmOxdyy12L0XiK/A5BED5xl/UMRw5QNxxsnHIc0J5aPhmh0+kK\ndTrdR1P8/sJlKsprHrODHwCg31rPvrb/w+G0jbkuwy+RRzPuQSHJMdrN/Lz4b1QPjp0RGbYwIp43\n195GoIcGJ/Czw9v4a+EBzhdIRwf48cbXb+Xa7HQAarp6uOnFN9hSrHP7M6XGhfLaL2/nrmvmIpdJ\nGExWfvvqTh787eRnO2QyGeuvm8Ur7z/ADbcvQC6XYbXYeOPlfdx9/dNs+7AAu90xqTEFQRAuJ1Md\ncAQBZ88D95z62/2qScLnUrr/LaT4Xg1As+EgRzr/Mm5gMCswnR+n34UMGUM2Iz8r/Bt1Qy0Tjpsd\nHME7G+4kystVTfSPJ3L56aFt2BznfkCrlQp+c/06fn7FChQyGQaLlYfe2cyvNu/GYhsbDI1HpVTw\nrZsX89L/3UZClKtnypGSBm575B+8vb0A+3nu4WzePhru+/56nn/rfmbNd+Vx9HTp+ePjH/DAnS9w\n4mjtpMYTBEG4XEz1kspPgOt1Ot3cM44lARVAok6nqx/nNXFc4JLKqTyQiAlOfxgRERG1Z8+eyQwp\nXGJ2p5WdzQ/RZjwOwJzg75IRcOu41+7rOM7vy/+BAyf+Sh9+M/1BYjzDxr0WoM2g56s730bX1wnA\niqgknll67YRVSc9U0NjCQ//dRNvAIADTIsP4881XEh3g5/ZnM1tsvPT+QV7ffAy7w/VzlZUcwU/v\nWUti1OQbuDmdTo7lVfH3P22jobZz5Pj8ZVq+/sAaYhPOXzlVEAThIlzWSyqduGY5zhSEKym0c+zl\nF+0+XImn4/2JGhoaugRvKVwMuaRkecST+CpjATja9VcaBveNe+3S0By+p70dCYk+q56fFj5Ni3Hi\nf0bhnj68vf52Foa7cj52N1fzpe1v0GEcPO99zYyJ5P377mBJcjwAxS3t3PDC6+wqr3b7s3moFHz7\n1iW88viXSY1zBQNFVa3c+ei/eOm9g1is7s2aDJMkiTmLUnj+P9/iOz++Ej9/Vzn0Q3t13HfLs/zp\nV/+ju3NySzeCIAiflqme4ZgBHAXCdDpdz6lj3wHu1el02RO8Jg6oAdLFDMcXx4Clic1N92K296GQ\n1KyP/htB6rRxr93WmsdfK/8DQLDKn6emP0CkZuLf7i12Oz8+uJn3a0oAiPb247VVt5Dsd/5ZBofD\nyd/3H+Gvuw/iOPWzcfvcGfxozRI8lOeuTnomm83OG1vzeem9g5itdgDiIgL40V2rmJ0R6/Y4ZxrU\nG/nPq7l88OZhrBZX8OLhoeT62+dzy1cW4+XjXoM5QRAEN03pDMelqMORBxQDPwCigE3A73U63fNa\nrbYM+LpOp8s74/p4XAGH2KXyBdNhLGJb8wM4nBY08iCuiHkRb2X4uNdubMnluar/AhCk8uOp7AeI\n8gydcGyn08kfTuTyTJHrn5qP0oPnll3P4sh4t+7tUG0jD7+7hc5B1yyZNiyYP950BUkhk1saaWjr\n5amXd3C8vGnk2BWLM3jgS0sJvMAGbh1t/fzz+Y/ZufHkSA6Mt6+GW+9azDW3zEWtOf8SkiAIghsu\n+4AjEngRWA70A8/pdLpfnTpnBzbodLrtWq32UeBnp16mAiy4ll5+rdPpnpyC+xABx2dArX4n+9p+\nAYCfKoEN0c/hIR+/lfyZQUeAypensh84Z04HwJsVJ/jZ4W3YnU7kksTjc9e6tW0WoGfIwE8+kCx3\nUQAAIABJREFU2M7eSleiplqh4NENy7kpZ9qktr06nU427y/lL2/spX/QBICvlwf337KEa5ZPQy67\nsJXN2sp2Xnl6B0cOnK5XEhjkzZfvWcb663NQTmJGRhAEYRyXd8BxuRABx2dHUc8/Od79PACh6ums\nifozCtn4dSe2tBzgmaq3APBX+vBU9neI9ZpoVc0lt6WW+/d+gN7qKu71tfTZPDprJQo3HvTD1Ul/\nv2M/VrtraWRNWjK/vHo1AV7ulzQH6NcbeeatXD7cWzxyLD0hjB9+ZSXTks/9Gc6l6Hgdrz67i5IT\nDSPHwiL9uf2eZay6YjoKpXvdbQVBEM4ypQGH6KUifOpC1dmY7QN0mUsZsrXTZ6klznsFkjQ2IEjx\niSVY5c+RnhJMDjP7u06QE5BGgGr8WRGAOJ8A1samsrelhn6LiRNdLRR2t7IyOgkP+blnASRJYnp0\nBMtS4jlS10Sf0URNVw8fFpaSHBJEXJD7nV7VHkqW5iQxJzOWspo2egeMdPUN8eHeYtq7B5iWHIlG\nrXR7vGFhEf6svWYmadOiaajppKd7kCG9iYN7dezeUoinlwfxSaHILnAmRRCELyzRvM0dIuD47JAk\niUjPufRb6ui31DFgrcdk7yPac+G4SxfJPjGEeARyuLsYk8PCvs4CsvySCfaYuBFboNqT6xIyKehq\noXlogDp9L9sbK1kcEU+g+vy5FKE+3twwM5N+o4nilnYMFisfFZXTM2Rkbnw0Srn7swjhwb5cuzwL\nPx8NRZUtWG12Kuo7+d+eIlRKBWnxoZNeZpEkiajYIDZcn0N8UhgNtZ309w4xqDdxcG85u7cV4eWl\nJi4xRDSHEwTBXSLgcIcIOD5bJElGjNdi2k2FDNna6DaXIyEn3HP8fIsk72gi1MEc6i7G7LCQ23mc\nNN8EwtQTJ3VqFEquTcik3ThISU87vWYj79eUkBYQQoLv+UuaK+VylqcmMi0yjEM1jRisVopa2tlW\nWklGRCgRfhN3rD2bTCZjWnIEVy3NpH/QREV9JxarnUNFdew8XEFkiB8x4f6TLpEuSRJxSaFceeNs\nYhNDaajppL/PgH7ASN6ecj7eUoiHh4K4pFDkIvAQBOHcRMDhDhFwfPbIJAWxXktpGsrDZO+lzXgc\ntTyAYHX6uNcneEeR4BVJXtdJLA4r+zqOk+gddc7dK3KZjNXRyQSpPcltqcNkt/FhbSkKScac0Gi3\nHvDxQQFcNyOD+p4+arp66TOaeK+ghCGzldlxUSgm8SD3VKtYNiuZ+VlxVDV20tk7RP+gie0Hyyms\nbEUbF3pBu1kkSSL+VOAREx9CfU0HA30GBvUmDudWsOOjE8jlMuKTQ0WOhyAIE7m829NfLkTS6GfX\nkK2TLY33MmRrBySWhP2CRN91E15f0KvjVyUvYnZYkEsyfqC9k2Whs877PofaGrh/7/v0mI0ArI9N\n5fcLr8RH5V6jNKfTyQcnS3lyy170ZldCakJQAE9et5aZMZFujXEmh8PJtoNlPPvWfjp7XcXKZJLE\n1csy+cYNCwkJGNvszl12u4O83WW88fI+airaRo77+Xtyza3zuOaWufj6X9g2XUEQPrfELhV3iIDj\ns23A0siWpm9hsvcgIWdFxFPEeC+e8PrS/hoeK36BIbsRCYlvJt/IVZFLz/s+zYP93LvnPUp62gFI\n9A3kuWXXow1wv2x4+8AgP/9wB/uq6gBXkPCV+TN5cMVCPFWTTwI1mqz8e/NR/rXpGObhAl8qBV/e\nMIs7rpyNt+bCO8c6nU4O51bw+kt7qShpHjmu1qjYcH0ON9y+kNBw98u5C4LwuSYCDneIgOOzr8dc\nxbamb2Nx6JFJKlZH/oEIz4lnLqoHG/l50XP0W12zA7fGrOXO+CvPu0xitFl59NBW3jtVmVSjUPLk\n/HVcnzjN7Xt1Op28d6KUp7buYdBsASDK35fHr1rN4uQ4t8c5U3uPnr+/m8em3BKGf0wDfDTcfd18\nrluRheoi6mw4nU5OHq3lrdf2c/zw6fLtcrmMpWsyufGOhaSkT36WRhCEzxURcLhDBByfDx3GInY0\nfxeb04RC8mRt9F8JUWdMeH2LsZOfF/2NNlM3AGvC5vNA6q3IpXPnKTidTt6sPMljR3Zgcbjqbdye\nOpNfzFl13q2zZ2rr1/PYpl3sqTjd1fXa6ek8sm4ZAZ6Tq9sxrLKhk2ffyuVgYd3IsfAgH+65YQEb\nFmVMKmdk3PHLWnj7H/vZv6sUh+P0/wfZs+K58Y6FzF2cIrbUCsIXkwg43CECjs+PlqEj7Gp9GIfT\nikrmw9qovxKk1k54fY9lgMeKn6d60FVOfG5gJj9O/xpq+flLfhd2tfKtve/TPORqijYtMIynl17r\n1i6WYU6nk60lFfx6yx66hwwABHhq+NHaJVw3PWPSO0+GHS1p4Jm3cimvbR85FhcRwH03LmLFnBRk\nsov7v6GlsYf33zzItv8VYDZZR45HxgRy7a3zWHP1DLy8Rb8WQfgCEQGHO0TA8flSP7iXva0/w4kd\nD5kva6OfJtAjZcLrDTYjvy59mZN9rvY8Wp84fp75jXMWCBvWZzby0P6N7G52LTV4KVQ8OX8d1yZm\nTuqe+wwmfrd9H++dKBk5Njs2il9cuZLUsOBJjTXM6XSy51gVL7ybR21z98jx5Jhg7rl+ActmJV90\n4DHQb2DLe/n8763DdHfqR45rPFWsvXom19w6l+i4C7t/QRA+U0TA4Q4RcHz+1Op3ktv2GE4ceMj9\nWRf1NAEeSRNeb3VY+aPudfZ1HgcgzCOQx7K+Sazn+A3izuRwOnmx5Ai/L9iLzekA4OakLB6fuwZP\n5eSaox2qaeDxTR9T290LgEIm46vzZ3L/svl4eVxYozW7w8G2vHJefO8gLZ39I8enMvCwWm3s21HC\nB28eoqK0ZdS5WfOTuOrmucxbnIJcIbbVCsLnlAg43CECjs+nmoFt5Lb/EnCilgewLvpZ/FXxE17v\ncDr4R91G3mncCYCXQsOjGV9nun+qW+93vLOZB3M/pGnQ9VBP9A3kr0uuYVrQ+YOWM1lsNl7Jy+e5\nfYcx21w5ImE+3jy8dglXTtNe8DKL1WZnU24Jr/7vMG3dp2cjkmOCueuaeaycm3LBzeGGOZ1Oyoub\n+ODNw+TuLMFud4ycCw7z5cobZrP+uhwCg90vfCYIwmeCCDjcIQKOz6+qgc0caH8CcKKRB7Eu+mn8\nzhF0AGxtzePZyrdx4EAuyXgg5TbWhM9z6/36LSZ+cnALm+t1AChlMr4/Yyn3Zsyd9MO8qbefX23e\nPdKBFmBWbCSPblhBRsTEBcvOx2qzs3FfCa99ODrwiAn35ytXzWXDonSUUzAT0d05wJb389n8Xv6o\n5Ra5XMb8pVo2XD+LnPlJooqpIHw+iIDDHSLg+Hyr7N9IXseTAKjlgayN+ss5l1cACnrLebL0FQx2\nV4v4m2JW85X4q5CP0yTubMO7WH51bBdGmyuhcm5oNH9YfBUx3hP3cJlorN26Gp7atpfGXtfMiQTc\nlDON761cRJD3hRfgGg48/rXpKM0dp5daQgO9uf2K2VyzbBqe6gtbxjmTzWrnUK6Oj/57lBNHakad\nCw33Y921M1l7TY6o6SEIn20i4HCHCDg+/yr6/8fBjt8BTjxkfqyN/guBHudeKqkbauGx4hfoNLvy\nKeYGZvJw2lfwVLi3ZbVmoIeHcj/iZHcrAD5KDx6fu4brEzMnvSxisdl47eBxnt93BIPVFcR4qVTc\nu2QOX52fg/oi6mzY7A52HtLxj4+OUHNGcqmPpwc3rJrOLWtnEOx/4ZVLz9RU38XWD46z/aMT9PcO\njRyXJImZcxNZe81MFi5Pw+MCOuEKgvCpEgGHO0TA8cVQNbCZvPYnceJAJfNhTdSfCD5HnQ6AXssA\nT5S+TNmAa1kjxjOMX2TeS6TGveqiVoedpwvzeKYoD8epn5/V0ck8OX89oZ6Tf4i3Dwzyh525fFhY\nPnIswteHh1Yt4qqstItK/nQ4nOQWVPOPD49QUnO6pLlSIWf9wjRuWz+LpJip2XFitdo4uEfHlvfz\nRxUTA/DyVrN83TRWXTmdjOyYC85ZEQThEyUCDneIgOOLo0a/nf1tv8KJHaXMi9WRfyRUk3XO11gd\nVp6tfJsd7YcB8FZ48kj615gZMHF9j7Pldzbzg/0bqdO7Zkv8VGoen7uGaxMurNZGUXMbv922j2MN\np0uOZ0SE8v1Vi1mUFHtRD2mn08kJXTOvbz5GbsHoJZA5mbF8aV0OC6cnXPTOlmFtLb3s3HiC7R+d\noL2lb9S5iKgAVl6RzaorphMVO3F3X0EQPnUi4HCHCDi+WOoH97Cv9Rc4sKGQNKyI/A2RnnPO+Rqn\n08mHLXt5qfp9HDiRIfHVhKu5MXqV2w93o83K7wr28lrZMYZ/ktbEpPDEvHUXNNvhdDrZVV7N73fk\nUt9z+kE9Lz6G769exPToiEmPebba5m7e2JLP1rwyLFb7yPHoMH9uWTODK5dk4u154f1azuRwOCg6\nXs/2DwvI3VU6qqAYQNq0aJatm8ayNZkEhZy/RoogCJ8oEXC4QwQcXzyNgwfY0/ZTHE4rMknJ0rDH\niPNZcd7XHe8p4zflrzFkc3WNXRg8nYdSv+x2XgfA4fYGHj6wmYZBV5Dgo/Tgp7NWcGvKdGQXMDNh\ntdt5O7+Iv+09PFKtFGB1WhLfXbmQlNCLXwbp6Tfw/u5C3t15ku7+07kXGg8l6xamceOqGaTGud/E\n7nyMBjN5e8rZtbmQgsPVo8qoS5JEVk4cy9dNY9HKDPwDvKbsfQVBuGAi4HCHCDi+mFoNx/i45RFs\nTgMSMuaHPkyq37Xnf52xiydLX6ZmyLWcEaUJ5dGMrxPn5f6MgsFq4XcFe/lHef7IbMfcsBienL+e\nZL8LWzoYMlv41+ECXjpwbKQpnARsyEzl/mXzSQ69+CUJq83OzsM63tpWQNkZZdMBslMiuX5lNivn\npqC+gM63E+nu1LN3exG7txWP6loLIJPLyJ4Vz5JVGSxemY5/4NQktwqCMGki4HCHCDi+uLpMpexs\n/gFmh2tbaE7Qt8gKvPO8rzPZLfyt6m12tR8BQC1T8UDqbSwPnbhD7XjyO5r4yaGtVPR1AaCSyfl2\n1gK+OW3+pBrBnanXYOSl/Uf595ETI4XDJGDDNC3fXjaPpJCpyYUorWnjnZ0n2XmoHPMZyy0+nh6s\nX5TOtcuzSImdulkPgObGbvZuL2bPtmLqqztGnZPJJKbNjGPRinQWLk8jNGJyW5AFQbgoIuBwhwg4\nvtj6LXVsb/4eBpvrAZbhfxuzg7+NdJ6aG06nk62teTxf/Q42p+uBuy58Ifcm3eBW87dhFrudF0oO\n8XRh3kj32QSfAB6ft5alkQkX+KmgQz/IS/uP8Z9jhVjspwOP9Zmp3Lt4DukXUTzsTP16IxtzS3jv\n40Ka2kcnfWYmhnPV0kxWz9fi6zW1zdzqqjvYv6uEfTtLxwQfAMlpESxcnsaC5WkkJIeJ3S6CcGmJ\ngMMdIuAQBq1t7Gj+HgPWBgDivVexOOxnyGXnT4gsH6jjt2Wv0WHuASDOM4JH0u8idhJLLADV/d38\n5NBWjrQ3jhy7Ik7Lz2evIsLrwpMk2wcGeXH/Ud7OLxoJPACWpSRw35I55MRGXfDYZ3I6neSXNfK/\nPUXsPlqF1Xb6vVRKOUtzkrhySSZzp8WhmOLqog21neTuLCFvdzlVutYx50PD/Zi3VMu8JalMnxWP\nykPU+RCEKSYCDneIgEMAMNl62dX6I7pMro6tYZoZrIj4DR7y8z/s9VYDf6l4g4PdhQB4yFR8K/lm\nVofNndRv1k6nkw9qS3ji2G66TK7kTE+FkgeyF3F3+uwLXmYBV+DxSt4x3s4vwmi1jRyfHRvF1xfN\nZlnK1G117dcb2ZJXxkd7i6lq7Bp1LsjPi9XzU1m/MJ30hKmfeWhr6eXgnnLy9pRTXFA/KuEUQK1R\nMWNuAnMWpjBnUQphYulFEKaCCDjcIQIOYZjNYWJf2//ROJQLgJ8qntWRf8Bbef7ZCqfTyUct+3i5\n5oORJZalITncn3wLPsrJlSDvt5j404lc/qk7PlIwLNbbn5/OWsG62NSLekj3DBn41+ET/PvwCfRm\n88jxxOBA7lqQw7XZ6XhcROXSMzmdTirqO9m0v4RteeX06Y2jzseE+7NuQRprF6QRFxE4Je95pv7e\nIY7mVXFon478g1UYhsxjrolNCGH2wmRy5ieRNTMOtebiy7kLwheQCDjcIQIO4UwOp50jnX9G1/8u\nABp5ECsjf0ewOt2t11fqG/ht2Wu0mly/2Qer/Pl+2h1ud509U0lPO48d2cHRjqaRY/PDYvn5nFVk\nBoZNerwzDZrMvHmskH8eKqBz8PRW1yAvT26bk82ts7IJ8Zm6LadWm528E7VsO1jO/oLqUYmm4Opa\nu3qellXzUokND5iy9x15f6uN4oIGDufqOJZXRWNd15hrlEo5GdNjyZmXyMx5SSSnRYjmcoLgHhFw\nuEMEHMLZnE4nJX1vkN/1LAByyYPFYT8j3meVW6832Ez8vfrdkeqkEhI3RK/kzvgrUMomlz/gdDrZ\nVF/OU/m7aR4aODUe3JSUxfdnLLmo/A4Ai83OpuJyXsnLp7LjdC8VpUzG+sxU7pg3Y0qKiJ1p0Ghm\nz9Eqth0s51hJw8gszrCU2BBWzElh+axkEqODLknCZ1tLL8fyqjiaV8nJo7UYDZYx13h5q8nKiWP6\nnASmz04gITkU2SS7/grCF4QIONwhAg5hInX6Xexv/xV2p+thNCPwHrIDv+b2A/BA5wmervwPepur\nIFeCVyQPae8gyTt60vdisll5sfQIfys+NNKF1kOu4K60Wdw/bQF+Hhe3C8TpdHKguoFXD+ZzoLp+\n1LmsyDBumzOdDZmpaKawxgZAd98Qu49VsutwBQW6Js7+byY6zJ/ls5JZNiuZzORw5JfggW+z2ikr\nbuL4oWoKDlejK2kek/sB4O2rYdrMWLJmxpGVE0+yNhy5Qj7l9yMIn0Ei4HCHCDiEc+kylfJxyyMY\n7a4p+Hjv1SwKexSFGztYALrN/fxJ928K+nQAyCUZt8as5ZbYtShlk8+VaDfo+eOJXP5bXTQyM+Cn\nUvPtrAV8RZuDWnHxAUFNVw+vHznJ+ydKMFhOlxj3VXtw7fR0bp2VPSWFxM7W1TfIx0cq2X2skhPl\nzWNmPgJ8NCycnsDinETmTovDWzM1ZdXPNqg3UnS8nhNHazl5rJbayvZxr1NrVKRNiyJjeiyZ02NJ\nz4rGy2dqt/8KwmeECDjcIQIO4XyGbJ183PIjesyuoCHII40VEU/hpXQvj8LhdLCpZT+v1n6I2eGa\nLUnwiuIh7e0XNNsBUNnXxW+P72FnU9XIsVCNN9/OWsCXUqZf1I6WYXqTmfdPlPDm0UJqu3tHncuJ\nieTGmZmsy0zF22PqEy17BwzkFtSw91gVR0rqR/VyAVDIZczQRrEgO4EF2fGXbOkFoK93iKL8OooL\n6ikqqKemop3x/j+UJIm4xBDSpkWjnRZFelYMsYkhIg9E+CIQAYc7RMAhuMPqMHKg/dfUD+4GQC33\nZ1n4rwn3zHF7jFZjJ3+ueIPifldLdrkk4+aYNdwauxbVJHM7hh1tb+Q3x/eQ33m67Hekpy/fyV7I\nzclZKGUXP+XvdDo5UtfEW/lF7CitxOpwjJzzVCpZl5nCjTMzmRUbdUke+gaThSPF9ewvqOHAyVp6\n+g1jrgkJ8GZ+Vhxzp8UxOyOWQL/J7QyaDP2AkZITDa4/JxuoKG3BarGNe63GU0VyWgQp6ZFoM6NI\nyYgkMjpQFCITPm9EwOEOEXAI7nI6HRT2vMaJnpcBJxJyZgV/mwz/W91+gDicDja25PJa7Ucjsx2R\nmhC+k3LrBe1kcd2Xkz0tNfzxRC5F3W0jx6O8fPnmtPncnJyNegpmPAC6Bw28f6KEdwtKxsx6xAT4\ncVVWGldnpZEYMvXbXAEcDidltW3sP1HD4cJ6SmvbxuR9gGvXy5zMWGZnxjIjNWrKutqOx2KxUa1r\npeREA+XFzZQXNdHZ3j/h9V7eapK04SRpw0lOiyRZG05MfLDIBxE+y0TA4Q4RcAiT1TR0gH1tj2N1\nDAKQ4LOWhaGPoJC5v37fauzk6cq3ONlXMXJsTdg87k68Dl/lhW1HdTqd7Gis5I8ncynv7Rw5Hqrx\n5t7MuXw5ZQaeyqlZ/nA6nZxoauW9ghI2F1cwZBm9yyMzIpSrs9PZkJlKmO+la6rWO2DgSHE9eYV1\nHCmuH3f2QyZJpMaHkpMWTU5aNNO1UVNeav1s3Z16dMVNlBc3UVnWSkVZC4MDxgmvVyrlxCWGEp8c\nSkJKGAkp4cQnhRAY7CNmQ4TPAhFwuEMEHMKFGLA0srv1EfostQD4qxJYFvEE/qp4t8dwOp183HGU\nl6rfZ8DmqoXhp/TmawnXsCpsLrLz9HOZiMPpZFuDjqcL8yjtPd1nJMBDw1fTZnGnNocg9dQtORgt\nVnaWV/FRYTkHquuxn/V/xazYSNZnprI2PeWSBh9Op5Pa5m6OlDRwtLiB4+VNGExjt7sCJEQFMT01\nkumpUWSnRBIV6ndJH+xOp5PWpl4qylqoKm+huryNal0r/X1jA6QzeftqiEsMIS4plLiEEGISQoiJ\nDyYkzFcEIsLlRAQc7hABh3ChrA4Dee1PUTfo+rejkNTMD32YJN8Nkxqn3zrIy9UfsKvjyMixNJ94\nvpl8Eyk+sRd8f06nkz3NNTxdlMfxM3I8POQKbkrK4p6MOST4Tu3SR9fgEJuLK/iosIyiltG7OyQg\nJzaS1WnJrE5LIibw0pYVt9kd6OraOV7WRH5ZIycrWiYMQPx9NGQmhZOZFEFmUjgZieGXfBbE6XTS\n2T5Ata6V2qp2aivbqalop6Wxe9xtuWdSa1TExAcTFRtEdFwQUTFBRMUFERUbiLeP5pLetyCMQwQc\n7hABh3AxnE4n5f3vcqzzrzhwJQ4m+17JvJAfTGqJBeBEr47nqt6hyeh6UEtIbIhYyJ3xV13wMsvw\nPR5sb+D54kPsa6kdOS4Bq2NS+Fr6bBaExU75b8yNPX1sLa1kS0kFpa1jO7pqw4JZlZbESm0SGeGh\nU9bLZSI2u4PK+g5OVrZwUtdMYWULXX1DE14fHepHWkIYaQlhpMeHkRIXgp/3pX+Ym4wWGuu6qKvu\noL6mg/rqTuqrO2hv7Tv/iwEfPw0R0YFERgcQER1IRFQAYRH+hEcFEBzqi0IpckWEKXd5BxxarTYW\n+BswH9ADb+l0ukcmuPZB4H4gHCgEvqfT6Y5P0X2IgEO4aF2mMva2/pxBWwsAfqoEloX/kgCPpEmN\nY3XY+LB5L282bMVod/X+8FZ4clvsOq6MXHJBtTvOVNbbwUulR/iwtnTUbhOtfwhfScvh+oTMKcvz\nOFN9dx9bSirYWV5FccvYuhYh3p4sTUlgWUoCC5PiLslW27M5nU5aOvsprmqluKqVkuo2dPUd2OyO\nCV8THuRDSmwIKXEhpMSGkBwdQlSY3yUpSHY2k9FCU303jXVdNNZ10lDbRUtjN0313ZhN1vMPAMhk\nEsGhvoRG+BMa7kdIuJ/r7zA/gsN8CQn1xcdPI5ZrhMm67AOOY8BR4GEgDNgMPKfT6f581nVXA68B\n64Ai4LvA94AknU43cRaW+/chAg5hSljsevI6nqJ+cA8AMknFrKBvke5/M9Ik8zG6zf28UvMBezrz\nR45FqkP4WuI1LAjKvugHQptBz2tl+fyn8gR9FtPIcR+lBzclZ/HllBmk+Adf1HtMpPX/s3fnUZKl\nZ33nv3eLfcnIfa+tq26t3dVbqVsNEkJgJDAeBNjMDNgM4EFjhgEzRmPj8Rzsg4+XYf7gAD5GB3PM\nLhsYYCSxS1hSI6m36q2qq+pWdW2577Hvce+dP25EZNaeWRWREVH5fM6Jc6MiIuPeyq7O+OX7Pu/z\nprP8tXWVL166yms35qg5t37AG6rK6alxXjo0zUuH9nF8bHhXPtABKtUal2+ucvH6MhevL2PdWOba\n3PodTci28hsa+8cHODg5wIGJAfaP97N/vJ+J4T70XejB4bou66tZ5mfWmZ9ZZ3EuyeLcBotzSRbm\nNu66ad39+Pw6A0MxBoaiDAxF6R+M0D8YpX8wSmIgQmIgTKI/QqwvJD1GREP3Bg7TNJ8DvgYMWpaV\nqT/2SeAnLcs6fttrPwdYlmX9dP3PCjAH/JRlWb/XgmuRwCFaxnVdrPQf8vraL+HUW6KPhZ7nG0b+\nBSF9aMfv9176Kv/p2h9xOTvTfOxk/BA/fOC7MGP7Hvl6i7Uq/9/1C/z6pTduWdkC8PzwJP/D4dN8\n+z6zJR1M7yZTLPHVqzf50pXrvHzlBhuFO3+HiAcDvHBgig/sn+LM/kkODe1uH4tSucqVmVWuzKxy\neWaVyzdXeH92jfI9em806JrK1GiCqZE+pkb7mBpJeMfRBEN9kbZPIYH37zGbKbK8kGJ5McXSfJLl\nxRQrS2lWl9KsLKXJph/u9zZVVYjGQ8QTIfoSYeJ9IeKJMLG+ELF4sH4MEY0Hica8WzgakJDyeOrq\nwPGjwE9blnVky2PPA68AMcuy8lseX6i/9ne3PPYnwAXLsj7VgmuRwCFaLlm+xstL/5JkxesE6lfj\nvDjyz9gX+fCO38txHb6y+ia/fv1zrJY3e1+8OPAkf3//d7Av/Oibq7muy2srs/zmpTf5y9nLt0y3\nxHx+/s7+43zvE6d4amCsbR/2tuNwfmGZl9+/wVev3uTduaU7VrwADIZDnNk/ybP7Jnh2eoLDwwO7\nNgKy9VrnV9Jcm1vj6tx68zizlMS+z5RMg8/QGBuMMT4UZ2I4zthgnLHBGCMDUcYGYyRioV0JJOBN\n1awspVlfzbK2nGF1Jc3acoaNtRzra1k21rIk13Lb+nttRyjsJxoLEor4CUcCRKIBwhE/ofDmLRj2\nEwr5CYZ9BIM+AkEfgZCPQNAgEPARCBgEgob0LukeXR04fgb4LsuyPrDlsUPAZeCgZVk1ps2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sZ4u4o0u40Eju2QwCG6VaYyyxtrv8Rs/m+aj0WNCZ4Z+Efsi3ykJb/tF2pFvrRylj9b/CrX8vO3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2x2PdOvDJuKE4GRz3lL9o/SEWrVf1LSKa1efNxwah1V61r2VxX5VTR6o+wmEqNLNumdolt1MP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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad8082eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(0, 1, 0.01)\n",
"f, axarr = plt.subplots(2, sharex=True, figsize=(6, 8))\n",
"f.suptitle('$U(r) = -(o \\cdot x - 0.5)(x - 1)^2$', fontsize=18)\n",
"\n",
"for o in np.linspace(0.6, 1.5, 6):\n",
" y = -(o*x - 0.5)*(x - 1)**2\n",
" axarr[0].plot(x, y)\n",
" axarr[1].plot(x, -y/y.min())\n",
" \n",
"axarr[1].set_ylim([-1, 2])\n",
"axarr[1].set_xlim([0, 1])\n",
"sns.despine()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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5h/dnf+e6LBGROmnOiOaMRAXNKYmMBcs3cvvfp1FUUg74F0u7duIxeL1hG+oV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\niIiIiFMKIyIiIuLU/wPFGMgPxaB/gQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad23cc8d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(0.5, 1, 0.01)\n",
"\n",
"F = 2*(x - 0.6)*(x - 1) + (x - 1)**2\n",
"U = cumtrapz(-F, x, initial=0)\n",
"U = U - U[-1]\n",
"plt.plot(x, U, '.')\n",
"\n",
"F = 2*(x - 0.6)*(x - 1) + (x - 1)**2 + 5*(0.73333 - x)*(x < 0.7333)\n",
"U = cumtrapz(-F, x, initial=0)\n",
"U = U - U[-1]\n",
"plt.plot(x, U)\n",
"\n",
"sns.despine()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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SmkReqavPhCavB1w21JSl37ehGbyjxmyHJVIphme9X4/bDL4QizAdsWDsQFZoGpKLe4XI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pDQJIQQQgjhAAlNQgghhBAOkNAkhBBCCOEACU1CCCGEEA6Q0CSEEEII4QAJTUIIIYQQDpDQVIiI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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad25ed630>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(0, 1, 0.01)\n",
"\n",
"f, axarr = plt.subplots(2, sharex=True, figsize=(6, 8))\n",
"axarr[0].set_title('Potential')\n",
"axarr[1].set_title('Force')\n",
"\n",
"for r in np.linspace(0.5, 1, 5):\n",
" F = (2*(x/r - 0.6)*(x/r - 1) + (x/r - 1)**2)\n",
" U = cumtrapz(-F, x, initial=0)\n",
" U = U[x < r]\n",
" U = U - U[-1]\n",
" axarr[0].plot(x[x < r], U)\n",
" axarr[1].plot(x[x < r], F[x < r])\n",
"\n",
"axarr[0].set_ylim([-0.01, 0.02])\n",
"plt.tight_layout()\n",
"sns.despine()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## $1/r$ Potentials"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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OGZPczMHNv7wywjFjIHDUuVyJiIiciwKHjElcrJ/MVOdMFa8FjsbOZnoDvS5XIyIiZ6PA\nIWOWExrl8FrgAKjVqbEiIp6mwCFjlpsxuDTWC/KGBg71cYiIeJoCh4xZeKWKV0Y4hgaO020KHCIi\nXqbAIWMWXqlS39xFoN/9zb+S45JIjU8BoLZDgUNExMsUOGTMwoEj0B+kqdUbW5wPrFRp00oVEREv\nU+CQMcv14OZfM1JyAfVwiIh4nQKHjNnw3Ua9McKRl+KcGqvNv0REvE2BQ8YsOyMRn8/53Cu7jYZH\nOJq7W+nuc/+MFxERGZkCh4xZrD+GrDRvbf6lpbEiIlODAoeMS67HlsbOSB2yNFZbnIuIeJYCh4zL\nQODwyuZfyUMDh0Y4RES8SoFDxsVrIxwJsfFkJKYDChwiIl6mwCHjEl6p0tjSRSDQ73I1jvBeHOrh\nEBHxLgUOGZfwCEd/EOpbvLI0VsfUi4h4nQKHjIs3N/8Kj3DoxFgREa9S4JBxCZ8YC94LHG097XT0\neqMmEREZToFDxiUrPZGYGGf3L+8EjtyBz9XHISLiTQocMi7+GB/Z6YmAd3YbHXZMvQKHiIgnKXDI\nuOUNOabeC3KTs/DhjLro1FgREW9S4JBxCzeOemWEI84fR3ZSJqApFRERr1LgkHHz2uZfoFNjRUS8\nToFDxi030+nhaGrtprcv4HI1jnDjqEY4RES8SYFDxi1vyF4cXunjGNz8q55gMOhyNSIiciYFDhm3\nnCF7cXiljyO8F0dnXxftPR0uVyMiImdS4JBxy/PgbqPDl8ZqpYqIiNcocMi4ZaQmEOv32OZfqYOb\nf6lxVETEexQ4ZNxiYnwD0ypeCRw5SZnE+JzbWYFDRMR7YiP9gsaYzwAPA29aa794lut+CPwF0BN6\nyAcEgRJrbW2k65LIys1M4lRDB3VN3mga9cf4yUnOora9XitVREQ8KKKBwxjzx8DXgYNj/JJ/s9Z+\nPZI1yOTI8+BeHDNScqhtr9cIh4iIB0V6SqUTWAccifDrisd4bbdRGLo0Vk2jIiJeE9ERDmvtPwMY\nY8b6JSuMMe8Dy4BjwB9Za1+LZE0SHXlZTuBo7eihs7uPpISIz86N29DNv4LBID6fz+WKREQkzM2m\n0SrgMHA/kA/8HNhojFngYk0yRjOykgc+P93gjX0vwntx9AR6ae5udbkaEREZyrUfS621P8cJGWH/\nYIz5Ak4A+eFYXsMYUwgUjvJ0fCDgjW23p6OCnMHAcaqhg5LCdBerccwYuhdHWx2Zie7XJCIiDvfH\nwYerAGaO4/oHOUs4aW9vn2g9MoqhIxw1Dd74Phek5g18XtNWy8LceS5WIyIiQ7k2pWKM+TNjzDVn\nPLwYKB/HyzwEXDzKfydSUlIiUaqMID7OT3a6c4jbKY9MqWQkppMYmwBATdtpl6sREZGhJnWEwxiz\nH/iGtfYDIAf4sTHmLqAS+B5QirOHx5hYa6uB6lHeq8fv90+8aBlVfnYyDS1dnKr3RuDw+XwUpOZR\n0VRFdasCh4iIl0R6H45OnM274kK/vhsIWmvD4+8LgdTQ5z8IXfsGkA3sA6611p6MZE0SPfk5yeyv\naPDMCAdAQdoMKpqqqGnT3nEiIl4S6WWxSed43j/k8x7g+6H/ZAoqyHamrE41tHtmGWq4j6Om9bRn\nahIREZ2lIhOQn+0MXHV2B2hp7znH1ZOjMHUGAO29nbT1eKOZVUREFDhkAvLPWBrrBYVpMwY+Vx+H\niIh3KHDIeQuPcACeaRw9c2msiIh4gwKHnLecjCRi/U6PhFf24tDSWBERb1LgkPPmj/GRF9oAzCtT\nKuGlsaApFRERL1HgkAkJT6t4JXCAszQWNKUiIuIlChwyIQOBwyM9HPDppbEiIuI+BQ6ZkHDgqG3q\nINDvjX/ctTRWRMR7FDhkQgpynM2/+gJB6ps7Xa7GUZA2uFJFfRwiIt6gwCETMmxprEf6OMIjHKA+\nDhERr1DgkAnx4l4cWhorIuI9ChwyIekp8SQlOEfkeGUvjqFLY2taNcIhIuIFChwyIT6fj/yBQ9y8\nMcIBUBCaVqnWCIeIiCcocMiEeXJpbKhxVD0cIiLeoMAhExY+xM2LIxztPR20dre5XI2IiChwyISF\nRzgaWrro6Q24XI2jUEtjRUQ8RYFDJqwg1MMB3hnlKNDSWBERT1HgkAkLT6mAdwJHZmI6CVoaKyLi\nGQocMmH5Wd4LHFoaKyLiLQocMmGJCbFkpjqjCV4JHDC446iWxoqIuE+BQyJi8Jh6b2z+BVoaKyLi\nJQocEhHhPo4aL+3FoaWxIiKeocAhETE4wuGdwDF0aaxGOURE3KXAIRER3t68vbOXts5el6txDF0a\nq704RETcpcAhEVEw7NRYb/RxDF8aqxEOERE3KXBIRHhxL47hS2M1wiEi4iYFDomI3MwkYmJ8gLca\nR7U0VkTEGxQ4JCJi/THkZiYB3loaW5jmBI6TracIBoMuVyMicuFS4JCIKQxNq1TXeSdwFKUXANDZ\n20VjV7PL1YiIXLgUOCRiZualAnDCg4ED4ERLjYuViIhc2BQ4JGKKQoGjtrHDM8fUF6XlD3yuwCEi\n4h4FDomYcOAIBqHaI0tjE+MSyUnOAqCqpdrlakRELlwKHBIxM/NSBj4/WeudrcSLQ9MqGuEQEXGP\nAodETH5WMv7Q0tgTtd4Y4QAoSlPgEBFxmwKHRIzfH0NBjjPK4aURjqL0QgCaulpo7/HOHiEiIhcS\nBQ6JqOIZTh9H1WkvBQ6tVBERcZsCh0RUeGnsyTrvBI7iIYGjSoFDRMQVChwSUUWhxtHmth7aOnpc\nrsaRnphGWrxT1wmtVBERcYUCh0RUeIQD4KQHNwDTlIqIiDsUOCSiioYEjhMebBxV4BARcUdspF/Q\nGPMZ4GHgTWvtF89x7R8A/w4oAHYDf2it3R7pmmTyZKUlkJTgp7M74LHA4YxwnG6vp6evh/jYeJcr\nEhG5sER0hMMY88fAPwAHx3Dt7cAPgfuBfGAjsNEYkxTJmmRy+Xy+wcZRD+3FEW4cDRLkZKuOqhcR\nmWyRnlLpBNYBR8Zw7beBX1prt1lru4EfAUHg9gjXJJOsKDd0iJtXl8a2qnFURGSyRTRwWGv/2Vrb\nOsbLLwYGpk+stUFgJ7A2kjXJ5Bs8NbaNYDDocjWOnOQsEvzONIr6OEREJp+bTaM5QOMZjzUAuS7U\nIhFUFNr8q7snQENLl8vVOGJ8McxMd06O1V4cIiKTL+JNo+Pkm8gXG2MKgcJRno4PBLxxRPqFpmjI\nIW4natvIyfBGW05ReiFHG49rhENExAVuBo5anFGOoXKAPeN4jQdxGk9H1N7unabFC8nM3KFLY9u5\naH6ei9UMCjeOVreeJtAfwB/jd7kiEZELh5tTKttw+jgAMMbEAKuBLeN4jYdCrzHSfydSUlLO8qUS\nLSlJcWSmJQBeO8TNCRx9/X2cbq93uRoRkQvLpI5wGGP2A9+w1n4A/AT4tTHm1zh7cPwx0AW8ONbX\ns9ZWAyMuOTDG9Pj9+gnWLUV5qTS1dntrL460oYe4VVOYNsPFakRELiyR3oej0xjTgbO3xueG/Dps\nIZAKYK3dBPwp8BRQD1wH3BJaIitT3Mzc0NklHloaW5CaR4zPueXVOCoiMrkiOsJhrT1rd6C11n/G\nrx/CmRaRaSa8xXlNQwd9gX5i/e7voh/rj6UgNY+TrafUOCoiMsnc/1dApqXwXhz9/UFONXSc4+rJ\no0PcRETcocAhUXHm0livGBo4vLIpmYjIhUCBQ6KiMDeFmNAuK15aqVIcOjW2s6+Lxs5ml6sREblw\nKHBIVMTF+pmRnQw4e3F4xdAzVapadKaKiMhkUeCQqBk8NdY7IxxFafkDn6uPQ0Rk8ihwSNSEV6pU\neWhpbGJcInnJ2QAc1wiHiMikUeCQqCkK7cXR0NJFZ3efy9UMmp1ZBMCxphMuVyIicuFQ4JCoCU+p\ngLemVUrCgaP5BP3BfperERG5MChwSNSEj6kHOO6haZXZGcUAdPV1U6szVUREJoUCh0RNXmYSSQnO\n5rLHalpcrmZQeIQDoFLTKiIik0KBQ6LG5/MxuyAdgGM1rS5XM6ggNY84fxzgTKuIiEj0KXBIVM3O\nTwO8FTj8MX5mhTYA0wiHiMjkUOCQqCopdEY4ahra6erx0EqVDK1UERGZTAocElUlBc4IRzAIVac8\n1Dga6uOoaaulq6/b5WpERKY/BQ6JqnAPB0ClBxtHgwSpatYGYCIi0abAIVGVlZZAWrLToFnpoT6O\nkoyhK1WqXKxEROTCoMAhUTV8pYp3RjjSE9PITHTqqtRKFRGRqFPgkKibHerj8NIIBwzZcVSNoyIi\nUafAIVFXEhrhqGvqpL2z1+VqBoVXqlQ2nyAYDLpcjYjI9KbAIVEXXqkCcPyUd0Y5SjKdLc7bezpo\n7Gx2uRoRkelNgUOizqsrVWYPbRxtVuOoiEg0KXBI1KWnxJOVlgB4q4+jKD0fv8/5I6AdR0VEokuB\nQyZFiQdXqsT545iZXgCocVREJNoUOGRSeHalypDGURERiR4FDpkU4T6OptZumtu8s5V4eIvzky01\n9Aa8s4JGRGS6UeCQSVFSOLhS5ZinVqo4gSMQ7OdEyymXqxERmb4UOGRShI+pBzhW7Z0+jpKM4oHP\nj2laRUQkahQ4ZFIkJ8aRl5UEeKuPIyspg9T4FEBnqoiIRJMCh0yagZUqHppS8fl8g1uca4RDRCRq\nFDhk0oSnVSqrWzy1lfjAFudaGisiEjUKHDJpwo2jbZ29NLZ6Z6VKeISjqauF5i7v9JeIiEwnChwy\naYZtce6lxtHMwcbRo43q4xARiQYFDpk0xTNS8fmcz73UODo7Yyb+GD8A5Y2VLlcjIjI9KXDIpEmM\nj6Ugx1kR4rUtzmdnzASgvOGYy9WIiExPChwyqcJH1R/z0AgHQGlWCQBHNMIhIhIVChwyqcJLYytr\nWujv985KlXnZswGo72hU46iISBQocMikmluUAUBXT4Dq+naXqxk0LzTCAVDeqGkVEZFIU+CQSVUa\nChwAR6qaXKxkuNkZM4mNiQXUxyEiEg0KHDKp8rOTSUl0/mE/UtXscjWDYv2xA0fVH9EIh4hIxClw\nyKTy+XyUFmcCcOSEd0Y4AOaG+jiOaoRDRCTiFDhk0s0LTascqWr21BbnpVmhxtHORprUOCoiElGx\nkX5BY8xs4P8BlwKtwJPW2h+McN0Pgb8AekIP+YAgUGKtrY10XeId4RGOts5eTjd2kp+d7HJFjnnZ\nQxpHG46xeuYyF6sREZleIh44gN8BHwNfAPKBl4wxNdbafxjh2n+z1n49CjWIh53ZOOqVwDErvZC4\nmFh6+/sob6xU4BARiaCITqkYY9YAFwF/Yq1ts9YeAf4e+HYk30emtpl5qSTGO1uJHznhrcbR2aGD\n3I40aAMwEZFIinQPx2qgwlo7dAJ8O2CMMSkjXL/CGPO+MabZGLPHGHNDhOsRD/LH+Jg7M9zH4a3G\n0fCOo9qLQ0QksiIdOHKAxjMeawh9zD3j8SrgMHA/ztTLz4GNxpgFEa5JPKi02JuNo+EdRxs7m2ns\n9M7oi4jIVBeNHg7fWC6y1v4cJ2SE/YMx5gs4AeSHY3kNY0whUDjK0/GBQGAsLyMuKC1yGkeb2rpp\naOkiJyPJ5YocZ+44enHScherERGZPiIdOGpxRjmGysFZfTKWlScVwMxxvN+DnCWctLd7Z+tsGS48\nwgFOH4dXAkdxxmDj6JGGSi6eqcAhIhIJkZ5S2QbMNsZkD3lsHVBmre0YeqEx5s+MMdec8fWLgfJx\nvN9DwMWj/HciJWWkthHxgln5acTFOrefp3YcjfEzJ7MYUB+HiEgkRXSEw1q70xjzMfC3xpjvA0XA\nfwR+BGCMOQB83Vr7Ac7Ix4+NMXcBlcD3gFLg4XG8XzVQPdJzxpgev98/kd+ORFGsP4aSwnQOH2+i\n3IM7jh5qqKBcK1VERCImGjuN3osTNGqAN4FfWWt/GnpuAZAa+vwHwMvAGziNpfcB11prT0ahJvGg\n8H4cXloaC4MrVZq6Wmjo9FYYEhGZqiLeNBoKDLeO8px/yOc9wPdD/8kFyNlxtJLaxk6a27rJSE1w\nuyRgcKUKQHlDJdmhBlcRETl/OktFXDN0x9FyD41yFKcXEuePA9THISISKQoc4po5henExDirqL00\nreIf0jgJ4wISAAAgAElEQVSqHUdFRCJDgUNcEx/nZ3Z+GuDBHUdDB7kdqq/w1MZkIiJTlQKHuGpg\nx1EPjXAAmNx5ALT1tFPdesrlakREpj4FDnFVeMfR6rp22jt7Xa5mkMkpHfjc1o1naxgRERmJAoe4\nauiOo+UnvTPKkZOcRXaSE4ZsvQKHiMhEKXCIq+bOzMAXOn3HSzuO+nw+FoamVQ5phENEZMIUOMRV\nSQmxFOU5e8EdOn7mQcPuMjlO4DjeUk17T8c5rhYRkbNR4BDXLZydBcCBSo8FjtzBPo5D9UddrERE\nZOpT4BDXLZrjnPV3uqGDxpYul6sZNCezeGADMDWOiohMjAKHuG5RSdbA5wcqG1ysZLhYfyylWc42\n5wfrj7hcjYjI1KbAIa6bXZBOUoJzrM+BCm9NqywMTascqq8g0B9wuRoRkalLgUNc54/xsXC2swTV\nSyMcMLgBWFdfN8ebdZCxiMj5UuAQT1hU4vRxHD7eRG9fv8vVDFqYM3fgc/VxiIicPwUO8YRw42hP\nXz9HPbQBWEZiOgWpeYA2ABMRmQgFDvEE49HGUWBgA7CDdWocFRE5Xwoc4glpyfEDG4BZjzWOhs9V\nOd1eT1Ond0ZfRESmEgUO8YxFc8IbgHlrhCPcOApwUBuAiYicFwUO8Yxw4+jpxk4aPLQBWHF6IUlx\niQBYTauIiJwXBQ7xjHDjKMCBCu+McsTExLAg21mtclArVUREzosCh3jGrPy0wQ3APHauSrhx9Ejj\nMXoDvS5XIyIy9ShwiGf4Y3yY8EFuHhrhgME+jr7+Po42Hne5GhGRqUeBQzzFhBpHD1d5awOwBdlz\n8eED4EDdYZerERGZehQ4xFPCjaO9HtsALDk+iTmZxQDsO33Q5WpERKYeBQ7xlGEnx3psWmXpjIUA\n7K89TJ8OchMRGRcFDvGU1OR4imc4G4B5rXF0ab4BnIPcyhsqXa5GRGRqUeAQzwlPq3htA7DFufPx\n+Zw+Dk2riIiMjwKHeE54x9Haxk7qmztdrmZQcnwSpVklgAKHiMh4KXCI5wzdAKys3FujHOE+Dlt3\nhL5An8vViIhMHQoc4jmz89PISI0HYPeROperGW7pDKePozvQw+GGCneLERGZQhQ4xHN8Ph/LSnMB\n2HO41uVqhluUOw+/z/ljs1fTKiIiY6bAIZ500XwncJyobfdUH0diXCLzs+cAsO+0dbcYEZEpRIFD\nPCkcOAD2HPbYtEq+08dxsK6cHp2rIiIyJgoc4klFealkpycAsNtrgSPUx9Hb36fTY0VExkiBQzzJ\n5/OxvDQPgD0eaxw1OfOIjXFOtdXyWBGRsVHgEM9aHppWqanv4HRDh8vVDIqPjWdhzlxAfRwiImOl\nwCGeNbSPw3vTKk4fx6GGCrr7elyuRkTE+xQ4xLMKcpLJzUwCvDetEu7jCPQHsHVHXK5GRMT7FDjE\ns3w+38Aox+7DdQSDQZcrGrQgZw5x/jgA9mpaRUTknBQ4xNPCgaOuqZOaeu/0ccT541iUOw9Q46iI\nyFgocIinLfd0H4czrXKkoZKOXu9sTiYi4kURDxzGmNnGmI3GmDpjzFFjzN+e5do/MMYcMMY0GWPe\nMcasjnQ9MrXNyEqmICcZ8N4GYMvzFwHQH+xn7ylNq4iInE00Rjh+BxwH5gDXA3cbY/7wzIuMMbcD\nPwTuB/KBjcBGY0xSFGqSKWx5abiPo9ZTfRylWSWkxacAsKN6n8vViIh4W0QDhzFmDXAR8CfW2jZr\n7RHg74Fvj3D5t4FfWmu3WWu7gR8BQeD2SNYkU1+4j6OxtZuq020uVzMoJiaGFQVLANhRvddTYUhE\nxGsiPcKxGqiw1rYMeWw7YIwxKWdce3HoOQCstUFgJ7A2wjXJFDe0j8Nry2NXFS4DoKGziePNJ12u\nRkTEu2Ij/Ho5QOMZjzWEPuYC7WO4NheRIXIykijKS+FEbTu7D9dxy+Vz3S5pwIrCJfjwESTIjup9\nzM4scrskEREA+vuDtHb00NzWTWN7O7VtTdS3N9PY2UpbdxtdgW66+rroDnTT19/L1fPXcufqS6JW\nT6QDB4AvStd+ijGmECgc5en4QCAwkZcXD7lofp4TOA7VEegP4o+Z0K0TMekJqczPLuFQQwU7qvdy\n5+Ib3S5JRC4AHV29zrEPjR3UN3dxqqmZEy2nON1RS2tfE13BNvpi2iC+E198Nz7/uf89fLysfEoF\njlqckYuhcnB6M2rHeO2ecbzfgziNpyNqb28f7SmZYlaZGbz8YQWtHT0cOt7IopJst0sasLJwKYca\nKrB1R+jo7SQ5Tn3PIjJxHV29VJ1u40RtGydCH6sbWjnVXkNnTCMxyS34ktqISWrHF9/tNEmkDn79\nmHomAn58wThignGsylkTpd+JI9KBYxsw2xiTba0NT6WsA8qstWfu2rQNp4/jEQBjTAxOD8jPxvF+\nDwHPj/Lc8ykpKRrfniZWLMgl1u+jLxBkW9kpTwWOVYXL+M2+FwkE+9lz6gCXFK9yuyQRmUJ6+wIc\nq2mlsqaFiupWKk42U1nTSkNLpxMoUpuISWkmJrUJX347vpgg8Wd5vZign6SYNNLiMshMyCI3JYuc\npAyyUzLIS80kPyOL7KQ0kuITifFN3nZcEQ0c1tqdxpiPgb81xnwfKAL+I84KFIwxB4CvW2s/AH4C\n/NoY82tgN/DHQBfw4jjerxqoHuk5Y0yP3++fyG9HPCQ5MY5l83LZeaiWbQdOcf/Ni90uacC87Nmk\nJ6TS0t3Gjup9ChwiMqrevgBHT7ZwuKqJw8ebOFLVTGVNC4H+IPj6nWCR1kBMYQOJC5rOOhWSEptK\ncVohJdlFzMoooCg9n5lpBWQlZeDzeWPaeaho9HDcC/wrUAM0Az+x1v409NwCQgM+1tpNxpg/BZ4C\n8oCPgVtCS2RFPuXixfnsPFTLkapmGlq6yE5PdLskAGJ8zvLYdyu3srN6H8Fg0JN/2EVk8tU1dXKg\nsoEDFY3YygYOVzXTF+gPPRvEl9yKP7+O+PR6YlIb8fn7R3yd3ORs5ufMYV7WbOZkzmJOZhGZSRmT\n9xuJgIgHDmvtSeDWUZ7zn/Hrh3CmRUTOae2SfH7+/F4APtl/ihsuKXG5okGrCpfybuVWGjqbONZ8\ngpLMYrdLEpFJFgwGqa5vZ9+RevaW17OvvJ5TDWd0E/h78WfXEZNRS1xWPcHYT/+MHeOLoTS7hMV5\n81mYM4/5OXPITsqcpN9F9ERjhEMkKmbmplCYk0J1fTvbDngrcKwoGL48VoFD5MJQ39zJrkO17DpU\nx65DtdQ3d33qGl98J0kz6kmeUU9H7CmCOKMY4a0CffgozS5hWb5hSd5CFuXOIzHOGyO4kaTAIVOG\nz+djzZJ8Xni3nB22lt6+fuJivXH+YFpCKvNz5nCo/ig7qvdx1+LPuF2SiERBd2+AvUfq2H7gNNvt\n6VF3P87N6yenpImOxGPU9dQQZPhGVFmJGawoWMLKwiUsz19EWkLqiK8znShwyJSyZpETODq7+9hf\nUc9F8/PcLmnAqsKlHKo/6iyP7ekkOV7LY0Wmg5r6draW1fDJgdPsPVxHT9+n+yxyMxJZvDCZuNzT\nVPcdpKL5mBMwegavKckoYm3xCtbMXMHcrFkXXK+XAodMKctKc0iI99PdE+DjslMeCxzLeGrvRvqD\n/ew+tZ9LZ+nwY5GpqL8/yKHjjWzZV8PWfTVU1rR+6pqkhFhWLMhl2YJMfBmn2F2/k09OHyBYP/xM\npYU587h01mrWFa1gRuqFvZG2AodMKfFxflbMzwv9tHGKb9yxzO2SBszNmkVGQhrN3a3sqN6nwCEy\nhQQC/ewtr+eD3Sf5aG81DS2fbuacU5jOxYtmsNrMICatiXeOfchvj2+n68Twa0uzS7h81houm7Wa\n3BTv7BnkNgUOmXLWLJ7B1rIajp9qo6a+nYKcM88FdEeML4aVhUt5u+IjPjm5m/7+fmJivNFjIiKf\nFgj0s/twHe/tckJGS3vPsOdj/T6Wl+ZyydIC1i4pIDGln3cqPuKXh5/mREvNsGtnpOSwfs6lrC9Z\nR0HajMn8bUwZChwy5Vy8OH/g80/2n+LWK+e5WM1w64pX8nbFR7R0t7G/7jBLZyx0uyQRGaK/P0jZ\n0Xre3XmC93efpLlteMhISvCzZnEBly0v5OJFM0hKiMXWHeFx+2u2Vu2kr79v8NrYRC6bfTFXz7kU\nk1t6wfVkjJcCh0w5M7KSKSlIo7KmlY89FjhW5C8mITaB7r5uthzfocAh4hGV1S289clx3t5eRd0Z\nS1dTEmO5ZFkhV1w0k5UL84iP89Pd18N7lVt45fDbVDZVDbt+Qc5crpt3JZfPWj0tl69GiwKHTElr\nFudTWdPKnsN1dPX0kRjvjVs5Pjae1YXL+PD4J2w5sYOvrv7cpJ5VICKDGlu62Ly9irc+Oc7Rky3D\nnkuM93PJ0kLWrypilckjLtbZl7Kuo4FXyjbzxpH3aO/tHLg+KS6RDXMu5fp5VzI7U8d0nQ9v/C0t\nMk5rFufz27cO09PXz57DdaxdUuB2SQMuKV7Fh8c/obGzmcP1FSzM9c4IjMh019vXz8dlNbz+8TE+\nOXCa/v7BVSP+GB9rFuezYXUxa5fkD/tB5UhDJRvt63x4fDv9wcFlr7MyZvKZ+RtYX7JOoxkTpMAh\nU9LiOdmkJMXR3tnLln01ngocqwuXEuePozfQy5aqHQocIpOgsqaFV7dUsvmTqk81fy4qyeLqi2dx\n5YqZZKQmDDweDAbZUb2X5w68xv7aQwOP+/CxtmgFtyy8hsV5C9SbESEKHDIl+f0xrF2Sz+ZPqvhw\nTzW/f89F+P3emLpIjEtkRcEStp3YxZaqHdy/4h79hSUSBV09fby/6ySbPqpkf0XDsOey0xO5bu0s\nrls7m6K84bt4BvoDfHh8O8/t30Rl84mBxxNiE7hm7mXcsvBaClK9s8fPdKHAIVPWlRfNHPhpZu+R\nelYs9M5fEJcUrWTbiV2cbq+noqmKuVmz3C5JZNo4fqqVlz44ylvbjtPeNbhqJNbv45JlhdywbjYr\nF87AHzM86PcGetl89COeP/Aqp9rrBh7PTEznloXXcn3plaTGe2OZ/XSkwCFT1iozg+TEWDq6+nhv\n90lPBY6Li5bj98UQCPazpWq7AofIBPUF+tmyt4aXPjjK7sN1w56bmZvCZy6dw3VrZw2bMgnrCfTy\nZvn7PLf/Veo7Gwcez0/N485FN7B+zqXE++Oi/nu40ClwyJQVH+dn3dKC0LTKSb5z93LPTKukxqew\nLH8Ru2rK2HJ8J19YfqfbJYlMSU2t3bzyUQUvf1BBQ8vgctZYv4/Ll8/kpsvmsKw0Z8Rpy56+Ht4o\nf59nD2yisbN54PGSzGLuXvwZLi1erc35JpECh0xp4WmV5rYe9pbXs2KBd0Y5Lilexa6aMk601lDV\nXE1xRqHbJYlMGYermnjh3XLe2XGCvsDgqpHczCRuvmwON1wym6y0kVeN9AX6ePPo+/y27OVhQWNu\n1izuXXora2ZepL4qFyhwyJS2yjg7AXZ2O81jXgoc64pW8K+fPE4wGGRL1Q4FDpFzCPQH2bqvmmff\nPkLZ0eFNoCsX5HHrlXNZuzh/1JHMQH+Adyq28HTZS9S21w88XppVwr3LbmV14TIFDRcpcMiUFh/n\n55KlBWzeXsUHe07yoIemVdIT01iSt4B9pw+ypWoHn116i9sliXhSV3cfr398jOffKae6vn3g8YR4\nP9dePIvbrpzL7IL0Ub8+GAzyUdV2ntjzPNWtpwcen5NZzH3L71DQ8AgFDpnyrlgxk83bvTutsu/0\nQSqaqjjVVku+ltqJDGhs6eKF98p5+YMK2jp7Bx7PzUzi9ivncuMlJaQmx5/1Nfaesjy2+xmONFQO\nPFaUXsB9y25nXfFK7fTrIQocMuWt9vS0ykp+sf1JAN4/to17ltzsckUi7jtZ28bvNh/mzW3H6e0b\n7M+YX5zBXRvmc8WKmcSeY6SyorGKx3c/w86asoHH8lJyuG/Z7Vw5e62aQT1IgUOmvPg4P+uWFPD2\nDmcTsAfvuehT6+/dkp2cyZK8BZTVHuLdiq3cvfgmDe3KBevw8SZ+8+ZBPtxTTXBwx3HWLSng7qtL\nWTpv5NUmQzV0NPHEnud5u+IjgjgvkpaQymeX3MwNpVcRp+WtnqXAIdPCFStm8vaOKprautlXXsdF\n870zyrF+zqWU1R7iRGsNRxoqmZ8zx+2SRCZNMBhkb3k9v3n9IDsO1g48Huv3sWF1MfdcPf+s/Rlh\nXb1dPG9f44UDr9MdcLYuT4hN4LaF13H7outJjkuK2u9BIkOBQ6aFixfNICnBT2d3gPd2nfRU4Lh0\n1ip+vv0JegO9vFOxRYFDLgjBYJBPDpzmqdcPDtt2PDHez02XzeHO9aXkZp47JPQH+9l89COe2PMc\nTV3Oia8+n49r5l7OfctuJyspI2q/B4ksBQ6ZFpxplcLBaZW7vTOtkhyXxLqiFbx/bBvvH9/Gl1d+\nlli//ujJ9BQMBtmyr4YnXrMcqRrcAyM1KY47rprHbVfNI+0cjaBhB2oP88sdT3G08fjAYysKFvPA\nis/qiPgpSH/rybQxMK3S2s3uQ7WsMjPcLmnAhjmX8v6xbbR2t7GzZh9rila4XZJIRPX3B/lwbzVP\nvmY5erJl4PGstATuvno+n7m0hOTEsfVX1LU38OjuZ/jg2LaBx4rTC/nyys+ysnBpxGuXyaHAIdPG\nmsUzSEuOo7Wjl9c/PuapwLE8fxGZiek0dbXwdsUWBQ6ZNsJB44lXLRXVg0EjNyORe69dwA2XlBAf\n5x/Ta/X09fC8fY1n92+iJ+Ask02JT+a+ZbdzQ+lV+GPG9jriTQocMm3ExfrZsLqYje8d5cM91bR1\n9JxzDf9k8cf4uXL2WjYefINPTu6hrbud1ASdSilTVzAY5KO9NTy+6cCwoJGXlcTnrlvI9WtnERc7\ntoAQDAb55ORufrXjN5wO7RAa44vhxtL1fG7ZraQlpJ7jFWQqUOCQaeX6tbPZ+N5Revv6eWfnCW65\nfK7bJQ1YP+dSNh58g77+Pj44/gk3zl/vdkki4xYMBvl4/ykee+UA5ScGezTyspK47/qFXLtmNnGx\nY98Do7r1NL/a8RQ7qvcNPLZ0xkK+turz6tOYZhQ4ZFopLc5k3swMyk8289rWY54KHHOyiinJKKKy\n+QTvVGxR4JApZ9fBWh55ZT+2cvCI99zMJD5//UKuXzu+oNHT18Mz+zfx3IFX6evvAyAnKYsHVn6W\ny2at1n4105ACh0w7162bRfmzzRw+3kRFdQtzCs+9xn+yrJ9zKY/s+i0H68upbj1NYZp3+kxERnOg\nooFHXt7P7sN1A49lpyfy+esWcOOlJWOeOgnbfnIvv9j+xMD0iT/Gz+3meu5ZfBOJcSOfACtTnwKH\nTDtXr57FL18ooy/Qz+tbj/HNO5e5XdKAK0vW8uju3xEMBnm3cgufX3a72yWJjKqiuoVHXtrP1rKa\ngcfSU+L53HULuPnyuSSMsRk0rK6jgV9t/w1bT+wceGx5/iK+sfo+ZqYXRKxu8SYFDpl20lPiuWRp\nAe/vPsnm7cf5yq1LxjXUG01ZSRmsyF/Mzpoy3q7Ywr1Lb9XhUuI5NfXtPLbpAG9vrxrYgjwlMZa7\nr5nP7VfOG/Py1rBAf4CXD73Fk3s30t3XDUBWYgZfWXUvl826WNMnFwgFDpmWrl83m/d3n6S5rYdt\n+2u4bPlMt0sasGHupeysKaO2vZ7dNQdYWbjE7ZJEAGhq7ebJ1yyvfFRBX8BJGvFxfu64ah6fvWb+\nea36Olxfwb9se4yKpirA2SX05vlX8/nlt2s78guMAodMS6vMDHIyEqlv7uK1rcc8FTjWFa0kPSGV\nlu42Nh3erMAhruvs7uPZt4/wzOZDdHYHAPDH+Ljx0hK+cIMhO338fRUdvZ08sed5Nh16e+CQtdKs\nEr615ovMy54d0fplalDgkGnJH+Pj2jWz+M0bh/jkwGkaWrrO6y/NaIjzx3HtvCt4dv8mtp/cy+n2\nemak5LhdllyA+gL9bPqokidetTS1dQ88vn5lEfffvJjC3PPbK2bbiV387JMnaOhsAiApNpHfu+hO\nbixdr2PjL2AKHDJtXb92Nr954xD9/UHe2nacz167wO2SBtxYup7nDrxKMBjk9SPv8sWL7nK7JLmA\nBINBPtxTzcMvlnGyrn3g8ZUL8vjKbUuYX5x5Xq/b1NnML3Y8xUfHtw88tq54JV9fdR/Zyef3mjJ9\nKHDItDUzL5Ulc7MpO9rAq1squfvq+cR45EC33JRsLp55EdtO7OKN8ve5d+mtxPvH14gncj4OVDTw\nixf2DTvBdd7MDL5y2xJWn+dxAMFgkDfL3+fRXb+jvbcTgOykTL5x8RdYq238JUSBQ6a1my6bQ9nR\nBk7WtbPdnmbN4ny3Sxrwmfnr2XZiF63dbXx0fDvr51zidkkyjVXXtfPwi2W8v/vkwGN5WUk8cPNi\nNqwqPu8wXtNWy0MfP8q+0wcB8OHjxvnr+b2L7lRTqAyjwCHT2pUrivjlC/tobO3mubePeCpwLM9f\nRGHqDKrbTrPp8NsKHBIVbR09PPn6QTa+Vz6w8iQlMZbPXbeQ26+aN+aD1c7U39/Piwff5Mm9zw8c\ntFaUXsB31t6PyS2NWP0yfShwyLQWFxvDrVfM5dFXDrDzUC2V1S2UeGTn0RhfDDfOX8/DO5/mUP1R\nyhuOqXtfIqa3r5+XPzjKE69ZWjucQOCP8XHrFXO57wZDesr5H2x4rOkEP/n4EY40VDqv64vh7iU3\ncffim4jT1KCMIqKBwxiTBfwU2AAEgJeA71lru0e49ivAL4Dwcz4gCKy31m6LZF1yYbvpsjk8+fpB\nevv6ef7dcv7951e6XdKADXMv5dd7nqMn0Mumw2/z++secLskmeKCwSBb99Xwixf2DWsIvWx5IV+9\ndQkz887/5NW+QB/PHtjEb8teJtDvLJ8tzSrhO+vupySzeMK1y/QW6RGOnwFxwGIgAXga+DvgD0e5\n/m1r7bURrkFkmIzUBK5eXcxrW4/x1ifH+fIti8lITXC7LABS41O4smQdb5a/z3vHPuaBlfeQGq9j\n6+X8HD3ZzM+e2zvszJMFszL5xh3LWDpvYkuvyxsq+cnWR6hsPgE4y7vvW3Y7ty68Fn/M+U3LyIUl\nYoHDGDMDuBNYYa1tDD32V8BTxpjvW2sDkXovkfG6Y30pr209Rm9fP698VMF91xu3Sxpw0/wNvFn+\nPr2BXt4q/5DbF13vdkkyxTS2dvHoywd4bWvlwFbkuRmJfOXWJayfQEMoQG+gl9/se5HnD7xGf7Af\ngMV5C/jO2vt1+KCMSyRHOFYCfdbafUMe2w6kAYuAfSN8zWxjzKvAGqAB+KG19rEI1iQCwJzCdFYs\nyGXXoTpeev8o91y9wDPnq8zJmsXCnHkcrC/npUNvcvOCq4n1q71Kzq23L8Dz75Tz5OsH6ex2jnhP\niPdz77ULuGtDKYnxE7uPDtdX8P+2/htVLdXOa8cm8KWL7uLG+et1BpCMWyT/VssBms94LLzQO3eE\n62sBC/wpsB+4B3jEGHPCWrs5gnWJAM4ox65DdTS0dPP+rhNcffEst0sacMeiG/hf7z9EfUcj7x37\nmKvnXuZ2SeJhwWCQj/bW8MsX9lFdP9ince2aWXz5lsXkZExsOWpPoJen9704sDkdOKuqHlx7v3bF\nlfM2rsBhjPkS8AiENsZ3hJs9/zz0+ZhYa1/CaSoNe9IYczfwNWDzGOspBApHeTo+ENAsjgxasyif\nwtwUquvaee7dcjasLvbMKZVrii6iKL2AEy01PLt/E+tLLtEW0DKiiuoW/vXZPcP6NBbPyeZbdy1j\nwaysCb/+maMaSbGJPLDys1w37wrP/HmRqWlcgSM03THilIcx5nogwxjjs9aGA0k4Cp8e41tUABeP\no6QHgR+O9mR7e/toT8kFKCbGxx1XzeOhZ/Zw+HgTZUcbJtxIFykxvhjuXnwT/7zlV5xsPcXWEzu5\ndNZqt8sSD2lp7+GxV/bzyocV9If7NDKT+NptS7hqZdGEw0C4V2PoqMZF+Yv5ztr7yU3JnmD1IpGd\nUtmBM8KxAtgZemwd0IgzdTKMMeZBoMFa+5shDy8Gysfxng8Bz4/y3PMpKSlF43gtuQBct3Y2j768\nn/auPp564yB/Oc87UxeXz17Dk3tfoLa9nmfKXuGS4lX6iVLoC/Tz8gcVPL7pAG2dzn4a8XFOn8bd\nV0+8TwPgSEMl/2/LwxzXqIZEUcQCh7W23hjzNPDXoT02koC/AP7VWtsPYIx5HXgoFDISgH8yxpQD\nu4DPATfjhJSxvmc1UD3Sc8aYHr9fS7VkuKSEWG6/qpQnXrNsP3CaAxUNLJrjjZ/eYmP83GFu4Ofb\nn+Bo03F21ZSxsnCp22WJi3YdrOVfntvDsZrWgcfWryriq7cuJS9r4tuG9wX6eLrsJZ7dv2lgBcry\n/EX8/toHNKohERfpVvjv4Gz8dRTowZl++fMhz88DsgCstf9ojEkFfgMUhL7mTmvtTkSi6M4Npbzw\n7hHau/p4bNMB/urBy90uacA1cy/j6bKXaO5q4Zn9ryhwXKBq6tv5xQv7+HDP4M9TpcUZfOvO5RGb\nBjzaeJwfb3mYY6F9NRJjE/jyys9y3bwrNaohUeELz9VNN8aY8uLi4rlvvPGG26WIB/160wEef9WZ\n6fu7713Jkrne6OUAeG7/qzy2+xkA/vLaP2Jx3gKXK5LJ0tXdx9NvHuJ3mw/T2+eMOGSkxvPAzUu4\nft1s/BE47bivP8AzZS/zu7KXCYRGNZbNMHxn3QNagSJnimjy1GJ/uSDdsb6U594tp72zl8c3HeCv\nv3OF2yUNuGH+VTy7/xXaezt5dv8mBY4LQDAY5L2dJ/nFC3upa+4CnHNPbrtyHl+40ZCaFJnzSY41\nneDHWx7maNNxABL88dy/4h5umH+V9tWQqFPgkAtSSlIcd28o5dFXDrDrUB17j9SxrHSk7WImX3Jc\nEs7WZzAAABwuSURBVDctuIbflr3Ejup9OtRtmjt6spmHntnDvvL6gcdWLczjW3ctZ1Z+WkTeI9Af\n4PkDr/HUvo0DZ6AszpvP76/7MgWpeRF5D5FzUeCQC9btV83juXeO0NrRy+ObLH/z77wROABuXngN\nGw++QXdfN4/vfpY/v/oP3C5JIqy1o4dHXx6+zLUgJ5lv3rGMdUsLItZHcaKlhh9veZjDDRWAcwbK\nF5ffyc0Lr9GohkwqBQ65YCUnxnHXhvk88vJ+9hypY8/hOpbP90boSE9I5XZzPU/ve5Hdp/azq6aM\nFQVL3C5LIiDQH+TVjyp45OX9A8fGJ8T7+dx1C7h7w3zi4yKzuq6/v5+XDr3Jr/c8T2/AeZ8FOXP5\n7rovMzO9ICLvITIeChxyQbvtyrk8+/YRWjt6eGzTAf5HqXf2HbjdXM9rR96luauFR3c9w/IZi7T7\n6BS3r7yef3lmD+UnB0+BuGplEV+7LTLLXMNq2mr5ydZ/Y3/tYQBiY2L5/LLbuMPcoHtIXKPAIRe0\n5MQ47rlmPg+/WMa+8no+LjvFuqXe+OkvKS6Rzy29lZ998msqm6p4t3IrG+Ze6nZZch7qmzv51cYy\nNm+vGnhsTmE6D969PKK9Q/3Bfl49/A6P7XqG7kAPAHOzZvHddV9hdqb2QRR3KXDIBe+2K+ay8b1y\n6pu7+Nlze1ll8oiL9camcdfOu4KXDr7JydZTPLH3eS6bfTHx/sisWJDo6+0L8Nw75Tz5mqWrx2nW\nTE2K4/6bF3PTpSX4/ZEbbTjdXs9Ptz7C3tPOcm+/L4Z7ltzM3UtuJjbGG/ezXNg0tiYXvMSEWL52\nm7PBVnV9O8++fcTligbFxvj54kV3AVDf0cgrh95yuSIZq237T/G9H73Fwy+W0dUTwOeDmy6bw09/\ncB23XjE3YmEjGAzy+pH3+E+v/NVA2JidUcTf3PADPrfsNoUN8QyNcIjgbBf90gdHKTvawFOvH+Ta\nNbMmfMR3pKwtWoHJLcXWHeF3Za9wzdzLSUtIdbssGcXJujZ+9txePi47NfDY4jnZPHj3ckqLMyP6\nXnUdDTz08aPsqtkPOIcA3rX4Ru5dciuxfv31Lt6iEQ4RwOfz8e27luPzQVdPgF+9WOZ2SQN8Ph8P\nrLgHgI7eTp4pe8XlimQknd19PPxiGd/9n28NhI3s9AS+/8XV/N33roxo2AgGg7xV/gHff+WvBsJG\ncXohf33dH/OF5XcqbIgn6a4UCSktzuTGS0rY9FElmz+p4pbL5rJ4rjcOsFqYO49LilexpWoHLx/e\nzLXzrqA4o9DtsgTnH//N26v41cYyGlqcXUJj/T7uXF/K569fSHJiZHtuGjqaeGjbY+yo3gs4gfQO\ncwOfW3ab+nvE0xQ4RIZ44ObFvLfrJO2dvfzLs7v5X/9hQ0TOr4iEL624m+3Ve+kN9PLQtsf4y2v/\nSBs3uezQ8Ub+5Zk9HKhsHHhs7ZJ8vnnHMmbm/f/t3Xl4VFWax/FvVSoLJGEL2SBhh0NIgEDCoiwK\nCNggoig2irgv3T5Oj8483dPbPK09Pd09M7Zttz3d2trtBm2LjmIAkX2XNWEN5IQkkAUSEkggCdmr\n7vxRoUgjSBXUrUqK9/M8PD65ucl9OV7u/dW5557j3cdehmGw+cRO3t33MXXN9QD0iozlubGPMKTn\nAK8eSwgzSOAQoo2uEaE8NFPx1rLD5JWcZ93uImaO7+vvsgCIi4jm/mGz+PDQ5+gz+azP3870QZP8\nXdZNqaqmgQ++OMq6PUVcXP+yV89wnr5nOOlJsV4/3td6NbAwe8hUFgy/mxBbiNePJ4QZJHAIcZlZ\nt/Zn9c5CispqeGdFNulJMe1mAOmcodPZVrSH4vOnWHLwM9J7j6B7p67+Luum0dziYOX2Aj5co6lr\naAGgU2gQC6Yr5kwaSLDNuz1OhmGw6fgO3tv/iatXIz4yhufGPoLqOdCrxxLCbNIfK8RlbEFWnrtv\nJBYLXKhv5vdL92Nc/BjrZzZrEM+mL8SChbrmet7Zt9TfJd009h49zT+9soG/ZGS7wsbU9ETe+OEd\nzJsy2Oth48yFSn655XX+tOcD6prrsWDhLnUH/zPjJxI2RIckPRxCXEHygCjmTh7Iss35ZOWUs2ZX\nITPH9/N3WYBzAOmMQZNZnbeZncVZZJ46RFqv4f4uK2AVn67h7YzDZOWUu7YN6dONZ+4Zjurr/UHF\nDsPBuvxtLD7wKQ0tjYBzrMZ3xy6SoCE6NAkcQlzFom8lkZlzmuLTtfwl4zAjB0cTFxXu77IAeHDE\nXHaf3E9V/XnezvyQ5OjBhAWH+busgFJT18Tf12hWbj+OvXU51x5dQnl0djK3j07AasJg4rKact7c\nu4Ts8lxA3kARgUUeqQhxFSHBQbywYDRWq4X6Rju/+2gfDkf7eLTSObgTT45eADhnIF184DM/VxQ4\nWuwOVmwr4NlfrSNjawF2h0GwzcoDdwzhjR/ewdT0RK+HDbvDTkbOWv519S9cYSOxay/+c9oPWDjy\nXgkbIiBID4cQ32BIn+7MnzaYj9bmcjj/LMu3FTB3cvvo1h6bkMrY3qnsPrmfNflbGB43lHEJo/xd\nVoeWlVPO2xmHKD5d69o2YUQvHrtrmGm9WyeqSnhjzwcUVBUBzjVQ7km6k3nD7iRYgoYIIBI4hLiG\nb9+h2JN9moJT53l/5RFGDYmmT1wXf5cFwDNjFpJXeYLK+nO8sfsDBnTvQ3R4lL/L6nAKS6v56/Js\nsvSlcRoDenfl6bkpXl3Nta0mezOfHvmCz4+uwW44ABjYoy/fHbNIVnYVAcnSXkbfe5tSqiAhIaH/\n+vXr/V2KCAAnSqt58bebaLEb9I6O4Df/PJnwTu3j0+eR8lxe3vQahmEwJGoAL039F1mwy01VNQ38\nbbVmzc4TXHxa1j0ylEdmJTElvY9pk74dPq15a+/fKK11BpyQoGAWDJ/LrMFTsFrlSbdoN7z6D0AC\nhxBuWrmtgDc+OwTAuOQ4fvzYWFMGDl6Pjw+v4OPslQDckzTTtcKsuLKGphYythTwyYZj1Dc6X3EN\nCQ7i3tsHct+UwXQKNafzt6axlg8OfMqm4ztc24bHDuWZ9IeIjYg25ZhC3ACvXuDkkYoQbpo1oT/H\nSs6xfk8xu7LL+GhdLg/OUP4uC4D7hs0iuzyXIxXH+PzoGlJiFCPikvxdVrtjdxhs3FvE4i9zOHu+\nwbV9SloCi741jOju5kzwZhgGWwt38/7+T6hudI4PiQyN4NHU+5nUdywWS/sIrkKYSQKHEG6yWCw8\nd99ICstqyCs+x99W5zAwoStjh8X5uzSsVivfG/8E31/9C2qaLvD6rnf5r+k/okdn7y6H3lEZhsE+\nXcE7K7I5UVrt2p4yMIon5iQzOLG7acc+WV3G25kfut4+Abit33gWpd5Hl1DvrrciRHsmj1SE8FBF\nVT0vvraJ87VNdA6z8eoLt9Hbywt1Xa+sU4f49dY/AtCvWwIvT/1XOt3k83PkFlXx3sojHMw749qW\nGBvBY7OTGTMs1rTehcaWJj49sooMvRa7ww4418N5Ku1B6X0SHYWM4XCHBA5hpkP5Z/jpG1/hcBgk\nxETwX89Pokt4+1hEq+14jlHxyfxg4ncJugkHkZ6sqOWDVUfZfuCUa1u3yFAWzhzK9LF9CAoyZ3Cm\nYRhknjrIu/s+pvzCWQCCrTbuSZrJ3KSZMqeG6EgkcLhDAocwW8bWfN5a5ly9c1BiN/7zO7fSOcz/\nNxPDMPjf3e+x5cQuAKYPnMRTaQ/eNOMEzpyr56N1uazZVeiaqK1TqI15UwYxd/JA0waEApTWlPPu\nvqXsK812bRsZl8QToxcQHxlj2nGFMIkMGhWiPZgzcQDllfV8viWfvOJz/Pwvu3jp6fGEhfj3n5XF\nYuE76Q9ztq6K7PJc1uZvJTYimruHTvdrXWY7V9PIJxuO8cVXx2lucc5rYQuyMmtCPx6YNoSuEaGm\nHbuhuYFPj37JCr2eFofzrZcenbrxSOp93JKYdtOEPSG+ifRwCHEDDMPgDx8fYM2uQgBGD43hp4+P\n8/rKodfjQlMd/77+FUqqSwF48danuCUxzc9VeV9tXROfbspj+dYCGpqcYyWsFrg9LZGHZg4ltkdn\n047tMBxsPbGbDw99TmX9OQCCrEHMUXcwL+lOWd9GdHTySMUdEjiEr9gdBq8uyWTL/pMA3Doinh88\nnG7aGAFPlF84y0/W/TfnG6oJslj551ueZHziaH+X5RW1dU18vqWAjK35ruXiASaM7MXCmUNJjI00\n9fg5Ffm8t+9j8qsKXdtGxSfz6Kj59IqMNfXYQviIBA53SOAQvtRid/Crd/ew+0gZAJNSe/Pig6MI\ntvl/sGZ+ZSE/3/Qa9c0NWC1Wnh/3KBP7jvV3WdftakEjPSmWh+8cysAEc18FLq89w5KDy9hRnOna\nFh8Zw6KR95HWa7g8PhGBRAKHOyRwCF9rarbz8ts7Xa9fpgyM4iePjyOiHUyBnl9ZyC82/54LTXVY\nsPDsmIeZOuBWf5flkXM1jWRszWfl9uP/EDTShsbw4AyF6tvD1ONXN9Twf0dWsSZ/i+s11/CQzsxP\nns2MQbfJdPIiEEngcIcEDuEPDU0tvLI4k13Zzp6OPnGRvPTULabNYOmJE1Ul/GLz71wzXT6VtoAZ\ng27zc1XXVlFVz2eb81i9s5CmZrtru6+CRkNzAytyN7A8Zy31Lc7ZSYMsVmYMuo35ybOJCDVnFVkh\n2gEJHO6QwCH8xW538OayQ6z66gQAPbqE8dLT4+nfq6t/CwNKzpfyH5t+R1XDeQDmJ8/mvuRZWC3+\nH29yucKyapZtymdTVjEt9kvXqXHJccyfNtj0oNHU0sTa/K0sy1nD+YZLs5PempjGguF3EyevuYrA\nJ4HDHRI4hD8ZhsEnG47x/hdHAec8EN/7dioTR/p/2fHSmnJ+vvE1ztZXAZDeawTPj3uMziH+74Ux\nDIODeWf4bFMemTmXloq3WmBiam/unzrY9ODWZG9mXf5WPj+6xhXMAFJiFAtH3svAHn1NPb4Q7YgE\nDndI4BDtwcbMYn7/0T7XJ/QZ4/ry9NwUwkycfModZ+oq+c32P5Nf6XzDIj4yhu9P/A4JXeL9Uk9T\ns51tB06SsbWA/JJLN/lgm5Wp6YnMu30QvUyePr6xpYkNBdtZlrOaqvpLNQzq0Y9vD5/DiNgkGRAq\nbjYSONwhgUO0F9kFZ3llSSZnztUDkBATwQ8Wpfv9EUuTvZm3Mz90LZUeZgvl+XGPMTYh1Wc1VFTV\ns2rHcVbvLKT6QpNre2TnYGZN6M/sCf3pHmnuXBa1jRf4Mm8zq45tpKZ1fAvAwO59mZ9yF6PikyVo\niJuVBA53SOAQ7UltXROvf7yfrw46J+GyBVl5ZFYScyYNwObH+ToMw2Bt/hbeyVqK3XDOzjm53zge\nTb2fSJNWMrU7DA7kVvDlzhPsyi5zTT8O0Ds6nDkTBzBtbB/TZ2ytuHCWVbkbWVuwjcaWRtf2Ad37\nMD/lLkbHp0jQEDc7CRzukMAh2hvDMFi9s5C3Pj/setsiMTaSp+emMEr5dwBiTkUer371FudaB0d2\nCY3gsVEPMKFPutduuuVVdazfXcTaPUVUVNW7tlsszjk07po4gNTB0Vit5t3kDcMgu1yz6tgm9p46\nSNvr3/DYodyTNJOUGCVBQwgnCRzukMAh2quismp++/d95BWfc20bnxLHk3enEBflv1csaxsv8P7+\n/2PTiR2ubaPiU3gybQEx4VHX9TvrGpr56mApm7NKOJBXQdvLTZfwEKamJzJ7Qn/T/94XmurYVriH\n1XmbXVO9g3PdmXEJo7hn6AwGyGBQIS4ngcMdEjhEe+ZwGKzfU8T7XxzlXK2zOz/YZmXGuL7MnTyQ\n+J7+Cx4Hy47y571LXEurB1mDmNLvFu4ddifRbgSPpmY7WbqcTVkl7Mkuo6l1ITVw9maMGhLDjHF9\nGZscZ+qaMw6Hg0PlOWw8voM9JftpdlyaLCwiJJypAyYwY9Dk6w5TQtwE2nfgUEqlAx8CFVrrb5zK\nUCn1beDHQH9AAz/WWq/1Uh0SOES7d6G+mb+v1SzfWoC9dSyD1QK3DO/FvbcPNH2uiatpbGli6eHl\nrMzdgKN1bMc3BY/auib2HD3NzsOlZOWUuxZRu6hXz3BuH53A1DF9TF1MzTAM8isL2Vmyj+2Fe1yv\n/l7Ur1sCdw6ewsQ+6YTYQkyrQ4gA0X4Dh1LqIeBXwGGg+zcFDqVUKrADuAfYCNwP/BkYorU+5YVa\nJHCIDqP4dA1L1+WyZf/JfxhEmdSvB7eNTuDWEfGmv61xJWU15Xx65Eu2FO66FDwsVlLjU1CRKTSc\nieLQsSqyC866AtNF3SJDmZzam9tGJzA4sZtp4yJaHHZyz+Szq2Q/u0v2fy1kRISEM7HvGG7vdwv9\nuyfK+Awh3NeuA8fjwCrgWWDmNQLH60C81vr+Ntt2AJ9prf/bC7VI4BAdTnlVHcu3FrB6ZyH1jZce\nAVgtkDKwJxNTezN2WCxRXX07SVfJuTIWZy1nX8U+DC5dM4yWYOxn47GfjcNxoRvR3cK5JSWe8Snx\nDOvfw5QVcw3DoPj8KQ6Xaw6ezuFo+THXlOMX2aw2RsYlcVu/8aT1Gk5wkP/XsxGiA/Jq4PDqe2da\n63cAlFLu7J4GrLhsWxYwxps1CdGRxHTvzJN3p7BgumL1zkI2ZhZzorQahwEH885wMO8MfwRienRm\nWP8eDOsfRVK/HvSODvfKyrSGYXCutpGS8lpKTtdQVFZDbnEVBSerabHHYAmdRFB0Mbaep7CENGKx\nNWOLLcIWW0SwNZj+0QOJirET3LUzzY4IgoJurFfGMAwq6iopqCzkeFUxBVVFFFQV/cN8GReFBoUw\nKj6FcYmpjIpPoXOw/2dOFUJc4s/pDqOAqsu2VQLD/FCLEO1KeKdg5k0ZxLwpgyg+XcO2A6fYuv8k\nxadrACivrKO8so5NmSWAczBmVNdOxEeFE98znJ5dw+gUZqNTqI3OocF0CrPhMAxaWhw0tzhosTto\naLJTVdPAuZpGKqsbqKpuoOxsHbX1zVety2jsTFxTGiM6z6B7r1pO2TVZZQdosjfT7Gjm0OkcDp3O\nce3fLawL8ZExxEXEEBMeRafgMMJsoYTZQgm1hWIYBo32RhpbmmhoaaS+uYGzdVVU1J2l4kIlFXWV\nNNuvXk+frr0ZHjuU4bGK5BhFqIzLEKLd8ihwKKUWAh8AbZ/DWFq/flxr/b6Hx7+h7hqlVDxwtbmY\ne5eWljJt2rQbOYQQ7YrdbtDUYqep2UFzi/0fxk0UmHA8q8WCzWYlxGYluPVPrsVC7ppL+xgYNNtb\nnKHD3tz6Noj3336zYMFmtWELshFstRESFMxZSy772Oj1YwkhoKSkZLPW2mtLSnsUOLTWS4AlXjp2\nBc5ejraigPIr7Hs1zwI/u9o37Xa7o6SkpASwX20f4VVBQBegGmlzXzG9zRuBC2b84uvQeO1dfEHO\nc9+TNve9IKCvUipea116zb3d4M9HKntxjuNoawzOV2rd9SaQcZXvDcUZju7VWmd5Xp7wlFJqNJAJ\nTJM29w1pc9+TNvc9aXPfa9Pm8UC7DhxXfFSilFoHvKm1/hh4C9itlPoWsAFYCAwGFrt7kNbUdcWG\ncHPgqhBCCCF8wKuBQymVA/Rp/b1WpVQ9zoe5SmtdDAwAugNorbNbx4S81vozR4DZWmtPHqkIIYQQ\nogPw9muxQ6/x/QGXfb0MWObNGoQQQgjR/vhvXWwhhBBC3DQkcAghhBDCdBI4hBBCCGG6QA4cpcDL\neOl1HuEWaXPfkzb3PWlz35M29z2vt7nXl6cXQgghhLhcIPdwCCGEEKKdkMAhhBBCCNNJ4BBCCCGE\n6SRwCCGEEMJ0EjiEEEIIYToJHEIIIYQwnQQOIYQQQphOAocQQgghTCeBQwghhBCm8+ry9L6mlOoD\n/BEYD9QAH2mtf3iVfb8HPAfEAQeBF7TWWb6qNVB42ObfAV4AegF5wEta6wxf1RooPGnzNj/TGzgK\nvKK1/rn5VQYWD89zBbwBjAXOAL/VWr/mq1oDhbttrpSyAC8BjwBRQAHwS631Ut9VGziUUjOB94AN\nWuuHrrHvDd1HO3oPx6dAMdAPuAO4Vyn1wuU7KaXmAD8DHgZigRXACqVUJ9+VGjDcbfN5wC+Bx4Du\nwB+ApUqpfr4qNIC41eaX+T3QYnJdgczd8zwMWA0sB3oA84AnlFJDfFdqwHD3PP8u8AQwHegK/ARY\nrJRK8VGdAUMp9X3gNSDXjX1v+D7aYQOHUiodGAH8m9a6VmudD7wKPHOF3Z8B3tFa79VaNwL/AxjA\nHJ8VHAA8bPNOwI+01ju11nat9V9xfmoZ77uKOz4P2/ziz8wChuK8IAgPedjmDwDntNavaq0btdaZ\nWusRWutrXsDFJR62+Whgm9Y6T2ttaK1XAmdbf154ph5nz1y+G/ve8H20wwYOnCfdCa11dZttWTh7\nOMMv2zet9XsAaK0NYD8wxvQqA4vbba61XqK1fvPi10qpbkAkcNInlQYOT87zi5+4X8fZ7Wn3TYkB\nx5M2nwgcVkr9RSlVpZQ6opT6xm5pcUWetPlK4Hal1EilVLBS6m6cH3A2+6jWgKG1/oPWusbN3W/4\nPtqRA0cUUHXZtsrW//Z0c9/L9xPfzJM2v9xbwA6t9VavVxXYPG3znwHbtdZy8b1+nrR5AjAXWAPE\nA78G3ldKjTS1wsDjdptrrT8D/gzsAxqAJcDjWmv5MGOuG76PduhBo4DFpH3F1XnUjkopG84BSUnA\nFFMqCnxutblSahjOZ9vyLPvGuXueW4BMrfVHrV+/3zpYej5wwJTKApe75/kinANG04HDOMd7/E0p\nVaS1zjSxPnGD99GOHDgqcCautqJwPlOqcHPfQ+aUFrA8afOL3fsZQBgwSWt9eToW1+ZJm/8R55tA\nX/t/ITziSZuX4RwU3dYJnKP4hfs8afPngTfbvB3xhVJqA7AIkMBhnhu+j3bkRyp7gT5KqR5tto0F\njmit666wb9rFL5RSVpzPDHeZXmVg8aTNAf6Os8tzmoSN6+ZWm7e+UjgJeFkpVaGUqgAWAP+mlNrr\n04o7Pk/O8yN8fbBiP6DQvPICkidtHtT6p61QM4sTgBfuox02cGit9wN7gF8rpSKVUkOBF3F+ykMp\nlaOUurV19z8BjyilxrW+wvNTnDfClX4ovcPypM2VUguBZOABrXWzv2ru6Dxo82IgEUgFRrb+ycB5\n7s/yR+0dlYfXlsVAT6XUj5RSYUqpB3FehBf7o/aOysM2zwCeUkoNV0oFKaVmAFOBz/xReyBTSh31\n5n20Iz9SAbgf52DEMuA88Cet9Rut3xsMRABorVcrpX4ELAWicZ7Ys1pf7RGeuVabXxxR/jjQF6h0\nzouEBWf36Ada62d9WnHHd83zvHXE+Km2P6SUqgOqtdblviw2QLh7bSlVSs3GOe/JvwNFwN1a6+O+\nL7nDc6vNcc7vEwQsw3k9PwE8JQOlPaeUqsd5XQ5u/fpewNBad27dZQhevI9aDMPwYvlCCCGEEF/X\nYR+pCCGEEKLjkMAhhBBCCNNJ4BBCCCGE6SRwCCGEEMJ0EjiEEEIIYToJHEIIIYQwnQQOIYQQQphO\nAocQQgghTCeBQwghhBCmk8AhhBBCCNNJ4BBCCCGE6SRwCCGEEMJ0/w+Zve/Vk9Vh1AAAAABJRU5E\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad2648400>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.gcf().suptitle('$U(r) = 1/r - b\\cdot(r - c)^2$', fontsize=18)\n",
"sns.set_palette('deep')\n",
"\n",
"x = np.arange(0.1, 1, 0.01)\n",
"\n",
"y = 1/x - 4*(x - 9/8)**2\n",
"y = y - y[-1]\n",
"plt.plot(x, -y/y.min())\n",
"\n",
"y = 1/x - 3*(x - 7/6)**2\n",
"y = y - y[-1]\n",
"plt.plot(x, -y/y.min())\n",
"\n",
"plt.ylim([-1, 2])\n",
"plt.xlim([0, 1])\n",
"sns.despine()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Leonard-Jones Potential"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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V/H7mOejbvwUseHlOwujTwUJdGDHkuRIGQdbNrYlngkMp9RLgvwP/h9b6o212Mw55H8dp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\nQymllFJx9/+RNoz8zTGlTgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad85667f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.gcf().suptitle('$U(r) = (0.5/r)^{2n} - 2(0.5/r)^n$', fontsize=18)\n",
"\n",
"x = np.arange(0.1, 1, 0.01)\n",
"\n",
"for n in np.arange(1, 7):\n",
" y = (0.5/x)**(2*n) - 2*(0.5/x)**n\n",
" plt.plot(x, -y/y.min())\n",
"\n",
"plt.ylim([-1, 2])\n",
"plt.xlim([0, 1])\n",
"sns.despine()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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S0VMq2jQqZ7HYCRS3Z5jsJc/hZGeA0qbQV7fjj/Uu+DpaPhFpLAUOaXlZV3s4pDYLF/Dy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\nDhEREWm6/wG99gCSDMenTAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad8611080>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(0.3, 1.2, 0.01)\n",
"y = (0.5/x)**12 - 2*(0.5/x)**6\n",
"plt.plot(x, -y/y.min(), 'o')\n",
"\n",
"r_min = 0.5*2**(1/6)\n",
"y = 1/12*(r_min/x)**12 - 1/3*(r_min/x)**6\n",
"plt.plot(x, -y/y.min())\n",
"\n",
"plt.ylim([-1, 0.1])\n",
"sns.despine()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def plot_potential(force):\n",
" \"\"\"Probe force and plot the integrated potential\"\"\"\n",
" r = np.linspace(0.2, 1.2, 100)\n",
" F = np.empty(len(r))\n",
" for i in range(len(r)):\n",
" X = np.zeros(6)\n",
" X[3] = r[i]\n",
" F[i] = force(0, X)[0]\n",
" U = cumtrapz(F, r, initial=0)\n",
"\n",
" plt.xlabel('Distance')\n",
" plt.ylabel('Potential')\n",
" plt.plot(r, U)\n",
" plt.ylim((U.min(), 1.1*U[-1] - 0.1*U.min()))\n",
" sns.despine()\n",
" plt.tight_layout()\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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brhr4rrX2ydD3vzfGrAHOBhSaZFj5ob9i1XJAJHEcx2HTzkO8vGoXr67ZQ0Nz14Db8/P8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\nGpsAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad80316d8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def leonard_jones(t, X):\n",
" \"\"\"Calculate forces for the potential U = (r_min/r)**12 - 2*(r_min/r)**6\"\"\"\n",
" r_min = 0.5\n",
" X = X.reshape(-1, 3)\n",
" F = np.zeros(X.shape)\n",
" for i, x in enumerate(X):\n",
" r = X - x\n",
" norm_r = np.linalg.norm(r, axis=1)\n",
" F[i] -= 12*r_min**12*np.nansum(r/norm_r[:, None]**13, axis=0)\n",
" F[i] += 12*r_min**6*np.nansum(r/norm_r[:, None]**7, axis=0)\n",
" return F.ravel()\n",
"\n",
"plot_potential(leonard_jones)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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OGPNF4DSgMOzuscAJgy1KJBUVKTSllUAgwK8eXklHpw9vjodvfOpEbZMiIoMS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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad808bba8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def leonard_jones(t, X):\n",
" \"\"\"Calculate forces for the potential U = (r_min/r)**12 - 2*(r_min/r)**6\"\"\"\n",
" r_min = 0.5*2**(1/6)\n",
" X = X.reshape(-1, 3)\n",
" F = np.zeros(X.shape)\n",
" for i, x in enumerate(X):\n",
" r = X - x\n",
" norm_r = np.linalg.norm(r, axis=1)\n",
" F[i] -= r_min**12*np.nansum(r/norm_r[:, None]**13, axis=0)\n",
" F[i] += 2*r_min**6*np.nansum(r/norm_r[:, None]**7, axis=0)\n",
" return F.ravel()\n",
"\n",
"plot_potential(leonard_jones)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"3375.0"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(4*np.pi/3*150**3)/(4*np.pi/3*10**3)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"3.7267799624996498"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.sqrt(500)/6"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"14.142135623730951"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.sqrt(200)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ReLU Forces"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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uJR1Z4wrh864fz6Vp0+gR52y3snDTWxptEhHp4gI90rQWGGSM6WmtrZsumwJk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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad23ccb38>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(0.5, 1, 0.005)\n",
"\n",
"f, axarr = plt.subplots(2, sharex=True, figsize=(6, 8))\n",
"axarr[0].set_title('Potential')\n",
"axarr[1].set_title('Force')\n",
"\n",
"F = 2*(x - 0.6)*(x - 1) + (x - 1)**2\n",
"U = cumtrapz(-F, x, initial=0)\n",
"U = U - U[-1]\n",
"axarr[0].plot(x, U, '.')\n",
"axarr[1].plot(x, F, '.')\n",
"\n",
"F = (0.8 - x)*(x < 0.8) - (0.9 - x)*(x > 0.9)/2 - 0.05\n",
"U = cumtrapz(-F, x, initial=0)\n",
"U = U - U[-1]\n",
"axarr[0].plot(x, U)\n",
"axarr[1].plot(x, F)\n",
" \n",
"# axarr[0].set_ylim([-1, 2])\n",
"# axarr[0].set_xlim([0, 1])\n",
"plt.tight_layout()\n",
"sns.despine()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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/gJktNrMqgtWgoWZWZWZHzex8d98DzAM+BrwDLAOeAW7vgO8j3czAPv2ZMPgM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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f8ad264a748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(0.5, 1, 0.005)\n",
"\n",
"f, axarr = plt.subplots(2, sharex=True, figsize=(6, 8))\n",
"axarr[0].set_title('Potential')\n",
"axarr[1].set_title('Force')\n",
"\n",
"F = 2*(x - 0.6)*(x - 1) + (x - 1)**2\n",
"U = cumtrapz(-F, x, initial=0)\n",
"U = U - U[-1]\n",
"axarr[0].plot(x, U, '.')\n",
"axarr[1].plot(x, F, '.')\n",
"\n",
"F = np.maximum(0.7 - x, 0)*2 - np.maximum(x - 0.8, 0)/2\n",
"U = cumtrapz(-F, x, initial=0)\n",
"U = U - U[-1]\n",
"axarr[0].plot(x, U)\n",
"axarr[1].plot(x, F)\n",
" \n",
"# axarr[0].set_ylim([-1, 2])\n",
"# axarr[0].set_xlim([0, 1])\n",
"plt.tight_layout()\n",
"sns.despine()"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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jAnbQtY4dGBcyqwkgPRIFTe6ngkNr0OQ+0I14Xox0mCnUTJNS1yYNmpS6hFwm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\nDzQM+7rnd71Bdae+euy2GdeSGe39otiIuEmAPoLR0XTI648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