{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The effect of tangential velocities" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It was first noted by [Rezzolla, Zanotti and Pons](http://dx.doi.org/10.1017/S0022112002003506) that there is one effect that is specific to *relativistic* Riemann problems. Thanks to the Lorentz factor coupling the tangential velocities more tightly to the other terms, it is possible to change the wave pattern in the problem solely by changing the tangential velocity. This cannot happen in the Newtonian case.\n", "\n", "The examples used in their paper use a *modified* relativistic Sod problem as a base. We set that problem up first:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from r3d2 import Gamma_law, Gamma_law_react, State, RiemannProblem\n", "from IPython.display import display, display_png" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/latex": [ "$\\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}= \\begin{pmatrix} 1.0000 \\\\ 0.5000 \\\\ 0.0000 \\\\ 1.5000 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}= \\begin{pmatrix} 0.1250 \\\\ 0.0000 \\\\ 0.0000 \\\\ 1.2000 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad {\\cal R}_{\\leftarrow}{\\cal C}{\\cal S}_{\\rightarrow}, \\quad p_* = 0.5974, \\quad\\begin{cases} {\\cal R}_{\\leftarrow}: \\lambda^{(0)}\\in [-0.2902, -0.0488],\\\\ {\\cal C}: \\lambda^{(1)}= 0.6407,\\\\ {\\cal S}_{\\rightarrow}: \\lambda^{(2)}= 0.8900, \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 0.7341 \\\\ 0.6407 \\\\ 0.0000 \\\\ 1.2207 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 0.3427 \\\\ 0.6407 \\\\ 0.0000 \\\\ 2.6154 \\end{pmatrix}. \\end{cases}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "eos = Gamma_law(5.0/3.0)\n", "U_left_sod_modified = State(1.0, 0.5, 0.0, 1.5, eos)\n", "U_right_sod_modified = State(0.125, 0.0, 0.0, 1.2, eos)\n", "rp_sod_modified = RiemannProblem(U_left_sod_modified, U_right_sod_modified)\n", "display(rp_sod_modified)\n", "display_png(rp_sod_modified)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see the wave pattern has a left going rarefaction and a right going shock.\n", "\n", "Now, by modifying the tangential velocity of the right state, the wave pattern changes:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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{\\cal S}_{\\leftarrow}{\\cal C}{\\cal S}_{\\rightarrow}, \\quad p_* = 1.1509, \\quad\\begin{cases} {\\cal S}_{\\leftarrow}: \\lambda^{(0)}= -0.3224,\\\\ {\\cal C}: \\lambda^{(1)}= 0.4549,\\\\ {\\cal S}_{\\rightarrow}: \\lambda^{(2)}= 0.7638, \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 1.0879 \\\\ 0.4549 \\\\ 0.0000 \\\\ 1.5868 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 0.4748 \\\\ 0.4549 \\\\ 0.5873 \\\\ 3.6363 \\end{pmatrix}. \\end{cases}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U_right_vt_0_9 = State(0.125, 0.0, 0.9, 1.2, eos)\n", "rp_vt_0_9 = RiemannProblem(U_left_sod_modified, U_right_vt_0_9)\n", "display(rp_vt_0_9)\n", "display_png(rp_vt_0_9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is a left going *shock*, rather than a rarefaction.\n", "\n", "A shock-rarefaction problem can be modified, via a tangential velocity, to a two rarefaction problem in a similar fashion:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/latex": [ "$\\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}= \\begin{pmatrix} 1.0000 \\\\ 0.0000 \\\\ 0.0000 \\\\ 1.5000 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}= \\begin{pmatrix} 0.1250 \\\\ 0.5000 \\\\ 0.0000 \\\\ 1.2000 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad {\\cal R}_{\\leftarrow}{\\cal C}{\\cal S}_{\\rightarrow}, \\quad p_* = 0.1546, \\quad\\begin{cases} {\\cal R}_{\\leftarrow}: \\lambda^{(0)}\\in [-0.6901, 0.0309],\\\\ {\\cal C}: \\lambda^{(1)}= 0.6206,\\\\ {\\cal S}_{\\rightarrow}: \\lambda^{(2)}= 0.8996, \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 0.3262 \\\\ 0.6206 \\\\ 0.0000 \\\\ 0.7108 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 0.1621 \\\\ 0.6206 \\\\ 0.0000 \\\\ 1.4302 \\end{pmatrix}. \\end{cases}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U_left_sod_modified2 = State(1.0, 0., 0.0, 1.5, eos)\n", "U_right_sod_modified2 = State(0.125, 0.5, 0.0, 1.2, eos)\n", "rp_sod_modified2 = RiemannProblem(U_left_sod_modified2, U_right_sod_modified2)\n", "display(rp_sod_modified2)\n", "display_png(rp_sod_modified2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now with tangential velocity:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/latex": [ "$\\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}= \\begin{pmatrix} 1.0000 \\\\ 0.0000 \\\\ 0.9000 \\\\ 1.5000 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}= \\begin{pmatrix} 0.1250 \\\\ 0.5000 \\\\ 0.0000 \\\\ 1.2000 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad {\\cal R}_{\\leftarrow}{\\cal C}{\\cal R}_{\\rightarrow}, \\quad p_* = 0.0513, \\quad\\begin{cases} {\\cal R}_{\\leftarrow}: \\lambda^{(0)}\\in [-0.3838, 0.1375],\\\\ {\\cal C}: \\lambda^{(1)}= 0.2809,\\\\ {\\cal R}_{\\rightarrow}: \\lambda^{(2)}\\in [0.7773, 0.8750], \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 0.1683 \\\\ 0.2809 \\\\ 0.9324 \\\\ 0.4573 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 0.0838 \\\\ 0.2809 \\\\ 0.0000 \\\\ 0.9189 \\end{pmatrix}. \\end{cases}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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ER0eTm5vLX/7yl3LdL3ryySeZOnUqHo+H6OhoHnroIW6++ebCQWyN+13euzlN6ybw1BcryffYWZSJHHsys1m25QCntw3uqDWWoMopKiqKUaNG8d5776GqRRJUixYtSu0k4d/F/Mcff2TGjBkB97abNm0ajz76KPn5+URHRzNmzBjuuuuuoAwua0InNiaKe89tz2/bDvDBfBujz4RGTp6HjEM57MnMZk9mNrszs9l1MJudB7PYeSCLHQey2L4/i237j7B13xG27DtC+t7DbM7w/mza4/3ZuOcQG3YfYv3uQ6zblcnaXZmk7cwkbedBPlnkHerw9HbBLQ9md9Ur4KabbuKpp55i586dnHLKKaxYsYIDBw5Qt25d8vPz2bdvX2EtJv9LfAVdzP/3v/8F/HDu8uXLueyyy8jLyyMqKoqrrrqKRx99lJo1a1bZ5zNVZ/jJjXl37iaenr6SIV0akljdLs+aqrM0fT/Xj/+F3ZnZZS9cSfVqxNK1SXAKrhawBFUBKSkpDB48mMmTJzNmzBh69uzJTz/9xODBg2nWrBmbN28ukqCysrLYtWsXrVt7h57/8ssveeutt8rcz+7duznjjDPIysoiKiqK8847j2eeeaawJ6DbiUgUEOUbG60i6w8GngeigddU9e/F5l8H/APY4pv0oqq+VvGIq56I8NcRnfn9Cz/wzy9X8bfzuzodkolQc9ft4aa35pNYvRoPD+tEVEEBTilaXNO/8Kb/e/yKeh4t4Fm0SCd+89s2qEl0VHBHrwlqghKRFqrq1iqbQTV69Giuv/56Ro0aVXiZb/DgwYVDHnXt2rXwHtTGjRtp0qQJ1atXB+Cnn34q8wwoJyeHM888s7DHXv/+/Xn11VdJTEwMxcerNBEZAzwC5IjIbuDf5UkeVVW22w06NqrNNX1SeWvOBi7r1ZyuQRj1ORKJyE/AX1T1W6djCTczV+7gtncW0qxedd658VQa1gnPe9XBvgf1UfEJvjIIEef0008nLi6O77//vkh9KP9RzQsGb/Ufg+/LL78kLS3tuKNHqCqXX345y5cvR0To3r077733XriVzbgH6KqqTYDBQD8RebQc6xeW7VbVHKCgbHdE+OOgdiTXjOPeKYvJybNyHKW4BRgjIt+ISB+ngwkXnyzawi0TFtCuQS0+GNUnbJMTBClBicilIvJ3oJaIdPQd/RYYF4x9uI2IcNtttzFx4kQ6duzIgQMH2Lx5c5G6UAWdJApGMY+JiWHs2LFs2bLluNt+4oknmDp1KuAdUmnq1Kk0aNCgyj9TkGUCOwF8NZpuBC4sx/qllXMv7iIRWSIiU0SkWQnzEZFbRGS+iMzftWtXOUKoOnUSqjH2gq6s3H6QF22cvhKp6jJVvQi4F/iLiHwqIhUbuPIE8c7cjdz1/iJ6tqjLezefSr0a4X2PM1hnUD8CvwF1gWeANSKyUEQ+BY4EaR+uc+211zJnzhzS09MLL/P5dzUvuAe1du1aUlNTOXDgAAsXLjzu6BHTpk3joYceAqBRo0Z89tln4Vo24z/AZBFp43vfHDhcjvUDLdudqqonAV/jLdt97Eqq41S1l6r2Sk4Obi+jyji7UwMu6N6El79NY/nW/U6H42ZpwON4D1JcVVLFTV7+Lo0HP17GwPYpvHVD76A+j+SUoCQoVd2iqhOAEao6RFVbAWfjvQcxMBj7cKPatWtz8cUX8/777xde5vPval6QoNatW0fbtm2ZPn06Z555Zqndw3/77TcuvNB7kpGYmMiXX34ZtmUzVPVl4F3gNRHJwPsls0pELhGRtgFs4oQo2/3IeZ1IrB7LH99fxJGc8o/LGMlEZKaIbAYWAA8Ae7HCgsdQVf7+xUqenr6KEd0a89+rewalWKArqGpY/vTs2VPdYOHChdq4cWP98ccfNTExUVevXq1xcXG6adMmTUhI0DVr1mhycrIuXLhQc3JydNu2bSVuZ8+ePVqzZk0FNCEhQX/++WfNz88PyWcA5msV/q3wdsY5CbgWeBaYGeA664CWQCywGOhcbJlGfq8vAOaWtV23tBt/363aqS3+/Kne9+Fip0MplxC0mx5AQlXuozw/bmw7efkevX/qEm3x50/1Lx8t0fx8j9MhBSTQtmMP6lZS9+7dady4MYsXLyY5OZm0tDTq1q3L9u3bUVUyMzPJzMykSZMmTJw4scR7Sbm5ufTq1YvMzExiYmL44osvIqpshqrmqeoSVX1LVf+oqmWeVesJVLa7f7tkbjuzNRN/3swni45/f/JEoqoLVTVibxFUVk6ehz9M+pX35m3i9jNb8/iILkQFuZu30yLjG9BhBcUMzzjjDL7//vvC+1Aej6ew48TChQt54YUXSrxcN2zYMNavX09UVBQffvihlc3w0ROobPc9g9rRq0VdHpi6lLSdB50Ox7jckZx8Rr09n0+XbOO+IR340+AOYXkroCyWoIJg5MiRLF++nNatWzNr1iyaNWtWmKA2bNhAamoq06dPZ9iwYcese9999/Hll18iIowfP54hQ4ZY2YwTUEx0FC9c3p2E2BhufGs+ew/llL2SOSEdyMrl2jd+5rvVuxh7QVdu7d/a6ZCqjCWoIEhISOCqq65i1apVLFmyhMaNGxcmqI0bN5Kamsrnn39+zPBG77//Pk899RQAzz77LJdddpmVzTiBNU5M4JWre7Jtfxa3vrPAno8yx8g4lMMVr85l4aa9vDCyO1ec2tzpkKqUJaggGT16NJ999hkdO3YkJyenMEEV1IGaPHkyPXr0KFx+yZIljBw5EoAHH3yQUaNGWdkMQ88WdXn6opOYtz6DBz5aisdGPTc+uw5mc/m4uazZkcmr1/TivJMbOx1SlbMEFSRt27ala9euJCUlsWXLFjZs2AB4B4mNiYkhKSmp8Brx3r176dnT2yP65ptv5oEHHrCyGabQ+d2b8Iez2jJlQTp/+2xFQY82cwLbcSCLkePmsDHjEG9cdwoDOqQ4HVJIWIIKottvv50NGzawfPlyNm/eXDjM0ZQpU/j1118ByMvLIzU1lby8PIYPH86zzz5rZTPMMe46uy3X90vljR/X89zXa5wOxzho674jXPbKHLbvz+Kt63vTr01YDXlWKZaggmjEiBHs3buXnTt3sn//fqKiovB4PKxYsYKBA709q7t27cqBAwc45ZRTeOedd6hRo4bDURs3EhEe+n0nLu3VlOe/WcM/Z6yyM6kT0OaMw1z6yhz2ZOYw4cZTObVVfadDCinrLhZE1apV46abbmLChAlkZWWRkZFB3bp16dKlC9WrV+eiiy5i5cqVpKamMmPGjLApm2GcERUlPHnhSUSJ8OK3aaTvPUynxrWPWa5PqyQbET0Cpe89zMhxc8nMzuPdm0/lpKbhUckgmCxBBdmtt97KM888U3hm1L59e8aOHcvf/vY3pk6dSmJiIvPmzaNu3boOR2rCQXSU8OSFXamTUI1xP6zj40Vbj1mmb+v6vHdzRBYNqLAAaonFARPwDo+1B7hMVTeEOs7S7DyQxVWvzeNAVi4Tbz6NLkEuBBguLEEFWdOmTenbty/ff/89Ho+HunXrsmXLFh566CFiY2NZvHgxKSknxg1OExwiwv1DO/LHQe3IL9ar77o3fyavCnr6eTzKF8u28+68jRzJDa8xAgOsJXYjsFdV24jISOAp4LLQR3usPZnZXPnaPHYdzObtm049YZMTuChBlXXEE07uvfdeZs6ciaoye/ZsJk+ejIiwePFimjUrsSKEMWUqaQDQ6CjhYFYeS9P3oyge9Y2vScE4mxRO8ygoCgXTSll+Sfp+pi3eyvrdh2hWL4HU+mF3n7SwlhiAiBTUEvNPUCOAR32vpwAviojocW70HcnNZ9mW/ajvd+f93//3BxSZ7l3Pf37B79//ffHt/HPGKjZlHOatG3rTo/mJfaXFFQmqHNVTw8KgQYOIjY0lOzubbdu2ATBv3jzat28fkcORGOckVItm7roMzntxdtC2KQKntazPXWe3ZdhJjUst4/3OTUHbZbCVVEvs1NKWUdU8EdkP1Ad2l7bRtJ2ZDPt38H7PpakWLbx6TS9OO8E6RJTEFQmKwI54wkZUVBRnnHEGX331FQCffPIJPXv2tORkgm7shV1Zkr6fKBGixJtcBPH+XzCt8L33dZRvngh4c4/fNKBRYjwptcL6ubxAaokFsgwicgveyr40aJrKuKt7Fv6e/H+nvn9F5nl34vvd+/bo/77gb+C/PAiNE+NpVMcePQH3JKhAjniKNBYgW0SWVXFcUXgvOVZUMrB3xIgSK5XnVWK7laEl7Lu9E4E4YcGCBbtFZCOQxHGOll3AzfEVxNbC6UBKUWYtMb9l0kUkBqgDZBTfkKqOw1cVXER2ndulkdvbjptjg3K2HbckqICOZoo1lvmq2quqA6uMcIgRvHE6HUOoqGoyuP9v4+b43Bybzy9AWxFpCWwBRgJXFFtmGt76ZHOAi/HWKDtub5NwaDtujg3KH59bElQgRzzGGFMm3z2lglpi0cAbBbXE8BbKmwa8DrwtIml4z5xGOhexKY1bElQgRzzGGBMQVf0c+LzYtIf9XmcBl4Q6LlM+rkhQpR3xlLHauKqPrNLCIUYInziDye2f2c3xuTm2UHDz53dzbFDO+MTG9zLGGONGNlisMcYYV7IEZYwxxpXCOkGJyCUislxEPCLiqq6VIjJYRFaJSJqI3Od0PCURkTdEZGcInidzJTe2Hze3mxO9vfiztlM+FW07YZ2ggGXAhcAspwPx5zd00xCgE3C5iHRyNqoSjQcGOx2Eg1zVfsKg3YznxG4v/qztlM94KtB2wjpBqeoKVV3ldBwlKBy6SVVzgIKhm1xFVWdRwtPzJwoXth9Xt5sTvb34s7ZTPhVtO2GdoFyspKGbmjgUiwkf1m5MRUVk23HFc1DHIyJfAw1LmPUXVf0k1PEEKKChm0zVC7P2Y+3GRaztOM/1CUpVz3Y6hgqwoZtcIszaj7UbF7G24zy7xFc1CoduEpFYvEM3TXM4JuN+1m5MRUVk2wnrBCUiF4hIOtAH+ExEZjgdE3iHbgIKhm5aAXwQwNBNISciE/GO5txeRNJF5EanYwolt7Uft7ebE729+LO2Uz4VbTs21JExxhhXCuszKGOMMZHLEpQxxhhXsgRljDHGlSxBGWOMcSVLUMYYY1zJEpQxxhhXsgRljDHGlSxBVQER+VZEBvle/01EXnA6JhMeRKS/r25OvoisF5F7nI7JhIdIbDuuH4svTD0CPCYiKUB3YLjD8Zjw0QCYjHdA0n1OB2PCSsS1HTuDqgK+2icC3A2MVNV8h0My4eNa4Gtgv9OBmLATcW3HElQVEJGuQCMgW1UPOh2PCSv/Bt4G9onIFU4HY8JKxLUdS1BBJiKNgHfxVrM8JCLnOhySCRMi0gF4GjgPSFTV9xwOyYSJSG07NlhsEIlIdeAb4GFV/UpEzgCeUtU+DodmwoCIPAssVtXxTsdiwkukth3rJBFEqnoY7/D7Be9n+b83pgzxlFzB1ZiyRGTbsTMoY1xCRFoBr+LtjbUNuEZVtzkblQkHkdp27B6UMS6hqutU9SxV7YK3XHcPp2My4SFS244lKGNcRkSGATXwdhk2JmCR1nbsEp8xxhhXsjMoY4wxrmQJyhhjjCtZgjLGGONKlqCMMca4kiUoY4wxrmQJyhhjjCtZgjLGGONKlqCMMca4kiUoY4wxrmQJyhhjjCtZgjLGGONKlqCMMca4kiUoY4wxrmQJyriSiLwhIjtFZFkp888Ukf0issj383CoYzTuFEDbERF5QUTSRGSJiERE7aRIZAnKuNV4YHAZy/ygqt18P4+FICYTHsZz/LYzBGjr+7kF+E8IYjIVEON0ABWVlJSkqampTodBvkfJ9ygePfp/QYkt/0pbAogI4nvj/14EokSIjXHmeGHBggW7VTXZkZ2XQlVniUhqsLdbu249TWnUrPBvUJoS50lp849dWgRqxMYgx9tJmHNju4GA2s4IYIJ6i+HNFZFEEWlUVon0QNsOVK79xMZEEefQd0GoBNp2wjZBpaamMn/+/HKvp74EogWvwffeN93/NeBRZeu+I6TtzCRtZybrdh1i+/4sth/IYseBLLLzPEH7TB/e1peeLeoGbXuBEpGNId9pcPQRkcV4S1xZSsscAAAgAElEQVT/n6ouL2khEbkF75EysQ3bkDd8bEiCG9k3lUeHdw7JvpwQxu2mCbDZ7326b9oxCcqJthOfUI25D55NTHTkJqlA207YJqjlWw/Q6eHpxyQUir33T0KVJQJNEhNonJhAt2aJNKwTT0qtOOokVKNWfAw146pRIy6auJjowuVFvPvO9yh5HiUv30Oe76wrN99DvkdJ25nJk1+sZP+RnMoHeeJYCLRQ1UwRGQp8jPeSzTFUdRwwDqBrtx760d39gaJnugXtiILXxd4X+d+/vVG8jXmnvjF7AxN/3sSYgW1IqhkXxI9tgqCkE5wSvyFKazveef5t4Gi78H9f8JrSlvPuo/D1L+szePKLlSxO3+/IwarbhG2Cqlcjlit6N/clAf9LZ+Kdhi9B+L3H75LaMcv5rsVEybHrp9SOo01KTVol1SQhNjron8W+wMpPVQ/4vf5cRF4WkSRV3X289eJiomiTUrPK40usHsvny7bx5o/ruffcDlW+P1Mu6UAzv/dN8Z6FH1co2k7L+jX4+/SV/Ji22xIUYZygGtWJ58FhnZwOwzhERBoCO1RVRaQ33g4/exwOq1Dr5JoM7tyQCXM2Mqp/a2rHV3M6JHPUNGCMiEwCTgX2l3X/KVTq1oilS+M6zE7bzZ1nlXhB4IQSuRc5TVgTkYnAHKC9iKSLyI0icquI3Opb5GJgme8e1AvASNVgXMgNntvPbMPBrDzemRuut2rCUwBt53NgHZAGvArc7lCoJerXJolfN+3lUHae06E4LmzPoExkU9XLy5j/IvBiiMKpkK5N63B62yTemL2eG/q1JL5a8C8Pm2MF0HYUGB2icMrtd22S+O/3a/l5fQYDOqQ4HY6j7AzKmCo0ekAbdmfm2FmUCViv1LrEV4vi21U7nQ7FcZagjKlCp7Wqz+/aJPHyd2vtko0JSHy1aM5om8xXv+3AZVetQ84SlDFV7J5z2pFxKIfxP21wOhQTJs7p3JBt+7NYtuVA2QtHMLsHZUwV6968Lmd3TOGV79dy1WktqJMQPj360vce5khOvtNhnHAGdkghSuDL37bTtWkdp8NxjCUoY0Lgj4Pa8fsXZvPaD+u455z2TocTkF837eWCl39yOowTUr0asZySWo8vl+8Im/ZSFSxBGRMCnRvX4fcnNeKN2eu5pk8qybXc/3D2jOU7iIkS/nXpyURHHTv4wnlPORDUCeTczg157NPfSNt5kDYptZwOxxF2D8qYELlnUDuy8zw8+/Vqp0Mpk6oyY/l2TmtVnxHdmjDspMbH/JiqNezkRkQJTF24xelQHGMJypgQaZVck6tOa8GknzexesdBp8M5ruVbD7B+9yHOO7mR06GcsFJqxXN622Q+WbQVj+fE7M0XkgQlIoNFZJWvQNh9Jcy/TkR2+RWfuykUcRl3i8TCc384qy0142IY+/kKp0M5rmmLt1ItWji3c0OnQzmhXdijCVv2HWHe+gynQ3FElScoEYkGXsJbJKwTcLmIlDSI3vt+xedeq+q4TFgYT4QVnqtbI5Y7Brblu1W7mLV6l9PhlCgrN58pC9IZ0D6FxOqxTodzQjunU0NqxEYzZUG606E4olwJSkTu9nsdaNeS3kCaqq5T1RxgEt6CYcYcl6rOAo536FhYeE5V5wKJIuL6a1LX9G1B83rVGfv5CvJdeOnm0yXbyDiUw7V9U50OpcIi5apNQmw0F/Rowv+WbGVPZrbT4YRcQAnKV3HyTeASEbldRH4HHPNHL0VpxcGKu8h3mWaKiDQrYT4icouIzBeR+bt2ufPo0xQlInOKva8lIt2DtPmA2pbb2k1cTDT3DenAyu0Hee/nTU6HU4THo7z2wzraptSkb+v6jsQgIkNEZJ4vwXwgIn3KuX5EXbW5pk8qOXke3p+/ueyFI0yZCUpEfgK6q+r1wKPAPLyXVKYGuI9AioP9D0hV1ZOAr4G3StqQqo5T1V6q2is52XWVpk3J4gBE5BkAVT0IvBykbQdUeM6N7WZIl4b0aVWff85Y5aoj48+WbmPl9oOMHtCmsEaaA14G7gZOw1ss8B8ictwBYIuJqKs27RrUom/r+rwzZyN5+cGr4B0OAnkO6hbgryLyIPCgqi4AFpRjH2UWB1NV/zo+rwL2hEXkEBFJAa4SkXt8I0knBGnbFSo85wYiwmMjOjPk+R94avpKnr745Apt56vfdjB92Xa/qr7e/z169DUKHtUi1Vw9vhkFVWEL5i/fup8ODWsx/GRHu5HvUNUffa+/9p2FzwMmBrh+SWfWp5aw3EUicgawGvijqh5ziuJf8r158+YB7j74ru2byqi3F/DZ0m2M6FbSBajIVGaCUtVleP+QPYDHfEdVD6rqogD38QvQVkRaAluAkcAV/guISCO/gmHDAXd3cTLlcT8wG3gPeFZEVhO8zjmuLTwXiLYNanHj6S155ft1XHZKM3q2qFfubbw+ex0LN+4jpXYcIr6K0BytMu1fcbpgPr75UVKsurQILerX4P/OaU9UCQ/mhtAGEfkb8JjvDCgXKE+//ECv2kxU1Wxfnai3gIHHrORX8r1Xr16O3TAc1LEB7RrU5N8z0xh2UuMSH5yOROUZSSINeBy4Hpgf6LqqmiciY4AZQDTwhqouF5HHgPmqOg24U0SGA3l4b4pfV464jIup6nSgHYDvXsIlwI2BrOsrPHcmkCQi6cAjQDXfdv+Lt/DcULxt8zDethlW7hzYlmmLtvLQx8uZNqYfMdHlz93dmifywahy3aZxOwUuBG4WkTVAc+BdEWmrqmsCWD/irtpERQl3DGzLHRN/5fOl2zjP2TPckCkzyYjITLz3nLKA33w/15VnJ6r6Od4vE/9pD/u9vh/vkbaJYKo6B2+l00CXD+vCc4GoERfDQ8M6cfu7C3ln7kau69fS6ZAcV/B3F5F4oAtwsu/nNRFppaoldqLyE5FXbYZ2bcTz36zhua9XM7hLQ6pV4GAm3ARyFvR/wApVPVLVwRhzIhrSpSGnt03iX1+uZnCXRjSsE+90SK6gqll4r9bML+d6EXnVJjpK+NO57bnl7QW8M3cj158ABzNlpmBVXWjJyZiqIyL87fwu5Ho8PPjxshO+SF0wqOrnqtpOVVur6hO+aQ/7khOqer+qdlbVk1V1gKqudDbiwAzq1IDT2ybx7FerXdX7s6pE/jmiMWGgRf0a3D2oHV+v2MFnS8Omn4cJMRHh4WGdOJSTzxOfuf6qZKVZgjLGJW7o15KuTerw6LTl7D2U43Q4xqXaNqjF6AFtmPrrFqYv2+50OFXKEpQxLhETHcVTF53EvsO5/O0EODo2FXfHwDZ0aVKbBz5ayvb9WU6HU2UsQRnjIp0a12ZU/1Z8uDDdtYPJGudVi47i2Uu7kZWbz6h3FpCVm+90SFXCEpQxLnPHwLa0Sq7BAx8tJTM7z+lwjEu1bVCLZy7txuLN+7h/6tKIrBllCcoYl4mvFs3TF53Eln1HeOKz35wOx7jY4C4N+b9z2vHRr1t4eFrk9QC1BGVcK1JKJlREr9R6jDqjNRN/3szMlTucDse42OgBbRjVvxXvzN3EAx8tJTeCBpS1BGVcKdJKJlTEHwe1pUPDWvxpylIyrFefKYWIcN/gDowe4D2guWH8LxHTC7Q8Y/FVmIgMBp7H+1T3a6r692Lz44AJQE9gD3CZqm4IRWzGtQpLJgD4BoQdgXeorRNCXEw0z1zajREvzeahj5fx4hXdnSyBYVxMRLj33A60qFeDv3y8lHOfm8VTF53EgA4pIY/lUHYe//pyNYvT91V6W24p+X4jsFdV2wDP4vKBG01IWKFLvL367jq7HZ8t3ca0xWFRScQ46NJTmvHx6H4kVq/G9eN/4Ybxv7By+4GA11dVPB4l36Pk5XvIzfeQk+chOy+frFzvz5GcfA5l55GZncfBrFwOZOWy/0guG/cc4qVv0+j/j+9448f1ACRUiy7xJ1ChOIMK5Eh4BN5iiABTgBdFRDTS7viVoqAEwq3vLCTmBBlGPwARVzKhokad0YqvV+zgj+8v4v6pS4vMy8rNp3fL8pfpiHQn8lWbzo3rMG3M73jrpw28+G0ag5/7gfhqUYW1v/CrC+ZfQyxY37Z9WtVn3DU96dG8bqnLvHtzYNsKRYIKpHhY4TK+gR73A/WB3f4LuaV4WLB1aFSLuwe142BWriP7f9CRvZYp4komVFRMdBT/ubInb8/dQE7esTfAB7QP/WUcN/O7ajMIbzv6RUSmqar/QXHhVRsRGYm37VwW+mirRny1aEb1b82lvZoxecFmdmfmeI/4/Ot/cbQeWJTvjf+0IssU1hHzrzl2dDmAuJgo+rdLoXn96kH7HKFIUIEcCQdcupswPhIuTbXoKO48q61j+3dpgorIkgkV1bBOPPee28HpMMKFXbXxqVsjllvOaO10GBUWigQVSFnugmXSRSQGqIN3CPxSLViwYLeIbASSKHam5SJujg2OxtfC6UCKq6qSCWHSbsDd8bm23fhUyVUbIFNEVhEefxu3KlfbCUWCKvNIGG/p7mvxFrO7GJhZ1pGMqiYDiMh8Ve0V9KiDwM2xgfvjq4pCl+HQbsDd8bk5Np8quWpTuKKLP7+bY4Pyx1flvfhUNQ8oOBJeAXxQcCTsO/oFeB2oLyJpwN3AMQ9lGmNMgMpz1YZAr9qY0AvJc1ABHAlnAZeEIhZjTMSrkqs2JvRCkqCq2LiyF3GMm2MD98dXldz+2d0cn5tjC/T+5evA276rNhl4k1ig3Pz53RwblDM+sYMGY4wxbmRj8RljjHGliEhQInKJiCwXEY+IuKIHS1kjcTtJRN4QkZ0isszpWJxk7aZ8rN0cZW2nfCradiIiQQHLgAuBWU4HAuUaidsp44HBTgfhAtZuymc81m4KWNspn/FUoO1ERIJS1RWqusrpOPwUPsmuqjlAwZPsrqCqs7AutdZuysnazVHWdsqnom0nIhKUCwU6Ercx/qzdmIqKyLYTNt3MReRroGEJs/6iqp+EOp4yBPSUuql61m5MRVnbcV7YJChVPdvpGMohkCfZTQhYuzEVZW3HeXaJr2oUPskuIrF4HwKc5nBMxv2s3ZiKisi2ExEJSkQuEJF0oA/wmYjMcDKe0sYfdDImfyIyEe8QL+1FJF1EbnQ6JidYuykfazdHWdspn4q2HRtJwhhjjCtFxBmUMcaYyGMJyhhjjCtZgjLGGONKlqCMMca4kiUoY4wxrmQJyhhjjCtZgjLGGONKlqCqiIj099U/yReR9SJyj9MxGfezdmMqKhLbTtiMxReGGgCT8Q4suc/pYEzYsHZjKiri2o6dQVWda4Gvgf1OB2LCirUbU1ER13YsQVWdfwNvA/tE5AqngzFhw9qNqaiIazt2ia8KiEgH4GngPOA7tQEPTQCs3ZiKitS2Y4PFVgEReRZYrKrjnY7FhA9rN6aiIrXt2CW+qhFPyZU4jTkeazemoiKy7dgZVBUQkVbAq3h71WwDrlHVbc5GZdzO2o2pqEhtO3YGVQVUdZ2qnqWqXfCWXe7hdEzG/azdmIqK1LZjCaoKicgwoAberp/GBMTajamoSGs7donPGGOMK9kZlDHGGFeyBGWMMcaVLEEZY4xxJUtQxhhjXMkSlDHGGFeyBGWMMcaVLEEZY4xxJUtQxhhjXMkSlDHGGFeyBGWMMcaVLEEZY4xxJUtQxhhjXMkSlDHGGFeyBGWMMcaVLEEZY4xxpRinA6iopKQkTU1NdTqMclOFPI/nmOkiQkyUOBARLFiwYLeqJjuy8xCrVz9JmzVv7nt39PctRd8eo8RZUvo8QRBn/pwhcyK1G/BvO94/bGlt5phJUtJiUuJypWwy4gTadsI2QaWmpjJ//nynwyiXrNx8hv17Nmk7M0uc/8nofpzcLDHEUYGIbAz5Th1yKLYu+899PCT7euS8Tlzfr2VI9uWEE6ndQOjaTpPEBN66oTdtUmpW+b6cEmjbCdsEFY4mzNlA2s5M/u+cdiTXiiucvjnjCC9+m8aeQ9nOBXeCaJqYwBMXdqWgjrQqKEpBYWktmOh7rQpa/H3hukerURffzmdLt/HSt2u5vHdz4qtFV/GnMqHQpKDt+P2tC9qLf1vxbyeFbafYOse0Oz06b8KcjVz52lwmj+pL8/rVnfioruGqBCUi0cB8YIuqDnM6nmDKOJTDizPTOLN9MmMGti0yb/Hmfbz4bZpDkZ1Y6taIZWTv5mUvWEldm9bhilfnMXlBOlef1qLK92eqXr0asVwegrZzTucGjBw3lytem8vkW/vQqE5Cle/TrdzWSeIPwAqng6gKT32xksM5+TwwtKPToZgQ6NOqPt2aJTJu1lry8o+952hMaTo0rM2EG3qz73AuV742j72HcpwOyTGuSVAi0hT4PfCa07EE24KNGbw/fzM3nt6Sdg1qOR2OCQER4fYzW7M54wifLtnmdDgmzJzUNJE3rjuF9IwjjHpnAdl5+U6H5Ag3XeJ7DvgTUOo3uIjcAtwC0Lx51Z9qB0NOnoe/fLSMxnXiubPYpT0T2c7u2IC2KTX5z3drGX5yY6Ic6qVpwlPvlvX4xyUn8YdJi7jvw6U8c+nJSJh0DX17zga+XbWr0ttxxRmUiAwDdqrqguMtp6rjVLWXqvZKTg6P3q3Pf7OaldsP8tcRXagR56bjAVPVoqKE2we0ZtWOg8xYvt3pcEwYGtGtCfcMasdHv27h3zPD4z71roPZPP7ZClZuO8Cug9kl/gTKLd+Y/YDhIjIUiAdqi8g7qnqVw3FVyoKNGfznu7Vc2qspgzo1cDoc44DhJzfhxZlpPPPVas7p3JBoO4sKGhEZDDwPRAOvqerfS1jmUuBRvB3kFqvqFb7p+cBS32KbVHV4SIKugDED27Bu9yGe/Xo1JzdLpH87dx+cv/bDOvLyPbxz06m0Si65q7zcGdi2XHEGpar3q2pTVU0FRgIzwz057T+cyx/fX0yTugk8fF5np8OJWCISLyI/i8hiEVkuIn91OiZ/0VHCHwe1Y83OTP63eKvT4UQMX4/fl4AhQCfgchHpVGyZtsD9QD9V7Qzc5Tf7iKp28/24NjmB937m2Au60r5BLe6a9Ctb9x1xOqRS7c7MZsKcjYzo1qTU5FQerkhQkcbjUe56/1e27T/Cc5d1p6Zd2qtK2cBAVT0Z6AYMFpHTHI6piKFdGtGxUW2e/Xo1udajL1h6A2mquk5Vc4BJwIhiy9wMvKSqewFUdWeIYwyahNhoXr6yB7n5yuj3Frq2Hb06ax3ZefmMGdgmKNtz3Tenqn4HfOdwGJXy3Ddr+HbVLh4/vws9W9R1OpyIpt4nIQuG5qjm+9HS1wi9qCjhnkHtuGnCfD5ckB6S57CCYdOew1w2bg6Hc1zZg6wJsNnvfTpwarFl2gGIyI94LwM+qqrTffPiRWQ+kAf8XVU/LmknbuqY1Sq5Jk9ddBKj31vIv2emcfegdo7GU9ymPYd586cNnN+9Ca2DcPYELkxQ4W7qwnRe+GYNF/dsylWnhscXUbjzXe5ZALTBe8Q8r9h8x79kzuqYQrdmibzwzRrO794kLEaX+GzpNrbtz+Lq01qUeO9siQMx+SnpZl7xA5MYoC1wJtAU+EFEuqjqPqC5qm4VkVbATBFZqqprj9mg6jhgHECvXr0cP/D5/UmN+GZFE176No2zOqQ4MjRaaZ74/DdiooQ/ndshaNu0BBVE363ayZ+mLKFv6/o8cUGXsOkSGu5UNR/oJiKJwEe+L6FlfvMd/5IREf50bnuueG0e43/awK39WzsRRrl89dt2OjeuzePndylxvsM3+9KBZn7vmwLFb/KlA3NVNRdYLyKr8CasX1R1K4CqrhOR74DuwDEJyo0eGd6Zn9bu4Z7Ji/n0jt9V6GAnJ8/Dp0u2cign/+gwS6p4/IZoKhiOyaPeoZk8hcM2FZ2mwIEjucxYvoN7z21PwzrxQfuslqCCZP6GDG57ZyHtGtTilat7Ehfj/iPkSKOq+3xfNoOBZWUsHnJ92yRxVocUXpqZxiU9m1K/ZlzZKzlkc8ZhFm7ax58Gt3c6lNL8ArQVkZbAFrydq64otszHwOXAeBFJwnvJb52I1AUOq2q2b3o/4OnQhV45dRKq8fTFJ3HNGz/z4sw0/u/c8v+Nfl6fwd0fLA5aTCLQvXkiN/4uuIMjByVBiUh1VT0cjG2Fozlr93DjW7/QqE48468/hVrx1ZwO6YQhIslAri85JQBnA085HFap7h/akXOfm8VzX68p9czEDT5b6h394ryTGjscSclUNU9ExgAz8N5fekNVl4vIY8B8VZ3mm3eOiPwG5AP3quoeEekLvCIiHrwdxf6uqr859FEq5Ix2yVzQvQnjZq3jwh7l7zFX0MnizetPoWuTOggQJd4SMeL7P0q8JUEKXuO3jP+8qrxSFKwzqNUi8gnwX1VdWubSEWTW6l3c8vZ8mtWtzrs3n0pKreCd3pqANALe8t2HigI+UNVPHY6pVG1SanLlqc15d94mru3bgjYp7hv6yuNRJs/fTI/miTSr597RtFX1c+DzYtMe9nutwN2+H/9lfgK6hiLGqnT/0A58/dsOHpm2nAk39K5QoqhbPZYkF5/JB6ubeXtgEfC6iMwWkatFxL2fOkgm/byJG8b/Qsukmky65TRLTg5Q1SWq2l1VT1LVLqr6mNMxleUPZ7WlerVoxn6+0ulQSjQ7bTdrdx3i6j6hG4VdRAb6/m/kO9gwZUipFc8957TjhzW7mb4sMkcqCUqCUtVDqvqqqvYGxgB9gRUi8k/fw3IRxeNRnvxiBfdNXUq/Nkl8MOo0V99PCAciMlBEXheRf4nI9SLSM1IPcurXjGP0wDbMXLmTWasrP15ZsL3543qSasYytGujUO52sG/A6P8Cz4Zyx+HsqtNa0L5BLZ6avtK1z0ZVRlASlIi0EZEeItIfb8+a2cDLwDDAnYeJFbQ7M5tr3/yZV75fx9WnteD1a3vZPafgeAf4FJgLtAIeBpY7GlEVur5fKqn1q/PotOWuGql6wca9fLtqF9f3axnqjj6JwJ/xDhidFcgKIjJYRFaJSJqI3FfKMpeKyG++UUbe85t+rYis8f1cG5RP4ICY6Cj+NLg9G/Yc5v1fNpe9QpgJ2j0ovD1pPgL24n1w8iDwuO//iDBn7R7+MOlX9h/J5ckLuzLylGbWlTx40lT1I9/ryY5GEgJxMdE8Orwz1735C6/9sJ7RAyr25H3azkx+2ZDh7e5brMKrx3NsddeSKrv6dx+evnw7STVjua5valA+5/GISC9ghaoeAh4DOqjqKl/nhbLWLRjqaBDe7uS/iMg0/84OxYY62isiKb7p9YBHgF54fw0LfOvuDfJHDImBHVLo1aIuz3+zhgt7NKF6bOR0zg7WJ+kBjAIG4B1yZIKq7gjSth13JCefZ75axeuz15NavwZv3dCbjo1qOx1WRBCRCcBCYI6I3KOq/3I6plA5s30Kgzs35N8z1zCiW2Oa1i1/h4S//m85P6zZHbSYRGDsBV1DNfL+BLzfHahquohkicgwVS3xbKiYwqGOAESkYKgj/954pQ11dC7wlapm+Nb9Cu+jCROD8JlCTkS4b0gHLv7vHN6es5FRYfCMXaCC0gpVdRFwm4jUwPsswscishlvr76ZwdhHVVHVokeYUOQoc9Hmfdz34RI27DnMFac254GhHW1sveB6CzgZaAicKyJ3Aot9P0tUNaLPph46rxPf/2sXj3/6G69c3avc6+fme+jWLJFXru7pHVqhSBdgKew+jPi6BPumRwkI3i7DcLQrcZRIKEdcz1LVwst5qrrb1008kF6YlRnqqKR1m5S0EzeMQhKIXqn1+F2bJF6bvZ5r+6aGxUglgQj2N60H+AT4FhgIvCwiqGrwxr7w+W3rAbo+OgOOk1y8lzuKX9I4ulygmterzns3n0rf1knB/hgnPFX9Bvim4L2IxOAdnfpkvEfJEZ2gmiQmcMdZbXh6+iq+XbWTAe1Tyr2N2JgoGtQOyx6k60RkiKp+4TctNsB1KzzUUYDreie6YBSSQN12ZmuufG0eUxdu4YoIGWYtWA/qFly7PQQc8P0cxHuTe38A6zfDe7rfEG+SG6eqzx9vncTq1bioR1PfUaH4HR0ePXKkpHl+7/F/2KyEbQDUjo/hop5NI+q6rpupah7eYd4cHuotdG76XSumLEjnkU+Wc9pd9UmIjYyj3wDcAXwhIlfj7RzTmcCHG6rMUEfpeJOW/7rflTd4t+nbuj4nNa3DK7O8NehiosO/WEWwvnXr+R6Kq6g84B5VXSgitfDetPzqeE93N05M4NHhVmfJhL/YmCj+dn4Xrnh1Hs99vZr7h3Z0OqSQUNVtItITOB9vqZQlFHuo9jgqPNQR3iQ41jfkEcA5eDtThDUR4bb+rbnt3YV89dsOhoT2MYEqEaznoCp16quq21R1oe/1QWAFpVwTNiYS9W2dxMhTmvHqD+tYml7mRYeIoar5qvqhqj6kqi/5evQFsl4e3mcuZ+D9vvigYKgjESkoQDgD2OMb6uhbfEMd+TpHPI43yf0CPFbQYSLcndO5IU0SE3hn3kanQwkK150Dikgq3pGF55Uw7xYRmS8i83ftct8DjsZUxv1DO5JUM44/fbgkIh+6DDZV/VxV26lqa1V9wjftYd84fKjX3araSVW7quokv3XfUNU2vp83nfoMwRYdJVzeuxk/pu1h7a7MsldwOVclKBGpCXwI3KWqB4rPV9VxqtpLVXslJyeHPkBjqlCdhGo8NqILK7YdYNysdU6HY8LUpac0o1q08O7cTU6HUmmuSVAiUg1vcnpXVac6HY8JDyLSTES+FZEVvtEC/uB0TJUxuEtDhnRpyPPfrImII2ATeim14hncpRFTFmwmK9c9o5RUhCsSlHi7zL2O96nyZ5yOx4SVgg42HYHTgNEi0snhmCrlryM6Ex8TxX0fLsHjcXXPZuNSl/ZqyoGsPGau3Fn2wi7migSFt2DY1cBAEVnk+xnqdFDG/SKxgxVUW30AAAYqSURBVE1KrXgeGtaJXzbs5Y0f1zsdjmuVNRafiFwnIrv8vlNu8puX7zd9Wmgjr3p9WyeRUiuOj37d4nQoleKKh3tUdTYlPzxnTMBK62ATLqMB+Lu4Z1NmLN/B0zNW0b9dMm0buK9ulJMCGYvP531VHVPCJo6oareqjtMp0VHCiG6NGf/TBvYeyqFujUCff3YXt5xBGVMpx+tgE46da0SEJy/sSs24GP74wSLr1XeswrH4VDUH7xigIxyOyVUu6N6U3Hzl0yXFn18OH5agTNiL1A42ybXiGHtBF5ZtOcC/Z6Y5HY7bBDqe3kUiskREpvhGrCkQ73tkZa6InF/aTsL50ZaOjWrRrkFN/rdkm9OhVJgrLvGZqpGZncfsNbt4d94mVmw7ptd+RIj0DjaDuzTiwu5NeOnbNM7qkMLJzRKdDsktAhlP73/ARFXNFpFb8Q5MPNA3r7mqbhWRVsBMEVmqqscMsxROY/EVJyIM6dKIF2auYdfBbJJrhV/9T0tQLvLPGat5Y/aGwto+Ht/Atvi99hQffV1Lnpbn8bBhz2HyPUqjOvEM7JBCtVLG5loQuo9YFQo62CwVkUW+aQ+o6ucOxhRUjwzvzJx1e7h5wnw6FCvzsmLbQdo3PCHvT5U5Fp+q7vF7+yrwlN+8rb7/14nId3jvXQY6DmDYGNLV+8jC9eN/pl6Nowkq41C2g1EFzhKUC7RMrsEZ7ZLJzMrlSG5+0RIJQFSUEOMrhVBQHqHgtfi/9hv8NkqEwV0a0rd1Eqe2rHfcgSPHhuAzVpUToYNNnYRqvHhFd56avooDR3KLzGuZVIOhXRo6FJmjyhyLT0QaqWrB9a3heHt44huD77DvzCoJ70HO0yGLPITaN6jFpb2asnpHZpG2ExMVxeltk2iZVMPB6MpmCcoFasdXY8INvZ0Ow7hYzxb1+GBUH6fDcA1VzRORgrH4ooE3CsbiA+b7hju60zcuXx6QAVznW70j8Iqvcm8U8PfjDUwdzkSEpy8+2ekwKkwqOc6rY0RkF7ARSAKCV1I0uNwcGxyNr4Wqhkf3tkoKk3YD7o7vhGs3EDZtx82xQTnbTtgmqAIiMl9Vy1+KNATcHBu4P76q5PbP7ub43BxbKLj587s5Nih/fNbN3BhjjCtZgjLGGONKkZCgxjkdwHG4OTZwf3xVye2f3c3xuTm2UHDz53dzbFDO+ML+HpQxxpjIFAlnUMYYYyKQJShjjDGuFBEJSkQu8VVT9YiIK7pYllWrxkki8oaI7BSRZU7H4iRrN+Vj7eYoazvlU9G2ExEJClgGXAjMcjoQKFKrZgjQCbjcZVVexwODnQ7CBazdlM94rN0UsLZTPuOpQNuJiASlqitUdZXTcfhxda0aVZ2Fd+iXE5q1m/KxdnOUtZ3yqWjbiYgE5UKB1qoxxp+1G1NREdl2wmawWBH5Gihp2Oa/qOonoY6nDIHUqjEhYO3GVJS1HeeFTYJS1bOdjqEcyqxVY0LD2o2pKGs7zrNLfFWjsFaNiMTirVUzzeGYjPtZuzEVFZFtJyISlIhcICLpQB/gMxGZ4WQ8qpoHFNSqWQF8oKrLnYzJn4hMBOYA7UUkXURudDomJ1i7KR9rN0dZ2ymfirYdG+rIGGOMK0XEGZQxxpjIYwnKGGOMK1mCMsYY40qWoIwxxriSJShjjDGuZAnKGGPM/7d3hzYRBVEUhs9xJFsAHoVA0QBiLTSAgCLoAoNYiSFZSQsIWqABkGt3CyAX8ZCEbG4ymTuT/6vgij+5mZeXmZJYUACAklhQjdi++n3/5Nv2l+2H3jOhPrpB1oztDHMX34BOJb1quVhy33sYDINukDVdO5yg2rmX9Cbp0HsQDIVukDVdOyyodjaStpL2tm97D4Nh0A2ypmuHT3wN2D6X9CjpRtJ7cOEhjkA3yJq1HS6LbcD2k6SPiHjpPQvGQTfImrUdPvG1caK/X+IE/kM3yJqyHU5QDdg+k/Ss5a+anaS7iNj1nQrV0Q2yZm2HE1QDEfEZEeuIuNDy7PJl75lQH90ga9Z2WFAN2b6WtNLy6ydwFLpB1mzt8IkPAFASJygAQEksKABASSwoAEBJLCgAQEksKABASSwoAEBJLCgAQEk/mBcH8FNegE0AAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U_left_vt_0_9 = State(1.0, 0.0, 0.9, 1.5, eos)\n", "rp2_vt_0_9 = RiemannProblem(U_left_vt_0_9, U_right_sod_modified2)\n", "display(rp2_vt_0_9)\n", "display_png(rp2_vt_0_9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Reactive case\n", "\n", "An interesting question is on the potential impact of this relativistic effect on detonations and deflagrations. Let us set up a reference reactive problem and add tangential velocities:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/latex": [ "$\\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\\\ q \\end{pmatrix}= \\begin{pmatrix} 1.0000 \\\\ -0.5000 \\\\ 0.0000 \\\\ 1.5000 \\\\ 0.2500 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}= \\begin{pmatrix} 0.1250 \\\\ 0.0000 \\\\ 0.0000 \\\\ 1.2000 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad \\left({\\cal CJDF}_{\\leftarrow}{\\cal R}_{\\leftarrow}\\right) {\\cal C}{\\cal S}_{\\rightarrow}, \\quad p_* = 0.1464, \\quad\\begin{cases} \\left({\\cal CJDF}_{\\leftarrow}{\\cal R}_{\\leftarrow}\\right) : \\lambda^{(0)}\\in [-0.7887, -0.4919],\\\\ {\\cal C}: \\lambda^{(1)}= 0.1532,\\\\ {\\cal S}_{\\rightarrow}: \\lambda^{(2)}= 0.7187, \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 0.3120 \\\\ 0.1532 \\\\ 0.0000 \\\\ 0.7039 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 0.1570 \\\\ 0.1532 \\\\ 0.0000 \\\\ 1.3989 \\end{pmatrix}. \\end{cases}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "eos_reactive = Gamma_law_react(5.0/3.0, 0.25, 1.0, 1.0, eos)\n", "U_reactive = State(1.0, -0.5, 0.0, 1.5, eos_reactive)\n", "U_burnt = State(0.125, 0.0, 0., 1.2, eos)\n", "rp_reactive_base = RiemannProblem(U_reactive, U_burnt)\n", "display(rp_reactive_base)\n", "display_png(rp_reactive_base)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that this is a deflagration-shock problem.\n", "\n", "Now add tangential velocities to the unburnt material:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/latex": [ "$\\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\\\ q \\end{pmatrix}= \\begin{pmatrix} 1.0000 \\\\ -0.5000 \\\\ 0.8000 \\\\ 1.5000 \\\\ 0.2500 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}= \\begin{pmatrix} 0.1250 \\\\ 0.0000 \\\\ 0.0000 \\\\ 1.2000 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad \\left({\\cal CJDF}_{\\leftarrow}{\\cal R}_{\\leftarrow}\\right) {\\cal C}{\\cal R}_{\\rightarrow}, \\quad p_* = 0.0464, \\quad\\begin{cases} \\left({\\cal CJDF}_{\\leftarrow}{\\cal R}_{\\leftarrow}\\right) : \\lambda^{(0)}\\in [-0.6382, -0.4005],\\\\ {\\cal C}: \\lambda^{(1)}= -0.2901,\\\\ {\\cal R}_{\\rightarrow}: \\lambda^{(2)}\\in [0.4159, 0.6667], \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 0.1567 \\\\ -0.2901 \\\\ 0.9377 \\\\ 0.4445 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 0.0789 \\\\ -0.2901 \\\\ 0.0000 \\\\ 0.8828 \\end{pmatrix}. \\end{cases}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U_reactive_vt_0_9 = State(1.0, -0.5, 0.8, 1.5, eos_reactive)\n", "rp_reactive_vt_reactive = RiemannProblem(U_reactive_vt_0_9, U_burnt)\n", "display(rp_reactive_vt_reactive)\n", "display_png(rp_reactive_vt_reactive)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, by adding tangential velocities to the right state the shock has become a rarefaction." ] } ], "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }