{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial 5 - Fluids in the Complex Plane\n", "\n", "This tutorial will cover complex numbers and the compelx plane, and how we can use that as a tool to develop fluid dynamics." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Complex Numbers\n", "\n", "A complex number is written as\n", "$$\n", "z = x + iy,\n", "$$\n", "where $x$ is called the real part and $y$ the imaginary part. Complex numbers are built into Python, so they're straightforward to use:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(2+3j)\n" ] } ], "source": [ "z1 = 2 + 3j\n", "print(z1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the imaginary number $i$ is called \"$j$\" in Python -- $i$ is too often used in loops, and $j$ is pretty typical in some engineering fields. \n", "\n", "You can add and multiply complex numbers as usual:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4j\n", "(-7-4j)\n" ] } ], "source": [ "z2 = -2 + 1j\n", "\n", "print(z1 + z2)\n", "print(z1 * z2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also extract just the real or imaginary part, and take the complex conjugate:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.0\n", "1.0\n", "(2-3j)\n" ] } ], "source": [ "print(z1.real)\n", "print(z2.imag)\n", "print(z1.conjugate())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using polar coordinates can sometimes be more convenient. In polars, the complex number is written\n", "$$\n", "z = s\\, e^{i\\phi},\n", "$$\n", "where $s$ is the distance from the origin to the point, and $\\phi$ is the angle measured from the real axis (the $x$ axis). The distance $s$ is called the modulus, and $\\phi$ the argument (or sometimes phase). We can calculate them as follows:\n", "$$\n", "s = |z| = z^* z,\n", "$$\n", "where the star $^*$ indicates the complex conjugate, and\n", "$$\n", "\\phi = \\tan^{-1}(y/x).\n", "$$\n", "Python has functions that do the work for us:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.605551275463989 0.982793723247329\n", "(3.605551275463989, 0.982793723247329)\n", "(2.23606797749979, 2.677945044588987)\n" ] } ], "source": [ "from cmath import phase, polar, sqrt\n", "\n", "s1 = abs(z1)\n", "phi1 = phase(z1)\n", "print(s1, phi1)\n", "\n", "# or\n", "print(polar(z1))\n", "print(polar(z2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Complex Plane\n", "\n", "Now that we have the basics covered, let's draw the complex plane and plot our two complex numbers. The $x$ axis becomes the real axis, and the $y$ axis the imaginary." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "fig = plt.figure(figsize=(6, 6))\n", "\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.set_xlim(-4, 4)\n", "ax.set_ylim(-4, 4)\n", "ax.spines['left'].set_position('zero')\n", "ax.spines['bottom'].set_position('zero')\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.set_xlabel(\"Re\", loc=\"right\")\n", "ax.set_ylabel(\"Im\", loc=\"top\", rotation='horizontal')\n", "\n", "plt.plot(z1.real, z1.imag, \"o\", color=\"black\")\n", "plt.plot([0, z1.real], [0, z1.imag], color=\"black\")\n", "plt.text(z1.real + 0.2 , z1.imag + 0.2, \"$z_1$\")\n", "\n", "plt.plot(z2.real, z2.imag, \"o\", color=\"black\")\n", "plt.plot([0, z2.real], [0, z2.imag], color=\"black\")\n", "plt.text(z2.real - 0.2 , z2.imag + 0.2, \"$z_2$\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's easy to draw shapes in the complex plane as well. For example, the equation of a circle of radius $a$ centred at point $z_0$ is given by\n", "$$\n", "z = z_0 + a\\, e^{i\\phi}.\n", "$$\n", "Here's how we can draw that circle:" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "def circle(radius = 1.0, centre = 0.0):\n", " # set up an array of angles between 0 and 2pi; we'll return a complex array\n", " # of points along the circle at those angles.\n", " angles = np.linspace(0, 2*np.pi, 100)\n", " circ = centre + radius * np.exp(1j*angles)\n", " return circ\n", "\n", "fig = plt.figure(figsize=(6, 6))\n", "\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.set_xlim(-2, 2)\n", "ax.set_ylim(-2, 2)\n", "\n", "circ = circle(radius = 0.8, centre = 1+1j)\n", "ax.plot(circ.real, circ.imag)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Complex Potential\n", "\n", "In fluid dynamics, we define a function called the complex potential, \n", "$$\n", "w(z) = \\varphi + i \\psi,\n", "$$\n", "where $\\varphi(x, y)$ is the velocity potential, and $\\psi(x, y)$ is the stream function. Given the complex potential, we can easily find the stream function in Python by taking the imaginary part of $w$.\n", "\n", "With the stream function, we can plot streamlines using a meshgrid as we did in Tutorial 2. For example, consider the compelx potential\n", "$$\n", "w(z) = \\frac{1}{2} \\alpha z^2 - \\frac{i\\Gamma}{2\\pi} \\log(z - 1).\n", "$$\n", "Here's how we plot the streamlines for this." ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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M34VGt7K5QgnnJxAJmSvR36ZIeRuLIu8qt7vaO7MD0ng9Sup0OAnK+fx/H4kYdYXfjwR+QZgpYAmUwd4jWE2I/XOICWsP/DxwPHOTpvbUfCi8OQSX2gt4CDkPlwrsPwtvDhoL+ZE6CHiPKoVMIjCCy16AD4go+4IQN8cR4X03ZWI4cHGCNdHb5vTYWFrt6B5odEv7Xkr0Mb0JoTcIyDES2OcPkA3cmwJRudZbeOY/BB60vkeivNOlQn47pJ2AuYVNOGyWgNahyHYUFNKIgg4yQ/yWgTQWRwiJLwkM00Te0dhk2X1NYJeuBWftF0PmnZtCeEHg9ZcQRC/UFnsRMm0EOQFt0XsiKraiaMMRIRt4gUZWyDLaUYUw3p7AwKAu6K5F4nDgTvpZwzbSq2PXeIk+Hap+/CUytZ1Iwvy2dfS/HLmWPxlBNjchtNxTBCP9EfZxPMrHGmrznBOz2yKHQKh3fWGblDcJr0iwhr2gHxNetHAV5NT4dcTcRh+jkCf4SQJB4OSa05YRz3U8gWXOjcbNKKAiSGCi08KXwOWRc5llBQvKC93B+vDAxrG02tGdyegelpJuJ30dTWCATmS/MyMUkEcVpCsrqdNJ/7OhU9OnBR5+TdmKNoGdb4jQAB6F8pV+sckzAn2Dwhijy68gDOugQDrbI83wVQLLqCBM4zfo+BWq3a2DNMwUJVhiHEe7EKHNoMQy4ykZRFNoPzvSqE6OGEMWxbZF5DxejQIEUtQi25EK8tUa7S8IxJGX7KfNNsSJJEBzBPS/JrnN9SFghQb339vkRVYyaBJydG9dj4IQ2uluyPa6ZmD7IUhF9wh7G1r1djEEJVo8pH07WochaFiopr080pLfJjCrETJLfG1zG2SDRAlpSuUyruI2gVe6QnCh/a/RUS5480GZn0YSkSfZlINPSZTbgFxLLFVWqU7aDxCYFyOgr+lQsMuIKjaQOvrvaUrW5zafN9Age287PuZDkZ5Znt3hwDldtqmT8ABUTWF/+7uNcM10DntQY1AehxAYlEPYyzHIhhsKmu+VCWyjGTqmaYyPdwhMnoyOh28hbSV0E5rJHv6rBNq8kFnipzQwQqcTPvoQCRdEddiCnXBGYzESBh4gG/OnFc3ZeSSqDlxnf3PZhvRh6LpPwMMAlBNjlG3SVzVJ+PYENkborS6fby1CPUy4fWYL76yYySn8fjQlUzEW2g4kz8d5L+HH+Kyi6DckKGqHPP2hArcfwll+R0CIs9FoQ6eHsYQHo/QEnreXqHRlBqMxl23Q0bliU9yxAog8SXgSoYKA/w9WNNYMEx6dHL1En0shJeoNAmGJifiYEZ3wviWvx9ZQs0OBly6Vt1qNn7GH+EjoAJD94yh7MKUjwjqg92tkS/pVqDaGnG5vIhvubhG8rAPsmmBMg03oBld1BY6wZ/WzCBqHE5HJy2hcZPMaZMs1GtcSUeLcaAQVnuyAzt0kyuCFTlNfA+eloNcB/cyGnTwHbo1+M+fxayQoQRT73BG64Wtym++WobKiEh5rDOAUBBQOdaasjpxC3naeUIB+LwwfZ0I8qHy2td8M2fk+J6LAnNEZiyJmgp2A5IU0Y/K8ZnWtboh4VnOjlJ23RNCY3zbE0uXcCzSWs/VySASN6ZDpKSqxN0q0Mw44PYZOgd7ssRtjDfrzGP29qqBfo+/V7L16h8BTbGJ+BiAI6ns2J++i+IFkpdqDeatowA7lrPQ26GAML9JKn0QIh+g0bMi58nSkJraLCZcnCCi1U6BzHPBPIgtiGq0liUtbeIdpKzGlxa8xwR18vAWutA0kJpghq8oRZKop0MlCX0unwuyE3qZEJO6pg34PEpQTiuh/eeRI+gJYuRk8dMBTTwQte9DmfhxCo6wTo+hE8ZT6oRd+P9nuIC+tLaDDkTY5HNgmgq/pgfnt974xwtt2T49yMgRH5ZDb3/5KuGbZk4AyR53QWpeIKDxUBtsDJ0XQGIKw1mdFjuVfyMYYa8+9BB1Tk8Tfo/SYkwm0l9fZxxskzutQsv8FkEN4LJFljSrgbVFUTTozPbyLnHDRUWal+Eg4oPWQKSFFgpoZUMifR3jA4LSGwLI2uS+m2NlQisMbiIMh7U6ekyG4SCRyHPgYrSJWMBXozI+01IERNE5GmMcYmNhQm5OjI8fT0zb7oHSWndC8A3gpFb1O+rgLeKrKPurgYTA5hvWCGCWnIv76ATsB99gm6JFP5cAYWVN3/wkGsCB5bPTbBFaobUezDbgeHeNDtUCHUiKOQ/H7pZNvF2j1xbCIRjfG/rqtCZa7iUhbR55MJ9gpQ56gKCgDWeobadtB6S8LNI63FymqAqzx4olwbraj12YaVhSErY5+zgeGdYNn2RP5hLwpY0s3m6dO+JwD5YvJgi0moVPs/lSExohl+DimLH0Ro/0tj46F0d5PZES/0SbxNuLsroORB3RYjBZXoLcE0pSDwfEIpjManQZicgrsQHxy7zZUMLLpzhPjZwYiI9CMzvk2x0li/O25eyqqN1boJ0tB2S20S1QI4ROTEyfEyIgG8Lqobdqv2hxOtnfs58CCyfoJYKw/diS23eB84hwn06GKvJPt4aySYPKyDF1HEKeVLoigZWOBHSJ5WoQ0YaT9kXPyQ+LMLrOg4/PjxJk4drcFGpSYp/C8jqXCDFkl+elpm2zpStdd0DyEhHjfLvrZzfrpFpug8TQDeeXfN4EfNpunOnheFPgNOWzWI3v5GegUFH5KLcFEL5T442PSRedsb4J2MirWNzCCVm/b5We0v6NwebZDj0Ce2KiNAHnBJwD7Jpq3HYmDzTmUH/Y7IrDTKBLvYxPcMZtbVo5nk8h5OTl2czQ6WZn6LVM8L6N5O/BGKnpd9LOB8b561X0F8LYeeZLwe6i4/E9CvudEpsq7kLnSI6TPLfb/+csoVPV02AMZnd8kz2kZBcUp0L4EwbeiIkcQrOwp42+/RLxdjew8c0fS2QHByx6J3FQcicIbUfrKcURgYY3O8TbnwZsSMk+8bHMdk6AnOkFOgVZU5eEO6PVDuOFKyum062tJeybBaJ+K+euNtP4vyZ3J3dLe2wn/0wCbo4ROb5Nrwe8hJNJO1LAF19PJdUb0eRQQEPNiDELq+TL297REaKRMCSsbRmSlCHs5Zrff+xMJ7UFHvUnI1BGV9NkE3DgCU052QG8B4rTTuZCmHHUER9FCHtgpks5v0YlpaCSdAciWe0GKeTaaGT630ly31tcQ6yvJqapCPgfaMxth/N6NIuqagp2NGMd8yMz6d3Iomu+yTR1E10NmgJgXNMsINMxejEMTDfhEclhZVLw5gho9a5tLiny28yCTwt1EZpQiB/sHY3qNTm/S4XqnR5n0Y4IpHAp8eZs4u3IvZKa6I8G49rC5Do5W7IDmxSjHR+WZ35Am5klQtbgRtwnfX5LnqH0dYeGThHE3eCw9UERllxGBjWBkffJQ4H8ReZQwAT6z/T4LEbCyAs3NbJf6mki7Yju66xLprUXVEyaiyLUokD4qgeTpJrY0dNK5BvhJJJ3tbFybJuDpIRIEVhTo9UZJ/q9o0Jw6U2xOaPbzDZinXcgrAY9HCKQtqbgicMPH2oDJPAZFqERneUeBDs/Yi5Ei0KFXQRA9Q/zRtAdwDrB5orlbAB11nybePJElQzk/wZxdQwTuuYI1thHwD+KdpwvYHP0yIW+bG82GeeyR/fi0Zj+XCP4XR9WAs1y5I1Dpqs1ilZjucFcxYfPZS7mN/d2XyGMVsrOdieyjn5LISWC8PYPykMZqpP1RPTIPHJ+IvzaUoS3WdDIbQmG8SCR+kzzV4RaRdJYiQfL5lDfCG08gYVSSaWtfUEEp7y76HAmc2ez5TDCOXihH7aXktt9v7T3biyZnNAseV8IJmgOF/E007SxJJiXkjf0YHZnOI7AcTzuaW2V0SJDBH9Vuesx4PCgBvaEkigc3wf0veyZRqTWRk2YUgj/F2JYdqtLxIRG2XKO1YaI10Qf5HG5MMe+FdTGeRFnKSvQ7CjijkX02YEy97VmfiyJMM9TAS6aQbUrCMumVjiXRhByJPOvjgbNTaAqYHQc5Bm4mwXEWBWJcag8rSegrAn6/g450UegJozc7CXNFGM2diAheKNC5HiEWYs0w65EgxSHKnToW+HOiOUqKMLD3wsdudgH9jicBdK673rZpL44ixe6xNeDRSfgphJDamgYmcy/Ff8TAh2RaIrAzSl49V4IJnd52rldJaEBHlX7ftQdzPOkyRzmEoojOUg/Miry3I4HlEtBLVocLpcLzxOdGcAjr/SHxJp0s5DUav2w8vZlwo+uBsJsPpHoGdfbblwQJf6am28a8tr3XD5pikGnCb6MSPgcBK8WuuST8BgxwbnTMH0fCcs8IlbA/Ck2djEwVwTlV29H+idF8iwR5Pk1wHERCmyTwA+AVZLOKhiuhEOYvSJCHwOj1QrC/WPt8Fu0VFcSCjpufAnclGFuWljIJlNFobkPChDkl+p3D+t2nkf12pxuZilZBaQBuRObJTAhPQIUH/oqiyVZJqZzUxV+JgSyG4qcnouPLBSQoE260ZyNPMvEAsFQiulmOiNnRkSM6jykKoMjiyIMrJHRA92Jkd40utYKwj6+Z0A1O1l6glwxfCuyL7HCxwjsLHd4wAU+X2NwPSjRGh1IFvk2Dy8QAq9q8bNzIfrv7bTJgK+AkBL8cXhDEk7E8xCjfwhbAvFQUqFGG6QdtYZ5BIq8hZnNBzp6rbbApksIMQNCtu1PQK9CdmzwBxjEpH4rxnMJE0QPlVZgArJmA3vLARyQwdxR5TEDjbBPesTDEmZFN8NyE41vT1sj+qWiW6HtPulnCm+5428Y4p8mcY1BE2VsFQexN3j2J/EC/ADZBTu44aGINxh7EMj+h42pwisR2dBdDuMoRqWgWaG+O7IWTUfayJFqa8fyV8RwNwjeacyOtOaXtNUtsHv3CoyP8iyZ0B0bS6oGCRVJuglHYZaNxjM3XQgn5uhdV0G54ekXk3R+ZUiH4X7pRwM5KCJJ2FnLUfdJOGH+HIlf/htLb7ohiCOpaj7UYOIWEIHgEPr/KBOI3qLJvEoFjGstNNikvkCgpT4F+L+BC0kG5FjZh9hWJbMO2e59Comqz5AltUkR6ZeaA9RPQSlXpt48Jx+jw4QLN1W2ch6eiWbL/V0lg527d/zWv0yPTzV7A6Qg2+TZyzBcF8ifAg13SaiDTc5FjeE8hvYY7LbJjHkk6ZMJcKOFPal5XQDalz4AlEtEs1qdLYaJZGpkoosNXTbi9h+A8URoYggqNJ02i8iynxXqJnoFDmOhPSZT8vGT/C9p4orHirbvuOe+Lcu9ujQKZLgHu7rJNxQwtSsGLiuxNMyekv4ntOL3t7yigfTva26NcDCOBtRLSXRchFJKVqjat+VUS5lQA/mC79gwJaB2SUMu9zOYvii8TkC+hY2KqPAsbkwB/HNH/KaZ5dYtk8K27k+dU0cNfgfyo/zWJoF8F+osAdxr910hYzZMpAygeS0nb6M+PHHxJ6i8hbO97pjUnQZMYXUea0kkDTau/NwGtOUz7jkaNFARkkvI5yGb9AjpyVp5NrJN5/hq4odF9t+6Szyrxg18UFXXLhO3xJDyao/wG5yIzxQiUAi7pAgf+QjUBFFun0qgKdKdDmMNviagk0Y7msok3seURTjKaP2RLm0iaIJz7kU09laM1M1Vsn/IZl+g/S9w01SQE/1+9UzzsvhgW1DSRd1Bi8WjPcqGPtuwnwj+eTcJ8myjUOENpzEJCJxzC9V5tL0SS7GOFeX/ANL9orKrRnM6eX1QVhw7oRgs2G+9XwFUJaC1nz+OIROMbgOy4j6beWOvsf3nbjP7a6L5bd8DzinjQsyK4xOcUDMekxa72QZFfr2caMwnttkZvXRM091egic6K6od5lKg5pSDrj/C4OyekeZlp+UkSeKMcCykDK+YksnyS0bkOoWdSRTyebM+44ekuUf6Jd1ESmOkb3X/rDnhmAQ95OdPcxiPo163AukmZEjxrb/JsQg+Q3rY6GEWBeRSNEh0J1o7+iuhY/S0JEuEU6PbIThGJhfiOpE0EtKStj6hcDRWMc17bWE5JRG8+FBJ/Wcr1U2ff05p2PZYEgTWtu0HPrc6HO4A869fPTUs4iwqiXsiPuJkja70KNNDlUIjsRNNSkoPYTYN+g0SQMKPZhmzOz5AQkoRKC41ESV+iTxLIhn0PKj4YrX2hnA//TKGZIp/AOBI4Mm2ct6NUikkcoyX6HojSY05Muam37gY8uxoPdjmUY2EUsKv9b1oS5DBo108/CnAiE4Q/rEDYZhvHtCjOOplALIxj88LfyRJXm8A9zzajpKVYkKniLBI4qIxeVogxRW7hnggR8HjsekABNN8BFyUaZ1YVoqGBEMjM8gKy52/XyL5bd4LnV+PhfoDyxF4KLJm8c+3WRyK40yQSJGfppJ+siOLLVFRvCQHTnzfNI7UppChwT0m5GZEe/dELwfheT7HpoBL2ngTZuoATkMljwQS0+iNb6kspN9c6+l0LndK+IVFQR+tu7N2Trq9tgDe99yNqfK/U5ZybCSWQ2BeZLu5B2u1HifvpiWzDx6Nk439B+QTGJe5nVyQUxwKbee/fTkkflareD+VVOMrb2xd7Oee2BU5yzm3gvX8/BU3kPPwO+I33fkIMIeecQ5vy6yhXRwytaVEqv5u996/H0LLraJQ7Y63YcdZzOed6WJ+/RWarrbz3r1Xdb3e5bPzT2N3f7r7I2d4bbfa90MmoBzL9tLUj49GmOxkpeRML9wS7x9s9rnCPtXt8inevS6HrvX8ytoPi5Zyb1nv/LZqcn6GKEKd5759J2Y/1NQQFISyCQjMP8d4/V0E/F6FIu4cQkiDpxmHXRQiXfGZCgbsgciS+guBOSS7v/QfOuWXRAo+91kfhyHt57ydH0toTnXhOjWXK5u4XwJXe+3/F0qujv3kQsmR1lLvkp977UVX3W/XlnBuENq45UFGEWRFkcyaEypgBGIROxNM2g8d2l3fOjUVKxXfICpD9HF34Odp7v1dnRFyid7jTyznXGwUGHASM9d6vY/+f3nv/dQX9zeS9H+acawOuRUUy/5FKWHXQ34HoZT7Jez8pId1+6CTwpwQCpz3taZGNdGYUOvxhIrrbA/ekeq72Uu6B0i4Gn07sxPMW8KH3fvVInhzazJdHZorPY+jV0ddPkGlsMnCA9/6Kqvqr6nLOzQgsgxAtiwELocjM6dt91aPoxWF2Z1n9RiBH7yhy4TaGXAsdT66pTiRPQjOZfPN35NpvG9KGexbuTFPubXefwt23cPcr3P3b3Zkm3td7P0enE1KV3QIlDT4eaVEelUI5mIrA4/Ywb0KRcJXhFW2yT6fCyCO0u//LFs2aiWk74AZbmMmgfkgjTQbFSjzmDA4XHZxCbmOuNL+CvT9ZqPv9JHJyNmi+Z0FZ5S7lv3PUfgLch8xxRwDborQBQ0iMwe+ud+rJ7oE5FUzATkaQmh9SVRZ2JXu5hjxd5G+oqPwGKu3xmi2e31XUx+woh+144EcV0J8OeISEHncT5P9G2smgRDRPJo3zzAFP23OLzXA2AGGvn6aiihDG7+5IuxsNHFDVu5OY7x+gsPzHCgJ2uClCv0A19qKTJ30f7lQTPhRptR8CP7H/DSRhApYu+p2EAhBOruqh2sv2JxPs71GR1xgdvz5CR6mkASft+ulNWgTErvaS7ZmI3gI21ycloLUWiWqGocxrnooiz5BN8zbr4yESo2Aq4nlJFCw1wfh+BuXJXnpq2CyaMmcRk+2A3VC0WGY/uZOEaRA76XcFCkc7ZPOaqeI+t7DxnU1ijHK7flZDx7ElK6C9NEIAJDW92Ob6GbIRp6qkeyGy1UWX0AZuQRp4VAAMcshOIBHGtwP6OyAb5nfolNitBRY6kV1j7/5IVME7uirz/8JddqJ7UigaiZJSv2k7WyUYW+vHoVR8mYD/nIoreKIore0K/S9c4dhWLfydHPOJ7GUfoZNI0sgpZL/7B4lqqJm2Nw44PwGt+W2zPD7BM7oX+QuSbvC2aV1p6/pxEmCIq76BXUzQfoewz4OazdPUdNczwW2oTMXZJuy+w8Ixkfe70qxKKIfBy7YoPyJxBrMO+uuPEvmMRSD0yioAIKfcZTa2pLkfCn0MQOkfR5E4Aq8ifk9GJqPoEHNbs+OBWSLpbGXP6IDEY10RBVhMBI6lmzuSTBacQW7+GNpsnqbGu9Ykb2TakTdhe70twEqTNCPc3kL2+1ymUf+4yn5tQe1UGO81wOwV9jc3csh4e+GSHyeR7fZue6mTpH8s0O6BUBypo+9+RAIEhGmQo4DLI+n0QblAXkwlFE1zPgyZK94FVq5qnSV8Lg4439brH7v7BtGd71oTvSjKIrZLldql9dWGktvcaEIiWbHAOvtfGB1FnwZWr7ivjVEymBEogq2qfua2TWSPCmjvby/gLo18TiX4O8j4izJ7oARPngSlhozeAATZ86js96Bmz1XJeUgahv6/eDedAXuguyPbcAYz+T0J8qbW0e8SwGGFv1etQuPsZLzPUUGWNqPvyANfkjv+gNkQPO/eVC8gAqbvn2Jzt/G/BjwWSWdG2xhvSzTGeZGpbCIyk00VwgslvpqITrpTBc/d+W7WQ+yJsLt97e+jUJq6XbL/Vdz/ggjmMhl5jCvHDyJ422aFv6s0lRyP7JlVYaNvROamZJuGPXsPbJKA1rpGa9dIOmci+3K0Vx4hU4ajE05lcMAKnnUb8CQKahjUbH6+D3ejH+DiwGnkUWoZOqAh8BjT0C63F2k0ctpUmm2fHOw+CgHrK91UUIUKD/y1Cq0E2MzoH5V4jp4zLTB6LZhG9mXMXCNfwjgSlMBBUVdjUeKeSk43Fa6nbVNsYFP7bWt0AEI1LY/8XTuh4JVfIwz3X4C/Abd0SatBDM+E0h565Dy4mQY45Ar997OfMyPM5h9IWAq+i35/QF4V+UEqDuVER1aPkqJUFTE1APgVaXMFr2d8/yTRnE8ATo+kc5EJ3SgoJLAXOlH9h4RFWht1A0/YZlHJeuoON3IKzwmsgU5cvwTOQTb3R1FA1BimDGduf49ByuTrwJNd9VdJwhvn3KwoLWQ/7/1plrjjWmRCuNZ7Pzx5p//Ng0OT+AuUWGNV7713zvX13o9tQP+DkV1xANoJz/QJE+J00N9hCE1wPbCT935iBX30rIjuXcBSaFOKSrvpnPsF8gks7ANTHzrnhqL0iX/23h8cwcsByMxzJ7Ct935MKK1mXM65pVGE2YHe+3OazU/MZfJgZgQOWBiZGOdH5ZbmQj6F4jUCmVQ+QVDZzxCEdBi5megru0d478fXy0utfLp1X8652VE2sW1QCjoHPOSc+4OXZN8hVV81+OiFjkSHIQfAMBTC2wOYWLXAdc5N570f6b3/0jl3MnCn9/7VKvu06w3gCqQtViEYNwJOd85t6r1/NyHdLCfqOQkErkNZyf4TKnDtOgo5jn4fwct+SODejJIj1f1SdqNrJ3RquLrZjJS5bB3Mi8wAy6BozCXQiTu7vkXO+2cQmuRdpNF+gLLRja6MwQiV3KFdo4f9/SekZr+EcKdNCQlEYcEeqfn7UUH9s0767YUE/Tckis6q8xlU3hfKevYR1VbeSGHLXYnIHBAovHU80nJDaexkfNxKg0xoFT2TN5HS0HReavDZE6UH+AUK+x5Ofuwfi3D+F6Hw6vVQhGbTUBhlB9fHmD4L1a3yWAgrMjA3NITRhM6qKIxyb/vfNMAmKV7iEnysicDzHiUsmatBC+0vyCm4TMV9XY40v6QCHpl9koUlo6KTY4goYIkcvRMJhCyibFrjkQ2/ciROhc98XiqIwkvI3xBgH+Qz+aYgZF9Hyfn3QSarhpVSqpv3OgbX034ujjzwHsGFbkdJtmdswoQPBg5BWrW3Sf95kx5+Vsb9PWDLRuygKFT5Zuv3hCr7ROYiT6LS7O1oH2uaSLRTE0XfDQeuiaAxwNZSEA2UHe1rW5cDq14HVd6ozJXHIkO7w22K3ZEIwpYJ2fdN+diBBAmSGjKOGoN8BPi9/d4b2ag2o8J8BF3w4gq/30ueIGQvKsz81Qkv02X8oEidYxs1J8g7/zjyiFeaSNv6u8MWeVKNAWXh/5x0gQc/tDURHOGHSkh5AlI3onIyryAfwtyNWAsVP/fL7Pk0NRjCNsK9Ub7mTNA+gezuizabv6Ax1RjwUcCOTZxwByyLkmx8mGlEyH7T8OQtKEHN4chzuVWT5uRn6Ai9RYP660VkwphO6O5uL1CS3MQmJL4m0IZqa+0lasB9umh7JTL1rNOMdVHB83kdlblqVv8LIXNRdrp+BUG55m723MTetQpTntzV51VdzrkfAD9FZVYWQB7U25CG+YX3/okG89MbOeh+jWxJdyObdiN5mNELancuykuRDEHQSX9bAA97779CcJmUtB25eei+BPR6o5zH//DhKIGVkOa0d0DbnYCdgWO99/cH9p/Ny0Io+9jCyKk3EEWFZcE1r6AT6KvepFPqyzk3EL13l1dBv0bfKyEc+KYIJ30tcAEK6a5kvA2/mi31bR4dqnG2pP09F9IaHkAG8Uqjxurg70G02/4HWLvBffdAdtuvaVAlASSAJqCCkFXQX8ye716J6G1IvGnhQhSlWCr3A8r/+7WtjaAAAgRtOgcJ1ewIPQ5t7E8j7/vrTAnQfwelIK3iFLKW9bFxI9ab9bk0eU24L5HJrtLiBM26m9exhMmqqCT2GzbZNxc+b7iDrtD3dAhekkWybWovdkPtRwhXeDd5WG8j8lLMgJyC71JhrD1yiiSB8yHtf3To/CBUztfAFQFtr0POwAVKtnPIDv0ouXP6RuSjWKgjAY403vmRNv5PZNf/DvgdCX0K6BTiqxDoHfQ1K3lO6S8R7KuhPprE42mjhkOv0Qz1Lfx+v030eFtA+zXiIdfgb3YEiB9hvEUXRozgZU3TfMbaS9YIVEQbMuOMB1aoqI+k4zDh9QFwUwSNLJ9EKc0OwcM88JuS7RYqrP93UPz+wAC+50cBMd4UlyUTzeklwGdVPP9CH2027pFIq/99lZt8BfxPh8xAu6McLn9H5rLvgPFdtm3AxC6DHHL/MmGWZRbbFiWsLr3YKuCzH0paPgEde68Dlm8yT39BR8qlGtjnYVSMzUT5WG8mUSw/MlV4DKcdSOMSSjrhbG0/i04EdWnYtkEcbBvpV8gpGo0KAda2DXo0CZLVoyitf1a4BoailAAeKVzdNgkQ+eliB3SiuN02eV+4xwOv2ro+Hdi/S5oVMJlBqbZB8JmMsWeN6UHNnkjjb1pgzcLfd9uEzd1EnhYBFrffp6HxULiZEQ6yEq0a4Yu/Am5ISDPbKIIS0yAz1zDgqpLttrd+d67z+/2QU8ijqKmkmFJ0TH/WBHowggKhVcYCp1W0BnZGTsERqLBtt4J8oZp/W5lycD9TBl5MAF5AYdFHI+ftApSsohHLoEPVCXZD2sK7WD5UBPW6HGXt6RagZeN3eeQNHYWOAoOyz5rIV08TdmOBB5rQ/xAaELmD7JW+uNkloHkH8FpE++WNp51KrqPnTbupqbGjo+hDyAZb5aY2Azrifk1g/TLyk0PSiiDIbp6V+3kImLPq9VYnX3MhE8ElqBJ3UXt9EvkL9kSOviQh8GUZ7IGZA1Bu2qKa/SWya6zW7InshPc1yCPYxgCXAqs0e6dF5pesVtqNjd6g7EV9k4hIrjr7yXLmvpBqzm2zGgWcF0HjKJv7uqPiyFNR7l7Hd/ujo/QElPim6uc5D9IiH6lnQ+ig/c42tsUS8jQTuTnh9zSxvho64W5hwrQoZIejkOIjgJWp0Gldi8HBqJ7Xcej4/Q3wF/uszQTXAShEuGG5Duqc3OkRtnYl+3sR5Cneh25gRzae1kE25E9R6r9G998H2drHUSgDX1Ffq9ni3ichzeWM5o8iaNwJvFyyzY3IJNGl5mMbzQ1Iw61c4Bb63ZVAOzfKNT2WRCcflDrxLXSq3KFRc9COh9kQ7v8uW+seZRm7FdnYGyq/ajGb7QSTkJZyHrBpMyauzsmdHpk6bkXHAw/8sdl8teOxDXMcIPvZMTTBzm18XEXJo3VEfzOio/U0CWlmxSeDqjbbHHwNXFByHBOAP9Tx3SOMv8Pr+O4syPxyMdJS37D7UVNu9qJObdyE/b8JqFSCsPFPJHo+S6DAmuGY8tOoG4XLH0CuYXubz9ORstO07G+1GN8cAaW7LW6OQkYpcrzvBza5y9ONDPXIy/w00mybOqco4MKTsOxOE8ZwFfBRRPv5bA7qDtIgTwSzVI3vLWYb/41drUHk+7jJFBuPEmU/gJxu16CIvc/JHTlXAfPXwWfdJpBCmzYE4QpOa1mgtTQyOX5Eg5LmoJPb9sjOP9HG/yLwG3TS7RayoOkMBExsD4SPOx5BW74gz+m7KcrL0C0mt8Dz0rYQPMqKtFOzeQSWRGajRuB/d6WCo6VtsjdFtN/ankndKSsRjvntGoLUIWfRcDqJqkK2xQvI/SGnoGPuf9E1ekugHCTfoiPyL+jiSGxtXkWh3PWObdGygroTOovbmN4n0KFXsr/5kFkky6P7IUJKLVp130H8NpuBkpO7a2FiJ6Ej1JE0IetZCZ6XNH6/QhnJGpJUvQt+GropIRPKRyTGfZrQmgwcE0HjV/Zs6jJ5oEx7o1GVi66+t7nR3beTz+dBCeEnoRPZwBI8z4LsxB5pvZ3aXpGG56kz6IgcXRKcFxvl4f3MnnllAtc2lXVtE8xOATegyNFuXc+t6Qx0MqEzIpzvObZbr2b/XxPB0HakGxf5Qw6e3QuLYx+6AT4ZORMaYsMt9Jnl4908Md0Vje6WETQuAT4O6LNLpyfwGNKG/8tLbwL3I9uEg/C0tqaONl4u6WwTRaaLup83CscdFropI5z3W0gxWrii9dQD2A6dcj0yvfwWmK2K/ioZQ7MZsInsZT/nIYd1eXSUugNYpdk81jGGNhRLf5/x/jHdqFQLcCA5ML9hfNl8vJ9a+yBPDVnTvtkFjXuBR0t8/wBqBGIgCKBHxRzbf5bl3P2KdqlJkT1yO5Rj43EUjfg00mZ3pwMfgAkbTycoBRNQo4Gz6hibQzk3ggJXUPDHYwiOmdxpZu/XDjZ/3uZnL7pJdQ5U6HIPhEV+oMvvNoG5PkhjOBg5Cz7APMH22W22i69CNyy10cmY1kQauUdazM+JKBmTmLeiVnRTgwXuwlTkrEM2uwlEYD5tg/97ie+fZwKzK3vu6ciB9l+Z8ZANd4qcu/Z8dkNVZzP77j3A3xCcLfv/Vyb02wpt29Cm9g2d246fBO6uY2yZU7F0YnwbwzXI3JM0z7TR3hChpzwyy2xPE00IyGS2MrBb4X8PGX8jgHu6bF8xcz2RA2CNwv+KARUf2uJqOEY1wdiWwryyyFP9BAKWdxvt1nhb3F70Kxu9iaGAlGc6EwiRtK8F3oqk8SmGO6/z+3dTA06FNLD/KuZIrgH/ofC/3uSwvUfowB5JXgcwyzZ3E1MmjlrInu8pnfBzA8q9W2tsWdWM0icH8gCTXyZ+xoug3AweJQbauVnCFoX7/hxhfb8lj1rLcsksh5SMmnjfKpjbBu3ojyNAtKcQpolU8G2AIc2YvMixDbbF+ZSN6/Jm89QFr0WNaJV6FsPUdJuQui+SxijgzBLf71IzRk4uTwe4XAQd+4o8ojPTDj1y6LVZ+8NNUN5nG8v+qBpzlvjdo4RMrh3tYXSwqaI8wTUzhiGt+s2AOdwYabhXky7ScAA6MUxEOOpDabAygyI1dyw8r5/b3L+CfE3bEljbL4SZvkh73RE4EfgHUv2zRDcX20TdbxO3Mw2uElzRQziPPODiOWQjbWpy9S54nRUl1f5hE3lYmAqxyMhOHLXpIehVhxpiJ9//GLioi883ooPcEigMdiJwauF/+9h3f2kC9TDyJOVv2vN7z/7+Gkusg6BinimPtlt11K99dg7wZY1xTWdzcXrJ+ZsHbSTPkQhBhEJ0PzJBfiENzKuN8sgciooWZDjfbe2zGUnkrKvFxIoolPbUgsTPQPXeGHsFmQimtc/7081wsgGTPw3Sxv9CjgH+pW0iSzWbvxq8r0Se5m+LJvHgECj9wQr7+I7ITFgo3PX3Jb7/FXB2F59nR/RZ2/0/C8tdtrC+hqEgCGfvl0cKzMHI5HAPcJEJ5yyqal+kET+GzHRZpe7p6cR2bjQ+qTGuXax93Q5rpHw9hWyY0RVNTKhlWdheoEERbIU5zGza3tbuSfYuJTdn1GLoOWNiHHkpnSVQHtwlSJR1pzvcyHSwJ8qJmZlFhlGyIkAT+XdI+x6P4EoNL9xZ4GVNm789K6LfjwQ2RBR9dVaJ739JFxhdcjRBe7vsOdZXm/2dCeE1gA3s97+QI1++RDbMkYXPbrf3cAFyzXaDQh+fABd3wNM/gBdrjOtOdHKo2wSFEsZ4EkABgU0Qtnc8qkNYqe8BmQ5+ik4Tl9n/HNrUKi+JVYu5pRHYuVuDjQMnvhdKwjKv/b0uecTYn1DIbtOyIQWMZ2NySFiza8pdj7TCSoJWUFy9p0ay6DrofNSRoOri+x8Cl3Tx+SnAuA7+fyfwVOHvq5ATz6GEQ+8gR+dEpqyT5snznxyLzA/nodPkBOCkAs0X6CA6DylOt3fB82zIEXdSZ9/poM0OxlPsSaMf8Gej9TwVKwoopcF15ElvXqIDaF/Vd61qwM929fnUdFml1SWQMF0XaWMD0ItyFDrCLQW84O0JTQ2Xc26I9/5j5FXdAri1mfw752ZHmtiZ3vsxFXXT337G0h+O7K1lvj9jF59PAHo559q895ML/x+IjuHZtRBKOD4AWB34I3KSvQPM2Y7mvOjksj96xht478c4595HNtXsakN20P+/nHO9kG39ni543tPaXtLFd4o050Oa96MIihh0OecWRAIwC28+2ns/LpReF/3MhGzak1FZpnXQxnUZ8Fwz3pW2RnfYqMs519c5t4pzbgP7VxvSKs5Ei/5q5IE8FcB7P957//zUInCdczM45y4BXnPOzeN13dIN+N8caXDnVthHL/s5IZLOx6guXr3XhyjpdWfXcDT2Gdr9fwI5z6AgiZHWt0OaJqiMTXtFaDKyAc+MjuBDOqE5CzKHFa9lESztiY6YtdL1+yEc71tdjCv7fh/kv5mI0mkGzb9zbltkDx6CnL2Hpxa4zrllnHOXodPMuvbvExBq6hDv/bPNele61HSntss5twmwPjKAL40W3EuoBM4k59w2wBve+w+byGbUZRr7rijBxwwoKfQnTWWqcHnvz3XO3e29f7fZvNRxvQOs7pxzdb6ArwMbOOd6eu8ndvB5Nub5kADOrk9Rzovs+hpp2KPt7z5d9OnsBqEMRjnn2pDAvgfAOTcb8km81q5thqZ4oBPaP0Lmhb276L94nY7wxpt77z+os83/X865HqiI48+RM3D7lO+ivRsbIYTHWghPeyEy0eC9H5Gqr6ir0faMBHaZXgjwvwtaBDeRw9WuQkfOh5AGuxXdpFRQwrFnnuxHSVT9NSF/DbH9I43QU4BNBdLJclHUVToGZYfzwNKdfD4HHYQAk0cEzmh/X4CiyPqgLHm3IDvjx+RQpeL9OYp4fB9FbGYlhnY1ertRQEfY/xxCFj3U2bMymnVV8kCnQk9JWFmh/SBkHvHoFJQcd2vz+Qk6kRxBA/OdWN/rUU/azUYxFTCIHsietRmWmQthGTMjuEeQnyewkFuk+U01zq8Sc/GDwu+/RzC+bhXsYC/5k8CvGtDXrPb8fxpJJ0tgs3Wd35/Tvn9IF995F7il3f9WoJAyEXnrPQpnPQWZEC4jRy4UBe4X5IltPDLf/BUhbKY3evciTG8xYCKr1NFhrmByBMV2dYx7PmQOeSxEWKJquq8hdEJw1eYO6LbZHN6Z8YXSUzYkkAKZR/ZBm+Zom8/f1WzXCOa6YNqhY1Z/+3tF5Pl+wQRqtvAyfOM6JnR2RqG33zsB225+hiKnxXgKWkx3vMmhT7s1oK/+pIGM9bF1dkaJNq8A93bx+ZlIMZi+8D+Hcv8+br/3MDpv2QbyDrLHXl9Y8xPs5xh0gpuETnUr2e9nGe1M6z2qHR+3mAD/r7SVCDXwPkqo0+Xmbd99zmjNFTDHa1jb4RTSAUQ+N4c2rufI8zFUnrfX+s42ul7klYLfQyiMTakjIKgRTA4gD5yYE9kib0Te2wyHuLl9vrYtzluB05BndWWanIO20TfKwXsFOmqORRC2bm0mQbkBPqEB2G176cYQeNRtR+s+auBY233/RBN6s3by+VK2po9o9/8sAm1r+3stpOHehBAGGTTsXwhbe5sJzpft/7cjs9rHSJseiHwyjyFtuFhBZVVr8+tOePytfb5WHfN8ifFZOroRRa2OQ1puEvwrQo88SA6nqzwfA9Kej0cb5YuF/29ln5UKBotd+INQUoo57H8zIDjGrQh395VNzgH2+cLoWPQaStl4NorAqRyQPLXcSIv7BjkBzmAqyBOKnJbRmmfJPt8Crk1A53DjfZ46v7+Afb9TMwoKgf+MgtaDNKPn7P+z2v+ydJsP2sv7W6ZMCOWRl//HqMrFMKQxLmbtT7bv7NhBPx/RsZa7kAnCmtWfEUzNA8eVnFOHigtkm0g0bpzcfNCGNqD9qT6IYlsUnebRxvMAijqMMu3V6nRDBCnZoPBAH0HHoSxqy2OhlEirHW4P/VZkMD8SczzYw+hWtshm3yje+7com1LmEFw3xUJt4BiuRaeWgQ3s8z7gsQR05im7Ydiz+pROTmDodPb/70Xh/4sh29/T5MfUXVDinXEoQf82yB67BtKGD0RmCW/v1fzW7hD73wXt+vid/X/LDvjqZbS+pMbJyfqfYAKuTKRaD6RMeZTQJ+rkg0xARyPnWKV5GBCUb3dM0UGO0/+glJp1Vd+oq58aTGTZtK4u/O82ZGP6A9ISdqSiLPHf1xvFyu9NfkyabC/yoGbzFjieeUmcR7WOPs9D0KvoPB8IEfJ6vbTIw5w7rfKLch5Mop0dEyW6H4+gjJkAHYJsgpmNsP39MlJ+epkQ+qP9/0YK2h55zbcOk/IUBHKX5eDRRjTM5qTuNWm8ZXbp08sI607orUdebPbvVHDqQ4rgCsh3Msr6+ln2WSVrtwZDQxGOb6pIJt6dbxS6Oth+394e7uso1rwuyFLrnmI+s+QynVZxKEEr8+RvUKLNnSjKrEMNCJ363kBwr6HtPlsHaZtjUFrHAfb/3siZvDPyZ2yZtUXH6s2Rac4jh13PAs210enzUTrQwMnrtnWZPxiZDF9GG1rdeUcQhvh+amxGddLqhcKiPcq4tmFFa6gPuWI5GmVIXK0qYfv//VZJ/H/5Jq9afAw60k3GjrDIbrts1Q+3AWNcEJmRGuI5btf3SpSAe9WgleE77y859nGmgXVWo2whE67vdiB4h1hbjzTci1C5ngVMYPdHARDro4xXb9p33wA2akdrcxO4L9HBERzZ3EchSF+nTmkT+vchs0Ld9duQQvGMtdsl0fO9HFWrTlqOB2nxexX+Ph3htRtW6aUhnfwv3CZkZ7bfeyKbX2Y6eBxVZl2o2XwmHvO1yOEXlMw5su/ScK8a9A6x51VG2GSJrTvFC6OKAl8ijfe/IFPoaHs5OZKno3si0iJ3ZkpzQk+UCGcywqv/V4UOhJH9DDnoOj2eI006S6q+a4k5GIqcmqOBjSPmf3bbhBa2v5MqJMjOfiMy+YzraK4atnab1fHUfqOwy41s0d+FjpqPFD7/BbJ3NywJc4PHn1WaPaGJPNyHEhSloNUXYVefpU4IkgmqO0zDW7uL7y2ENNRJCGfeEaqgF8Lc7mbC/EiUanBdOnBQmjB/wp7B5XSQ0Q1pzR8h+2ynfhdk1zzfaP2ixJwtZQL9SwLz31rfP7b3ZzSJS3chdFUWxfkVQnxUWrWGGubYyjr+vtz2Yg1FGbwOK/z/JnJN9kUU2vmjZvPboDnJUhIO60ggNJCPI+wZzJWI3nZG79ASbQYhG+hIYIUuvjcdMiF4dAo6tOzckddLu9HofAbs0Ml3V0D43S/oImWi0cwccyeX4GVtZBb5oCuBXoPGTOQmloeB+RI9xzYMnYFMH68CB1FtJZO5bbN8ghpwvEoYmBpvBBdZirwc/C7IyJ6F92UCdqB9vrItvG5R9bfBc5V5yfdrMh/zksBxU6DnEDpnDCVMQehonCUd71Tjte+uQo5aGYO8/XvSQfiq8TMrQjycSu7J/xqB9Ttce8gM8Z3x1KkzzIRTBu86g/rRG9uhI/rLwOwR832i0fk5CQIcyMOCX0bQ1gyCWZnvBDlhHyvIiKeokaO30peiu9zkgRyLkXuKV0HpHR9F9rZs0ha1z3dCUVZnAXshx01lO+XUdCNHz+EpXpQEvDxOnUlb6qQ3K9LgX6ADM0AX7Wa3l30Ccsx0yQ8yz5xLXmI929S/QGGlHzMlFn48yrGwZ2frECkOfyEPSujU1o7MGZfad08rIXAPNj7/DcwQML/9yKFyfbP3LfKZOXQSfcHG8wrKoJZc2KI0mzuRl/k5GZmkjqTeAJvUTDXqtokeiI7+K6K4558UHugytvDeZEptdSP7fBOkCdyPjn1HoR18ULPH1p1vulm+C/Lw2lUT0tzQBMt1lAsMGIRsvB4dm2uGbts6XhidrI5DttXLUFKb0xAwf81aG4Ct5/eM75Ppwq6INs2Mz2PqEU5IizyjMLbSoflI6XkJJWVPlpQG2YQ9OgnsRGJlwJ7R6ghSlpVfX98+K/0+JH8JSgykDdlb5kXH+tXRMWqhwgI+AR1/rkDHvv9gdlOUn8B3cO9VeMAPIQ/7GUgz24GEkSX/azeKkHqNblQ3DmkeX9FBqZpIupm9+Kx6hFKhXRs6Lo9DZoBDqDAfBXKo/ZNcw+ty80G2x+cRImKfOvvoT25H/lNZoWZC66dIc/+MBLhb5CBb237vixyQyRUClC/mdRv7KLQZrl5mTfwXzRodboh24D2QJ/UAYJPC579BkWnnoGPNFZidzyb6YYTfy3KBDsNKXtvL0pHQPME+nxl5e79GOMdnkLc6K4k8yF6M3dEuv4ItqO9NsczudKO8Gh8ibaLuY3eDeDve1s6SCWk6E7geIQ7KJTURYuFua/8h2vRLH8c7od0LHafvMfpfIsdcl9ojwvwOR0iBugJBkLnlSaRBHxLA67TkzrI7iUzchJxv55lseD5G+HXx3FfDHJRoE73e5EySdV+Lgac7EIp/L3z+CVK3v7Tf36EQb46OMLehY9qlyIa1bWEw+6OjwVbkFR9mLQx+qg4e+L7c9qxuQ3bF5ZrNTwf8TW+b8z9Trhkbd1b19kJKalK2htcjd5yNRRrjrnSSpawLWgNRbunzyXPsfoRsiV06c01In2iC8yXqPKkgu/NH9o4HVf1F+PW7kYIUHBZsYzjMNoyJ6AScDI6JbM17kaeLfKMq+VOLkXkQuHpuFA48Uypp37qnnps8Zj+q+m7FPB5iPCbNAWGC8ySjfU/oi47MYX9kSsfZe8DNKCrqCHvpd0POskORhn09OilOtjbfojplm1NHeD5CRTxpbf9a7/tLjoB4n5InCNusDsVMeTHCtkBzC3JtOWmuF2R2HG70n0d5USqTc5UQbd3fn9s0jH8hHHK3PXmQpzT8FMtxkZj+HshO+yE18tDWoNNmGuThJjxfQtCxjkxt40zjuhk5vNamTvOZaW4noNPJMGCbEvN4FnUgIDppPzN5WZ7YJPNzkOfadsDqCZ9nMSXtKiiH8VqNWOOVEm/dU/eNOUyQo6LbJz1CDtnx9gJVARda1oTgZOTHGJiIrkPBE3MgNM6cyGRSegwm1HdEWrRHiWPqCnm1/h8hdyCWeuYokc+nyIyyb+gzMMF/BNLqvyBhEQNkwrzZxnhuI9fn//PQjE5bd/e/kdP0IaYybDI61nrala9JSH8aZCaYjPDd+3aHDcmE7VbkNslngTVLtN8c+WZG0UmUW432O9icvIqqb4eOY2VyvO0twNyJ5mdN5IjPHI+/JXGIPnWaUZq6UFp397uZ8nh5c0oto0H8OxT04kOER4l+liWP6X8HQaL+K/9BA8Y7HXJIZykf30T22PoEgDaR86ztM9RRzbb9fNvPGRCuONgWinxIk5AJZ8vE83SBaeGHp1YkEM76NOO7Nja70YukdXff2xb9f8jztTY94ixwHH1NS58AbFZhP1mBxKyyw9fIq74CFdoGUQrGjVAQRRb48ySKwqobYYGgUW+ahnoaJeGWqJzNP4kMdMDKD9nv22NRo5E0V0eokZXs7xlSKhAIu7x74X2ZgPKx1MwfUcmiaN1T520L6Bu+B4l7EMTqCWTjrUzjtb4ybOfV5FWs30PVILYk8hiLTAeLIFPG9eQVJkYgfPyKZYQ8ikg724Ttu5QwQ1j7acjDjR+vR7vrhM4sNp7JwDKJnsWy5I68TwmEunVBP6vVNrfx/RqyP9c9B9nRoHX9D17OuTYkFB723g9zzi0GjPTef9BcztJczrmBKMn66sAvgVN9xQveOTcI2Va3QmkZ+9tH7yJb5RtIIH+KbIujkZbUhjT0gQiaOTuK1lwIwc0GGJ2PkVC5GbjHez+2BG8OaadnIgjoOcDR3vtvS9BYHpXrmg9B2o7x3k+ot32Bjx8bH/1RcMtpZel0QPdCBPf6CjgF+LP3fkwMTaPbA9m8DwDGeO83s/8vgaoDl1tTKXeB1j113EhT2Yu8vHeHpbq/DzeCTl1r47yOxhbP7I004F9Y368gGFhH8LCO7i+Q3fjPCLK2AOGIgCXJHUnPAisG0GhDjroPCITNoVPBTcbHv4EFI+d4RnK78qEIJpfkGZNHvb5n/L5vzzLKdNSlpuucW8kWzihglPf+rdpivHV158s5dy4K7R6AgOCnAX/z3k9sKmMVXqZZ/RwFeXwE7OG9f6BJvPRAWNZZESxsGuS8nIxMEyMRUP9jX0ID7aK/uZCnfjdkcz4GVRCu+3k75xYEPvXej3TOzQ8M896PKMmH85nUde5gNN4/e+8nl6FToNcPZTw7Ctjbe39dCJ0affwKRfI9hBArtyR5T2pI+mfId91vCv+/CtmVPkY2jSeB6wuf749e5mNR6N7eTJmzYX67Z0Wx2a2y7IlvFH65BDoSnVn4/6XAJTSgAF93uxFGM6s19leaUGaogWOdC4Uwj0fC/DSs7HvJNXQ4ikz7YwQvQ1E2v7oCNGrQcgie9h45rCxKWy7QXhYFrGxjfw8Glkr9bHrWkMl7IPvStDDFd+9CUS4D7LMByC6VXeujZDn9Cv97Drjdfr8KlSbJLu+cu997vx6Ac+46lIFsFAJIfws85b0/3z7f1Sb/28L9iff+Pfu8PzDWB+6iU9NldtnZgM+89xOdczugSrnLIC0K4D3n3K+996O997s3idWmX977x5xzSyLN71BgW+fcycDZ3vvRTWUu0WXjOwylOPQoHeFJ3vsPS9JZBG1MKyHBdkoAL21o0z8Z5UvoU5ZGB9dVKPjjeeAn3vv7Y4jZKWgt4GiUJ2Mk8ACA9/5LZHdPelXqSLOjVCaYe3jv37f/r4MERVFof+y9v8A+/ysy1E9b+Px+7/0u9vkwZMspXld673e1z0cjA/0YJJBHA5d574+zhXCzfTbafo4B7vPe/9M51wclJPnO7rF2v+m9/9A51wtpEeOQFjEebThjfeDRw3jCez/Zjk2zIIE5AOEwBwIPeDm7VkMnidmQs2UOZAJayHv/unNud3SyeBp57//jvX83hK/v8+WcWwhpf5siBeIs4Hzv/VfN5CvksjW7JcIKr4nW80XAH8oKW6P3IwRHG4WO8Ff7koLCObcAEtqroXwJ+4bwYrRmQg7ecc65zZFCdrH3flIIvXa0r0Ib1Gfka+CbWLpdXqlV50bcyCY2L3IOrIq06qULn/8cJYT+A8rKdAWwu33WFzkSXkdg5i+RcC2mlOzIqZGVTx/ayec/s8+XQIL4OyTUR6HdM8sDvIr9bzQS3JOs/Rb2+Sad0F/XPt8cVV99GDmITkUvW9Oqm07Ntz2PO22OxxAAwWoS3w5poWeTJ2t519Z+KTNCgWYGh5oHmaGCzS9IkH2NbMmhzr+eSFMeQaIIQ3JsdT/7e1t7f5KUekd2+i6La7YgY3Zlhn7TzmdDppF+SEj3Bd7z3r/vnJsOZTzqgzTM3sgRcq/3/lnn3GxoofRE3t42LErKe/+kc26ofT4ZCdwJdl/nvX/VOTcEmWdGIy19JLKfv+MTwF9aV8eXwX8ORMKiP9qU/4Zywb7gu8GL4pzL0BCbI0janGjjvhmZEe7xASY159ysSOufAflegsbqnFsUld+5zo7tM3gd0UNorYpQG0uiMkUHee9fDaFl9BywMYKnLYs07wtD6XXSxx/QKbSf9951+sVG7s6tu3V39xuZcvZCdr0sneKH6Ki8MzItNUQLRpv9ykh7vZ28VMxYhD/ejQh4FFIcjkQnr3EIblW+/IwUj9+gE977xEeoHWXj/ADYJna+USKeR8lDtvcgQb4MpGxthQEBkK/gAmo431qabutqXZ1czrkfIJvvD9GLO8g++gwhe55HCV7eQEf7YT7ghXLOTYu01nmBBVEO3CVRyale9rXXEc72n8j/EOX4M83+H8iUcCtwmA+AhFqwxF+BxdHJ4EDv/bAAOm3oiD/GaG6DTH6x43Qoc9rsaFO5xMcHYQxG0YE/Q6fi9b3399bdviV0W1frqn2Z2WkJ5ENYAVgaRYsVUT3jkUAehuyQo5BWOgFpWT2RdjkN0qgHI6fQwHbdfYai155BztBHvPefJxrHIO/9CDOT3YTKZ90TSGsu5F/4HCW4vyWQzlLI9/KC936fEBrt6C2A8MiHee+/MD4/9yWi9zqhOxAhMXZHpsd7EH73Tl/CrNMSuq2rdQVeZmOdFyFt5kZIklkQsmYQQt70RdqqQ7CpcchePxI5cb9AePcP0NH3DV8BgsICnY4HhgBL+AjPv3NuIe/9a/b7j5DQKe3xNw3/eISQGI6E5FURfM2MYgP2QfO8nff+zlB6Bbozeu+HG3LpFRQscab3/qUggilsT627dbfu7nkjzTxLAPMFwvAG2TPRhnItsnVH1cpDqJEPja8LCERcGC2H7MCj0Mb2Z+ILYGb17e5Dm2If+3+0LbjL4Ajn3BzACO/9qCCJ3rpaV+tq2uWc2xgVhx2GEv782QeEFptpZV8URt0POYxeDOQpCwf+CAnd7b33j4bQyi7vvbegkPuAI733r4fSMhvwpsCvkRnpU+AMhELCR9qDoYZ5wTn3FIJXfI28ku8V7nftfq8llFtX62r+5ZybBuXVmOC9v9g51xMVubzCB8INTQg9gIIu7gd+6r1/I4BODwSVXAPhWKPsmmYu+QOwn/f+Jedcb+/9+BiaRnctNN53URa1S73342LpTtFHDaG7OcqKPpfdc9vPadp99Utkj8rutwv3x/5/IBy3dbWuZl0WXbcvcvAMAm7zln4wguZAFAXmnXP7I8fgNSHC0jm3NAo6yXLdbh+qqBkO/hQUNfopCnq6O4SW0XMIdz+b9/7cwt+3p9BqO+yz7BwaUzMiqMncKEJrHvuZFdUrmi3GIUH8JvJ0vokgNm/SEsitq3VFXc65E9BReAIK5DgHhX6HBjj0QGHkJwH7eO9vjOBtGuQoOwSZOA5GQUChvGWpG3uhsvUnRwjvLFjiBJSn5Dlg2UbIo1oJb/7rsgkbZvcT7T+3I80c5F7d+ez3+YENkDc3u75zzr2JMpW9bj9fA17335MEJK2rdaW6zHu+LgrSOMGO+feioIlLfSSszI7Wf0TQuAfROxlz9UDldy5CYfRfR9KbCY33cO/926FEDKJ2DnIyvouCJa6MEbiWH+KnwGO1NO+GQsYMAD0EJWOe334uaPc8mLHarg8QPCO7XwZebtmPW9f/0lUQtNug6KfB6Ki/h/f+Hwn7OQeB/d9HEXA3BJoShqB0kL/03o93zk3nvR8ZyNM8KAnNed77u5xzPXwc1K2H936SBYbcjrT5i2NswRbWfzgS3P2A33nvf9Vlm0YK3a4uy5Q0H7IhL2Q/F7Hfi9rx+8BLyHv6gt1vVGV/aV2tq9GXaU0/MAfRdOhUOR5Fjv0NuCuFc8ciq0Z778c657ZHitAZ3vvvAmj1QJre79Dxfz3v/X8C+eqLBP/RKD/Jgd77S0JoGb25kRkBn2ci7OkjE5JbroVDjccrgNO996/UbNddhG5nlz3MeZAAXqxwL0xuHhmHNOHn7H4WeC4EHtO6WlejL0vnuTLCha6PHE6Pee9Xsc9XBJ73kRFVhf76AwchbOvx3vvTI+ktjbC2ywN3o+i0oOO/c25dFJ02HypaeZj3/qNAWtMDv0KJjCajmmy/ikFO2LN4zivN5F7olH6m9/6TuonEAn2bdaMkG0sgiMxp6GF/QZ4KcTKKi78SGfJXBfo3m+/W3bpR2O+ahb9vJi/j/W+UPGbZCvrtBeyHwP4eac6LRtJ0yLfzGUouHpucZm/kaF8/ks66qEDlZFQpZfZIequjsF8P7BlDq9trumUu80jOhuLil0VeyeXsf6BjwIuobPTjKPPQ6/77NAmtq9tdZpvcEGmCK6JTm0M5kIebA2ta4F++Qp+Fc+5qJBj/g/LTPhxIxyH78oPe+6+cc/MBX/oAR5k53g9AQViXmt+nlw8wnxhf03nvv7FkRRcAx3rvny9Lq0BzdRQMsg5S6v6AbMzBp+jvldDt7LJ8ocujCJPszpKMfIWyEP3b7qdCHnjr+t++7IX/ATJ9LYGyhJ3ovX/TObc3cCHCsz8OPIY2/IerXGtmmtseVR35zI7GMwJ3hCoazrl5UeL0jYHfeu+Pi+BvBSwVIso3vXMErcWR+aAfsFoKRcqe6dNIafs9KugZn9O61tEh5fGmu9wIJbEIitb5K4KpZWaJ71DkzTEoeqZPs/lt3d3ntrUzN7ARMNT+txISqMVKH58C69jnMyC/RKPy8PZEZrdXjZejE9Dsa+/EWJTj4BACcu8arYEIsjUZmTq2DZ0bhOY4B51iv0L22x4R41wKOStnsL/nI7FZshYD96BKvxegiJdlv69CCGEAt0K75TPkCazHoCiaw5EG873ciFr3FGsh01pnsb9nBG5EpqnvCoL1cPt8VqTJHoSOoU0rnYSgS28Zfy8A25Gg2jZKIuNNIA2JpLWeCck/IXNAKJ3lbLObZIJ3cASt+VEyH2/Ce82qnlGtMODfIgPyMuQJnCfYw3zS7ieAV32CInHd6TLP55rIIL8egq4BfIKE8B3A3b6FG55qL+dcm1cx0DakxS1AjiGfDpUdP8TgjM8iYfYGChp4HXjRxwP+oy/nXF9vyAaz286PMKi3+DjA/9xIyXjXctLO70sk6+6A1ure+yvs76He+3cCaQ3w3o8y1MeFwKne+9AEPD2RuWRvhII6ExX0HBFIbxCwsff+mk6/05XQLRBy6Hi0LNpdsns6+8q3SAA/lt3e+y9CmO6ul3NudhRRt5H9HIg2oAeQ9/kfvgxspHU19HIqKb40Oq0shqozPOG9394+/wg9zzfIw9Qf8d4/1RyOa1/OuVnQcfqnSDN70XLUjvb1vNid081wskchxWLLCFo9EZb1OGSamMcHVts159jvkdlvUR+AJy7y5Q2n65y7HiViP9F7/1kgvRmRyeVApL2nr5GGbFsLAT9GR4+nyDPke7RoL0M7yCIkOOJ0lxvZzNZEULU3CmN+BC2wKHhK645+PnMiL/3Bhf89Zc9oHDqpXYNyC/z/M2023yXGtyjyRYxDZrAbgYUS0HWo6OXbNlfXAXNE0FsB4eY9UkyCaKFw4p+hSLzxqHpDkJ3V3t19UVrJBbJxR87bAkjxnAzcQKEyeYffT7wY+iFzxC9Q/aUibna4/e8wpDEHG7u7020LdRGUdOTZwnj/ZRvOoGbz+L9wI1vqRSiWPnsGn5Gf5lbEao41m9fIcU6DHFljgHPRkT8V7X1s3l4G1o2kNTPSbD8Gto6gM1Nhw7wXWDCC1oYomtUDDwOLRNCaEdjIfnfAifXSq3qBONsFfoJKRGcGfo/Kit+KNMMl+Z5owjbe35B7jsciA/3635cxdocbmXf2QOWuQTbZEaju10HIlDDVaK9djHNaZD64rrCBbEiE06iDeVzYfp8OaZTBGxOwfOH3TQl0lJFX2G2zsf+IQI3UaPzD3se3gK0jaE1vAnaUybBpStNowiIago5+FzLl0XyYCac9gTkbzVcF43TI7n028oZ6lOLySGDGZvM3td7olHQJ0vQ8sIn9f9rvg5AtjHNelL5whI3zyVSC1uj3QKXmv0CojNgj9hCUWtIDa0fQcSZgX8PQIxG0pin8/luEQAoqD2/r6+jC8/hbtlmVptUNFtfswG7A5QgZkAnhV5EncQOmcpgawjjuiNLlZdrvRUSGYP4v3QiPeZ/N3ygUn79SrLDojjc6FU1GPpJrUT2xZONE/ojMFPZvIkKOTYv8GSq0+R0qCxRag20oeT23Jwk0JdiGso8pcsEbQDuaS9szuQVYMopWsxdYu4E5ZHc7DPinCSePqqfejGykszabz8gxLmoCI9PUbgNWbTZf3fUG+trPNgTTOxwY2Gy+Eo9xIErw/eNszMhENVsFfW1k6+59Io7sBXq3G717gHkDaTjkBxpjG+pBBPp8UOKgp8n9KosF0mkzRemkwv+S2M+bvuBqDLw/sAlCR7xf0IIfR3CWaI9tE8c22F6sYeROglWazVd3uW3RH4oKGDYt2KDiMS5mG/C3tgaurqifgcBK9nuW6yA4ygo5zDOb606odE6s8L4S2eODkT/oZOyR8y7GBrw2ufPuaRKftJu+8EpMhAMWR6nanigI4FdQrszFYx98k8Y1DdLsPyfP/BTsVf0+3LYhZcfMm4ksp90dbwQ39OhIfjHVZBXL4FFf2PqKFh4IJfImsG8knWlRld0l7O9QW2uPwgawH8LxThtIa257/7KTwK5U4PyuxcSxyEazbBWdRz602W3Hvh+FAWZ24GMx/N3UdJvwPQoZ6ichOFAyx8nUcqNY9zcRBnW/qXEj7WRcM9rzHWJ/r4eO1JU8Y4RweNHei4eA5SLpDUYOTG/PJ8ZZtiGqKO6BQyPoLItsv3skmrMhyK90JGbWCqCxGPD7Lr9Tg8CDBY1yGHA1CoboVpoHipPfz/jNciY8iexkMzebv5JjGYwQDxMRtnmP74vgqXP8l9u4vxemFnQCu4jcPxGVi7XOPpe3vt5GZX5ij/6b2/s/AVWG6BdIZ7A930xBWi2QznQob8MklFhoq0A6vVEU2U3kcLwgjdvaLmfy55suv1cHoVlQxqIryI/AHtk8jkdRJ91GC0Zp2A4jN6ZPREfULZmKgPH2sv6b3N47d7N5atC4+wHzNZuPBOPoSW4iGYNst5WZjVAwwpaFv7cjkS0SIYgew0wBEXSOMcF9QihvKKXkxybcziHQqYocill2wbuAAYF0ZgM2s98dcgLO0GWbkh20oeQ3v0KJkLNj/WcoLHELulF1BoQUONV2w4zPU7CUfN39tvneF8FxRiJo3fdO6zXN5SKmcvyyaU4bFP7+EzLPdfkSRvbZFx2Hv0EOuUEJaPYEjgB+U/hfqFNqVsy0YbwGoQkK9DZBcLcVAtv/AMG+MjPJpiFjQwnATrYN9UtKaP+xD2cw0oKvJQcNj0Hq+o+B6atabAGLaDOk8WYbxV024d0+HBmYC8FfPDpxBDkKuuNt2sF16ESyZrP5CRzDtOh0lZXBqdynYPO2A3nY862kyb+wDPkp8cYIYeuA3YGvkSkh6DSMHGUHAkcW/xf5rF5F9vTS2jbQB6FqvkTa9pUoiU/9NBIugt7IOXAOgvl4dJS4C0W+dAunEDKWH1t4Qd5Gdp3gvJ4N4rsHgphNQvHjU/0R3Ma1mz2HXzablwDeB6BT33Abw/3ISVT5aQQ5HCeihDJReRKMXn+EqMjspDGJxecA7iTPcRC0CaGT6qNG55YIfjZHuP8+9neM0F7G+LmbGoltOqVR0YJwyNb7e/KMRRPtQexGNwC3oyJ92yMziUfHs1OpAJCemO/1bJetNNFyg8byA9OEHgrVhJrM/0zoSH8bhoOtuL/ZgZ8V/l41RoC0o70oQoxcSISJAlXpHokCmg4Mea6mwB2DMooNR6fpEBPA3OSmhJcoqZEW6KwIHFH4O8623YCF4mx3OIX8KDQWpUDbkghvYUIeV0Cx1JMKC6/b2n1RXP4rtii3bzY/EeM418YwVQS5mDA4CJmpMm93VH6AOvvth045oxGuNzjdYju6g5kyvWVMGsfe9rPNlK3g9wc5kScgtFTpwBhkTjwSmTq/Rfbp0k502+SuJA+4CHK2/RfdqhdMu0E4FC//J3IkxJfIJLFcyG6WmL+hwHm2KUxEuMRuKXxRtqOHkV1pr2bzEziGwcDmzeajDj4dOm5np7b7Y7TBgH7fs36vD9XWOqC7g72DE4gwVRmtvVAwQfApETnZtin8HWwXR6a4J5FvqfRGYpvcr22TG4uqcCQRuN43WOi2G1hP4IfICZfVnXoR2Veb6sVGMJAzja8JqEZcVF2oivjsR24727vZ/Hwfb9N2/lVYnxs1SjlABS1HAM+TyJSEfBo3k2PZl4ycm2z93R8i4IzOiuSpUENzJQxE5dEH298xtdfmRFryDSGbXK31UfnCqZPJQQgalYX3jkNHizUbtcA74Ws2pIWPt4fwu5iHWRGPfVAimMnAjs3mp06eF0K4z26fZc02tidtfVaOdDHhcSh5aOviqfpFfoz3bC0fQUQqTIROGmHa4AGE2W77IrPjJOADYMNAXrZEx/9JwI8CaSyA8MOZ2SjG1HJel5/XaLwqDc7qZYvsT8jB4lEW+5+RUL0P4Gke4Crj53OU7azbQM1MMDyItPJoT3YD+D0XHdu6ZbQgOoE9QJ4gvRFoBAfsjJADk4GVE9KevSDENyYB8gVBFx8mLrNYhkz4S4gygxyx1xuN5ykkUC9Boz8yH4xHzvTS5kQby6bZegaW6fL7NYi9bwvgPpRcfFDVi6/dZOxhWoZHHtGzQh9yIp6WI48SewpYsVm8dMDbQHT8HUE3dkwhnOQo4NJm89LJHF5C7u1uiD3ftKwsV/ATROZJKNBtQ1roaGC/BPS2xo7/KFdIacUDaduZNvkjrORNID+X2+Z9NGGOsk3J7eWXE+AURYVO7zUax9fVpgbBhVGob1bhYaztLJuHDDJicldEXsTxtgn8nSbF5tuutiN5KOJ5jdyMavA2F8oo9VqI5tAgHvewtdStciugU9176Ih6Eg1KnG+C8VXbLH8aIsg6oTsvuS36TuKOywNRkVkfs1miWoJPE5F/Amntc9nvs4YqGEip+wSdpNcMaD8TCu2ehMAAB9UrE+vtIMPd/om82OQXyNkUhVkrOdBZ7YX40nj4D4o0a7jdFwHjz7RJ/4Ru4oVHdvCJCALX7UKGkUb3Znfizdb3fxA6oXK8rfW5PHmC9mVDtKwuaO+CtNtvUH3C4LkG1kIn3omojHqIRpnlRh6LEueUflfsGe1hY7ojcCw9jEYv+3thwlNKXmZz8kdKhnmHdNbLBN0NSPPMvKD70SDtCh1tDiQ/GryAAh0abmdFJofnyY8ogxrNQwc8/ZIGZbQK4O2nwO7N5sN4mQ4L1EFe/crXr2lYZ6BT0tEV9bEecq4GJwQ3Opsan28QaEpD0WmZ6eQWAjIU2rO5g7waRGkTIyp+mznqgxzOKJfwgoVxNb5GGsJZHmxCz9vuehGJbFJ19N8LeVEzuMkryE7U0OgmBJo/zna+D2hypJhpFvcj22k0rvP7eJMHmNzUwD5XJjfVnUsqsH2uBSYR4gVNsA/Cq5aueFug9UNbh3sRFlW2EnKqj0FH+FLvNkJI/M7ezc8JqCiBTBp/s+d2SfT8JnzoK5jAHU2u/e5OYO7Nkv33QGDvl8k13y1CHnIkHyvYSzXZhHDTEA7IvjsS1a7qFkd50xSaXnrHXuRhyEyVpHBhHX3uh0xR7wHrJKQ7E3l58fti1py9xweaEjMwgs5ACiYEIvKuIMfr1QTWJ0Mnco8cpOXMAFLqjkBRbd+h0OSg5OZT0K1gcQ1EHtNMAA63nSbqqFNn3z2QkyvTJh6hwUUfbZFcWngJmgaLAvY3PnZuFg8FXnrb4v1zk/nY2LSmt0Jf5MB+F0VBNslMGEiL/Azh2g8n4oSH8vFmRSZvJzBACVUufteEVFCxA5S+8b5QhQ2ZHwfY78sA6wfSOZI8g1uyE2OVi8yZZnOT7fBZLHXyWlAd9N0TYWmzku430uCsXOi49x3wIQH4wUQ8tCE71qc0EedsvKxhz2LLJvLQ157HM43YDNFJr0ugfATt2UzYvgAsHklrAxPeY01hCjED9DBNcCLwDgE4YxOW55GfVucKoLEWcoheGDgXM2BBO6ZAbZr82VWxIDoYyDzIeTDSJvQB0zgqPfYip8WvTcMaj7KINQxKBSyNjpNjaVK0GILbeeDEZvRf4ONYZHZpao5lFA03sOI+piE/7TxAwsT+FFAOqGpt1HHXlKP7EC45SHibwM2cZVeGvGPIIZ2Z5k6jJGTP5vxPxsNbwOoB87Ajsvu+RFiE3fzUEVZd2cLrhKnp0DHoQ5uc55Bhu1LbJ4KaXWx9foLKRjcqfn4mlLrQ2wbQDHjb1ehI3bS0lQhA/myT+t4YOLERc48CHV404fHbVGubPLHMGAJrgrWjN08mwG2NRvle7L3eNWJsj5hcKG1jB5ZCMESPIFylNjnk/8jQEU8AS5VsPw2Cso4D/lXz+zWIVYICQPa93clRB68jFEJwLHid/a5AHuF2Hw2qGoy8wFlBvguqHmcH/c+LzDtnN7LfQv890GnjnCb0vZIJqmfKvowBffVGmNbhBNoRO6E7gDwM/V4iMb3AVigY4+8RNPqYgNs4gsbs2MnHBF/QKQjlzX0eWCug7VK2Nr9FSKy6N0nbLLZCiCVPnVFttYjeg7SklahAS0A2x22Rxuttt9q1zMAD+uyBsKIj0LH/KBoQXWcP6Hc2zhtoUMRTof+/2E7ccG3Xxj4vDS6uiVJ1DkPHzcoqWNv4stDWtQiwRXZBezEUYTgJnZRinGW9USh9ptGFJvUeisLgPfDbQBqbI/TI5YHtF0cmy2zey8LA/r+KBHB6yDNDxT8z+3PdlY1rET0LRYBkD2mnKgSULdotUME5jzTg7WIWWB19zkoOJ3mGBkXWocgcjzzE0fCTEv0OtRf3tEb12cwbaYcvowoblZ1oTJBdChxaEf0fIyfXWpF0hqDMbtkRPDQSa2uTCV8DWwS070tue32m7LMhj24bh+yvc5Vs3wPBwD4gLEF6b6yqM4KU7UnJk2s9nUyLoEev20R9hIq6DapggbUB25DDzZ6i4qxZtog+R462X9KY9H17k8fEN1LwXo2cmQ3Ny4CyZ/2kwX1uiDDjyTCxHfQxCAWheODXCen2olDtlgSOP+SVfx7YNoLG6jbWxwk4tdjG/4zROJPyzrLZ0Onbo5zApRAowILIduwRtrls+1WQk+1TIkxVZTpsQ7jAzEs5EiUNTp7c23aj3ZB9zCMjd2W5V4EZyVPEPVR29wzsc0/y0MiGJA9CHmIPHNyI/gr9/ht4uJF9Wr+VBWKYAHgB2cqDHEid0J0RIR7GxL5b9s7+hEIpnUA6Pe1nVuE3VEueDZ1iNwscy4u2ke5DCXOC8X0wgnB+ZUpAmfYDUQShN5kUBSMLfZhLI61pItIQ/0IFOFh0FDkC2V8n2cArqSphD2ZX20y+plA6pKob2ZY9cpI0JHQZ5TB9vcyiSzCv3wDnNqi/ZYjQ5ursoz+yE39LWofZ4iiwYGysIEdIoX/Y+totgs46yNcSGhHWF4Xv9rC/S50kUa7oTOiviuU+KEnDocyEt1EyP7htFB+Z/DkTmDb6OUc+2HmAP9simYQwekFJIGr0MyNwtgn5rxGAuxIEADoCZYkx/hS6q5fo7yjr6/Qq+yn0t6v116jw19mtv/0b0Fc/pEl9RPVIhb1IGPSCorBGoZShUXQRbO1Ve18ODtlgTVD93N7rVwKF3VCUytED6wW0XwSdJo4L5H/XbLOwtVFGuy1q92dQMPdEP+tEC2YWBGgejfCJV1NBIm0USpklDH6OitLwIWP5mdbPo1RYH80eauZYOKCqfgr99UMnhyur7sv628DGtlYD+vqD9ZVM+2xHf6GqxmEv9tOxaw1ppiMQaiOIV+THuc7m8joCtDuUoexru0uZE8gT+IxBKWRLJTpH9uvMXPinAN63QyeOkCoSs1IjyCT1wpkJ1Tz61nbIS0mc5coeyHZIm/EokfCglH0U+toWaR+fUWEOB2TDvtnmLKhOVMn+zrMF3YhUhpntutJS5chePQm4oCL686PAmndIZINHdsrZC2sgWjtHELOHifBLoMIFk5CmG6IlH0aOTij1/pvAv4K82GVZc8A6JhtKO8ZNfmWbzZOU0O7tWf4UmdKe6vK7qRZlOwZmRlrHdzb4s0mMk0SQoDNscXwKbF3RWBZBNq3xVJgH1hbb86YZVJqIBXlho2x9JfsrdbQLoN8DIV0+oYIQX5Q79X2kPSZx6KLggmtNQESFRiO0w44EYlYLdDKHW19K4E47oLMSUoZKI3OQTT7L6FXW/rslOmm/Ro06ZZ20/QJB0Y6ihPnSZMR/yINXunx/ky7ODpgZYpM/EWmMxxCRm7OTPpYlx/deRwUea2B6crPGSVQXqTc3Aoy/SIU2SXRaeBe4s8rn36jbxrMTAbjROmgPRvbRb4ClE9Gclhz69IuYDQnB1rK1GVTMkjyl40sEnhpRkvCfR4xjucLvZbXbrOhmf5RStbSMQae/ZyhZAh4pMONRFOKP63mWSRdoF4wtQB6I8AmCnSQTXLbT/8oG/wUVZLKyPi4kT+pRiYMN2UAnkyBZco1+fo/gTqVyjAb0cx4N0qgr4v9Y5CheIxG96VGQwkQiT04odPZlW/dBc2zr+nxy7GvpbHQol/UYpLUPKtm2T6H/EGfbjsjxHWJ3XhvTiNFprG6zUdYfymh4IiWUvXoGlAwfa7tCFhXzNIntpMielYGvLw5ZQDXoO1R51AP/DHnQdfZzPBXnwUU1uio1MSA71zjg1Ar7+CWBtscSY1gqIb3zbE62jKSzFDKrjSAQicKUJ7hTyipCyKxzsrV/mJJ2e2BOcqTQ7yl3pO+PoKoeHe3r7tsEfeZ0vaUkz/2M148JTM5eq4NPkdZ1DYnQCORHwSzT2JWUPE7UoN8bmQAmISxl8ly2yLM6CSEbkqcqtN3zYYQZnjs1/cJz+IiIpCd19DEbFcLFEGpmDHBVBbT3AeasgO4AIuylBTpbobShwUoReYXt3QLXT4YQuICSJz9gXWQjH1l2A0IokiyT2+9KCutFyWsanksJMx5Kk5ol6foLgY7oWp0Mtp0sQyNckkoIoHRoJ6JdfyTCEybD3qKQxffREfowEmtCtujHI3ty8oANZN8dCTxIdTbkc+3ZVpJ8BzlUPBUkgjb6Z6FjetLAHBQa7oEzEtGbCZmm4oH1BUgZ8bl0Z6Fk3tl27XcN3VCRifFlwvC/95rA3qBkuxWQk+4LYJMS7TKNfhLK2RAFSay305lRJp6xJiTPIpHDCpgPuIscYpKssgQ6Pv2d3F41KBVto7+RPcTnKxK8exjvB6ambfQ3oVpc67ZGf8kKaP/A5v7ixHQXQk7fx1JsRuQ5D8YQCbBHOTui7MsosdQNoQoOsBqBEX/IJLB64e+65xeZBKaz3+egBJ6ZHNXRExUyKIWkQlr9zcBfSQCzLDtpsyO1ehLSwo4mDbYww95+YrRPT0G3QPtgpPG+ReJsYqjc9XcoWCOpqcF4vxNpo3OlpG30+9tLXEk0HIpx/4yIwoRd0M40j2TwOpuPl5AWFV3TD5kSHkeKSpx2lGenuyP03SAvjvl4yFq15znONpGycK45kB9nNCUVNnLb762UPLHaJvFYQJ89kK9gXvu7jJOty7kJXQALm+T3yDa7CwmOwAj+knky3yZhKXPkxPsYaRw7pKJrtDe0xfgY6Z13c5nQva3sgquT/j3Ai6npVn0j89GRiWmehOyEpY6tndDqg47BEylUxg2k9St7J64nADVjm/dxRuM2SkKqrP0x5OWHylbVXdk235GUNDUxpe237ooZyAF6NLlvZ5ESbecmr/ZyTMl52hN4o8vvRS6GNciTGT8GrBi7WI3umjZRHoXIptJ6Z0EZrzyyJ6eErW1hL9i9JLaRkkf4bJmSrtHOKp5WGjE2NdxIM02S6Aglbf+I+MQ1WRj15YSbBDKEwV/L0jDhdYm1v6ys0Ed233H2Ptedl4Upcz+8TIm8u8iG/k/j+RpKmASQk/8bE/J14W6t3RzkZtIHu/xugsXVhtIwZpV3LyFB9BlTFpp7nUQJJxC64SJyzSFl0cAfG91rEwv0Xshb+y6Rtaw6oJ1Bx36Ukq7RPhs4JTHNNlRBIV1JbNldk+c1Jo3jzCEcbHCeZxRAdFy9AqSD9qeiem8hIcFnonDeUiYm5MT/1N7RUvOI0g+MpXwKyJ+QQ9DqXl9Ik/8GmU5+VuvdT7nABiCs33hj4MCYhVKguw7yGE60ly0FTYcK6U0mwN5Tg/Yv7MElxaYiILcHjk5Mt6c9r/NT0jXaLwI3Jaa5ns3DLonoZU6SpxKtrf1ReHoULeAQAjz7hfb9iMB5o1Ph4tkcBfS9gP3eg3L20NnI00DOUW/f9hwzR9uMlMBWZ/whRe9g6jwNkDvopkEnkXnrahe7yDpgZEHgbvIAiOUS0ByEMpd54F8kcHIY3a2QE+yteieszof/Z+N1r8RzexPyrKfOY3EH8EoFa+GL1MIc+BsKlU6imaIAIA8cnoDWBug4fGuM0EU5pD2BkDUUZnyfKRVLBrSfDyX2eateAVRoOzNSZD6k5KkM2emHUTKVI1L4rkdVIcoI+DakfD1PeTv3FsjuW/qkHL1oO2EoOxJ9aovwDCKPWkbzx8ip9CUlcHY16K5s9D4rszvWoNkT2XcmkCh81OgugDT+pFV1yXP6JkMZIA1nEnBCQpqDMchiInoz2MbwRIyQNFrzo2RFLxDhTEVHYm+bS2meTAA9bHNf+jSAIt0+R7kESpn0kML1NgFl4lF+4vHIlFjGfrsQyvdbKisa0oZvs7n+O3UmSrINLYuEe5aAAJpaHcSCrweisEeP7JGlY6s7oLkAefXgUtEoXdBcGO3MI4BVYukVxv4a2rmTRTYhdMd40to017D5LF1GpQuaMxrNgxLS/BkJcb8oYGFiLD3yIpjDiQgeArZH2untBKSPRNUiHrExbR/QfnVkavqAkhGoCB30pW1idTvUyavxeuT8GlSi7RbI4fUFJUKhjdcP0QZ+QAlBvTzKODgZOSfDyhbV6OT6REJtNRNAH8YKcqPXr/DCpMr8NCfwBvC3FPSM5oJI+9k9Ic0hSBPZMiHN/jb2ZFA6hOl+MrEgPxZ4NBGtPkjDjcYoo7Lro4gogolOcvciLTUUh7uZCZKgNKfIfPUaMEdA21tsDZUy06F8KWOR07xMOG9vpBU/WYZfm+f/II287vSP1u7ftiGtGbNeMkNw62pdrat1ta4GXG3NZqB1ta7W1br+l66W0G1drat1ta4GXi2h27paV+tqXQ28WkK3dbWu1tW6Gni1hG7ral2tq3U18GoJ3dbVulpX62rg9X89CcGjI4cTxQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def w(z):\n", " U = 1.0\n", " a = 1.0\n", " Gamma = 10.0\n", " alpha = 0.0\n", "\n", " return 0.5 * 1.0 * z**2 - 1j * Gamma / 2.0 / np.pi * np.log(z - 1)\n", "\n", "# set up the meshgrid as usual\n", "xx = np.linspace(-3.0, 3.0, 1000)\n", "yy = np.linspace(-2.0, 2.0, 1000)\n", "xx, yy = np.meshgrid(xx, yy)\n", "# but now we'll also create one that is complex:\n", "zz = xx + 1j*yy\n", "\n", "# The stream function is\n", "psi = w(zz).imag\n", "\n", "# Plot it!\n", "fig = plt.figure(figsize=(6, 4))\n", "ax = fig.add_subplot(1, 1, 1)\n", "plt.axis('off')\n", "plt.contour(xx, yy, psi, colors='black', levels=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conformal Mapping\n", "\n", "Conformal mapping transforms the complex plane (keeping local angles the same). In fluid dynamics, a common mapping is the Joulowski transformation,\n", "$$\n", "Z = f(z) = z + \\frac{c^2}{z},\n", "$$\n", "where $c$ is a parameter. The Joukowski transformation takes a circle centered at the origin in the $z$ plane to an ellipse in the $Z$ plane. We can do this easily in Python by transforming the coordinates of the points in the circle from above.\n", "\n", "Interestingly, the same transformation takes a circle offset from the origin by a small amount and makes an interesting shape; play with the parameter $c$ and the offset $z_0$ below to see." ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def joukowski(z, c = 0.5):\n", " return z + c**2 / z\n", "\n", "fig = plt.figure(figsize=(6, 4))\n", "\n", "ax = fig.add_subplot(1, 2, 1)\n", "ax.set_xlim(-2, 2)\n", "ax.set_ylim(-2, 2)\n", "ax.set_aspect('equal')\n", "\n", "# offset of circle\n", "z0 = -0.3 + 0.2j\n", "circ = circle(radius = 1, centre = z0)\n", "ax.fill(circ.real, circ.imag)\n", "\n", "ax = fig.add_subplot(1, 2, 2)\n", "ax.set_xlim(-2, 2)\n", "ax.set_ylim(-2, 2)\n", "ax.set_aspect('equal')\n", "\n", "# parameter c; the close it gets to 1, the flatter the transformation\n", "circ = joukowski(circ, c = 0.7)\n", "ax.fill(circ.real, circ.imag)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Joukowski Aerofoil\n", "\n", "Let's use these ideas to create a nice plot of the streamlines and pressure field around an aerofoil shape. We know the complex potential around a circular cylinder offset from the origin by an amount $\\lambda$ is\n", "$$\n", "w(z) = U\\left[ (z+\\lambda) e^{-i\\alpha} + \\frac{(a+\\lambda)^2}{z+\\lambda} e^{i\\alpha} \\right] - \\frac{i\\Gamma}{2\\pi} \\ln (z+\\lambda).\n", "$$\n", "To find the pressure, we'll need the derivative of this as well:\n", "$$\n", "\\frac{dw}{dz} = U e^{-i\\alpha} - Ue^{i\\alpha} (a+\\lambda)^2 / (z+\\lambda)^2 - i\\Gamma / 2\\pi(z+\\lambda).\n", "$$\n", "While we're tkaing derivatives, we'll need one of the Joulowski transformation, too, since the flow in the $Z$ plane, $[U, V]$, is given by\n", "$$\n", "U - iV = \\frac{dw/dz}{f'(z)},\n", "$$\n", "where\n", "$$\n", "f'(z) = 1 - \\frac{a^2}{z^2}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [], "source": [ "def flow_around_shifted_circle(z, a = 1.0, U = 1.0, alpha = 0, Gamma = 0, lam = 0.0):\n", " return U * ((z+lam)*np.exp(-1j*alpha) + (a+lam)**2/(z+lam) * np.exp(1j*alpha)) - 1j * Gamma / 2.0 / np.pi * np.log(z+lam)\n", "\n", "def vel_around_shifted_circle(z, a = 1.0, U = 1.0, alpha = 0, Gamma = 0, lam = 0.0):\n", " return U * ( np.exp(-1j * alpha) - ((a+lam)/(z+lam))**2 * np.exp(1j*alpha) ) - 1j*Gamma / (2.0 * np.pi * (z+lam))\n", "\n", "def joulowski_deriv(z, c = 0.7):\n", " return 1 - c**2/z**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's test our functions by plotting the flow around the circle -- we won't bring in the Joulowski transformation just yet. We'll start with the meshgrid for the complex plane, but we need to create it using polar coordinates. This is because we don't want any grid points within the circle. It's fine for this, but when we apply the Joukowski transformation those points get mapped outside and are unphysical." ] }, { "cell_type": "code", "execution_count": 142, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 142, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# various parameters\n", "a = 1.0\n", "lam = 0.2\n", "Gamma = -4.0*np.pi*(a+lam)*np.sin(np.pi/6)\n", "alpha = np.pi/6\n", "\n", "# create the meshgrid\n", "radii = np.linspace(a+lam, 5.0, 200)\n", "angles = np.linspace(0, 2*np.pi, 200)\n", "radii, angles = np.meshgrid(radii, angles)\n", "zr = -lam + radii * np.exp(1j * angles)\n", "\n", "# calculate the stream function\n", "psi = flow_around_shifted_circle(zr, a = a, lam=lam, alpha = alpha, Gamma = Gamma).imag\n", "\n", "# plot\n", "fig = plt.figure(figsize=(6, 4))\n", "\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.set_aspect('equal')\n", "ax.set_xlim(-4, 4)\n", "ax.set_ylim(-2, 2)\n", "\n", "ax.contour(zr.real, zr.imag, psi, colors='black', levels=50, linewidths=1)\n", "\n", "# draw the circle, too\n", "circ = circle(a+lam, -lam)\n", "ax.fill(circ.real, circ.imag)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To also find the pressure, we can use Bernoulli's theorem,\n", "$$\n", "\\frac{p_\\infty}{\\rho} + \\frac{1}{2} U^2 = \\frac{p(x, y)}{\\rho} + \\frac{1}{2} \\vec{u}^2,\n", "$$\n", "and solve for the pressure $p$:\n", "$$\n", "p(x, y) = \\text{constant} - \\frac{1}{2} \\rho \\mathbf{u}^2\n", "$$\n", "where $\\mathbf{u}^2 = u^2 + v^2$. We find the velocities from the derivative of the complex potential." ] }, { "cell_type": "code", "execution_count": 135, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho = 1.0\n", "\n", "dw = vel_around_shifted_circle(zr, a, lam=lam, alpha = alpha, Gamma = Gamma)\n", "u = dw.real\n", "v = -dw.imag\n", "\n", "p = -0.5 * rho * (u**2 + v**2)\n", "\n", "fig = plt.figure(figsize=(6, 4))\n", "\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.set_aspect('equal')\n", "ax.set_xlim(-4, 4)\n", "ax.set_ylim(-2, 2)\n", "\n", "ax.contourf(zr.real, zr.imag, p, cmap = \"coolwarm\", levels=300)\n", "ax.contour(zr.real, zr.imag, psi, colors='white', levels=50, linewidths=1)\n", "circ = circle(a+lam, -lam)\n", "ax.fill(circ.real, circ.imag, color=\"lightgrey\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's draw the same thing in the $Z$ plane under the Joukowski transformation. It's actually easy to do so: just transform the coordinates as we did with the circle above. The only thing we have to be careful about is the velocity calculation -- it has to change to include $f'(z)$." ] }, { "cell_type": "code", "execution_count": 140, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 140, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "zjt = joukowski(zr, c = a)\n", "\n", "dw = vel_around_shifted_circle(zr, a, lam=lam, alpha = alpha, Gamma = Gamma) / joulowski_deriv(zr, c=0.99)\n", "u = dw.real\n", "v = -dw.imag\n", "\n", "p = -0.5 * rho * (u**2 + v**2)\n", "\n", "fig = plt.figure(figsize=(8, 4))\n", "\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.set_aspect('equal')\n", "ax.set_xlim(-3, 3)\n", "ax.set_ylim(-2, 2)\n", "\n", "ax.contourf(zjt.real, zjt.imag, p, cmap = \"coolwarm\", levels=300)\n", "ax.contour(zjt.real, zjt.imag, psi, colors='white', levels=50, linewidths=1)\n", "circ = joukowski(circle(a+lam, -lam), c = a)\n", "ax.fill(circ.real, circ.imag, color=\"lightgrey\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 4 }