{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# An $F \\rightarrow F+1$ MOT with small ground state g-factor\n", "\n", "This example covers calculating the forces in a type-I, three-dimensional MOT\n", "in a variety of different ways and comparing the various results." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pylcp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define the problem\n", "\n", "We'll define the laser beams, magnetic field, and hamiltonian that we'll use:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Laser beams parameters:\n", "det = -1.5\n", "alpha = 1.0\n", "s = 1.0\n", "\n", "# Define the laser beams:\n", "laserBeams = pylcp.laserBeams(\n", " [{'kvec':np.array([1, 0, 0]), 's':s, 'pol':-1, 'delta':det},\n", " {'kvec':np.array([-1, 0, 0]), 's':s, 'pol':-1, 'delta':det}],\n", " beam_type=pylcp.infinitePlaneWaveBeam\n", ")\n", "\n", "# Actual linear gradient:\n", "linGrad = pylcp.magField(lambda R: np.array([-alpha*R[0], np.zeros(R[1].shape),\n", " np.zeros(R[2].shape)]))\n", "\n", "# Define the atomic Hamiltonian:\n", "Fl = 1\n", "Hg, muq_g = pylcp.hamiltonians.singleF(F=Fl, gF=0, muB=1)\n", "He, muq_e = pylcp.hamiltonians.singleF(F=Fl+1, gF=1/(Fl+1), muB=1)\n", "\n", "dijq = pylcp.hamiltonians.dqij_two_bare_hyperfine(1, 2)\n", "\n", "ham = pylcp.hamiltonian(Hg, He, muq_g, muq_e, dijq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate equilibrium forces\n", "\n", "We'll do this with two governing equations again, one `rateeq` and one `heuristiceq` for comparison." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "rateeq = pylcp.rateeq(laserBeams, linGrad, ham, svd_eps=1e-10, include_mag_forces=False)\n", "heuristiceq = pylcp.heuristiceq(laserBeams, linGrad)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let now define a coordinate system over which to calculate and run both:" ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 2:02. \n" ] } ], "source": [ "x = np.arange(-20+1e-9, 20.1, 0.1)\n", "v = np.arange(-20, 20.1, 0.1)\n", "\n", "X, V = np.meshgrid(x, v)\n", "\n", "# Define the three-vectors used in the calculation:\n", "Rvec = np.array([X, np.zeros(X.shape), np.zeros(X.shape)])\n", "Vvec = np.array([V, np.zeros(V.shape), np.zeros(V.shape)])\n", "\n", "heuristiceq.generate_force_profile(Rvec, Vvec, name='Fx')\n", "rateeq.generate_force_profile(Rvec, Vvec, name='Fx', progress_bar=True,\n", " default_axis=np.array([1., 0., 0.]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot up the resulting forces:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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F3T9HtObo64EfA63A+e5+iCjTfhLImtka4Aqi+OwTRBMh5bdra9CURUtDdkWWimpDdkuEYcg73vEO3vrWt9Z8vdB61i0i5cxsE9E38s8DLnX3q0uuvQz4XMUtu919dU2ePP70Vpi4Jz9SLogOPCyf4AgoTHI0Op5kvDUDQFv7FAC9vaOFCY4mxqJrhUmOJhOFiYiClngfT3I01W2MDxQnOAJo3zlB9+bD0XFXdK4wydFAgmxncYIjgDATv6Skl01wBPEkR9UmOMq/+MpPsTOc5EgTHIk0J3e/EriyyvkbgDUlp5ZkZ6ECUpGlIAxhbJoe0rEDMLYfDu9pfLtEpKbM7PHALUz/bfpG4NvAH5Wcq0UngIjIImQE859lV+pMAanIUjB+MOqayCvNIf3wGZAbh0CfSUWawGbgN4iGgP1BlesnAZvd/XBDWyUisgCc+a1Dqk9GjbEku4VFlpzS4brJDLSULIcVr0WaTMBVH3xbXYbUJpNJrrrqKg3XFakzdx939/uPUmQj8ECj2iMistBCEnPepDHUQyqyFLR0wQVvigLTMChZ5R1o74eh7STMuPTZT4RE7d+AE4kEl156ac3rFZFZOwn4ZzN7O1FgeoW7/3fdnq2ie8GgLJ8UwPJzneWShLk4n3Qi+vJqvDWgtS3KJ+3pGQNgsj366DIxmiEYL+aTAmU5pfl80mxXtB8faKNtMM4n3TUJUMwp7W4tyycFynJKS/NJo31FPmnhxVXklOYTREt/DjPMJwXllIrI0qCAVGQp6DkBnv7O6tfa+wHIBk7vOX/EoaGRmi/Pks1m6e3t5dChQ1r6RWRhPQ8YBU4AXg580cxOcPd/mcnNZjbdAu0n16h9IiI1424E8/hmx/WtUEMoIBVZ6uIhuwBjE1N1e5qxsbG61S0iM+Pud8aH9xOtcdcJ/JOZfczdswvYNBGRupjfpEbSCApIRZa6koBURJacm4EXAV3AgWMVdvdN1c7HPadn1LZpIiLzF85jUiNpDAWkIktdSUC6pr+9bk+zZs2aYxcSkUY7B3jE3Y8ZjB6Tc+z1N73KpXhInHvJGqW5KIc0zCYYi/NEJ1pzALS0RR25XT3jTMX5pJNjUSpAaU6px59w8vmfuVYj2xXnpg60AcU1Sjt2ThbySTu6ovVLS3NKp7qOXKO0NJ+07AVpjVIRkVlRQCqyFNz5X9GERp0rYN2ToH9j8VpblEOaTho7PvpMqEOOZzqdZseOHTWvV0RmzsyeTDTL7i1ASJRD+jLgkoVsl4hIvfg81yE94kslqQv1YYssBXdcDTe8E77+l/DILeXX4kmNgtD5yP/eRRAEVSqYnyAI+MhHPlKXukVkxvqA1wO3xttTgKe5+zUL2ioRkToK4omN5rJJYyggFVkKStch7Vhefi0eshs6vPHLWwnDkFoLw5A3vvGNdalbRI7k7g+7u7n71SXnrnX3J7p7n7sPuPtT3f0HC9lOEZF6cua3DmnlCHupDw3ZFVkKRgeLxx3Lyq9pUiMRqZej5UtWW6O0JJ8U4pzSeN3SMBelE4xPxDmlLUEhn7SzZxyAqbbo2tRYhtx4lNyZiNcoTaQhjNJCyeXXKO0u5pS259co3TkBQNd9+TVKWxhb0xqXi+qa6rJCPqnHWQ5hKm50kvJ80pK91igVETmSAlKRZpedgMmh4uPKHtLeE+EZ74F0D/zzy4ufBEVERESOc4Fm2V30FJCKNLuxwfLHlT2kbX1w/utIBAGf+MQQiWSSWkskEnziE58gkdAfBREREWkMxwjnMTGRJjVqDAWkIs2uNH+0pQdSLVWLJZNJXvva19alCfWsW0RERGQ66iFd/BSQijS7o+WPlshms6xZs4adO3eSrvHSL/WsW0SOI9UyAuzIa4V8SbPyfFIo5JR61piYiEZ0TLZGM3hnWqOc0o6e8ZJ80ug9J5xIluWTQnlOaXGN0mg95rb9Ud5o+84Juu89FB335NcobS3kk2bjNUrzeameLsknzX8Ozu9L1igt5Msa1fNJS382VWiNUhFpFkviKwMze66Z3WJmB83sejPbdJSy68zss2YWmNk7pynzd2Z2r5ntNrPPm1lP/VovMk9Hm2G3wuDg4FGvz0c96xYRERGp5EBAYs6bZtVojKYPSM3sYuCrwOeB84BB4GYzW1Ol7DJgM9DGND8bM3s/8Bbgr4DnAGcB365L40VqoSwgnaaH9Par4Ruvi47vvbb+bRIRERGpN4fQbc6bItLGaPqAFHgXcI27X+Hum4HLiF73qyoLuvsgcJ67/2G1isxsOdGi4m939xvc/ba4nvPM7KI6tV9kfmbSQ/rQD+GuL9LTAuy7ry7N6OnRQAIRERFpJJtXD+lRx81LzTR1QGpmG4FzgK/lz7n7BHAjcHG1e9z9rqNU+Ryi3tOvlZz7GXBguvpEFtzYgeLxdAFpWz/ppHHobd2kpw7XvAnpdJpDhw4pf1REREREyjT7pEbr4/22ivOPEA3fnUt9Y+6+J3/C3d3MtgNr59ZEkTp7/hXwzPfByD5o6axepn2A0J0r78jyZ5sGa/5NVRiGXHnllfzZn/2Zln4RkXKlQ+IqOyO8fIIjAPKTGyUoTnCUi/aT8SRHUy0B6dYcAB09E9G5tiTZsUxUxUQ8uVF+kqMUhNElgnhyoqnu4iRHbYPFCY4Auu89SHtPGwBja1rjcsVJjkonOIKKSY7it8D8RERW8qAwOVG1SY5mOMFRniY6Eol+hcJ5zLKrEbuN0eyfDFfF+0MV50eAvjnWV1nXjOszs7urbcDJc2iLyMyYQWsPLDsFulZVL9PeTxDCq66dIBip/eRDQRDwqle9iiAIal63iIiIyHQCbM6bNEaz95DmP1l3V5zvAXbPsb7KuvL1bZlDfSKLQ/tA8Xh8/8K1Q0RERKRGHJtnD6mC0kZo9oB0e7zfANxecn59ybXZ1tdpZgPuvh/AzJJEw3W/fqyb3b3qcjNxL+kZc2iPSG209xePxw8uXDtEREREZElp9oB0c7w9H7gGwMw6gIuAf5xDfdcBQVzfZ+JzFxD1kH51nm0Vqb0wBA8heYxf9fYBEgYffHoLifEDRy87B4lEgg9+8IPKHxWRo6uWsGXVr1lY0nORPw6iQp4zpuJ80mxLlHSaas3S1h3lgOba4mvjUZJnOJEo5JOGcd5n0BLvW42prmI+KUD7YCvtO8cB6L4nes/sKOSUtjG2rJhPGtUV7cNMRT5pvC/LJ4XynNJq+aRlhaurzCtVTqksVRp6u/g1dUAaTzj0XuAqM/shcDPwbuBwfO4ZwBeBl7j7MdcSdfdHzexq4P1mto0od/STwP+5+x11eyEic3VgG3ziHGjrg67V8Jc/Lk4MUqp9gGTC+Jsnt0BuFLITkG6tWTOSySR/8zd/U7P6RERERGZiPkN2pTGa/l/I3T9HtFbo64EfA63A+e5+iGiuvkkgO4sq/wL4T+BzRL2uNwJ/UMMmi9TO6D7AYfwAjA1WD0YB2vrJBs6GjwyTDeLyNZTNZtmwYQPZ7Gx+1URERETmzoHAE3PeNMtuYzR1D2meu18JXFnl/A3AmmnuqfrJ3d1zwJviTWRxG91XPC5Zg/TQ2BT/e9dOzljdzTkb+qPe0EwnDx8ejgqM7Yfuqr8ac/bwww/XtD4RERGRozPCeQ3Z1XDfRlgSAanIklUWkC4DYNu+EV5x1c959MA4qYTxg7dcxIn97dC5EtgFK06HUMuziMgiMYMuikK+ZP675NAK+aTk4nzOiSTZlui9Lb9GaWvXZFSkNUluPPpI5HHuaTgZ532mS/JJ24prlI4t6wCgfTDKHW3fPgZA170HStYojfb5NUqnuq0snxTinNKSfNLSl2wJjlyjtKDkBzODz8ylOaXKJxWRxaTph+yKLGmjJWuKdixn8+5hXvSpn/LogWgyjlzo3PpQPDz3tT8jlUrBq38Eax5f86akUvr+S0RERBpHQ3aPD/qEKNLMKobsfvDb93FgdKqsyO6haNbJdCZTtxzPdDqt/FERERFpLIdwPkMCFJE2hHpIRZpZxZDdX+44fESRvUPRkLUwDPmv//ovwjCseTPqWbeIiIhINQ4EJOa8KR5tDPWQijSzkb2Fw8mWAfYNTx5RZPfhqIc0CAJe+tKX8uIXv7jm64XWs24RWaJKPylWrFVqTjH3Mv4ezAIgiD72ZCfjdUgz0cVka46WQj5pVCYYj8r4RJJwKs77jD81BZlofVKAbGGN0k4A2gbb6cjnk969H6CYU3pCO+PxGqVT+TVKW62YT5qMX0DyyJdZmCTd8udLe32qfGw+SqeQ1igVkcVEAalIMxveWTjcS1/VIvkhu4WJjPZthkwLLHtMvVsnIiIiUkc2vyG7mmW3IdRVIdKs3GFoV+HhI7neqsX25gPS26+K9p88H7711nq3TkRERKTuQhJz3qQx9JMWaVbjByEoDtHdOt5dON4w0F443js8SRg6iY5lvPPCDAkjWoe0hhKJBO985zs1XFdEREQaJppl1+a8KYe0MTRkV6RZmcFFfwdDO2F0kPuHiklJ527o56H9UY5TLnQGRydZ0bWCd13UGhUYO1DTpiSTSd71rnfVtE4RkYKjfGq00iTM/Lxq+aWWc9H7YjCVIEjn80njtUo7oxnJg9YkYX6N0slEvDfCdFxVvEZprmSN0vFlUT5p+754jdId0VJbXXcP0tETfSE4dkKcV7osyVR3MZ8UKNQdpryYT5pfozSfJ2tUzyfNv+DKn8kMc0qVTyoijabuCpFm1dYHF70Nnvcx+OMv8HC89ijAGWu66cgUA9Q9hyfJprvZ9G8jZAOveQ9pNptl06ZNWvpFREREGip0m/MmjaGAVGSJeDjuEQVYP9DOyp7WwuM9QxPQPsA9++Lug+wYZMcrq5iXe+65p6b1iYiIiBydEXpizpsmNWoMBaQiS0A2CNlxqBhgruvvYFV3MSDdPTQB7f3lN9V42K6IiIhII0XrkNqcN+WQNoYCUpElYOehcYIwels1gxP721jZXdFDmmopv6nGw3ZFRERERCppUiORZvXzT8PEIehaw242FU6v7m6lJZU8IiBNpVJMXb6J1NAj0ckaBqSpVIqpqSlSKb3liEiDVHZtOIXRdxbEB4VJjgxy8cRCU9F39UE6yrNPtAakOqL89zCedCgYT2H5CY6monOen4goA7m43FRX9J43VjLJUfuOKH2i8+7B6FxPO2Nr44mOlkXPme2K7s+1GmEmrjcVv6CSSY7KJjgien1eOcSw2iRHmuBIlhDlgi5+6iEVaVa3fxa+/8/wjdcw8fCthdPr4iVfVnUXe0R3D03i7ly3teQzSw0DUnfnuuuuw12DX0Tqzcw2mdk3zMzN7BUV11JmdrmZPWhmj5jZx80ss1BtFRGpJ3fmlUOqjy2NoYBUpFkN7SwcPjjRVThe398BwKrSSY0OTxAEAS/85N0E+R6D8YM1a0oQBLzwhS8kCIJjFxaROTOzxwO3A9NNaf2fwO8Dfwi8LD7+XGNaJyLSeCE2500aQwGpSDPKTsB4cVKi+0aLAWm+h3RF5aRGlZRDKnI82gz8BvDmygtmdiZRIPoad/+5u98Ul3uxmZ3U2GaKiIhElNAl0oyGd5U9/PVQKxAFnesLQ3aLAenh8SwT2bj38hnvge4VsPqshjRVRGrH3ceB+81sfZXLLwKGgRtKzn2LKKPwWcAV9W/hAptm+J05xYTJfH5pnFMaZhOF/E1rid4nk51ZwpY413QiSuoM45zSRMpI5PM+48yIXFucU9qdYmxZ9AVhx97ovbht+yhdv9wLQHtfNIJlbG28X5Yk213MJwXKc0pL8kkhGp5Ymk8aveSSXp5q+aQlZav+XEooFU+OP0Ywr/+4+k/fCApIRZpRSUDqHcvZdrA4ei8/ZHd5VwtmxUkx9o1M8Za3vIXE+a+BZJJaSiQSUd0JDcoQWUDrgUfdPZc/4e6HzWwIWDuTCszs7mkunVyD9omI1JRDvJ7o3O+X+lNAKtKMSvJHcx2rGNtfzN3MD9lNJxMMdLQwODIJwL6RLB/60Ifq0pxkMlm3ukVkxlYBh6qcHwH6GtwWEZGG0Cy7i5+6K0SaUUkP6WhmeeG4tz1NT1u68Hh5V3Gm3b2Hxzj33HPJ5QqdJzWTy+XqVreIzNgg0LJE0vgAACAASURBVF3lfA+weyYVuPumahuwtZYNFRGRpUM9pCLNaKgYkB5IFgPS9f3tZcUGOoqrPQyOTnLbbbfVZWkWd69b3SIyY9uBi80s6e4BgJkNAB3xtfkxpk+3Wqy/+n7kcSEHM9+rEhrkoouejdchTTmWiaYkT3REX7R5SU5pIZ80GZVPpKP7w4wRxLmg2e54jdLl3bTvjVIp2rePAND1yz3R495OxuN80tEV8RqlJTmlVdcoLcknLXs9NV6jNE+dT7LYabbcxU8BqUgzGi4O2d3lxZF46wY6yor1lwSkh0anooPv/gNMHYbJIfij/6pvO0Wkkb4B/C1wIfD9+NxziJaIuXahGiUiUi9RDuncA9LF+l1as1FAKtKMDj5UOHwoWwxIK3tISwPSA/mA9JZ/g/hbfabGIFN+j4gcn9z9p2b2feCTZvYSop7RDwCfdvcZDdkVETm+2LwmNdIsu42hHFKRZjQ1Vjj85fiywnF+QqO80oD04ETIwX17SJW+K9RoLdJUKsXBgwdJpfQdmMgCez7wU+A64P8B/wH81YK2SEREljR9OhRpRq/7OUyOwIFt3PzpRwqnj9ZDenBkklvvvIunZbqx7HB0cmw/9J447+a4O7feeitPe9rTMNO3jSL15u4PU+WrfXcfAS5teIOO9mu/2MbEefnejCiPFLB4jVLPOWSjb+/CVJRLSpxTau05PBPnk8a5pD6ZL1tcRzRoiXNB24ypnjifdEUPAB17ovSKtu0jdP4q6rxu7+2MyqyN9yuSTHUX6wAI0xDG+aqWzyXN720Oa5TO4O1aa5XKoubznGV3sb0/NSn1kIo0q5ZOhvtOZ9dY8Y14fUUOadmkRiMTPOMZzyBoLVn9YfxATZoSBEFUdxAcu7CIiIhIDTjRpEZz3RSPNoZ6SEWa2MP7i0N3W1IJVpQs8wLQV5ZDGq1HSns/DMe9qmO1CUhFREREFoLWIV381EMq0sQeOVAMSNf1t5NIlL8pD5TNspuNDtoGigVqlEMqIiIiIlLNkghIzey5ZnaLmR00s+vNbNNRyp5nZjeZ2SEz+6GZXVhx/bfNzKtsLdPVKdJQBx+CiSGgvId0/cCRs+WW5pBOhc6f/8WrSXTUPiBNJBK85jWvIZFYEm85IjIbdpRtMfCSLYw2CwzLxttEMtpGU9hoCh9LFcpbW4C1BYSdOcLOHEFHQNDq0dYWbdlOZ6oHpnpgbKUxttI4+Jg0Bx+TZvA3exk9YyWjZ6yEMIQwpPNXu+j81S6W3X6Ivi1Z+rZkad/ttO92MkOQGjNSY0ZiMt6yRFsAFkZb4XXkNydK/izdKl/7DMcumhc3kcUgdJvzViuzjEXWmdlnzSwws3fWrBGLWNN/OjSzi4GvAp8HzgMGgZvNbE2Vsr9JtDbbzcC5wG3At83s7JJiG4F7gN7Szd0n6/k6RGbsv18K7z8RPnQKmYdvLJxe199xRNHe9kxhkgtLJHnHey4n2bW8WKBGQ3aTySRXXHEFyWSyJvWJiIiIHIsz92A0dCuf+GuOZhmLLAM2A20sgTgtbym80HcB17j7Fe6+GbiM6HW/qkrZvwd+6e7/4O5bgDcBDwJ/XVLmJGCLux8u3er7EkRmyB0ObI2OR/exZThduFSthzSZMHrbojIeBvzBc36PXKa7WKBGPaS5XI6LLrqIXC5Xk/pEREREZmIR9JC+ixnGIu4+CJzn7n9Yqyc/HjR1QGpmG4FzgK/lz7n7BHAjcHFF2TTwgoqyDnynouxG4IG6NVpkPoZ3QbY4TPfGwa7C8WNXdVW7ozhs153bb/kx3t5fvFijgNTduemmm4h+pURERESa32xikZLrdzWkcYtIs8+yuz7eb6s4/whRl3mpE4DkNGWXmVlr/B/oJOD3zexlwMPA1e5+xUwaY2Z3T3Pp5JncL3JM+7cWDoO2Zew+WMwRPWNNd7U76O/IsHXfaPFE2wAkM9A+AG29dWuqiMgxLeD6paU5kEd0lJTkVBYuxWuVEhhk4/VKU3Gh/L41JIyPPV7H1CYNj7MZEvGglrB0jdLu6OTYimhJrvY90ZeLbY8O03HXzui4Nzo3vq6L0ZXRR7vCGqXtxTVK8+3JP9+81igtXKtyruK2/HOILIRw/sNuT57uM7y7T5sLGptNLLJkNXtAuireH6o4PwL0zaIsRLmiu4G/BKaAFUQ9qh81s9Pc/a9q0mKR+ThQDEgPt6+Hg9Hxuv52ulvTVW8pndgIgNOeA7+xt+TTiYiIiMjxx5nfsi81+N5rNrHIktXsAelgvK/sGuohCi5nWjbMX3f3X8fn7wd+ZGYOvNnM3u/uO47WmOm+RYm/dTnjaPeKzMj+4mjyHYlirvymaXpHAfo74gmiE0n+9uofkMpkah6MplIptm/fTirV7G85IiIismj4PNchjSLSrTPoCZ3ObGKRJaupc0iB7fF+Q8X59SXX8nYQ/berVnaXu083G8vNRANWVs65lSK1su/+wuHmbHG23KMHpPmeU+fhhx+qS56nu/PQQ/WpW0RERGQ6Czyp0WxikSWr2QPSzfH2/PwJM+sALgKuKS3o7uPA9RVlE8CzKstWOAeYJFoKRmThuMPOOwoPbx4u7SHtmfa2Qg9pGPLf/3gZQRDUvGlBEHDBBRfUpW4RERGRRWrGschS1tTj59zdzey9wFVm9kOi3sx3A4fjc88Avgi8xN2/DXwA+K6Z/UN8/q+BZcDHAczsNKL/QDcBo0T/ud4G/F084ZHIwjm8HUb3FR7+cHRt4fhoPaQDlTmkEC3APrYfhndC73pNbiQii0+dJzzKd46Yl0/OM125wiRHAYUJjiyIJzfKxpMJpRyS8XFLEJ8zfCrqH/CpeAKikkmOwkz55ESlkxx15Cc4eiRafa7jrh20xxMcja2L3vfH4kmOJnuMoC2qI8hPrl4yyVHpBEcQZ24UXpuVv9b8D6bkdRfPH/kzKi1eSZMdST3l1yGdz/3zev7ZxyJLUrP3kOLunyNa5+f1wI+BVuB8dz9ElBs6CWTjst8HXgg8D7gVOB240N3ziXm9wJ8Q/Wf6dXz8Enf/cMNekMh0SnpHxzvWcjBOV1jW2cKK7tZpb+urFpB+6gK4/BT496fAwz+peVNFREREGsHd5rzV5vlnHossVU3dQ5rn7lcCV1Y5fwOwpuLcN4FvTlPPLcBT6tFGkXnbUQxId7SfBvESokfrHYWSHlIzes96OmYGHcuKBYZ3zbtpZsYrXvGKqG4RERGRBqnBsi/zNptYpOTawje8QZZEQCqyJDzptXDiE2HHHXzv/s7C6WMFpPllXyyRpOeZbyDASHWtLhYYnv8kcKlUis9+9rPzrkdEREREmosCUpFm0bkCTruY3GOexRU/vB6IJoY+e93Rl7nKB6QeBuy75t3s+5sLWdu1qligBj2kuVyO5z//+XzjG9/Q0i8iUn/T9SvMIbe0Wh9FaT5ktdxIrziwkpzSfK5mIZc05XhLCECQjsvFuaQ+ZWX5pABhuphTOtWTzycdAKB9T3cxn/TOR6JzfdGXkuPrexmN80mnesrzUsM0hOliPinEOaVW/jMo/VEckVtXLad0Bv07pT+/pdMfJI2yCNYhlRlo+hxSkaXmru2HGZqIgtF00njSyQNHLd+aTtKeSYI749tuY3BkAmrcQ+ru/N///Z+WfREREZGGWugcUjk2dVWINJmb7i/OtPuE9X10thz713ygM8Po+CQA+0emoKyHVOs2i4iIyHHI59dDqi7SxlAPqUgzmBwpHN5cEpBeeOqKGd2+sqs4C++eoYmKgHT+Q3ZFRERERKpRD6lIM/j070AixcSGp7Fn+6lANEz3wlOXz+j2VT2tkEiy5pX/zr7RXHlAOjYIuSlIVVkeZoZSqRT333+/8kdFZGHVaO3S0g6Xajmk0665SbxOKRTXKs0ZXpJPCuCZaB+knER+jdKslZUJ0xDk1yiN1xed7MkwtiKaJb1jTw8ArQ8dBKDt9odo64/OjW+I1pYeW5mO77NiPmn8Vh+mKLSLZP6FFV9/4TXmz1Hlh6J8Ullw8x16q/+IjaBPhyLHuwMPwuD9ALTuvYckHwFgeVcLp6/umlEVq+J1Sj07ya7DE9C5rrzAyB7oPXFezRwdHZ3X/SIiIiKzoUmNjg8asityvNtyfeFwd2Y92z0apvuUxyyf8bqfq3paIQzY9dnXs/vgKKRboa1kdt6RPfNqYi6X4+yzzyaXy82rHhEREZHZcJ/7Jo2hgFTkeLflu4XDayfOLBw//fSZ5Y8CrOwu5pDuHpqIDspm2lUeqYiIiIjUnobsihzPpsbgoR8WHn4vdxYAyzozPO30lTOuZnVPMSDdmw9If+vVkB2L8klPOKc27RURWazmmF96rHVKpz2fT7O08nVKATxRzN0M4zVKLRVfi3NJEwkr5pzGn+bCTDEXdKonSgZtWRHNJdCxq5eWhw8A0Hb7g9G+L8opndjYz2g+n7Q3v0ZpVB9E+aRQklOaoNClke9FKgzIsWnWKK38mRxjAE/lz1A5pTJXofJAFz0FpCLHs4d+CLkogByljVvDxwLwoiecSCY18wEQK7tbwYz2xz6Z/WNZJnMBLU94Rc2aaWa86EUvmvEQYhEREZFa0Hqii58CUpHj2b3/Wzi8KTiTXPwr/cdPnN0ERCu7W7FEkuUv+DsA9g5NcmJ/e82amUql+PKXv1yz+kRERESORZMaHR+UQypyvJo4DL/+auHhd4JoWO0Fpyxj/UDHrKrKpBL0tybZ9/X34WFQzCOtkVwuxyWXXKJJjURERESkjHpIRY5Xv/xSlOMJHPROvh0+EYBXnL9hTtWt7Gnhzs0/Bnd2H65tQOrufOUrX+ELX/hCTesVEWmIWeaXHq1DpjI3smztzTA+F+eUEgCJ+Di/Vml+jdKkY7l8zmk+19NJRKmghOl8LmjU9zDZ00LLqmhugY5d/QC0PrQ/2t+6ldaBaG3SyfXRtdHVaSZ7E3EdcXPyOaXpinzSkr17eT4pzGCN0sK1KucqbiulkZhyTPOdLVddpA2hgFTkeOQOt11VePiV4ClMkuGc9X2zml231Kqukpl2D0/A8B746cdheDdMjcIff3HezRYRERFpJOWQLn4KSEWOR0M7YHhn4eEXg6cC8PaLT5/zxEEreloKx7uHJiBIw08+XiyQm4RUS5U7ReR4YmYJYAJIV1x6prt/ZwGaJCJSJzbPgFTBbCMoIBU5HvWs5cGX38anPvmvnBpuZZuv4Tm/sZqz1/XNucoT+jpZfenHIJGMAtLOU8oLDO+Cvg1zqjuVSnHnnXeSSuktR2QRWEsUjJ4EHCg5P7owzRERkaVMnw5FjkOTuYDXffle7p46Hzif7tYUf/fs0+dV58qeViwd9YDuOTwBqQx0LIfRfVGBoZ1zDkgBOjpmN9GSiNTNScBhd39woRsiIlJv85llVxpDAanIcSYInbd8+ZfcvXOocO6DLzqLE3rb5lXv8vYUOz/9F6x7y9fZlZ/UqPuEYkB6eMec687lcpx66qlMTU2RTleOEhSRBtsIPLDQjWgaNZjwKD9hzxET93hJHfmJjvITBSUcT0cXw3hCIcsVJzjKTzqUn9woSJdPcATQumoVAB07+2l5aBCAllu3RNcG+pjYuAyIJjgCipMcdRQnOPL4k2SYKpnkqGSCI4gnOao2wVHliy59/TOIISp/Xoo7pJIzv0mNNKdRYyggFTmO+KFHeMf3D/PNu4r5oy9/0nqe+bhV8657ZU9xUqO9wxOEoZPoWQu7fhGdHNo+7+cQkUXhJOBxZrYPGASuA/7J3YePdaOZ3T3NpZNr2D4RkZrRpEaLn9YhFTlOTO2+l6mPnsvj7ngnLUwB8NuPWcbbL57fUN28VSUBaTZwDoxNRT2kefPoIRWRReVK4CzgWcCngEuBG8xsfsMsRERE5kA9pCLHgcGDhxj7jz9mnU/wktT3OMl2cfnqy/n3lz2BllSyJs/R3Zqm45RzCwvI7To0wbKekoB0aO4BqZnx7Gc/e84zAItI7bj7QyUPbzOzB4BrgRcAR13fyd03VTsf95yeUas2iojUhM+zh1RjdhtCAanIInfzvdtJfOllXFAy/8jNy17MZy57Iu2Z2v0Kp9Npnvyay9m8Jxq199D+Uc4s6yGd+5DdVCrFddddN98mikh93BzvVy9oKxaz2XyenWkeZGnq5Ezq9/K9hVbM1cznZ6bB4txRz0UnE/nHSfB8PmkmKl+aU9qyeg0AnTsHAMhs20fmZ/cB0LqsPyp30nIARldnmOiL80nbieu0QhvC+DnJf1+aqMgnheLPxu3I129+ZCAwy5xSjdKUPMWUi5+G7IosUnuHJnjzF37G+BdewQV+R+H8jf2X8IbXvp6ettpODpTL5Xjoqx/CwwCAbftGoWdtscA8ekhzuRyXXnopuVxuvs0Ukdo7J97fuaCtEBGpA3eb8yaNoYBUZJE5PJ7lX767mRdf/lVect9r+L3kbYVrD614Ohe+9pM1G6Zbyt25/0fXFr7GfnBwpDyHdGw/ZMfnXPfVV1+Nz2eqOxGZNzNLmdk7zOwJZrbazJ4PXA18091/sNDtExGRpUdDdkUWiUf2j3H1Tx/iS7c+wgXZn/Dl9GdZbocL14c3/C4bXvZFSDZm2ZRtg6PQdSYkW6BzRRScTg5DWvOeiBzH+oDfBF4N9ANbiSY2unwhGyUiUjf6LnzRU0AqsoAOjk5x3a928fU7d3DbwwdZb7v5WOpqfidzV1m58OyX03Xx5Q0LRiEasuuJJPb2XZCofY+siDSeu+8Dfn+h23HcmU0+47FG+eXrmuX6pVWFFVWVrvcZr1EaxG/fiYQV1ia1VL5MVDjMGLn26HgynnG9ddVaOnZE65BmHtwLQPqn9wDQv2yAqZNXADCyJlrTtJBT2lGeTwpxTmn+z0i+fSW5pJU/irK1SvOJofNco7TsOWVJ0dDbxU8BqUgDuTtb9o5w8/37uHnLID/dOkg2KP7VdIzfTvyq+DjZgj3rAyTOuazubUsmk3z7hht51XeHABiZzLFvZJIVXa3HuHNmdf/oRz8imVRgKyIiIo3hFCfUmuv9Un8KSEXqaHwq4O6dh7lr+2HuevQQP3twP3uGJmljgickttAZrucg3YXy6WUn8WDXc3nMzm/Axgux5/wrDDRmvXkz43GnncLAj+/mwFgWiHpJaxGQmhkbNmzQsi8iIiIiUmZJBKRm9lzg7cBjgduAN7j73dOUPQ/4ANGi4b8C3uHuN1WU+Tvg5US5ONcDr3P3w5V1ydIQhs7gyCTbD43z6IExHtg7wpY9Izywb4QHB0fxMGCd7eGx9iiXJrbyW5l7OdMeJG0B78hexnfan8PzzlrDCx5/Ao87oRs7tAF2vxhOu7hkfvz6y+VyrF27lhd+/KaygPS8kwZqVvfU1BTpdOOGHYuIiMhSNt/ZcvVFeiM0fUBqZhcDXwXeANwAvAu42czOdPedFWV/E/g+8C/AnwOvAb5tZue7+51xmfcDrwT+EDgEfAb4NvCkhrwgaQh3ZyIbMjyRZf/oFPtHptg/OlnY7xueZMehcXYcHGfn4QmmcmHh3j9Kfp+zbRfPsf2sS+3hMbaDNpuq+jxvOfE+3vXKD5NKlkx43bch2hbIxmXt3LE9Wov0wcERCEMYG4zWIQ2ysO63FqxtIiKLwizzGcvMJHd0rvml1a7Ff17CjGNBXH28Rmk+pzRMQlhYozTa5zqMyd5oErvWNesA6NgR5Y0mtu0m+ZPoe/3+FVGe6dRJKwEYPaGFib6ojmxHMUc1zOeTpuI81vwaqonyfNKSXfySKn4Y1dYoLVyb5nzJraWUWrgEOPP7h9aY3YZo+oCUKAC9xt2vADCzy4BdwKvia6X+Hvilu/9DXPZNwO8Bfw1cambLgdcDb3L3G+IyrwJ+amYXufuNdX81S5S7EzrkwpAgdHKhEwTRPhuETGQDJnNhtMXHZedyARPZkMlsltzkBLnsBGOTOQZzbQxP5BiezDE8kSM1sY+1Ew+QmBqljXHamaCDSTpsnA4m6GKcE22UPhumj2FenX0jU762rK1/mvwWpyZmsGZnSze9vQPVZ15YQCct7wT2APFapPd9E7708ujiijPgNT9duMaJiIiIzIJWnFv8mjogNbONRAt+F6azd/cJM7sRuJiSgNTM0sALiIb25su6mX0HeGl86jlAG/C1kqf5GXAgru/GOryMo7rul7vYsn0vZ+3+CuDxOo8e/fZ5xeN4v63zbB7sOCv+BXXCEE4euZWNI784omy1vTt8vf9PyVoG9+hx6M6LD/47qTBb/V4cy7fHnV+lNvGd1FPLAsyzc3dxce4GEoSYByQ8wDwkQUjCA5KEJC16nCLg9dm/YrsvL/t5XJ1+PxtsN0kLo/KEpMmRIUuGHOn818PA94Kz+bPs35Td/4zEL/lk5l9hhqNKl9shtsQBaXdrihP62slNnQCjlQGpQf/GKKBbfz6sfzKsOnNRzV5rZlx44YWctKyzcG7b4Ch0lwTch2cQaB+lbuWQzpM7hDnwcJrNyx+39kK6Igd4aCdMjZaVcw8JgjC6PX4fcXc8mSFYdlp0TFw8N05i7z1xmfw9YcnbTlh2Lde9gVznysL7hAOpg1tJDu+Kvnh2J/T4/tJ6iF8PxtDaCwtr2DrQ355hw7KOhv7oRUTkOKWAdNFr6oAUWB/vt1WcfwQ4r+LcCUSTklcru8zMWuP6xtx9T/5iHLRuB9ZyDGZWNW8VmPOsNd+9Zzc//MV93NH6sRnfc2f2Er4Q9JWde0vqJn439Y0Z1/GGPc9ijPIPule0fJN2m5zR/ftHp9icO7fs3G8nH+WZ6R8VT5RMX19NG0c+1xrbz/rE3hm1IUP2iHMjzG6Nzb+/aAXp33gKa3pb6WqNo9hb/gD2ngY9J0bb8sfC8tMg0z6ruhstlUpx44038sDe4cK5Rw6Mke08tRifTx6GiSFo7a5ax7HqPq6NHYBDD8PE4WjLjkdbbqJkPwbZCcLsOGNPeQdj6T7GpwLGswFjUwEnfu91ZEa240E2Gv4c5rAwh3mORMk+4Tm2dj2Bq098L9kgZDIIyeZCHjvyM9689+9n3OQ3p9/Bj+03CdwJ4y9+rgjfwwX2i7JyRvU/BtvCVTx16sNl5zbaLn7Q8uYZt+Ed2cv4z+B3y869O/UZXpa6YUb3T3mSUyc/X3buhWefwL/+4eNn3AYRERFZvJo9IF0V7w9VnB8hmpBopmUBeuMyldenq68hEmaz/uKn2h1H5GjMqY7Z3H+kHLPrLUxSzNtMJYyWVGJWPY7re1K86exT6WxJ0dUabavGOpn80UbIdGAtnSRbu0i2dkKmAzJd0b6tD9oHoL2fx61+PHR1lVd83qtn9ToWiyAIeP3rX8/lH/4IyYQRhE4QOg9PdnBKIg1hHMAP7Zh1QJqv+2Mf+9jiWfpl7ADs3wrDO2F4d8m2K5pQ6omvxN0ZnswxODxJ8uefYf2t755R1Qng+T87i61+Qtn5GzJ3cEpiZ/WbKuw/cJD/2fNo2bnxxBBkZnQ7AAdGJ9kdTpSdm0rDTH/VZv/uUvs6qr1X5HtLRRaFav8d5zoYpBb5pUf59fD4d98TcR5nPqfUimuUhvEnwzBthXzSfC7oRF8+p3Q9HTuinNHE1l3R/se/BKBvxTKyJ68GYGRta3yfkYvrCFrivNJ0vk1e0q7iayy83Ir80qprlJa+/sK16X8O090OyittRlqHdPFr9oB0MN5XfnruAXbPomwYXx+scj1fZsuxGuPum6qdj3tOzzjW/dX81sZ+OtnIr3c8hWh16fyMAIl85fGbt0V/cDDWD5zLX/SfhGEk4lvWHXgSvz4YFOuw8nssfhy9wRtvecwmwlQrBnEdxoNbXkIizEZlC+VL7zUSCcMswan9m/j0ieeQShjJhJFKGF2HetixswtLpLBkikQiiSWSJJIpEsniufzjr5zyuyTb+0gnrTgp0CN9US9VIhUFp5aEZBpSLZBsgVSmsF+XauX16coe0dXwxF+wFIVhyL/927/xkY98hA0D7WzdNwrAvbtHOaV7TdQ7CNGw3RWnz7nuBQlIs+Nw+9Ww6xcwuAX2PwAT1b5bity8t4X/70ensv3gGBPZ6IuPFyX3cvksJghu5ciJrLKz+NKldHh5XjjLT7mJki9t8nIkmfQUjhGSwIEwnvUk/ohaOK42YiBHgkHvrlK+GHpGx9HjcVowi748M6K3hsOJbrb78sIHy8IHTKPwfpWvP7Ak/R2Zwr0Ana3N/qdLRERqRt9hLnrN/ld9e7zfANxecn59ybW8HUT/ZTdUnF8P7HL3XDw0t9PMBtx9P4CZJYmG6369tk2fmT964jp44jrgmzO+58yqZ08DZt6zVzWyPv9fZ3x/dRfE2zxoBtia2LSmpxCQ3rNriOf2rC0GpEOVvzqLjPuRy+UkUnDDO6NhtTOQO7ybB7IjZecOeSeHvIMhb2eYdsZpYdwzTJBhkkzhOL/tj4M2M2hLJ2lLJ7kq+TJ6k5MkU2kSqQzJVAZLprFkOvqiJZU/zhC2dPK69rWkkwnSKSOTTNBqp/D18GkkEkmSiQSJZBKzaJ9MJknEx4lEkmQywZ8nM/xFMkkyAclEgqQZicQFPJgwkhZ9GZRMGAkr7hOF756M1QZ3lASSZhbteVkUYMbl8t9BFb/kKt5zuVkxib/g2bP6J71jVqVFRESK1EO6+NUlIDWzFNFkQicCK4F2YG+83eXuc5sZZfY2x9vzgWvitnUAFwH/WFrQ3cfN7Pq47L/EZRPAs/L3AtcBQVzmM/G5C4h6SL9ax9ch0lBnrOnmf++Khpbes3MIekqGns5xYqO6codHfw53fh4euAFecwu09eLu3L1ziO/es4eLbSOP5d6y24a8jR2+nL3eyx7vYw997PVeHqgYaptMGHd1nM+fdP4Oy7paWNaZobctQ3dbip62NN2taXrb0nS3puhuS9PVmuKlmRRtmSQtqUTJZE7luZTSIVCxbQAAIABJREFUHBbR3zwREZF5WYi/aTUNSM3s6cDrgKcCHUyT/mNm9wBfAq5w9wO1bEPZE0UTDr0XuMrMfgjcDLwbOByfewbwReAl7v5t4APAd83sH+Lzfw0sAz4e1/eomV0NvN/MthHljn4S+D9315f4clxLJpN897vfJZlMcsbq4sj0u3cOwbqSAG1o9u9DpXXXVBjA3V+DH34Y9hbnDHvoZ//LF8bO5Vu/3sWjB8YBGEqey4m2gfv8RLaFq3nQV3OALsBIJ411/e2s62/nxP52ntbfziv62jmxv41V3a30tWdIJPQNq5RbbH/zZBGpHCJYi7ePqv+7ZlmmIg+1NKfUguhkYX3QpOMl+aRQzP/MdiSZ6Ism6ms9YSMAHdujvFF/YCf2k7sA6F0WrVGae8waRtdGKQCFNUo7i+ueFvJJ4zVKPUlh/dRC0+O257OAopdT5QXnE0PnuFZsaV6pOtaawDHyqmd0/xKxkH/TahKQmtkZwH8QzVz7M+DDwE3Aw0R5l+PAALAC+E3gd4A3Am81s38GPuTuRyY71YC7fy5e0uUNwPuAnwDnu/shMwuBSYimW3X375vZC4l6T99ENMz3Qnd/oKTKvyAKaD9H9N/0urisyHHNzDj33HMxM04vCUgHRyYZbllJYeqmw7Mfsltad81suwm+9VbYd98Rl+783n/z/7IDZec+GzwTgJZUgrM39nLJib2csbqb01Z1c9LyDtLJxBH1iFSzmP/miYhIJX2zcDSL4W9arXpI7wCuBc45Sk/h7nj7JfBZM2sH/pTiup8fqFFbjuDuVwJXVjl/A7Cm4tw3OUpCprvniAJQBaHSVHK5HH19fUxNTbG8q4UVXS3sHY6W1nko21vMPZ5DD2lp3en0LGYGqmbiMHzrb+GuLx5x6SfBGfxPcBE/CMuXBHnC+j6edvoKfmtjP2ee0EsmpeBT5mVR/80TEZESS6iXc44W/G9arQLSVwFfiIO1GXH3MeATZvafRDPqiMgismlNN3s37wPgntHuYkB6eEf1iYMaYd9m+O8/iWbJjYUY3wyexMdzL+CB/5+9O49ztKryP/45SW1dVV3V1Qv0AjbdzaI0gigyCo6Iyoiioo6Iy6DyY5ifo/5GRx1f48KIo+CMC8Ios7iMwqgjjA5u4waOsstOs8m+Nb1AL7V07ZXk/P64T5In6VRVKpVKUtXf9+sVk3qe+9zcpLEqJ/eecz2/HfCxBy3llCNX8aqNK1nZ3VaqN5FK/am7/0/2BzP7mLt/bqoL9DdPREQaVN3juGoFpN8ChoEfzPRCd+8Dfl+lcYhIlRy+uovfRgHpTf3dnH7yP0DXmnCrh8evh++9Bcbz1W83Zdbz8YmzuNdDDlNz0jjtmAM587iDOGT/xZP1JDIr8WA0cp6Z9br7v5Zqb2Gt+jvc/Tv6myciUmOaIZ1O3eO4agWksRRzEZmPzIxjjjkml+d5+Kru3Lk7t6fgz/6yan1XZGIE0hO5Hy9KvYmLUm/K7aH55hccwF+fdChrluy9d6bIHPs24ZvifncvWEtuZqcDnwIOA75Th7FJIygqJlQ1Myl0VKq4UfxQMjqYzWhIG5nslubRuXiRo1yBo85QGSlb5GjRmvW5Akc8HFI87IZNdC8Pef0dh4SVLEMHhJUro0sTTHQUFk3KNMcKHGXHE7svKHAUf42UKHRkPnlAMs2/h5V6n/Rpd/7RP9p06h7HLfR9SEWkTE1NTdxyyy25nw9fnS9s9NiuIYbGUnS0VvYro7jvihzySnae+h2a//v/8JHxs7kycwwA61d08Pk/PZJjDlo6u/5FKncWkCTk1Qy4+/+Y2ZuAcwnbNu8Bzqvj+ERE9lmuGdKGp8oeIgJAOp3mb/7mb0in0wCsXdpOR0v45tsd7t8+ULW+K7F59zCn/ryJF49elAtG33j0Gn76/pcoGJWaMrPW+M/u7sC7gcuA/zKzTYSlTwcAfw+sdfe/K+5HREREFJCKSCSTyfDFL36RTCZU7k4kCrd/uW9r5QFpcd8ztWd0gj+/5Fa29I0wTFjm9ZE/OZQL3nJUxbO2IrMwYGa3mdm/mdmfm9lRhL+n7wJ+CDwX+AJwkLt/2t376zlYEZF9ms/iJjVRzU9yJ5jZjEpZuvt/VPH5RaTKDl/dxa1P9AIw/uBvYMsNYduX1c+Hk8+f2ye//3/gsWtJv+JcPvD9u3ng6T25U5963eGcefy6uX1+kcn9hrAX29HA2YSPLaPAHYTy+U9G54fqNUBZeMpOgyuRQrnX8Sk+aGefx83z1ybDQYsWuViTF+STAgU5pSNLOwBoO/BgADo3r8nnk964CSCXU9p58BqGDgi5/yNLE1EfVpBPCuDJ7L0X5JNCbEmm7Z0IV5BTWpwUGv+xzPd3ry6UntjY3Gb3j7Tv/APXNY6rZkD6l9GtHEb4NaCAVKSBHR6bIR3Z8Rg8FhVgszleXJEah19/EnY/yq57f8dDu/4C2B+Av3zZBgWjUlfu/hoAM1sDHAO8IHZ/XNTsWcDuaPnuHcAd7v7t2o9WRGTfVqo4leylrnFctQLSc6vUj4jUSTKZ5IorriCZTOaOxQsb3dnfEcq2APQ/Neu+p3Tbt2D3owAs23M/rYTqun9y+P78zZ8cNqPnFpkr7r4F2AL8OHvMzA4kBKbxIPUlhD/e3679KEVERKZ0br0HUJWA1N3/Pv5zOZuEi0hjMTNOOeWUgq1ZDt1/McmEkc44T6SW5gPSga2QyUCivJnSUn1ParQfrv7H3I+XpU/kYT+A/Ra38oXTjiKR2GeWz8g85O6bgc3Aj7LHzOxZhMBURERqTTOkU2qEOG6uqoGUvUn4HD2/iMxQKpWipaWF8fFxmptD0k5bc5KDV3TywNN72OaxSraZCRjaAYv3r7jvSd36LRjeBcCQt/Ll1JsB+MwbjqB70TTXitSAmbW7+3C57d39SUJeqezrnLnZ7W+KNYk+1feGpcaSzSFNeP58tv8on85Sho2Hx4loe+hEKtyn24zUonBuvCt8izmyrIO2tYcA0PnUgaGPR7aFC26+l67HQj5p+/qwf+nQAW2M9uTzSQHSUW3rTLMV5pNCyT1Ks2O32Hu+1x6lBa+t9Pswnfhbv++kG84z+oeZqZrHcXOVCPZtwibhbys+EW0Sfi9wyRw9t4hUUXbZ7iDtjCXa8ycGt1f/yTKZsFw38q30yexgCa8+YiWv2riy+s8nUpntZvbPUXVdERFpZKqyO1PfpsZx3FwFpGcB3yVsEn4KgJm9yczuAr4HrEabhIvMC/HCRrsSsVnSPXMQkD72O+h9HIC0G99LvYKEwUdPfnb1n0ukcucALwVuN7ObzOxMM1tU70GJiIhUQc3juKoEpNokXGRhOPzww/c+FitstCXVnT+xZ9us+97Lrf+ee/jbzPPYynJed9Rq1i3vmNFzicwld7/I3Y8gBKX3A18FtpnZV8zsufUdnYiIFNAM6ZQaIY6rVg7pgJndA9wK3BLd7iFsEm7AOwibhJ/n7gNVek4RqaLm5mbuvffevY7HZ0i3pLt5Ybaw0QxmSCfru8DANrj/57kfv5t+JWbw/hMPLvt5RGrJ3a8HrjezvwLeSdiT9L1mdhPwr8Dl7j5azzHKPqw4bc7yxzyb+Gjxc0X5mEkn0Rw2Hk1G94vaQsJo96JRElH73cNhccBgf7j3oSYSo6GTZJRnOtEFY9Eeo0MrQ+pH68HrAejcdiDJR0PdgKY/PA7Akm3djK8NeaVDq8Jn5dEloa9Uh5FuCUPM7oHqTWEsnmDvPUrjb0FRfqlb9n9KNCoVjEyTijhZKq9SGOtotoHlvhGU1j2Oq9aS3d8Aawh/jL9G2Bh8ALgW6EWbhIs0vHQ6zbnnnks6nS443tPRworF4QPB096TPzGDGdLJ+i5w34/Aw/mnfDlXZ47iVYev5JD9F5f/IkTqwN373f0r7n4kYYuXB4B/Braa2UVmVsbyABERmRNuld/2DXWP46oSkLr7a9x9JXAg8EbCuuKrgUOA9xM2CH8FYZPwa6I/0O+uxnOLSHVkMhk+/elPk8lk9jq3YUVYMvtMQUBa/gzpVH3nPPir3MOfpl9MhgSnv/DAsp9DpBG4+43ufiYhx+Yc4ATgbjO7zsyOq+/o8szsdWb2ezPrNbMrzWxjvcckIrJQzeR3rpm9yMyuNrM+M7vWzE6Yy7E1QhxX1aJG7r7F3X/s7n8Xvbj9gbXAmwgv7gbg2cD/A75ZzecWkbmzYUUnEGYud7eshgNfBCuqXGjoFX/HPQf/JZsy6/lN+miWdbTwkkOWV/c5RKrAzHrMbMqUF3cfcPeL3f15wHGEXNMX12SA04iKVPw38B/Ai4CdwDVmtrquAxMRmQPmld+q8vwz+J1rZs8H/he4BnghYRntL83s6OqMZnL1jOPmah/SHG0SLjL/ZQPSX2WOZWi/1/Cds/6o+k+y5vl8dniM34//MQDvOnIVzcm5KgQuMis7gbcC/1VOY3e/CbhpTkc0M+cCP3T3iwHM7ExgG/AX0TmZS7Pc77LkKsLswYJNMYv6j52y6KAXZlhG7fI5lJ6J2mXC7+JM9DwJc9Z1hbzPN6zZDMDS5CAAD46u4pZdawHY3LsEgJE9rTASChBk80tHVoW+9qxtoWVj2H+0bWfY3qtzyzgtu0fC4/GwsqZpNKSOjPQkmVgc5ZNGta0z2XE2QSaZH394wr3fkqJXHM5Z8QP2jkhKvF3lMN+XVn82oPrngZ5L+b9zPw7c5e7nRG0/BLwK+ACh0FBN1SqOq8unPXd/0t2vqMdzi0hpyWSS73znOySTyb3ObdivM/f4kR2DVe07a2vfCL9/dHfu51OPXjPj5xGpkXn70dLM1gHHALm/wVHhpd8Bp9RpWCIiC9JMfueaWTPwhqK2DvyquG09zUUcN+czpCIyPyQSCd7xjneUPJfNIQXY1j/K4FiKztbyf31M1XfWlfc9nXu8dlk7Rx+4pOz+RaRsa6P7R4uOP0lYSjYlM5usXPaG2QxKRKSBbZjsd5+7T5d/P5PfuWuA5CRtl5tZ20Kt3D4nM6RmdmiUjDtsZjvM7DYz+7qZvcfMjjWztrl4XhGp3MTEBM3NzUxMTOx1bnX3Itqa878uHtsxs0JrU/VNahzcueGRnblDJz1nf8zm7SSUSCNbGd33FR0fBHoQEVlg6pxDOpPfuVO1BajJN/X1iOOqOkNqZh8Avg78O6GIw2ZgB6E609HAWYSV3Gkz+4O7H1XN5xeR2UmlUiWPJxLG+uWd3LdtgBX0sevBG2BPGvbfCEvXzapvbv13/Mav8or+57DTXsxtfhgv3rCs0pcgIlPLfvPTVXS8G5i2dPZkswHR7IG2txGRxjP7BN5HypgJncxMfudO1TYTOz8n6hnHVXvJ7t8RqkgdDXzV3f8qe8LMDiDsYfOC6Dbn1aJEpHo27BcC0i83X8xLrolWrpzyJVj657PreOvtWP9m3sJmBpJJ7kgfxgvXLZ39gEXm1gkz/ZbY3f9jrgYzA09F9wcBt8WOr42dk1pyZlwgJ3dp8XWlCvJMMctjuWJI4LmOs8WNwDMh7z8VFQ0azoTCQhMTSYbGWwDoHWsH4JieJwB4ddcm3rP0RgAemOgG4Jf9R3L77rCN19MDYW/pkaFw/cRoE6MTof/BZ4WVOL0bW2gaDM/V0h+G0zzoueFZtINY8b3HZrWytZkKijkV1W2Kv9ySRaNKFYvKnSu8fjp71UfSIqDacGZX1Gj2s6Qz+Z27JXrGg4qOrwW2ufsk3+xXTd3iuLnKId0M3BU/4O5PEd74n8zRc4rILK1du3bSc9k80qepbC/SSfvecnvu4V2Z9Tx3TTddbc1l9ytSJ38Z3cphhA8ZjRCQPhDdTgV+CGBmHcDLCB9GREQWlvpW2S37d667j5jZlVHbL0VtE8Crs9fWSM3juKoEpGbW6u5jsUPfAE6P7kVkHmhububxxx+f9Pz6aOuXZ3zmAemkfY/2w66Hcj/e5es5eYP2HpWGd269B1Apd3czOx/4lpldS9jr7jNAP/Ctug5ORGSBme53rpn9CfCfwDvc/ZfAPwK/NrNzouMfAJYDX5mrMTZCHFetGdKBKH+kE3gb8EvgeWb2ZeAj7p6u0vOIyBxJp9NccMEFfOhDHyq99Ut2hrSCgHTSvrfemXvY7+087iuVPyoNz93/vt5jmA13vzTaXuCDwOcIm50f5+7FhTREROa9KhUnqthUv3PNLAOMARNR2/81szcSZk8/RFjme4K7PzyHQ6x7HFetgPRK4CigGfgHwps9CrQBLzezbwK/Bh6I9tMRkQaTyWT46Ec/ygc/+MGSAen65WGGtJKAdNK+t96Re3hXZj1NiQTHrFWhT2lsZnaEu99T4bVJ4GB3f6DKw5oRd/8m8M16jkFiJvtkNE2eYcnURit+EGtcnFdZkHJqBefcYu0yIbczkw5txiYSpCbCR8jBkZDruX0o5Ibe1bWG43oeAeBVHfcBcP7+t/Lg0hsA+PngEQDcuHs9AJsHehgYCunYE2Ohz4nxBBNLwnOOrgzPaVGeaWLcSKQK82M9WwTeYi+71Hs3xfupnM4FrAEij8l+57r7VcDqomM/BX5ao6FBA8RxVQlI3f21AGa2mxDNryFsAnsM8FzgQsJ/DiNmdhdwJ3C7u2tJr8g8saglydKOFp4ejgek22bX6dZY/qiv58gDuumYwf6mInVym5l9Afiyu+8q9yIzO5mwHOsHhCVbIiIy1xogIG1kjRDHVfuT39PAb9x9c/aAme1PeEEvJP/iXkR4YXMekJrZWcD7CSWLrwXe5+5bpmj/OuATwGHArcAH3f3e2PkzgEuLLtvu7quqPXaRRrOqu41n4gHp8M6wj2hTS2UdbonPkG5g4+ruWY5QpCZeSyiN/9dm9gPCN8fXAU/Gvz2OClccDbwceCtwKCFP88Kaj1hERGRqdYvjqlXU6Ah3v8fdn1N8zt2fBv4numXbH0goGTyny5fM7D2EP/zvBO4DLgKuM7PD3X2kRPtTCOWOPwhcRShccY2ZPdfdt0bN1hHWVr81dqm+e5F5L5lM8rWvfa3kct2sVd2LeHhrUdA4vBO6Vpe+YKq+h3ZC/5O5Hzdl1vP+lYsrGrtILbn7lWZ2KPBu4H3AGUSbC5hZHzACLANao0uGgB8Bb6l0qa+IiFSm3jmkja4R4rhqzZBmly9d4O67p2scRd6b53L5kpm1AOcAF7r75dGxMwgli08Hvl3isnOBH7r7xVH7M4FtwF+Qr6q4nrCGur+a4xWpt0Qiwdlnnz1lm9VL2hijhT2+iMUWfacztGPagLRk37H80R3ezXaW8mwFpDJPuPs48DXga2a2GjgROBDYD2gnbCb+DKF0/vU12D9OFqIS+2VOZ9L9LksmScZyMa3wkJkV5pPGH6SddJRPmh4PCZwT4+EjZf/QIp4cCCtpft8d8kSPX/IIr+kMi83+ZmnIL31k8SYAfj64kWt7DwbIXdc/tIjxKJ80MxH691Q+j9XS2XFEY83E8l/LCD5KBig1DlrMlbdaE+Grwtldv/DVPY6rVkDaiMuXjickCV+RPeDuW81sE3AKRQGpma0jTEN/MdZ+1Mx+F7U/Nzq8DvivORivSF1NTEywYsUKduzYQXNz6X1AV3UvAmC3L44FpDsr63vng7nzf8g8CzAOVUAq84CZtbv7cPbnaAXNd+s4JBERmcy+EVTORt3juGoVNWrE5Utro/tHi44/CRwww/Yviv28HvismX0CeBi42N2/X86AopLKpWwo53qRudbfP/XE/+oloRLiLrpYyzPhYBkBacm+93sOW9adxuZH7uEOP4Q1SxbR1VY6EBZpMNvN7DvAv7n7pnoPRkREpFKNEMdVrahRAy5fWhndF++rNkgoWDST9vF9KF5P+IdYQ8hN/U8zW+PuX5rdcEUaX3aG9ILUaezX5lxw5ith+cGVdbbh5fzoyWfxhT+EtIOXa3ZU5o9zgLOB/2tmtwL/Cny/VG0CERGpH2N2OaT7yqrqesdxc7K/wlwvXzKz04HpZiXPje67gHhZ/m6g1OaJ2WmerqLjBe3dPZv49iDwWzPrBD5tZv/k7hNTDcjdN5Y6Hs2cHj7VtSK1sHz58inPr+oOM6TXZZ4Lw/C5Vc+ntWnyIkjT9X3/9j25x4cpIJV5wt0vAi4ys+MJNQa+CnzZzP4D+Jq7313XAcrCVPyhuoKc0r1S6QoOlNrUNOrDSu1Rms8nBUhHOZ7p8UQu/7N/KHyJ+WjfMq7tDl9eZvcofV1nmFj5fz1P5PJLfz4YPiZd37eBx/uXFvSRzVFNjydy+aREuaSeCWOweH7pFEGIF+XLhosL26gQzgKif8sZqUcaSmL6JtMzs/Zq9FMud7/M3W2qG3BT1PygosvXEgobFcseK7d91jVAB6BP0zKvNTc3T5k/CrB/VxsW+6P9dP/YrPp+MBaQqqCRzDfufr27v4tQr+Ac4ATgTjO7wczeaWZt9R2hiIiYV37bF9Q6jiulKgEpIZ/mn83sqCr1Vw3XEJbfnpo9YGZrgSOAH5Zo/0B0i7fvAF42SfusYwhJv9NWpRJpZOl0mosvvph0Oj1pm5amBMs7W3M/b+0vb4Viqb7HUxke2TGY+1kzpDJfuXu/u3/F3Y8EXkL4W/LPwFYzu8jMtAJGREQaVd3juGoFpOcALwVuN7ObzOxMM1tUpb4rElVAvAD4iJm90cyOAC4lrH3+CYRtXcxsp5kdGVWROh94h5mdbWaHESpH9Uf3mNnxZvZnZnawma03s3MJib8fqvkLFKmyTCbD+9//fjKZzJTtVnfnJ322lRmQ7tX3ltvp/+VneTXXc4g9RVPCWL+8s+Kxi9STWX7dgLvf6O5nUjhrereZXWdmx9VrjCIi+yyfxW3fUPc4rlpVdhsyn8bdP2NmaeDzhCW1/wu8wd2z0zQZYBRIRe0vNbNm4IPA54AbgOPcPVvoqAf4K+Ar0bWbgFe4+29r9JJE6m5V9yIGt9zH3zRdzlG/HYe7uuFdP51ZJ49dw4pbv8RXWuCq9NF8fumnaWmq1vdjIjW3ycw+5O5XZQ+4+wBwMXCxmf0RoQjSiwl/V0Rmr9SH5WnySidbgliQE1rqCbIPoyYl9yjNfpeZTpKJcjxHoz1Ex8eaGBgKX2Zmc0Ov68rmlD7KaxeHj4nvXfIYAK/qvI+fLwn5pDf0ho0IptqjlOj5PEF+qiW7R2na9n6vrOi+6OUWvK74ZVUOUKz4PZTqm21guQ8EpY0Qx1UlIDWzA9z9KXe/HrjezP6KUIH2bOC9ZnYToQrh5e4+Wo3nLJe7n0+Y+Sx17hLgkqJj3wS+OUn7nwE/q/YYReaTVUvaeJIJTk7eAgPAaAUzm7sfyT18zFexdllH9QYoUnsHAb8ys18BH3b3P8RPuvtN5OsaiIhIDe0ruaCVaoQ4rlpTEnebWS73Uvk0IvNPIpHgy1/+MonE1L8WVncvYqd35w+MD8LE1Et39+p7Vz4gfdxXsmZJXVf4i8zWOuAiQs2BTWZ2sZmtqO+QREREylL3OG7WAamZNQGdQDJ27Ktmdggon0Zkvkgmk3zwgx8kmZx6G5dVS9roLS4qPbSzdOPJ+t4VnyFdyeolKkYq85e773L3DwGHEFbdnA08ZGYfNbOW+o5ORESktEaJ42YdkEYbo94J/LWZLY0Ov5dQzTbebsDdL3b35wHHAfcT8mlEpAFMTEywZs0aJiam3E6XVd2LmKCJfo9VCR/aUX7fY4MwmN8K+PHMSlZrhlQWAHff4u5nAxuBXxDSRR6M9s4WEZF6UFGjSTVKHFeVHFLg48BPgc1m9r3o2KTLlZRPI9KYtm7dOm2bVVGV3V3eRbcNh4PDu8rvO5Y/OurNbGOpluzKguLuDwFvM7NPAR8FLjWzD7q7voSVuRX/AD2DQjnxHLtcgZ2SlXY8fxcvcBR7PjfPX5sOky6ZVIKx8fB4V1SQKFvk6In+pVzXFQoXvXjpowC8pvMe3rck/K14Vcd9APxiMHw+/n3fulxhpD3DoY94kSPPFjpKZscApMJjyxY6ypR4iVO83NyPc1ToqLgPFTmqLuWQTqvucVy1quxeaWYnAV8CziL8X/hfzOyLhG1W7iBE33cA97j7eDWeV0Rqb8XisA/pLrpYTzTTOc0MaYHex3MPn/D9cRIKSGXeM7NO4LDo9uzofj2h4FEzcGzdBiciIjKJRojjqjVDirtfCxxrZuuBh4FfAS1AdmoXwgtMm9kfgDvc/d3Ven4Rmb329vZp2zQnEyxubWJ3pit/cJoc0oK+B7bljm3zZTQnjeWdrTMeq0ijMLOngFXZH6P7IeBe4EfA3dFNRERqTTOk06p3HFe1gDTL3R81s18AX87uyWZma4HnA0dHt+cDZwDvrvbzi0hlmpubGRoaKqttT0cLuwbiAenUM6QFfe/JLwve7j2s6l5EIqH1STKvDQDXkQ8873b3x+o7JBERARSQzkC94riqB6QA7n5K0c9PAE8AV2SPmdl+c/HcIlKZTCbDpZdeyjvf+c5pt37paW8uCkinniEt6HsgH5A+zVJV2JV5z921lZk0nlIfwsv47q9kPmnJA15wl8spxfLPk80rDfMqAGSifM6xiZBTOjHWFMsn7QHg+q6DObbncQBes/guAN6z5H4AXtl5H79ashGAm3rXAfDkQLhuYKiNifEonzTKWfWUQfZLz2gMxTml8ZeRfyOY+v3Kvvwp2lSau1jqOuWVVshnmUO6Dwaz9YjjqrUP6Yy5+zP1em4R2Vs6nebMM88knU5P27ano4VdHgtIh6cOSAv6Ht6dO77de1izZPplwiIiIiLSGKodx83JDKmILGw97S1s9WU8nFlN25L9OWC/GUwQ/dkP+dh/Xs8td9/LLu/iDM2QioiIyFzZB2c55xsFpCIyYz3tLVyReSG/Hn8h79qwlk+fdMT0F2WZ8chAkof9AADtQSoiIiJzRtu+ND4FpCICQCKR4LOf/ey0+aPFSAeyAAAgAElEQVQQckizdg9PzLjvLX0juXMKSEVEaqT4g/k0eYmTfZB3o1SC6aTPZ26F+aQAmXxO6XiU79kb7Se6Z6iNJ/uXAPD77pAnms0pffXiu/iLJfcAcFK0R+mvoj1Kb+o9iM1RPume4VC9fWKsqTCfFPBoj1JLGZbNJ82UGPpU70+N80unzO2VqSkgbXgKSEUEgGQyySc+8Ymy2vZ0tOQe9w1Pvx1VvO90xtk+MJo7p4BUREREZN9Vt6JGItJYJiYmOOSQQ5iYmH7Gs6c9H5DuHpo+IM31PbyHZ3r7SWfyX1euUUAqIiIic8VncZOaUEAqIjkPP/xwWe16OsKS3YNsGwcO3gX3/xyGdk3f990/YNVX1nJb6//l803/xtKOFha1JGc9bhEREZFiRljuXPGt3i9gH6EluyIyY9kZ0v9o/gcOHN8B3wfO+BFsOHHqCwe3A7DM9rDIxljZpQq7IiJ1U829SkvtUVriuSzbLptTmiGXT+rRPqETEwn6ov1EB6Nc0M19+ZzSF/Q8CYR8UoCzltwJwImd9/HrPc8F4ObegwDYMtDF4HD4WzMR5aj6RJiP8YQV5JMW3MdzSrNjLXcaZ5b5pTB1jmnxOeWUTmG2M52aJa0JzZCKyIwtjXJIe+nMHxzZPUnrmIGtuYfbfSnLOlumaCwiIiIiC50CUhEBoLm5GXenubl52rZLoiq7fR4LSIcnD0hzfY/k91He7j0FuagiMvfM7EAz8xK3w+o9NhGROaEc0oangFREAMhkMvzXf/0XmUxm2ratTUk6WpL0sjh/cKR3+r77tuSOPe1LczOtIlIz64BBoAdYErs9VM9BiYjMldnkkEptKIdURABIp9O85S1vYXx8vKy9SJe0t9A7WN4Maa7vz63PfQu23Xs4VAGpSK2tBx5x9756D0QaVPxD+AzzSWGSPUo91jDbPptKapbPq8x+H5qx3J6hE1G+Z3+U/zk03MqW/m4AbulaC8DzezYD8Cddd3PWkluBkE8KcNWeI7ilN7TbOtAF5PNSU+NN+Hg2nzT66xTV2fOUkUhFY4xyW8kACc+/ztjrKCdvdCbtlBdaRQosG54CUhGpyNKOFvoGZ5hDOrQDogIS21lasJ+piNTEOqC8ctoiIguAZjobn5bsikhFejpa6PXYkt0pZkhLecZ7WKocUpFaWw+82syeMbNNZvZJM5s+cVxERGSOaIZURABIJBJ8/OMfL2u5LkBPezO9Xt4MaSKR4OPvexcJ+28AdvlixmnO7WcqIjXzmei2FDgJ+BhwLPD6ci42s3snObWhKqMTEak2zZA2PAWkIgJAMpnkvPPOK7t9T3sLj1JeDmkymeS8974JLr8CgGc87CenokYi1WFmpxN2BJ7Ky9z96tjPvzez3cBXzezF7n7j3I1Q5qXiD/KV7lG61w+xzp3CfNLoWPH+pvGc0v7xkOg5FOWCZnNKb+16Vi6f9BVd4buTM3tu5oTO+wG4as9GAG7vPRCAbQNduT5SUZ8e3ZM0Mtk9Siei8aUMm4iOZYeajHJKE+z9/kyVXzrTPWAVVFVG+5DOC1qyKyIATExM8LznPY+JiYmy2ve0Fy3ZnWKGdGJigue94f1MpMNv9p0ePjxoya5Idbj7Ze5u09yuLnHpNdH9qjKfZ2OpG/BI1V6MiEgV2SxuUhuaIRWRnE2bNpXddmlHM73xGdLRfkinIFn618qmhzYz8MJP8qub7+ERXw2ESr0iUlfHRPd31nUUIiKyz1JAKiIVWdLewg5fwofG30P3sv351Ftekl/DNIknj/wAH7/hJgAWtzbR0qRFGiK1YmbLgTOBXwG7gJcDXwK+4u6P1nNsIiJzRstuG54CUhGpyNKOFsZo4b8zL+WA1CI+deCx017TOzSev75Ts6MiNbYUeAXwIaALeIBQ1Ojr9RyUiMhc0rYvjU8BqYgA0NTUxODgIE1N5f1aWNKer5AbDzSn6vvKB3tzx3q0XFekptz9QeDkeo9D5rEZFuIpFQgUFysq6Djb3goLHBVf5+l8gSOA1Fj4uzU83MrWgS4Ablv8LACO7NnCSV33AHBmT6jbdeLi+wD4zcDGggJH2T4A0uNJPOrfs8WNYkWNEkX3buBRPSQSsUJHuTej6I2YaQEjFTyqnN6fhrfg18uZ2VlmdoeZ7TKzH5nZmmnabzSzH5uZm9m7SpxvMrMvmtljZvakmX3FzPTJWuY9d+d3v/sd7uX95o4HlEPjacZTmWn73jU4ljumCrsiIiIisqADUjN7D3Ax8DngBGAxcJ2ZLZqk/fOA24Cpyox+B3gTcDpwRvT40ioOW6Qu0uk0r33ta0mn02W171pUuIfo4Fhq2r7X/+HfeEvyt3QxpBlSERERmXs+i5vUxIINSKNZy3OAC939cne/hxBAriUEk6U8ABwJfHiSPp8bXfted785KqH/YeAtZra+2q9BpJG1N4e1Se9K/oqvN3+Rju+8Bu74TunG6fAdz0s2/yufb/46XTbM0o7m0m1FREREqsS88pvUxkLOIT0eWA1ckT3g7lvNbBNwCvDt4gvcfQR40MzWTtLnm4E9wFWxY78grOx/NWE2VmSfkEgYna1NPCf9BCclb4dtwK6XlG48vKvgx12+mB4t2RURmf+KP7RPs3lj8Yd8NyjMJ406jeWTQiynNBPLzcxE+ZvRHteplDE4Hr4sfTTKBd22ZzF3Lj4AgCOXbAHg5d0hh/TdS2/kpYsfAOA3A4cDcFfvmtx1I1EfqbHQp08kcvmk3rR3LmkiKqfgiahNlFPqSc+/xPhLney9KnV8quBI+aWTm+1M577+/tXIQg5Is0FlcSn7J4EDZtHnZnfPrU10934zGyinTzO7d5JTGyocj0jVJBIJPvCBD5BIlL9woqM1Sd/w4vyB4d2l+x7ZxQf+qIWEwZC3MkIbS7VkV0RERGSft5AD0pXRfV/R8UHgsFn0Wdxfts+eCvsUaQjJZJILL7xwRtd0tjbRO9SZPzBSOiBNju7mwpPbANiVCZUMNUMqIiIic8mY3dLbaSb8pUrmZQ6pmZ0eVcGd9Aa0Rs27ii7vBrZX+NQ7S/RXdp/uvrHUDXikwvGIVE0qleL4448nlZq8OFGxzrZmeokFpMO9Jdul+p/m+H8fIpVxdtENwDIFpCIiIjLXVNSo4c3LGVJ3vwy4bKo2Zpbda+0gIJ7AthbYVOFTPwWcYmZJd09Hz7MM6IjOicxb7s4NN9xQ9rYvAJ2tSfp8+hlSH9rBDZvTuMNONEMqIrJgxf+ElDG9FJ+9KnuP0rTlHgPk/mxljGxSVSraQ3RwPJnbW3T7QEgxyeaUPrdnKy/vyuaT3gDAI4uXAXD1wLO5q29NwXUjIy2ks/mk46H/TDK6b4LEeDafNIwhkd3pLGFkok/cniyxR+leb8o0x2YSKCm/VMWJ5oF5OUNapmsIy2tPzR6IihUdAfywwj5/DCwhbCGT9VrCNjE/q7BPkXmrs7WJXp8+h5ShHbmHuzwEpMohFREREZEFG5C6+zBwAfARM3ujmR1B2C/0LuAnAGZ2ppntNLMjy+zzRuB/gX8xs2PM7ATgH4Gvu3uly4BF5q2O1qbCJbsju2NfVcfEA1K6SNje+5iKiIiIVJ2W7Da8eblkt1zu/hkzSwOfBxYTgsk3ZJfbAhlgFCg/aS7MuH4V+B/CDOw3gL+r2qBF6qSpqYlnnnmGpqbyfy0sbm2iLz5Dmh6H8SFo7Sxo1zS6m2c+0klTAnalulnS3kIyoVIBIiIiMscUWDa8BR2QArj7+cD5k5y7BLikxPEnmGTVvbsPAu+u4hBFGoK7c++99/LSl740v9/bNDpam+ijo/DgyO69AlIf3MG9OzK8dG2Snd7FEs2OiogsfFXPJy3uNLounlNalFfq6STpbD5plP85MhJSRp4eWMymxSFP9Lk9WwE4oSvsS3rG0ht5vCvkk/5u4NkA3N27mmf2hL9v2T1KszmljCfIRHuTenZv0mxO6TgkR4v2Jm2CTPSYhJd+qQUvcpLHWZUEXZM930IK4HyWOaQL6b1oYAt2ya6IzEw6nebEE08knU5P3zjS2dZEiiYGfFH+YIk80vTIACdeMkw6E5bsLlZAKiIiIiIoIBWRWehsDYssHvY1PNV8EKw9HhLJvRu+90YAThz7IrdnDmFx64JfnCEiIiKNQDmkDU+fCkWkYtmA9E3jf88xq3r4wZnHlW4YLQHe7PtjNOWuExEREZlLNoPt7KQ+9KlQRAAwM/78z/+87PxRoCCwHBybvDaYmfFHJ5/Gtqjvzjb96hER2adMFhNM8ienOO+vZE6pFzX2fH/m+bzSXDySDit40qmwQHBoLMlolE+6I8oNvasz5JQe0bONl3bfD8AZuT1KV3DdwKFAyCeNXzc60kJ6NNqjNNqb1KOc0kyz5fYkze5RmhwxEtGepJnmovzShOf3Kc29biZnZbYr10Lbu3SejNnMzgLeDzwLuBZ4n7tvmaL9RkKdnNcD745q48xLWrIrIkCosvv1r399RlV2yw1Im5qaOPkvP4VFy3k1QyoiIiISmNl7gIuBzwEnEHYHuc7MFk3S/nnAbcBEzQY5hxSQiggAqVSKk046iVSq/F2Q4jOdkwakqTFSo8N865Nn4ZlQMKlLM6QiIiJSA+aV32oyPrMW4BzgQne/3N3vAc4A1gKnT3LZA8CRwIdrM8q5pYBURICw7ctVV12FzyDXoiOa6exghP1Hn8CfuAG23lnYaNP38fNW8uTdN/GFpn8BtGRXREREaqTxixodD6wGrsgN2X0rsAk4pdQF7j7i7g/WZnhzT58KRaRi2Wq5b05ew6ebL4FvAQe/Ev7sh/lGQztyD1sIs6idrdr2RUREROZYdfYh3WBm95Y87b5xFr1nrY3uHy06/iRwQBX6b3gKSEWkYtkZ0l7vzB8s3od0aGfu4U7vAjRDKiIikXiwMEUxnVJBRclCR9kOcwWPCgscQWGRo1yBo/Fwny9y1ME9i1cBcHjPdgCO73qIty/9PQCPL14OkCtydE/vKnbs6SjoIzMWFTlqSuQLHE2E++Q4JMbC46bhaFxRUaN0S6zAUVT4KDf2eAGjopdcEwut4FFjWBnd9xUdHwQOq/FY6kJLdkUECIWHHnvssRkVNWpvSWIGfcQC0pHigHQHTQl47AOd9Fk3gPYhFRERkdqY/ZLdR9x9Y6nbdE9tZqebmU91A1qj5l1Fl3cD22fxyucNBaQiAoQc0h07dswoh9TM6GxpotcX5w8O9xY2GtqBAzuGnF2EgFQzpCIiIjLXjNkVNSp/I7zS3P0yd7epbsBNUfODii5fCzw1yyHMCwpIRQSAdDrNscceSzqdntF1nW1N9MZnSMf6IR2ruDu0k3QGjv3GEDvTod1iBaQiIiJSC41f1OgawnLdU7MHzGwtcATww8kuWkj0qVBEZqWztYlt8RxSgJFe6FwRHseKGu30LjDtQyoiIiWUmU+aa1IUMLhl/6eo01g+abgun1MazycFSE+EuZrh8QRPjebzSQHu6VzFc2L5pABvW3YjAI93reD6gUNCu90h93RndN3YSHNBPmm4NxLNYRyJ8SivdDTKKR2yXA5ppiW6z/7ZTAIJz7/e3JtB/Sm/tCLuPmxmFwAfM7M7gIcIe5LeBfwEwMzOBL4AvNzd76rbYOeIPhWKyKx0tDYxyCImPEmzRbOr2YA0k4HhfFGjXYSlvYtVZVdERERqoFb7ic6Gu3/GzNLA54HFwP8Cb3D37LK1DDAKlL9Z/DyigFREgJAP+va3vx2zmX3NGpbfGn10soL+cDBb2GikFzyDGbz9uU1sYgkAHa3JKo5cREREZBIzqI1RT+5+PnD+JOcuAS4pcfwJGmN+fFaUQyoiQKiy+93vfndGVXYBOlqm2PolWq7blDD+/Y1dDCY6WdScpCmpXz0iIiIyx2ZT0Ki2eaT7NM2QiggAqVSKN7/5zfzgBz+YUVCarZjbS6zS7khhQJrKOKdePoK/PqMKuyIiMr3iQGCGOaUV71Gaic5lkvl80ij/c3SkJZcXem9nyBN9Ts/TABzf/RBvXVa4R2k2p/QPvSsL8kkh7FGa7T8T5ZJmYjmlTSP5fFIAj/50plscj9p59N2uJ/LlYHMvt9HmzOqZX6qgsuFpmkJEgLDty49//OMZbfsC+QJFfaVmSLtWwwl/y1Pr38qvHhgBd1XYFREREZEcfTIUkVnJBqSXpk+i91mv4q0vOxpWPDucXLYBTvwYd9z6BPB1ABarwq6IiIjUiGWmbyP1pRlSEZmV7BLc6zPP5Zr2V8AhJ8GSAwvaDI6n9movItVnZi82s2vNzM3shBLnO83sm2a21cweNLNzbaaVzERE5pPG34d0n6dPhiIChKJG99xzz8yLGsVmPPeMlq5GPjIBq/7PxZBIag9SkTliZq8Dvg9cNcl5A64kfBn9KmAd8F2gDfjbGg1TpDKlgoMpvkqZPp806rR4j9Ls9zMezyeNcjxTxsh4yCfdNhpyQXcPtgPwh979OWzJMwAc1/0wAG9bdhMAj3ct5/r+Q3LtAHbt6cjlk3qUo5puyuaSJshEu6Mlx6L7aI/S5iEjk92jtNWj9vl9S7N7lO6VUxo71nBKjauKY50P277s6zRDKiKzEl+COzRWOiDdMzqRe9ypPUhF5sqNwKHABZOcPwV4EfAud7/b3X8CnAe8z8wWT3KNiIjInFJAKiJAqLJ7xBFHkErNbM/l+AzpYHFAeuPFcPUXWP/E5Wz79/dBJq2iRiJzxN13uvuWKZqcBtzv7vfHjv0C6AReOqeDExGpByfsQ1rxrd4vYN+gT4YiMivZJbgH2DP89Z6vwXcvBjN4+2Vwyzdg96O8Np3/ja6AVKRu1gKPFh17Mro/oJwOzOzeSU5tqHRQIiJzSUt2G58+GYrIrGQD0lYmeHXmd/AQkGiCdAqGdk7aXkRqbiVwW9Gxwei+p8ZjEZm9MvcqLQ5Iyt6jNJZPClFOaSyfFCjIKc3mk97ftx8Ahy4Je3G/uPsRTlt2MwCPd60A4Kb+9bl2u4v2KPWxJOnsXqPN0V6lLWEMiTH23qM0Aek2Ctpl9yglGdujdK83pvjAAqWAtOHpk6GIAOEP76mnnspMC25mq+Y+5StIu5E0h0wKdj4AYwNR39BzyPPBTFV2RWbIzE4nFCuaysvc/epp2uwEuoqOdUf328sZi7tvLHU8mjk9vJw+RERE4pRDKiJAqLL7ox/9aOZVdlvCt8NjtLDZ98ufePz6fN8JY/mbzsFUZVdkxtz9Mne3aW7TBaMATwEHFR1bGzsnIrKgGGGGvOJbvV/APkIBqYgAoajRO97xjhkXNWqPBZgP++r8icfyn4/7MovY8tMLcRU1EqmnHwNHmNn62LHXAjuAa+szJBGROTabokZSEwv+k6GZnQW8H3gW4Q/u+6aqQmhmG4HzgdcD73b3S4rOnwFcWnTZdndfVdWBi9SYu/O9732Pb3/72zO6blFzMvf4YV/DK7kj/HD/z3LHH2c1w/ddDa/5a237IlI/PwA+BVxqZu8B1gMfBc5197G6jkykGuLxw1ztURrPJ4WSe5Rmc0GzuaEP9q3I5ZP+UVeoK3ba8lt4vGs5ADcNhO+I7u8Nq4x697QzHvWRaQp95nNJLZcnmtujdMRojrLBM9m9TFvDz+kWYnuUZu/z+bJ7vewFOCWookaNb0HPkEZ/cC8GPgecACwGrjOzRZO0fx6h4MNEqfORdcAvgSWx22FVHLbIvJJMGG3RH8pH4jOkMXdm8gU4NUMqUh/uPkH4W/gMcDXwWeDj7v6Fug5MRET2aQv2k6GZtQDnABe6++XRsTMIeTKnA98ucdkDwJHAGPCnk3S9HnjA3furPWaR+aqjpYnRiXEezqwpef6WifwKQeWQisytKJ+05DyHuz8NvKm2IxIRqRNndlV2NbtaEwt5hvR4YDVwRfaAu28FNgGnlLrA3Ufc/cFp+l0HPFytQYo0imQyyc0330wymZy+cZFFUWGjh710QLrJDmHlOy+AREIzpCIiIlIzsylqJLWxkAPSbOXAUpuAl7UB+CTWA581s21mdq2ZvXUWfYk0DDNjxYoVM972BcIMKcAe2hldtF/BufSiZWz2/Um2dwNGh2ZIRUREpCYcMrO4aYq0JhbyJ8OV0X1f0fFBZpfz+XpgCFgDvBP4TzNb4+5fmu7CaJ+2UjZMclykZlKpFOvWrWN8fJzm5pkVHsrOkALs6VxP28gzuZ9H9ns+7Myw5V/P4tCP/YTm5EL+HkxERBpCBQWOYLIiR/kiQAUFjuKnMhQUOAIYjYocbR9tyhU4ur8zfGl7yJId/FH3YwC8efktAGzuWgbADf0beKhvBRAKHAH5IkdjyYICRwDpVkiOhsfJ0TCe5j3hPtlspKMCR5mWMNhMMrT1JFj2DSh8OYUWYKEjaSzzMiAtc5Pwc6P7LmBX7Hg3ZW4AXoq7RyVEeRD4rZl1Ap82s3+KCkaI7HM6WvMB6a7OQ1lBHyw/FJ59Co8lD4f7wh9dVdgVERGRmtIkZ8OblwGpu18GXDZVGzM7OXp4EIUB6VpCHmm1XAO8mVDBd/dUDd19Y6nj0czp4VUck0hNtbfkf5Vct/6vefYf54sY7X5wBxAFpMofFRERkRpSLmjjW8hr564hLNc9NXvAzNYCRwA/rOLzHAM86e5TBqMijc7MeOUrX1lRDml7bMnuyHi64NzQWArMaFv7vIJ2IiIiInPKAfdZ3Or9AvYNC3a6wt2HzewC4GNmdgfwEGFP0ruAnwCY2ZnAF4CXu/td0/VpZscTquz+HsgQckjPAE6bkxchUkNNTU1ceeWVFV0bnyEdKgpIB8dSWCLJ/m/9LIvb22Y1RhERkRkrDipmkFMaLp8knzTWl2GF+aRQkFOazSd9ZjT8vezd057LE93QHRby5XNKb2Vzd8gnvbEvlBl5uG957rqJbD5pU5hX8uZELJ803Ddlc0pH8vmk3hSOpaI/xZlWz+WT5qaoEp7PJ83l08bfoL3fH5HZWsgzpLj7Zwgbf38euArYArzM3bOfmDPAKJAqs8se4K+AW6LbS4FXuHs1Z1xF6iKVSnH22WeTSpX7f4e8+Mzn8Hjh9cNjKTyTZtcv/on2BfsVmIiIiDQibfvS+BZ0QArg7ue7+yHuvtLd3+7uvbFzl7j7Ae5+X9E1T7i7ufslRcd/5u7HunuPuy9z95e7+29r9VpE5pK7841vfAP3mf8G7igISIuW7I6nwZ3Bu37NouYF/ytHREREGonP4iY1ofkKEZm19tjeosUzpINj+Z87tQepiIiI1JBV8EW71JY+HYrIrMWX7A6NFc6QDscC0niuqYiISF3MMCcyvnTTiy/wWKNMtsuoTfSzJ8glZGb3KB0bT/LMWD6fFPJ5ogcv2ZnLJ33LipsBeKI75Jve1L+uIJ8UYGKkmcxYPp8U8nuUJtuM5EiUVzoSxtMS5ZRmRox0lE+abg0vxJssjBdCPml4QXu93L0ot1RmQZ8ORQSAZDLJb3/7W5LJmVfCjQeaxVV2B8fSkEiw/9vOZ/GillmPU0RERKRsmembSH0pIBURIGz7snHjxllv+zJUXNRoPAUYzcvX0tnWPNthioiIiJQlFCeqfMmuChvVhiqMiAgQquzut99+s66yu/cMaQoyaZ76yjtQCqmIiIjUlIoaNTx9PBSRWetoje9DWhjQDsWLGrXMfDmwiIjInJnBHqWw94xZfq9OK8wnjV+TtsJ80qh9PJ8U4JnRsIqob3BRLk90fbRH6bFLoj1KV9zK493h3M1964CQe9q3ZxEAqaiPXE5pS4J0do/SRdm9SaOc0mFoHgjDSTZHbdpi+aTRseyY3cASha+t5F6luRde4phICQpIRWTWFjXHtn0pLmoUmzHtUFEjERERqSVV2W14+nQoIkDIIT3uuOMqyiGNz5AOT6Rx91w/g2MpMKN1zXPoUA6piIiI1JDyQBufAlIRAaCpqYnrr7++omvjOaTpjDOWytAWzZoOjaWwRJKVf/YFujvaqjJWERERkbJohrThKSAVEQDS6TQf/vCH+dKXvjTjrV/ai3JDR8bT+YB0PI1n0vT+7zdZ9IHjqzZeERGRqpthLmTBHqVW9KBETqml83uUxvNJATybUzqRKMgnBXi0fxkQckqP6X4CgD9dcRsAT3Qv5+b+g0K7vtAum1M6MdKMN4W/x9mc0EwuX9QK8kkBWgby51PZPUrbsjml4JnCvFLLvjaLvf7cGxJ/oxCZlKrsiggAmUyGiy66iExm5ht2tRflhmYLG02kM4ynMuDOntt+QluTfuWIiIhIjThYpvKbKu3WhmZIRWTWkgmjtSnBWCoEs9lCRvEKu1CYayoiIiIyt3yWS3YVkdaCpitEpCoKChtlA9KiPUk7tO2LiIiI1JL2IW14mq4QEQCSySQ/+9nPZpw/mlW49UuYGc3NkCYSrH7LubS2qMquiIiI1I6pqFHDU0AqIkDY9uVlL3tZRdu+AHS0xgLSvZbsGisOPbrivkVEROqmzOI8xduLFBQ5Ki5w5GCeL3AEsSJHGSsocATkihz17mnn4b7lAKxfsguAY7sf501RgaOnukNRo2yRo0d6l9OfLXA0Gj72p8fC3+tMi5FpiQocLcoWN7KCAkcAmajwUWoRZFrD+DPN2THnixzFCxzt/R6wN30kkIiW7IoIAKlUis7OTlKp1PSNS1gUK2yULWo0NBYt2c2k2fTZUyvuW0RERKQi7pXfpCY0QyoiVRHPD83OkA6OKQAVERGROnFyM9AVXy9zTgGpiFRFfOuXbEA6PK6AVEREROpHOaSNTwGpiOQcddRRFV/b3jJFUSOg58BDKh+YiIhIIyiObcrMKS3IJy3uLJt6mT1nsdWimShHM8opHR9PsHMsfHzvHwy5oY/2Lcvlk76g+wkA3rD8DgA2dy/llr6DAHisL+SXxnNK4/mkAJlmIxXLJw33YSit/eE8hHxSgHRbPqc0nk+afQOK37Ck+LUAAB5GSURBVJ5SLz9HOaX7LAWkIgJAc3Mzd955Z8XXFxQ1msgu2Q33lmzirZ/7T5qbVWVXREREakgzpA1PRY1EBIB0Os0nPvEJ0un09I1LWNQcW7IbzYxml+x6Js3tP/yXivsWERERqYiKGjU8BaQiAkAmk+H8888nk6ks+z8+QzpUXNTInZuu+GbFfYtIeczsxWZ2rZm5mZ1Q4vw50bn47cZ6jFVEpCYys7hJTWjJrohURbyo0che+5CKyFwzs9cB3weumqLZOuBrwEdjx7R0QaRSs9mj1PfKsMzdxfNJgXwuacbxdD6fFGDnWFMun/SR3rBH6bpcTumTvGnF7QA80R3O3db/rKjtMvZE102MhJSadHOCzHiUTxrllaba8zmlzUNhOC390bCG8zml6bboWHN4HZ60gnzS+MvJvQclXv5ej2XBU0AqIlURL2qU24d0XJ9zRWroRuBQ4GDg9ZO0WQ/8yN37azYqEZF6cZ9dlV0t260JBaQiAkAymeTyyy8nmUxO37iE9hL7kOZmSBMJ3vuZr1bct4hMz913ApjZwVM0Wwc8XJsRiYg0AAWVDU8BqYgAkEgkOO200yq+vnAf0qioUbbKriU48dWnkkgobV2kXsysBTgAuNTMRoB7gS+6+69n0Me9k5zaUIUhiohUnwLShqeAVEQAmJiYoKWlhfHx8Yq2Z2mPb/syVljUyNMpTjvmwIr7FpGqcOAFwAhwEPA+4Odm9nZ3v7yeAxNZEOZwj9JsX+ZWkE8K4GnL5ZPuivYoHRgKCZ2P9S0ryCcFOHVF2OLtqe6l3NK3Nmq3NFy3p53UaOgjHfUZzylNR3uUJqPc0eZoj9KWfshEj7M5p+m2WD5ptEdptpyqJ6bZo1T2KQpIRaQqOgpmSKMlu+MqaiQyW2Z2OqFY0VRe5u5XT9XA3SeA7GbDD5jZlYS8088AZQWk7r5xkjHeCxxeTh8iIjWlGdKGp/VzIlIVJYsajamokchsuftl7m7T3KYMRifpNwNcB6yq/qhFRBqEtn1peAs+IDWzs8zsDjPbZWY/MrM1U7Q92cx+aWbbzGyHmV1hZmuL2nSa2TfNbKuZPWhm55qZFhnIgnDwwVPVQplaZ2t+hnRoLEUm4wXbvjxr3fpZjU1E5sQxwB31HoSIyFwwB4sq7VZ2q/cr2Dcs6CW7ZvYe4ELgncB9wEXAdWZ2uLuPlLjkXcCPCXk1y4B/Ba40s43uPhEFnlcSAvlXEaoVfhdoA/52rl+PyFxqbm7moYceqvj6no6W3OOMw+7hcUYmoqJGySauvfVu5Y+K1JGZvRZoAW4HWoEPAscBL6nnuEQWrDnao7QgnxQgYwX5pJDfo3TXaBP9g/l8UoC13bsBeH73Zl6fyycN527vP7AgnxQoyCnN7k2abgn9p0MTkrE9Slv7PGpjuXzSTCvRseh1JKwgn7TgfdA0zz5nwc6QRtUEzwEudPfL3f0e4AxgLXB6qWvc/W3u/i/u/oi73wx8BDgE+OOoySnAi4B3ufvd7v4T4DzgfWa2eI5fksicSqfTnHfeeaTTlS2z7WprojmZ/yuyefdw7rFn0vzbRV+suG8RqYoVwKeAu4BrgAOBY939prqOSkRkLrlXfpOaWLABKXA8sBq4InvA3bcCmwiBZTl2RvfZYPM04H53vz/W5hdAJ/DSWY1WpM4ymQyf/OQnyWQqS5owM3ra87Okm3tjixDcOe/vP1Vx3yJSPne/ulReqbt/y92Pcvcud9/f3V/r7lquKyILmIdlW5Xe9iqdPHeqnWY4nyzkJbvZf5RHi44/SdiHrRzHE/5LzFYlXDtJf5TTp/Zvk4VuaUcLz+wZAwpnSOMzpyIiIiI1Mw9mOqudZlijYVfNQp4hXRnd9xUdHwR6prvYzDqBTwA/cPcnYn2W6o9y+hRZ6JZ3tuYeP7FrKPe4vWUhf/clIiIiUpk5SjOcV+blp8Qy92Q7N7rvAnbFjncD26fpvxn4IZAiFH3I2hn1F9cd3U/ZJ2j/NmlsyWSSb33rWySTyekbT2JprLDRA08P5h4v62ybdd8iIiLzVvEkXZlFjnK1jQqKHHnBHVZY4AjIFzlKJZiYiAocjYWP/dkiR0/0Ly0ocATw+hV38mT3cgBu7zsQgMejIkd7BhflCxxFxYkyY1FxoxZILwpDaBoOY2gagtbeqF1UDClb5CjdBpnm6Fx2FVW2yFG1F1U1/gxpyTRDM8umGX67jD6K0wznlXkZkLr7ZcBlU7Uxs5OjhwdRGJCuJeSRTnZdArgUeAFwfJR3mvUUUBxUro2dE5m3EokE7373u2fVRzwgvX/bQO7xqp72WfctIiIiMiPO7ALScOmGydLuJptsmqG5SDOcVxbykt1rCMtrT80eiJJ9jyDMfk7mn4DXA6e4+wNF534MHGFm8Q0VXwvsAK6txqBF6mViYoKOjg4mJipPPVgWC0jHUvkCRis6krPuW0RERGTGZlXUqCbmIs1wXlmwAam7DwMXAB8xszea2RGEmc+7gJ8AmNmZZrbTzI6Mfv4ccDZh3fb9ZtYd3aJFCPwAeAC41MyOMLPXAx8FvuDuYzV9gSJzYHh4ePpGU1ja2VLy+Mqutln3LSIiIlIHj7j7xlK36S40s9PNzKe6EfaFhtJpgZWmGc4r83LJ7v9v7+6jJCvrA49/f93TMw0M88LIDMIMgyQRsmAYlBxfiAHJGgwMJCcnvAVYDbvOMY7nZI0L6272JDmakIjRVTOJRjAK8QRNMFlcEoJ4VNZNjEmQAMubycSdkXEltE4Dw2tP92//uLea2zXV3dVvdauqv59z7rlTt+596rnPdNXvPvc+L+3KzPdGxDhwHUWb6i8BP5OZjckQJ4DngIMR8Vrg3eX25ieonwJ+ITPHIuIs4KPAXcA+4L9m5oeX9kyk3lB9Qlp1zNrhDudEkqQuVn341mZ/Uij7Vx7SyTKn9CctjovJ15nF86c8WKyrfUob/Um/VfYTfdm677NtbdEL7cKNRQ+3R9cV731jdMuU/qQAB58t+5S+MMDEyrI/aVm9Onj4i/1Jh8phJVaOlv1Gh4KDR7zYn7TY1uhTOn15zF1CLmTKuYU9Ja2xm2FP6esKKUBmXgtcO817NwI3VjbN2o06Mx8DfnZxcid1l2OPPXZBx2+ojLJbtenI4QWnLUmSNGfdP6hRtZvh3TClm+GvznBco5vhOS26GfaUvm2yK2luhoaG2LdvH0NDQ/NO46hpnpBuecmaBactSZI0J8nC+pB2oC67RN0Me4oVUkkAjI+P86EPfYjx8fHZd57GdE12X7J6xYLTliRJ6keZ+V7gNyi6GX6Rolvg2bN0M1xJ0c1wtLL8foezvij6vsmupPZMTEzwzne+k507d857vtA1w0MMDgTjlZHpVgwERx02tOC0JUnqS52ao7RcVfuUNvqT7i/nKH3q6eHJ/qRb1+4H4JXryjlKN97LnnKO0nvKOUr3PrEOgCcPHMZ4pT8pwMTKgSn9SQFWPF32Ka3OUTpUbBur9Clt7ju7IN3fZBdY/G6GvcQnpJIWzcBAsP7wqU9JN60ZZmCgr343JUlSr8ic/6KOsEIqaVE1N9t1hF1JklQbK6RdzwqpJAAGBgbYtWsXAwML+1loHtjomLXDi5a2JEmS+ot9SCUBMDg4yM6dOxeczobVTRXSNcOLlrYkSX2v1YO5Fj1fZu9PWiY2xzlKq/1JAfY8sR4o+pSetnYfABc0zVF6z+gW9oyun3Lc+LMrpvQnLdbFR7eao3SyT+nKKIbwWRQJE/XNQ6r2+LhCEgBjY2McffTRjI2NLSid5ia7L107vGhpS5IktS1ZWJNd66Md4RNSSZNGRkYWnMZRR6ya8nrTmuFFS1uSJGlO7Ava9ayQSlpUR60+9AmpJElSLSaskHY7K6SSJq1du3bBaTQ32W08IV2MtCVJWpaqdapZ+pNOPWzuc5RW+5NCZY7SA4dN9ifdsuYJAE4v5yi9YOO97F23AYB7RzcDsGd0/ZT+pAAHy76kAysHmGieo7TsU7ryKRgYb30+6k9WSCUBMDQ0xOjo6ILTaR5ld9OaYYZWDCxK2pIkSe1Kksz5D2qUdiLtCAc1kgTAxMQE119/PRMLGo0OfmjjalatKH5aTj1uDStXDCxa2pIkSW1Liia7812sj3aEFVJJAIyPj7Njxw7GxxfWTmbD6lV87MpX8ZbXncAHL962qGlLkiTNyUJG2VVH2GRX0qJ7w0kbecNJG+vOhiRJ/ae5ntSiT+nkW9W5Sg/ZcZo5Siv9SaEyR+kLg+x/YRAo+pMC7H1iHQDHrx3ltHWPAnDexvsB2LduPfeMbgHg26PFfpN9Sp9ZwcQLL/YnBab0KZ0YnP6c1H+skEqSJEnqT3YX6npWSCUBMDAwwHXXXcfAwOK35F/KtCVJkqZl09uuZ4VUEgCDg4NcffXVPZe2JElSS5nkQp6QWpntCB9XSAJgbGyME044gbGxsZ5KW5IkSb3LJ6SSJu3Zs6cn05YkadmqPsRrc4Cj4rCY8mpyVR3gqJJmJuR4UXUYKwc3Gn2+eH3g6eEpAxwBnLbuUbZvvA8oBjgCJgc52rN/PU83Bjh6tkirOshRLuagRj7l7HpWSCVJkiT1pwkrpN3OCqmkSStWLN1PwlKmLUmS1FI6ym63sw+pJACGhoYYGxtjaGiop9KWVIjCpRHxlYgYiYh9EXFjRGxo2m9TRNwSEY9HxH0R8fa68ixJko8sJAEwMTHBzTffzGWXXbbo07MsZdqSprgKuAH4KnAi8IfA54CzASLicOBvgAeB1wOvAW6IiInM/FgdGZa0iJpbp7bZp3Ta/qSVNCJjSn9SgBwvOnuOjQ1M6U8KsPeJdVP6kwKcd/T9ADy69ijue+I4oOhPCkztU7pYlwqZ5EKa7Nr/tCO8MpQEwPj4OFdccQXj4+M9lbakQhZ+MjM/nZl7MvPLwHuBsyLixHK3q4DjgCsz8+HM/BRFBfaaiPCaQFL/yYn5L+oIg48kSf1rpFwfWa4vAr6cmaOVfW4HXgb8cCczJkmdkBM570WdYZPd7rBl9+7dnHLKKXXnQ8tYls1STjvtNCJmaOPTZWlL7dq9ezfAlrrz0WFnAs8CD5evtwJ/0bTP3nK9GXhgpsQiYrr3Tx4bGWHfb79/vvmU1AumC+HV9r8Dxb8HItk9WLSM+trgQQBWULw+mIM8N1GMKzE2Xjwfm5gon5MljD3+PWJw4XO/PM2TfG3irxZ0vJaeFdLu8Mzzzz/Pgw8++O15Hv8D5Xr3YmVoGbHsmjz00EPt7Davcmsz7X7n39z8LbTstgDPLFJeul5EbAZ2Arsy8/ly8zHAaNOuB8r1+nl+1A8AAxwcf2rsu4/NN471I7/rh7JMDtXXZdL44Tkw414tnZwHxxfaZnY3LEqlsi//b7qJFdIukJnHLOT4xh3rzPQR6xxZdvNjuc2fZTd/y7nsIuIS4DOz7HZ2Zt5V7r8WuA14BHhPZZ8RYE3TcWvL9Xdny0ersl/O/y8zsVwOZZkcyjJpbYbWGG3LzAsXIy9aelZIJUnqcpn5WeCz7ewbEcPA54HVwJmZWX048ShwQtMhWyvvSZLUUQ5qJElSn4iIQYonqScD52bmY0273AqcExGrK9u2A/dn5j93KJuSJE2yQipJUh8oK6M3Usw5ehEwEhFry2VVudv1FN25boqIkyLiKuAK4DfryLMkSVZIJUnqDxcDl1P0Cb2LYvCixvJugMwcAV5PMQ3M14FfBP5d2SRYkqSOsw+pJEl9IDNvBm5uY79vAm9c+hxJkjS7aMwPKEmSJElSJ9lkV5IkSZJUCyukkiRJkqRaWCGVJEmSJNXCCqkkSZIkqRZWSCVJkiRJtbBCKkmSJEmqhRVSSZIkSVItrJD2qChcGhFfiYiRiNgXETdGxIam/TZFxC0R8XhE3BcRb68rz90mIl4bEV+NiIyIs1q8vzoiPhER34mIb0bEr0dE1JHXbhMRF0TE30bE/oi4MyJOqTtP3SgiTomIW8u/sTc3vbciIn4nIr4VEXsj4ncjYmVdee0mEfGmiPiriPh/5W/Xn0fE1sr7fje7gHFoesaXQxk3CsaFqfy9F1gh7XVXATcArwKuAH4c+FzjzYg4HPgbYBXweuCDwEci4m2dz2p3iYgLgC8C35/m/QDuBE4FzgX+E/Au4Lc6lcduFRHnA38G/BHwGmAE+F8RcWytGesyEbENuBsYm2aXTwM/C1wCXFn++6bO5K7rvRm4Ffgx4HxgK3BnRAz53ew6xqEmxpdDGTcKxoWW/L0XZKZLnywUFwYJnFi+fgfwHLCuss/HgH8BBurOb81l9RLgOOCssszOanp/e7n95Mq2dwNPAUfWnf+ay+7vgc9UXg8D+4Ffrztv3bQAhwEvpwiuCby58t4rym1vqmy7FJhofH9dppTlOWV5neN3s7sX45DxZZoyMW6kcaHNMvL3fhkuPiHtLyPl+shyfRHw5cwcrexzO/Ay4Ic7mbFuk5kjmblvhl0uAh7OzIcr224HVlM8AViWIuJlwBnAnze2ZeZzwFco7myqlJnPZuY3p3n75ygC6hcr224HAvippc5bD6r+tvnd7G7LPg4ZX6YybrzIuNAWf++XISuk/eVM4Fmg8cXdSnEXumpvud7cqUz1KMuutUa/jlZls5zLZa62At/OzIONDZn5BPAklmMrZ1LcJf9H/G52O+PQ7JZbmRg32mNcKPh7vwxZIe0TEbEZ2Ansyszny83HAKNNux4o1+s7lbceZdm1dky5blU2y7lc5qrV3xdYjoeIiNXArwC3ZOYe/G52LeNQ25ZbmRg32rPs44K/98uXFdIuFBGXlKOvzbScVdl/LXAb8AjwnkpSI8CapuTXluvvLulJ1GSuZTeDZVd2bWo0pWlVNsu5XOaq1d8XWI5TRMQQxQA5B4H/WG72u9kBxqFDGV/mzbjRnmUdF/y9X96skHahzPxsZsYsy10AETEMfJ6iPf15mXmgktSjwAlNyW+tvNd35lJ2s1h2Zdemxrmf0LR9K8u7XObqUWBzRAw2NpRTZRyB5QhARAxQjC75KuDczPxO+ZbfzQ4wDh3K+DJvxo32LNu44O+9rJD2sPJH6zPAyRRf4MeadrkVOKdsAtGwHbg/M/+5Q9nsVbcCp0bEiZVt24HHga/Wk6Wu8Ei5/HRjQ0QcAZxNZaoHzepWYB3FKJwN2ymmAritlhx1n48AFwLnZ+Yjle1+N7uIcWheltvfsHGjPcs5Lvh7v8xZIe1R5UXAjRQ/6BcBIxGxtlxWlbtdT9HW/qaIOCkirqKYJ+4368hzj7mFIoDeFBGnRsSFwDXA+yt9o5adzEzgWuDyiHhrRJwEfBJ4olyrDZn5NeBLwEcj4oyymd/7gOszc9k3Q4qI3wLeSjEP38OV37bD8LvZNYxD87as/oaNG+1ZrnHB33sBzkPaqwtwGcUoZK2WX6vs93KKSYVHKeYBu6zuvHfTwjTzxJXvbaKYyPt7wH3AL9Wd325ZgH8P3E/Rv+PzwPF156lbF1rMN1duXw18CniMIuD+Bn06L+Mcy+u1M/y2fbLcx+9mFyzGoVnLx/gy9ZyNGy+WhXEh/b13eXGJ8j9bkiRJkqSOssmuJEmSJKkWVkglSZIkSbWwQipJkiRJqoUVUkmSJElSLayQSpIkSZJqYYVUkiRJklQLK6SSJEmSpFpYIZUkSZIk1cIKqSRJkiSpFlZIJUmSJEm1sEIqSZIkSaqFFVJJSy4izo6I19edD0lS7zB2SMtDZGbdeZDU5yLiO8AjmfmGuvMiSeoNxg5pefAJqdTDIuKXIuKpiFjdtP2NEfFCRPzIEn72xyPi/0TESEQ8GxHfjIiPRsQxTfu9AngpcFO75xARt0XEWEQcNsPn/1pE5AzLhojYHhHPR8Spi3XektTrjB3GDqmbrKg7A5IWZAfwx5l5oLEhIlYBNwAfyMz7luJDI2IAuBz4v8DVwEHglcAvAudFxBmZ+Xi5+xuB7wOfafccgG3AA5n5bBvZ+ShwV4vtT2XmbRFxG0V5vKaNtCRpOTB2GDukrmGFVOpREXEm8G+AK5veejOwEfjgEn78y4HDgTsy85Pltj8qm1ddB/wcRbCH4qLiE60uEJrPISIeBjYB64BNEbG/svt7MvO/t8jL1zPzszPk9VrgHyLiJzPzC22foST1IWPHJGOH1CWskEq9awfwD5n5jabt7wBuqdxlXgqnl+vmz/5WuV4NEBErgTOBt0+TTvM5nAucA/wh8KvAH1f2HZlPRjPz7oj4OkW5eFEhabkzdrTB2CF1jn1IpS4REe8q+6+8rWn7+8rt76hsWwdcBPxB077HAa+gRfCMiDvK/jqDTdvfWqZ/8Ryye8hFRUQE8PMUTbD+stx8JnBXZn6LJq3OITP3AMeWL28v3/8C8BDwhYg4eQ55rLoDOKe8yJGkvmHsMHZIvc4KqdQ9PgZ8D/jlsp8NEXE5cA1Fn55dlX2vpAjeNzel0RiJ8H+3SP904L7MHG+xHQ69Yz2TbcDzwGMRcWxE/ARwK3A+8LbMfKDc7wzgd6dJY7pz+FHgOYr+RT8FfIDirvfrgOvnkMequ4AjyvxIUj8xdhSMHVKPssmu1CUy8+mI+DDwHmB7ROylGFDhcxQBtmoH8OnMfLpp+xYggb3VjeXd76OBP2vx0acDTwK755Dd04FVTG0KtQf40epgGJn5/hnSmO4czgCGKS6wrshybqqIuJDigmM+9pTrLfM8XpK6krFjkrFD6lE+IZW6yy7gKYqLiD8B7qESWAEi4rXAqcDHWxy/ERht9052eTf9R4B7KsH75oh4LCKejIh/atEMbDPwEuBPgbOBnwZ+p/zsP20eur+V6c6hPPY44AHgXdXzBh4Hmi9A2tW4+Nk0z+MlqZsZO4wdUs+yQip1kczcT9Ev5scoWjBcmJnPNe22g2J0wH9skcThQKvh7hsXFfc0bT+pPOYbMNmX53zgEuAoYCewKyJe3SKtOzLzrsz8fGZeDfwHihEU/8usJzr9OTSaRX0iM8ea3jueprv3c9Aok8PnebwkdS1jh7FD6mVWSKUuUg7WsL18OQiMNr2/FriYpgEpKh4HNrTYfjowDtzftP115bpxsXEiRX+ZuzPzIPBF4JmmNBsXFc0XBH9Rrl81Td6AWc+h0azqjqZjtlDcWZ9LX6WqRv7/dZ7HS1LXMnYYO6ReZoVU6hIRMUTRT2c1xZ3i44HLmna7AhgDpps77V+BVRFxZNP2VwKPVe+Yl3e0f6F82bio2AY8kplPRcRLgd8H/g64s5LWNooBJR5gqpPK9WxTBsx0DmdQ3JF+pEX+Ae6eJe3pbCzXXlRI6ivGDsDYIfU0K6RS9/g48OMUk5Pvohgs4poy+Dc0BnN4Zpo0GoNCNO5EExHrga3A+ogYruz73yiG1ocXmzNtA34wIp4GvgMckZn/tqkJ1OnAw00XKMPA+8qXN8xynjOdwxm0Hs2xced8vne5Gxcl987zeEnqVsYOY4fU06yQSl0gIn4FeAtwTWZ+KTMPAJ+gGLzh/HKfV1MMIjFdkyuAvwYOUEwQ3tC4wBgC/mdE7IiIT1LcQb+xfO+scr2NYlCMdWUaZ0bEZL+eslnYCcBYRPx8RLwlIq4F/qlM492Z2Wh+1eo8pz2HsmnVRg5tzgXFRcE4L140zdUbgAcz89vzPF6Suo6xw9gh9QMrpFLNIuIS4L0Ud34/WHnrIxSB9D+Xr3cAX8vM5r48k8q70f8DuLRyd7xxUXEpxWATH6AI3m+imKPtSWBzuc824IHMHMvML1PM3XZp5SNOBP6F4sLiRoo72+dR9AE6JTPfx8xmOofGoBTNg2dAcVHx8Ax396cVEUcAF1CM7ChJfcHYMcnYIfW4mDoytqRuFRFXUwTkVhOXV/d7BUXzou2Z+ZcRcRNwOTDcYvTB6nEbKIa4f2lmfrfc9nvAcZn5M508h8UUEe+guPjZmpkjs+0vSf3E2DHvzzR2SB1ihVTqQxFxA/BqirvDXwU2Z+bmWY75CeBPMnNDRKyiaJb1e8AFmfmlpc7zUij7QD0EfCQzr607P5LUzYwdBWOH1Fkr6s6ApCXxy8A7gR+kaCq1u41jjgcyIkYpJli/Fzi3k3ekl8DJwIeB99edEUnqAcaOgrFD6iCfkEp9LiL2A3dm5sV150WS1BuMHZI6xQqpJEmSJKkWjrIrSZIkSaqFFVJJkiRJUi2skEqSJEmSamGFVJIkSZJUCyukkiRJkqRaWCGVJEmSJNXCCqkkSZIkqRZWSCVJkiRJtbBCKkmSJEmqhRVSSZIkSVItrJBKkiRJkmphhVSSJEmSVAsrpJIkSZKkWlghlSRJkiTVwgqpJEmSJKkWVkglSZIkSbWwQipJkiRJqsX/By7/hcuKhahvAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "F0 = heuristiceq.profile['Fx'].F[0]\n", "F2 = rateeq.profile['Fx'].F[0]\n", "\n", "# Now plot it up:\n", "fig, ax = plt.subplots(nrows=1, ncols=2, num=\"Force F=2->F=3\", figsize=(6.5,2.75))\n", "im1 = ax[1].imshow(F2,extent=(np.amin(X[0,:]), np.amax(X[0,:]),\n", " np.amin(V[:,0]), np.amax(V[:,0])),\n", " origin='bottom',\n", " aspect='auto')\n", "cb1 = plt.colorbar(im1)\n", "cb1.set_label('$f/(\\hbar k\\Gamma)$')\n", "ax[1].set_xlabel('$x/(\\mu_B B\\'/\\hbar \\Gamma)$')\n", "ax[1].set_ylabel('$v/(\\Gamma/k)$')\n", "\n", "ax[0].plot(x, F2[int(np.ceil(F2.shape[0]/2)),:], '-', color='C0')\n", "ax[0].plot(x, F0[int(np.ceil(F0.shape[0]/2)),:], '--', color='C1')\n", "ax[0].set_ylabel('$f/(\\hbar k \\Gamma)$')\n", "ax[0].set_xlabel('$x/(\\mu_B B\\'/\\hbar \\Gamma)$')\n", "\n", "ax[0].axvline(-det, color='k', linewidth=0.5, linestyle='--')\n", "ax[0].axvline(+det, color='k', linewidth=0.5, linestyle='--')\n", "\n", "fig.subplots_adjust(wspace=0.25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Why is the oppositely directly force dissappearing at large magnetic field?\n", "\n", "It turns out that we are getting an interesting effect when the non-cycling\n", "transition from other beam starts to affect the population in the cycling\n", "transition ground state. Let's start by going figuring out the line to go along\n", "for to stay in resonance with the rightward going beam.\n", "\n", "Let's first look at this along lines that are going along $\\hat{x}$ for various $v$:" ] }, { "cell_type": "code", "execution_count": 168, "metadata": {}, "outputs": [ { "data": { "image/png": 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F6e4pGIulwBp3H04N7r7VzLYB+7VuWkII0VnUluZYNINONgr2BraUad8BLK52spmtrHDo4MlMquWUy+WTrZ+QkRPyQ7GkcnTV26wgJ3TPj3LCrCg3FGomxFLMM8L5XcnVP6s4MiH819y1+wIA5j0V5II5a3cCsODepwCYuzjUVdi1X9wnOWHh+OWEqomOJCcI0QCsppBELTRsDp1sFGwA9i3T3gs82eS5CCFER+LAcL6WjIaiGXSyUbAWOMHMut09B2BmS4B58diYuPvh5dqjB+Gwek5UCCGmM5IP2odONgquBP4ZOBb4RWw7ERiicghjbRhje7qmislbIUKh4GbPlmMeDh18KEYfJDkh1lDomheWb3glOaHb6JoZzsn3lCYnGkpywh4LAZj7VCzHvHYHAAvuXR9eLwrRC31RTti55zjkhPEkOoK6yQkgSUF0Lk5t0QdT5WtzqtOxRoG732JmvwC+YmZvI3gIPg983d0lHwghRFOwmJyoej/ReDrWKIi8DjgP+DFh0eE3gE+1dEZCCNFJqHRyW9ERRoG7P0YZM9PddwDvaPqEqv3/b/f//F66L7jZo4yQkh95lBMoRCfEbEhRTrC5UU7oiXLCQFehbkIqv5zc/LlZ0f2fohN6o5ywZy8A89YHuWBOlBPm3xecPUlO2LVf3O9ZWjshjZefCfkoXViSEdLeMu+zznJC8akJyQmiU3BqW1NQr69FM3st8AngUOB24IPuXjaazMwOAD4NnAJ82t3/rU7TaFumdfIiIYQQ7U/erepWD8zsBOB/gG8BLyFEof3SzPYp03d3QlbcOXTQb2VHeAqmHFNtkWKlBYmFhYixPVZdTJ4DT4v8YvVFm5MjH//NYKq0GPfx1EI1xJ7ShYODC8OBnXsuAmDe+uAZmLN2OwDz71sHFC9EnB/7h4/AYK+VeA2K55euLc+BEI2hiWmOzwAud/fzAczsNGAdcHo8VsDdN5jZS9z9HjN7c7Mm2Go6xvoRQgjRfjjVvQR5t9FG9zgxswOBFwJXFK7t3g9cD5xQdm7u90zqolMQeQqEEEK0lCZ5CpbGfbbY3WqClCCQUTD1aKNFilVd3NkFiak95TVI6ZJjXgOf4ZAkhdlBRkh5BDxKDjYQ+0aXfleSE7ILEaOcsGvPkLF67vqQLnnOmiAnzLvnifB6UWjvO2ABO/eKUkJahDi3SXJC0TmVkJwgpjPjSF50cKUU85USyhWxd9xn09vXlNq+U5BRIIQQomW4w3C+upJdhyqJG+J+YaZdqe2LkFEghBCipYxDPni4Bo9AJVL6+mXAHUXtS6khtX2nIKNgutFEeaHgNvfSfbX+BTkhF18X5TfwoeiiL6Qfjq9j5UWPlRU9RScMRhd/Vk7oKZUAsnLCvCQnrN4aXt/zOHOjlLDrgPAgsSvKCQO9MeVylCZyMXfCeOWEdGDU9595XVIllx1biDYnLTSspd8keSBurwMuBzCzecBxKGldAUUfCCGEaCnuVnWb/DXcgTOBt5nZu8zsUOAiYCtwkZm9wsw2mtmrJn2xKYw8BUIIIVpKs6okuvslZjYT+CDwOeBm4Gh332JmeWCAUBSvY5FR0Gk0QF6oZMRnXdwVXd5F/7BsquTky+oulRV8VohOyM2M/QeTrFBBTpiZkRN6k5ywBIC56xeOSAl3rQ5ti4OM0Lc0JEQqRCf0lo9OSGmSs3JCIRrBSl4Wvf+ilkkkPCo+vTC25ATR5jS7SqK7XwhcWKb9OmBUZsN4rGM+STIKhBBCtJQO+s1te2QUCCGEaB2qkthWyCgQpdSx7kL2c15JPijXnppGRSgMp+RFGTmhJ+xz8XVXik4oTozEiKs/l6ITYkTBQG8Pu/bcHYB560PlxdmPbgZgzh2Phv1uob1vWZATdu01M56bkRNidEKq9JjmSnd6U7G9OHqjAfUTik9P6IFMtB+1LiTUf95mIKNACCFEy2j2mgIxNjIKhBBCtJQ6ZCsUdUJGgaidSUYu1BqlULYtedGTy31UlEKpiz4foxMsJTuKMkJXV6mc4PETkO+xosiE4P+fteceAMxbF+SCWY9tAmDOHX8I+8VBTug/cDcAdiY5YVGSE0bGhjJyQopO6Br5UmxkOebi0xOSE0Q7kHOlzGkXZBQIIYRoGZIP2gsZBUIIIVqH1ygfyCpoCjIKRP2YoLww1kNCtQRIno/thXLM8UCUCQpJj1J0QnxdiGLoSq59L5PoKLg0B3pnATBr770AmLcuyAWzH90Y9rc9HPZLgswwsDTKCc9IckJXHC9OMckJqSRzt5dICVAHOaFwvEJ75vRiJCmIZqM8Be2DjAIhhBAtRCGJ7YSMAiGEEC1lHKWTRYORUSCaxwTkhWoRC5WiFAr7JCsk93uMUvBYpyAf3fU2PCIlpOiAJCPkops/KyfM3ntvAOY9EeSCWY9uCPvbHgzHl4Qyzf0HhqRIo+SEeWHcXI+NREHMGB2ZABOQExITiFJQhIJoJk5tawq0pKA5yCgQQgjRUrSmoH2QUSCEEKJ1eI1GgVwFTUFGQYOY0TWSjCOXz+OZNoDhfJ4uM7rMJtQ3707evWxfA7qL2hvdt9sM67Ix+7o7udTXrPAhL/Ttrq0v1foW30svvZeei327Q99U5jhnebw7vOcUmWDDoa/NiPd9VkxuNCuMy/zw8cktDoN0P2MfusxY8GRIetTzh6fJ55yeW1fRPaObebsHOWHgwD3I5fL07TML6zIGFnUxPBdynmd4pjGjqwtPkRDdHv72aQ4pyCLe95npPljpvezqzvyNyJf/e9r4//bp+7vkb29j/+3H07fS3zP97WfUuW+5z1zqW8vnczx909ya1bfen/uioeuKfu/bCHfXVscNWLnXgcu8mA9cfZUvO3u5Dw4PF9rWbN3iy85e7mf+8vqSvh+79hpfdvZy39rfV2jbsHOnLzt7uX/yF9eV9P2363/hy85e7uu2byu07Rwc9GVnL/cPX3N1Sd8v3HSjLzt7uT+yeVNJ+7Kzl/t7r/pRSdt5t97iy85e7iufWl/S/pzzzvbTfnh5SduFd97uy85e7rc9vrak/fkXnO8nX/a9krbv3nePLztnud/42KMl7cdceIGf9N1vlbRdcf/vfNnZy/2ahx4saX/5xRf5yy++qKTtmoce9GUrlvsV9/+upP2k73zLj7nwgpK2Gx991JetWO7fve+ekvaTL/+eP/9r55e03b5mrR/8+bP8olvvKGk//ZIr/Hn/9qWStlVr1vuL/nq5/9cVt5S0//u7L/JXzD+1pG3Nmo3+Z8ef6V++9MaS9o9f+lM/9P//ou8cGCy0rdu23Z/572f5Z679RUnfT/3sOj/o82f5hp07C21b+/r8oC+c5f/y05+V9D3z+hv8wLOW+5otWwptg8PDfuBZy/2DP7mqpO/ZN9/kB35xuT+w4emS9kPO/qKffuUPS9q+dttvfNmK5X73unUl7Ud++Vz/m8t/UNJ2yd13+bIVy/2WNatL2l98wVf9jd/7TknbD1be58tWLPefP/JwSftxF33DX/3ti0vafvzAKl+2Yrn/+IFVJe2v/vbFftxF3yhp+/kjD/uyFcv9ByvvK2l/4/e+4y++4KslbbesWe3LViz3S+6+q6T9by7/gR/55XNL2u5et86XrVjuX7vtNyXt7/rRD/2Z53yxpO2BDU/7shXLfcUtN5W0f+AnV/myFWW+I1ZU+I5YUeY7YsVy/+TPy3xHrCjzHbGizHfEr270ZSuW+yObMt8RK0a+Iw477DAHVnodvy979tvDD/nBp6tuPfvtUddrayu/WfzD1A0zmwG8ENgf2AuYCzwVt3vc/fG6XrDNMLOVM/fe67ClH//nQttUeQqYTN+yT4BW+xNgxadFanwCzI/vCXBUX8/jVt6rMCPXRZdZoWJjfiiM25MPHoKuwdi/L/yNenaF17O2OPl8nrlr++nu7qLn0afC+Rs3kxvOMWPP3bEuY/CgPdmxzyzy+Tx9i7qY0dVVtAgx3p+e8LfPx0WQua74N4oegfT0PuyjvS55d3Jk/p7mo++7Te5vX5iDPAUV+6a5TVVPwerPfZ7BJ9f/zt0Ppw6Y2cqe/fY47IAvvr9q39Uf+hKDa5+u27WnAq34Pa2bfGBmfwH8PXA8MI/y65zdzH4HfB8439031ev67Ub6UqrWlj6I9e7r45hDPfrmfHRaskb1rTS3SfW1Mn3j4XTfLV/StdC3K7Z3x77D+XDijNzI+Llcntxw6JgfDtZFPu+Q93AsN3Ld4Xye2JXUnOaQj6EBnplvQZK1CvfSMm1pnOK+RZ/Yifzti2XhKfW3H6Nvoz6f7dB3Ip/7Oj9DFsauZdxOkhha+Xs66SoUZnaYmd0M/IxgyXwR+AvgmcAiYBawD/A84J3AncA/Ao+Z2T+bmSphCCFExxKSF1XbOiF5UTv8ntbDU3AncBXwQne/s0KfJ+N2L/BNM5sL/C3wiXj883WYh2g3JljJb1znpGtMMMXymMfjxysfUyQn+aCQIjnlM0iVGVNeg5jGeHhe2A8smgPA7H0OAGDe43uG4R95EoDum1ey254hl8HgQSGV8s59Qy6E/sVhjKE4Vj6TIjnlNUhfBanYXLHnoGhX9HaLWiaZKjk7TOEa0/87XNQDp7b/LJ3hKmj572k9ntLf6O5/ld6Amf1LtRPcfZe7nwc8B7ihDnMQQggxRUmKzlhbh3A68JYxDIJR1Pv3dNJGgbv/ONP0WTN7d6X+FvibeO4Wd//1ZOcghBBiCuM1bJ3BRcDrJ3JivX5PG5Gn4JvAeWa21d2/W3zAzE4G/hU4FPh2A64t2plJuqcndO545IUqXzwpp0FKlVyQEywjJ6SUxRk5IUkA/YuTnLAUgHmP70XXw+sA6LrpXgAWRzlh6OBnALBjv9nx3FJpIjerVE5IcxiZa5x8IS1ymvNIeyNSJZcbpjCcZAWRQRkNC7R88UQjjIJ3EhZif9PMtrn7j83sDcAZwOHAduCzDbiuEEKIqUjneALankkbBWY2y90H0mt3dzN7B8Ha+YGZPQgcCWwBPg2c7e5bJ3tdIYQQ0wN5CtqHengKtpnZb4Hbgdvi9lvgVIJh8DbgC8Bn3X1bHa4nphvFTwn1/m6oNF4tLvFsn4wUMVpOiOmRUwRAcuVn5YRZSU4IA/QvnsvsfQ8EYN7aIBf4Q0+EsW6+B4BFuwc5YfiQfQDYud+ceG4ca36pVFGQE2aUygnZVUTuNVReTFSKUhjn36xYVtBvgah5zYC8CU2hHkbBz4HnA0cB7yL86fqBuwjhFavj8Z11uJYQQojphqzDYo41s9njOcHdv1Wvi0/aKHD31wCY2b6EdIwvKNofHbsdAGwys3sIxsJd7v7NyV5bCCHENEBegGLeE7daMMLdax+jIBFzMD8OXJnazGx/gnFQbCj8CeFNfLNe1xbTiFqjBSZLLXKBVWivtKo+ygUFF32UE/KptMAYcsLQ/BEpAWDOvgcBI3ICD4UU50lO6N19STh+yH4A7EzRCbuFiw1Vik5IckKaY9fIfFMseFZOGHnbFaIUJhFVoggFAegPPsIZrZ5AQ0snu/saYA3ww9RmZgcQjAMhhBCik5ITjYm7f7r4tZn9i7t/rplzqEftg7nj6e/uq939isleVwghxDRByYsqUXMywHpRD0/Bk2b2beBr7n5PHcYTom6MyytZKYfP6MIBNV3T4wCFcbpjdEJKejRjRE4YFZkQ5YS+3UIN5dn7PxOA+Wv2DScnOeGWUjlh/jPD8RSd0JfkhPkV5ITuMrJHRk6oqX5CyRstdMgcp2ZUR6GDcKux9kFH/if4Jk1OBliP2gefBF4G3Glmt5rZaWY2pw7jCiGE6ADMq28dyjuB/yYkAzwBwMzeYGb3At8hVEysazLAetQ+OMfdjyAYBquA84B1ZnaumR052fGFEEJMcyQfACEZYPFrd3fgHcClhGSA9wCXAfsRkgEudfdP1XMO9Yw+uAm4yczeD7ydkLPgvWZ2K/BV4Pvu3l+v64lpTtOiECp/23g1k7nS3JJ80OWl/Qqr9aOMEEsw26DRNRQOdQ2HfW52rHEwJ+wHF0Y5YUmUE5YeAsD8tfuHMWLtBH6zEoCFfwhywtyDQvRCITphcVZOGJEuCsmYapUTssmcGpj0SHLCNPQdfQwAACAASURBVEd/0ETLkwHWQz4owd23uvu57v5cQvjhA8CXgSfM7BwzO6ze1xRCCDGFkacg8XNgX8JD9QWEBIDbgBuBzTQhGWDdjYJi3P0Wdz+NoHt8EjgWuM/MfmVmR499dnMws9ea2a/NbLOZXWtmh7d6TkII0TE4kK9hq5NhMJ7vfDN7iZndYGZbzOxGMzu2PrMoj7u/xt33BvYH/pKwXuAG4BDg7wmJAP+ckAzwl/FB+x31nEM9CiItBra7+3ClPtHNcT5wvpm9mGAFvRS4ebLXnwxx4cb/AB8EriMkjvilmR3p7k+0cm6ihWQ9mdnaAJaVBdI+43aPbviumSHcoDvu58wOWkHvnKCmdZmzaVdYm7tja9j7zvDR7OoPg3UPxqiEhWHogRhVsHPvEBE865kh2dH8dUFO6H5kIwAz7n8UgEXregEYXBpkhZ3PCNJl/yIbKcPcE8YuyAnlEh0V7UepAVk5oZD8aRxJj1SWuTNp0h9uPN/5ZvZ84BfAWcDfAe8FfmpmR7v7XY2cZyuTAdZjTcEG4C3AD2rp7O63ArfW4br14Azgcnc/H8DMTgPWAafTBpmlhBCiE2hidMEZ1P6d/3HgXnf/ZOz7IeCVwAcIi/+aSrOSAdZDPpiStrmZHUiwtgqJlOJCyOuBE1o0LSGE6DyasKZgPN/5ZjYTeH2mrwPXZPu2kkYkA2xomuM2Z2ncP5JpXw28pNrJZraywqGDDZjR1dDlGp3LBE3Qqt7Jco8q45URRq5Wsk/duuMkusgDMLMrvD5w4Waeu+99ACzu3gHAg/0hauD2TQcAsHbzIgD6tge3f64/hAoMR3lhaDDs+w4MUQY9R4YkRrM2hlLL8x8fDK839wEwY22Y06yhWfQPl0YkJB0wn95FqtWQcfsXZAUraR4tq6Rxyv0Nqj0iNurvLSaEtf6+Hlzpu9fdq60HG893/r5Ad4W+u5vZ7OkaTdfJRsHecb8l074DWDyZgZ+52xJW/sM/TmYIIYRoOw7/2jf43ZPr6z5uk+SD8Xznj9UXYBHwZP2mVh4zexbwdeCPCREHqwkRCXfE/b31Nk462SjYEPcLM+291PDHrmSVmtnKhzZtPOyQc1dMcnpiTCb5xDLmk2Slb6gKT8CVFyBmFh7OCM/eXTOjp6AnPJMvmDvAPgu2AvCCRasBOG7+/QAcMGMXAL8fCgsFr9ka8oHdtTlUR3xq2wIA+naGVYL5/viRjjkQugbiQsWB8HrGjrDvCZdj5k4vzDflRBiO+UhTKuSRlMilCw+znoJ29BiMeU0xblZv2tiYgWv/Az1cg0egEuP5zh+rb77oeEMwsw8QjIH/Ao4mrCV4mhB9cBQh06EDOTO7393/qF7XrpdRcKyZzR7PCe5et/rPEyQ6UFlGsLoSS4uOTQgHhvP5qv3EJGhno6CgHGVW2Xs0CuLe4n7Y8+Tiv/Pk4inJiT9c8jodzxWdW7zPxz35aBTk06WtbLvlioyCeGw4DZHZp/dXKo4go6CDaEg1w1rXDEz+2uP5zn88XnFZpn0psG6saLs68SlClMRRwHnu/v50wMz2I+QqSJEIR9XzwvUyCt4Tt1owws1utVHwQNxeB1wOYGbzgOMIfxAhhBDNoDnyQc3f+e7eZ2bXxr5nxb5dwKvTuU1iDXBvZm5rCUbMjxpxwXoYBWfUYYym4+5uZmcCF5nZjcAvgc8AW4GLWjo5UZ1KXyKTiHOvOa6+Qgpm89JH5ZHx4j4fXAj5XDgwMBReDw/NYEdfWED45M4gB9y7MCwUPHrxwwC8ct7vADhzr9sB+P1uIcXHT3YcAcAtm0KegjXbgjS6bWdw3A0NhI94Wog4tCjs+/eOKZaHjK6YA6FruMpCwkqeEqq0kzlfiAzNWFNQ7TvfzF4BfBd4m7v/FPg88DMz+2Rs/wCwO3Buo+ZoZrPcfaCo6RvAyXHfFCZtFLj7p+sxkVbg7pfE0JMPAp8jJFM62t2zi0uEEEI0iiblKRjrO9/M8sAAMBT7/sLM/pLgRfgQQXI41t0fauAUt8XoivnAW4GfAs8zsxXAR9w918BrA/XJaHiEu/92gud2A8909wcmO4+J4u4XAhe26vpCCNHpWBOXYFX6znf36wgp+Yvb/hf43yZNDeBa4I+AmcB/EAyXfmA2cLyZXQj8DHgg5k2oO/WQD+4wsy8AK9y95qWpZvYqgnvmMoILR4jJ04hKfBX93hlZISMXmFWSE+I/cuFALmfkknt/MHwkt+4MIQCroxzw694gDxyzKMgJr5kfQrX/abfw+uEF9wDwkx1hYfaNm59Zcn4abzDKCfkoXfhwV0HOsFyaV5x/PrNysMavoIqu4BYWtbHs30C0D05tf5gOKIrk7icCmNkmgndiX0LCpRcCRwJnE+5En5ndC9wN3OnudZMX6mEUnEgInfhHM7uMYMX8ClhdbMnEBR1HAccT0iI/i6Ddn12HOQghhJiqdMAP/jhZD/w8pjYGwMz2IhgHf8yIofASwt1rH6PA3a+NCRbeAbwPOIVk+5ltAfqAJcCseMpOQu7mN09UdhBCCDE9MGpbaNgJTp4kx7v7c7LH3H098OO4pf6pSFLd5Pi6hCS6+yCh9vMFZrYP8GeE0o97AnMJSReeIoRW3NSEGE8hAo2QEyo3jDmHMeWEJCXElMNJTkju/uT+f2RLqHJ4Y2+QB1J0wmvnB/v6HxY/BozIC0lOuGnLwQA8unW3kvGGBmcUruXx2kQZwfMxTXNWXqjyBT4q6iJRIahDCHkKCiQ5/ovuvqla51QkqZ5yfD0WGs51913pdSw/+d+THVcIIURnIAOxQMvl+Hp4Cp40s28DX3P3e+ownhBCiE5CRgHQHnJ8PYyCTwLvAv4/M7sd+CrwPXfvq8PYQtSXSSQ9qvQ0UzlKIas/lF6rWE4onJpCs3KhCmI+uvT7h0rlhJScKMkBv1qY5IRQ1O3EBaHq4nsX/QGAV84PyY9+sijICTdvDnLC6m2LK0YmEK9dSGKU9ik6oZKcUCnJUTU5hsY/MSoKoQ1pXprjKUGr5fh6LDQ8BzjHzI4BTgfOA1aY2beAC9z9vsleQwghxPRF8kF5WiHHd1XvUhvufpO7n0pI/vBJ4FjgbjO72czePt6CSUIIIUQnYWZzWz2HupdOdvethNzQ55rZSwnegy8DZ0fvwdfc/Xf1vq4Qk6L4SWWcruV6JD0qSAnZiouFREelcsLAYHi9MSMnPFaQE4I88NLdgpzwmhid8L5FpbUUrt5xBL/eciAwIkVs3xXGGpXoKMkK3aVJjlKZZiskParw9svdjhokBaj/k2TxeJIS2gB5ChItX6NXN09BwgrfbuDut7j7aZR6D+4zs1+Z2dH1vrYQQoiph+Wrbx3CJ4GXAXea2a1mdpqZzWnmBOpuFAD3mNlfFDe4+zZ3P9/dnwccDawCXtqAawshhJhqeA1bB+Du57j7EQTDYBVhjd46MzvXzI5sxhzqLh8Ay4BrzOwa4MPufn/xQXe/Fbi1AdcVoj7UuSxzTUmPspEJlMoJBVkh9Ysr//PDqQxzkBOGRskJofbBTTE64UWLHwXgNQtCifZ3L1rFX8TIhGtiZMKtm4OcsDpbhjnWZchH6cLjtelKckLcZ+SEondZilH9ntYYLTAZeaFqVIloLF7j368DDAMz28/d17r7TcBNZvZ+4O2ECL/3mtmthAi/77t7fyPm0AhPwYHAOcBxBK/B+Wa2RwOuI4QQYjogT0HiPjN7XXrh7lvd/Vx3fy7wJ8ADhDV6T5jZOWZ2WL0nUHejwN03uvuHgEOAiwkWzoNm9lEz66n39YQQQkxtzKtv0x0zmwHMB7qL2s4zs0OgeWv0GiEfAODujwPvMrP/BD4NnElwf/yzu1/aqOsK0TAmWEdhfEmPqtRP8FJZoSAn5EvlhMHo4t8c5YTtUQJYvXURAL/uDRLBixY/yqujlHD6ohCh8PIYmXDNjiMAuHXzMgDWRDlh+66QTC1JFVk5wWN0gg1n9pnFYl70PirSQnmhqgwk6kcH/OhXw92HzexuQorj62Ptg/cCPwceLOq3DTgfON/MXkx48H4pcHM95tEI+aAEd3/Q3d8KHAZcB1xiZrc0+rpCCCGmCJIPEh8nlEZeY2Zfj20V5Xd3v9Xd/87dz6rXBBriKTCz+cChcXt23B9EWIQ4E3hRI64rhBBiaqHSySPE2gcvB84C3kkwh75iZssJaY3vAu6O+9/GlMh1pe5GgZmtBZ6RXsb9TmAloXDDfXETYmpTxyiFmusnZJpHyQnJRR/lBI8RAUMx8dCWGEGwI0oAa7YsKkgJL1i8GqAgJ7xz0d0A/FmMTvjZ9hAR9ZsoJzy+bWEcK0YnRDkhJTnyrnHICWn+4/Vd1klegOo/TJITGoRqH5Tg7jcCLzKzg4CHgGuAHiCF9EO4Gzkzux+4y93fUa/rN8JTsI1Q6jH9+N/n7n9owHWEEEJMBzrkB388uPsjZnY1sMLdrwMws6XA8wllk4+K/z6FUFWxLjQizXHdQySEmFJMYEFizamSC/kMRqdKhtLKi1DGczBc6jnYOjCDndFr8PjWXgBuW7gUgOcvXgPAKxYGx947F90OjHgOrtseFiLetjn0f6LgOQjjDUevhA8mz0FKk0xhLl2xvluh4mKab5eXvv1KlRezjOfe68m/beigjIXjwt1PyLx+DHgMuCK1mdme9bxmw6IPhBBCiFrohJDDRuHuT9VzPBkFQgghWouMgrZBRoEQjaaeckLlhtJrVZITMrKED9uIlBDzDWTlhNsXHgCMyAl/vnAlAKct/g0Ax85fBcB120Oa5Ds37w/Auign7CzICTGfQdzTbeTTIsShON+0CHEo7tP0u6OckBYiVqrAWKUwZdlzKqEfquaghYZthYwCIYQQLUXLOdoHGQVCCCFai7wAbYOMAiGazQRc2eNLlVx0kVrkhCQlZHIaDMe8A7ui+z9FF9yxIMgJz138OAAvXxjSI5+2OCQq/bMFITrh59vKywlpvNxg90hOg2wugygfdGX2XpAT4vvqysgKiUryQjkmmm9CP2R1QwsN2wcZBUIIIVqLjIK2QUaBEEKI1iKjoG2QUSBEO1CnCowTkhNi4piCC76QIjl0Ho4u/R0xauCR6P5ft30BAHcv2A+A5y4KcsLxvUE+eMduQU542YIHAPj5tpDX7N7N+xbO70uRCQMxMiEjJ/iM8jJC12Cac0qlHF+nKIVK0Qjl7ut4IhZqOa/W80UByQftg4wCIYQQrUMhiW2FjAIhhBAtw6gtzbHCFpuDjAIh2pFmyglJSkj1B9IK/zRWoW5CeDkcXfxJTkjRBE9uK5UTjlz8BADHL0xyws0APLxgCQA3bHs2927Zt+Tcvr4eAHJJToh1E/LdcR+/sboGk5wQXw/EuUY5IfUblfSoHJXubY0FK8c97kTGmuZIPmgfZBQIIYRoLTIK2gYZBUIIIVqLjIK2QUaBEFOBhsoJ5b+Rs3JCVlbwXHDx55KcEF3+SQJYHyWBexYEiSDJCccuDNEIp+x2C48uDFLC9dueDcB9m/cB4Knt88NYKdFRHJskJ8SoBC9EI5RGJXT3Z6IS4jddvijpUdVSybUmQJrID5oiF0bwGuWDTronLWQspU0IIYRoPF7D1kTM7J1mdpeZbTSzH5rZvlX6H25mV5qZm9mpzZpnI5BRIIQQoqWYe9WtaXMxezdwPvA54FhgAfArM5tTof/zgDuAoaZNsoFIPhBiKjLBfP1l5YSsH90znbMJj7xClEKSE4bDs8bO6PLvj3LC01ESuHd+eOg6YvE6XtYbyi6fUohM2AOAX217FjAiJ6Rz01i5/hidEKMSUpKj/MwoI8RohBSd0N0X22M0Qn6mjUgL2foJBYmFsckmSKrn71anyQtt8n7MrAf4JHC2u38/tp0CrAVOBr5Z5rQHgOcCA8AbmzPTxiFPgRBCiJZiXn1rEscA+wBXpAZ3fwK4Bzih3Anu3ufuv2/O9BqPPAVCCCFaS+0/+geb2cqyQ7gfXoeZLI37RzLtq4H96jB+2yOjQIjpxDijFMo9gY27fkKtckKMHBiRE+bx2wXPAOCwxU8CcMzCBwH4691+DcCjC3YHRuSE325+RuHc4rHyKdnRjIycEKMTumNUQtdAeD1j10hkQq4nzjtTP6HwfirVUWily3s6yQvtFX2wd9xvybTvAA5tygxajIwCIYQQLWOcaY4fnqhHwMxOBr5XpdsZcb8Q2FjU3gs8OZHrTjW0pkAIIURraUJIortf6u421gbcGrsvy5y+lLDYcNojT4EQ05kJJD2adDnmanJCTHa0a7CLtf0jUgLAb+cHeeA5GTnhrUtCGeZHF4bohJu2HRL6bwr9N8TzB/pmApXlhK4UnTBohQRHM3aWJjrKRzkh1U+gKOFR2dvQjpV6pljdhTaqffBLgnTwOkKYIWa2FDgC+FQL59U05CkQQgjRWtyrb02Zhu8Cvgh8xMz+0syOAC4B7gV+BGBmp5nZBjN7blMm1WSmtafAzF4K/CfwJ8Bx7n5D5vh84Bzg1YSFJN8B/s29iZkyhGgm7eA5SPpxvnvEa5DJaZCe/FcWPAfrATimN3gO3rKkdCFi8hzcv3nvkvOznoN0vfxMG8lpEFMkz+jLeA7it2OuJ3oIYv+UzyDlN6i6ILHdaLdFiu210BB3/4yZ5Qi/HQuAXwCvd/dc7JIH+oHh5syouUxbo8DMXktYVHJdheMGXEvwlrwSOBD4b2A28LEmTVMIIUSbPYa5+5nAmRWOXQxcXKb9MdrfJKzKdJYPbgGeRXAFleME4CXAqe5+n7v/CPgs8D4zW9CkOQohRMdj+eqbaA7T1lPg7hsAzOyZFbq8CVjl7quK2q4m5Lt+GfDjxs5QiDag3BPaRFIll/wjM3hWTjArtI9ICTGvwHDY9w0Gd/+6/uD+37RjLgD3b94LgEMXPQXA0b0PAfDWJWHR+KMLo5yw9ZCS/hszcoIPdJMrpEZOkkKYSndMkZwWIs6MckKqsJifNZIqGUYWKFJJTkhMlWfIsebZqPfQZp6CTmbaGgU1sJTyWaugQzJXCSFEO9BG0QcdTycbBXsTQ06K2BH3i6udXCnVJnDwZCYlhBAdhVNbdIEMh6Yw5YyCGrNSjYo0KMMGQtaqYnrjviMyVwlRlkmmSh6PnFAsJcD45YRVW/YE4FmLngbgpb0PA/CmJb8BRvIa3Lr1oJL+m7bPK5ESAHJJDkhyQsxXkCoujopOiCuycrMp6V+otphNl1x8K6aKlNAktGagfZhyRoG7XwpcWoeh1gLZdJlLi45Vm0fZVJvRg3DY5KYmhBCdgVGbfCA7qjlM5+iDalwJHGFmBxW1nQg8DdzYmikJIUQH0ibJi8QU9BTUkcuAfwUuMbN3AwcBHwXOcPeBls5MiHaikXLCGJEJUF1OSBLAphhd8PstQS5IcsKLF4a1xG/a/TZgJDrh1m0HsWpzkBI2bw9SxGBKdDQjpkguyAjx2lEeKEQnRDlhZlyJlE/RDLPC62z1xcIjWNfI+56yEQp1RgsN24eONQrcfcjMjgW+AtwAPA583N3Pae3MhBCig6i14JEMh6Yw7Y2CuOCwrP3t7uuBNzR3RkIIIYqRp6B9mPZGgRCizjRETqie6Agqywn9UU54sj98pSU5YdX8IBEckuSE3j8A8Fe738aahUsAuHlriCJ+MEoPo+SEgfJyQi7KBCnJUXd/eD1ze2yfWdovH2so5LutIClYujnlIhSKmdaygkNeroJ2QUaBEEKI1qLf+7ZBRoEQQoiWIvmgfZBRIISYHJOUE8IQNdZNYHxywlNRTkiSQJIIDu7dWCQl3A7Amt4gJ9yyJcgJD23ZveTcoUJ0QpARRssJMblRkhP6wtSSnOAxOmF4dlH9hO74foojE4re74jUUnp3ppWcoIyGbYWMAiGEEC1FnoL2QUaBEEKIlmI1LTQUzUBGgRCivkzA1T0qQiF7kmc65tPQVvK6UHfAS+WEgSQnDIzICUkeeOaiDcBIZMKb9wh1Ex7rTXUTDgTGkBMGyssJ3bOTjBBlhSgn9GyHfGxLdRNyUU5IEoNXkBOyt2MUU1VWUO2DtkFGgRBCiJZhDlbDmgJJDM1BRoEQQojWoh/8tkFGgRCisdRDTsgmPMrKCellrnY54alYhnnLjjnAiDxwUO9GAF60KEYn7BGiEx7tDcd/s6VUTtiyPZw/3J+RE3rCPpeiE+aMyAkzdoVpzdwW9oVER1k5YWapnJDevnWVvu+KUQqJdpcVVPCobZBRIIQQoqVIGmgfZBQIIYRoLfIUtA0yCoQQzaXc9/9k6ydMQE7wJCUMhcasnPDI1pDMKMkJL+x9DIA37nEHAI8lOWHrstB/S+if5IQUneCFUsxRwphp5LKRCVFO6IlyQn7mSKIjgNzsJCfE6edLZYVRNRQq5IIq7tM2OFgt0QeyG5qCjAIhhBAtxGv0FMgqaAYyCoQQrafelReznoP0IO0jnoOC1yA9dVfwHKS8BIWFiIviQsTeRwF4Q/QcrI1pkpPn4OHNof/W5DmIKZdzA92FXAb5zCLEGbsqeA6iR2F4Tnyd0iQnz0HX2J6DhBvtuRhRv/dtg4wCIYQQLaWWPAWiOcgoEEII0TocyKkgUrsgo0AI0X7UW07IDuxFUkJSHNIYGTlhcDD45DfEFMlb00LEuLAwyQkviAsRX7/7XQCs6d0NgNu2LAPgD7H/1u1zSqQEGJERCgsMK8gJs7aS6Rdep4WIleSEdIOK78aYixGznRuMPAXtg4wCIYQQrUVGQdsgo0AIIURrkVHQNsgoEEK0Pw2REypEJqQuSUaIZX09N7ackKINDizICasBeMMedwIjeQ3u2HoAD28OUsL2HaU5DXKp0uJgaXTC8NxSOWHmzjDFniQn7MrKCbF9Zpx7d5GcUEZKGHVriu5L1bZ6oCqJbYOMAiGEEK3DvbY1BfImNAUZBUIIIVqLfvDbBhkFQoipRz3khDEiE4rHHEl4NLacsDHKCdt2Bt99ijbIygmv2+Nu1hYiE5bGvuH1tpgoaThFJwyWlxMKFReTnJCSHRXkhLBPskOxnJAiE0iVF7tqlBMaiYyCtkFGgRBCiNYio6Bt6KreRQghhGgg+Rq2JmJm7zSzu8xso5n90Mz2HaPvq8zsp2a2zsyeNrMrzGxpM+dbT+QpEEJMfSYhJ9SS6Kh4zJrlhP4UnVAqJyzt3cTze9cAcNIedwMjdRPu3Lp/7FtFTkgyQk94nQvdRuSEGJ0wa4vHfiNRDPlZxLb4xirJCZn33SjMwfLVf/WzElCjMLN3A2cDbwd+B5wD/MrMDnP3vjKnnApcCbwPWAJ8FbjWzA5396HmzLp+yCgQQgjRQhzy7VEl0cx6gE8CZ7v792PbKcBa4GTgm6Nm5f7WopcPm9lHgJ8Dfwr8otFzrjeSD4QQQrQW9+pbczgG2Ae4YmRq/gRwD3BCjWNsiPsF9Z1ac5CnQAgx/RiHnDCRugnFY1aUE4bDM9fQUGl0wtYds3lsa5AHlvZuAhglJ6yOiY7u3BLkhEejnJCSHRXkhCgB5AeijNATppKLSYwKtROSnLDZRyVEyiY6yndn5IR0Gxrpv2+fhYZpLcAjmfbVwH41jnEM4X/J3fWaVDORUSCEEKJ1OLUZBaHLwWa2suxh98PrMJu9435Lpn0HcGi1k81sPvAJ4DJ3f6wO82k6kg+EEEK0lrxX3yaJmZ1sZj7WBsRlmCzMnN4LPFll/JnA5cAw8MFJT7hFyFMghJj+tEJOKJRkDs9exXJCsZQAI9EGBy4KcsLzetcCcNKe9wCwdlE4XlFO6MtGJ0Q5If7EDcfohBm7jJk7wr97tqRyy1FOmFdJTojvr6tRYQgOXkvMoQM8PFGPgLtfClw6Vh8ze1X85zJgY9GhpYR1BZXO6wIuAV4AHBPXIUxJ5CkQQgjRWtpnoeEvCdLB61JDzDlwBMELUIkvAScBJ7j7Aw2dYYORUSCEEKJ1OLXJB02wC9x9F/BF4CNm9pdmdgTBA3Av8CMAMzvNzDaY2XPj688B7wJOAVaZWW/c5jR+xvVH8oEQovMo/oGpSxnmokFrkBOykQmbo5ywfWepnLC0dzMAz18UoxOinJDKMN8V5YTVWxcBsC3KCbkx5ISClLAzk+hoc6mcMJSVE3q8cQEI7RN9gLt/xsxywH8Swgp/Abze3XOxSx7oB4bN7KXAx2J71pPwTeC0xs+4vsgoEEII0VrayCgAcPczgTMrHLsYuLioqZmloxqOjAIhhBAtxCGXq96tGfqBkFEghOhwKv3WVHj+q4ucMEZkAoyWEx7buhgYkRP+qPdxAF6biU5IcsJjWxaXnF8sJyQpIR8THRVHJgCF6ISCnNBTJCc0ojDR+PIUiAYjo0AIIURraTP5oJORUSCEEOWoMbdBpcV3PuqEIs/BOHIaQJHnIC4kTJ6D/RduBeCouBAxeQ5WLwpVF+/ZEjLzFnsOktdgOHoMupLnoExOA4Ce7eH17E1OVy1e/olQh+REoj7IKBBCCNEyHMdrSF7k0g+agowCIYQQrSPlKailn2g4MgqEEKIWxpEqGcosSCw5YYIpkgdDzuHNcZ/khJSn4IDeUMfnjxaFNMmv2fM+AB5fFOSDu7bsz5otoW9hEeKu8DOQH6wuJxRSHtcbrSloG2QUCCGEaC35RoQ1iIkgo0AIIURrkaegbZBRIIQQE2EScsKYkQlFY42WE+I+F766k5ywJUYn7IiSQCU54cQ97y2REgAe2xxe7yzkNAhjlpMTvBHygTtei6dAhkNTmJYFkSzwFjO7PhaueNzMLjazJZl+e5nZZWb2tJnda2bvbdWchRCiY8nlq2+iKUxLoyDyt8A3CPWt/wZ4GUUFK8xsLnAzMAv4U0JlrC+Z2bubP1UhhOhgPF99E01hWsoH7u7AK4qaHjOzzwAXmtlB7v4IwWjYF3iBu28hlLx8CfBRM7vAawmcFUKIxDjkhLEjE4oGMrsiQQAADfRJREFUq1lOCH79lOxoLDmhEJmwR4hMWNsbUiTfu3VfoIqc0IjHSHe8ppBEyQfNYDp7CrJsiPsFcf8m4P+iQZC4GjgQeE4zJyaEEB2NPAVtw7T0FFTgGKAPWBVfLwV+nOmzOu73A1aONZiZVTr+7KENG3j8P74w0XkKIcTYVPJCZF0QXeF1V2x/uDvHLd3DAMwg5CwejqsH+/MzARjKxYWF+fjMmIZ0Y+jpDQD7T3r+RexiBzcPX11TP9F4OsIoMLP9gPcB57n7QGzeG9iS6Zr+1y2exOW6GM7lh55cv6p6V1HEwXH/cEtnMfXQfZsYHXnfBmCyP63PBubUYy6Rh508O9lWc/86XluUYcoZBWZ2MvC9Kt2Oc/cbYv9e4CrgAeDTRX02AAsz5/XG/ZPV5uHuh1eY38qxjovy6L5NDN23iaH7NjHG8JBOCHc/qZ7jickz5YwCd78UuLSWvmY2G/gRMB84xt2LjeS1wLLMKUuLjgkhhBAdxbRdaGhm3QSPwrOBV7r7+kyXK4HjzWx+UduJwH3u/lCTpimEEEK0DdPSKIgGwcXAcYQogw1m1hu3WOaDrxPktUvM7FAz+1tCPoPPtmLOQgghRKuZlkYB8GbgbYQ1AjcQFhSm7WMA7r6BkLRoAXAr8B7g7VGeEEIIITqOKbemoBbc/bvAd2vo93vg5Y2fkRBCCNH+mCtLlBBCCCGYvvKBEEIIIcaJjAIhhBBCADIKhBBCCBGRUSCEEEIIQEaBEEIIISIyCoQQQggByCgQQgghRERGQR2wwFvM7Hoz22Bmj5vZxWa2JNNvLzO7zMyeNrN7zey9rZpzO2FmLzWzG83MzezYMsfnm9mFZvaEmf3ezM4ws0oV5TsGM3utmf3azDab2bVmpop/ZTCzw83syvj/69TMsRlmttzM/mBmq83sXDPradVc2wUze5WZ/dTM1sXvqyvMbGnRcX0mpykyCurH3wLfAF5AqKHwMuDydNDM5gI3A7MI6ZW/CHzJzN7d/Km2D2b2WuA6YFOF4wZcCxwBvBL4CPBh4HPNmmM7YmYnAP8DfAt4CaEU+C/NbJ+WTqzNMLPnAXcAQxW6fBt4A3AycEr89yXNmV1bcyqhaNyfACcQKshea2Yz9Zmc5ri7tgZsBCPBgYPi678H+oFFRX2+CjwCdLV6vi28T7sD+wLHxvt1bOb4ibH92UVtHwO2AwtaPf8W3rfbgO8VvZ4NbAbOaPXc2mkD5gDPIvyoOXBq0bEjY9uritreAuTT51Zb4b4cH+/V8fpMTu9NnoLGsSHuF8T9m4D/c/ctRX2uBg4EntPMibUT7r7B3R8fo8ubgFXuvqqo7WpgPsEb03GY2YHAC4ErUpu79wPXE57qRMTd+zzUOCnHXxF+yK4rarsaMODVjZ7bFKP4+0yfyWmMjILGcQzQB6QPzlKCV6CY1XG/X7MmNQXRfRtN0nbL3ZdOvScTYSmwxt2HU4O7bwW2ofuY5RiCd+Bu9Jmc1sgoaABmth/wPuA8dx+IzXsTSjcXsyPuFzdrblMQ3bfR7B335e5Lp96TiVDu/xboPpZgZvOBTwCXuftj6DM5rZFRUAUzOzmuWh5rO7aofy9wFfAA8OmioTYACzPD98b9kw19Ey1gvPdtDDrqvtVIcuWWuy+dek8mQrn/W6D7WMDMZhIWTA8DH4zN+kxOY2QUVMHdL3V3q7LdAGBms4EfEbS117j7jqKh1gLLMsMvLTo2rRjPfatCR923Gknve1mmfSmde08mwlpgPzPrTg0xjHgeuo+YWRchEuMFwCvd/Yl4SJ/JaYyMgjoRv1i+Bzyb8AFan+lyJXB8dMUlTgTuc/eHmjTNqciVwBFmdlBR24nA08CNrZlSy3kgbq9LDWY2DziOojBYUZUrgUWEyJfEiYTwxataMqP24kvAScAJ7v5AUbs+k9MYGQV1IBoEFxO+lN8EbDCz3rjNit2+TtDdLjGzQ83sbwn5DD7bijlPIS4j/ABeYmZHmNlJwEeBLxSt1+go3N2BM4G3mdm7zOxQ4CJga9yLGnD3W4BfAF8xsxdGOevzwNfdvaPd4Gb2OeBdhNwNq4q+z+agz+S0RkZBfXgz8DaCrnYDYRFO2j4GIfSOkLRoAXAr8B7g7e5+aSsmPFVw9yHCk9xThHv778DH3f0LLZ1Yi3H3S4DTgfcDNxHyFBydCXkV1XkdcAvwY+ACQgKyf2jpjFqMmb2U8L3VQ/A8FX+ffVmfyemNhYcOIYQQQnQ68hQIIYQQApBRIIQQQoiIjAIhhBBCADIKhBBCCBGRUSCEEEIIQEaBEEIIISIyCoQQQggByCgQQgghRERGgRBCCCEAGQVCCCGEiMgoEEIIIQQgo0AI0SDM7Dgz+9NWz0MIUTsqiCSEaAhm9gTwgLv/WavnIoSoDXkKhKgDZvYBM9tuZvMz7S83s0Eze26m/SozG4r16SuN+a9m5mNsS2qdR70wswvM7LdmtsHM+szs92b2FTPbO9PvSOAZwCXx9YlmNmBmRzRiXkKI+jCj1RMQYppwOvAdd9+RGsxsFvAN4Cx3vzfT/3nASnfvq2HsrxDq1mfZXss86oWZdQFvAx4F/gkYBp4PvAd4jZm90N2fjt1fDmwCvgfg7leZ2VWE+/GSes9NCFEfZBQIMUnM7BjgMOCUzKFTgT2BLxb1XQXsBSwC9jKzzUX9P+3uK8pc4lZ3v3QS86gXzwLmAte4+0Wx7VtRJvhP4K8IBgwEo+DCjNFzJnC7mb3C3X/WoDkKISaBjAIhJs/pwO3ufmem/e+By4qengFeCRwP/BfwKeA7Rcc2NGge9eKouM+O/4e4nw9gZj3AMcB7izu5+x1mdivhvsgoEKIN0ZoCITKY2YejZv/uTPvnY/vfF7UtAt4EfC3Td1/gSDI/fu7+GLBPfHl1PPdnwP3Az8zs2ROcc6V5XBO1/+5M+7vie3nzOC4zyigwMwP+miAl/CQ2HwPc4O5/YDTXAMdHw0EI0WbIKBBiNF8FNgIfijo6ZvY24KOE9QHnFfU9hfCD+N3MGGnF/a/KjP/HQD9Bl381cBbBc3A08PUJzrnSPI4C7nX3XJl2GP3UPxbPAwaA9Wa2j5n9OXAlcALwbndfGfu9EDi3whg3APNiHyFEmyH5QIgM7r7TzM4BPg2caGarCQvkLif8kBdzOvBtd9+Zad8fcGB1mUu8EJhNMDz+xmNcsJmdRDAYJsKoeURvxR7A/5TpfxSwDXh4HNc4CphFqczxGPDHxQsp3f0LY4zxWNzvP47rCiGahDwFQpTnPMLq/n8Cvg/cRdEPOICZvRQ4ArigzPl7AluyT+gxdG9fYCXw4eLxgKeBrHFRlTHmUdYbEL0fzwXuyryf75rZejPbZmYPFssnZrYfsDvwA+A44HXA8vg+f5ANSRyDZFDsVWN/IUQTkVEgRBncfTNBn/8TgkftJHfvz3Q7nRAZcHeZIeYC5cINk9v8Qncfyhw7gPKehWpUmkcyCu7KtB8a55ddG3ACcDKwG/A+4Dwze3FmrGvc/QZ3/5G7/xPwd4SohH+pca7pnsytsb8QoonIKBCiDHHh3onxZTewJXO8F3gzmYV9RTwNjEouxIg8cE1mvP0JT+LjihyoMo+jgBxwX6b96LgvNhYOImj9d7j7MHAdsOv/tXf/IHZUYRjGn68ILkQhS0AIWRMJAQURNptACkERhYgasMtGLGKTykowKrETAikUDMZCIhLLYCFIbAKxEkVIYSMRxUYQTZqQqM0Kn8V3Rifj3ess3l0WfX7NcGcOM+dW854/cw5//YcuFAyDx8V23D+yyt39ro0sL2kDGQqkgYjYQo3D30m1gHcBRwfFngNWgNXWD7gG3BERdw3OH6Bay98Mzi+145U1VndaPZaAn/s9HK1H4Pn2sx8KFqkliW9FxA7gHeBL4FLv+u/UsEfffe14nXHubkdDgbQJGQqkv3sXeJhafOhtakLeifZC7XQT+35b5R7dxLt9g/MHmPw1QNfSXusaAxPrERHzwG5gPiLmepdeoz4ZhNuHKhaBvRHxK/AjsDUzH+8NcewDrg4Cxhxwuv08N7K+Xfj5amR5SRvIUCD1RMRJ4BhwIjMvt+WC36Mm8j3VyhykJuqtNnQA8BnwC7VQUXfve6iW8qQ5CEtUV/9wOeRpdZ1Wjy6MbAE+jojjEfE+1eNxvl17pFd+kZpUua3V+aGIeLU9ZxtwL7ASEc9GxLGIOAV82+7xSmZeZJxHga8z84eR5SVtIEOB1ETEEeB1quX9Zu/SGeqF/XL7fRz4PDOHY/V/ai3sj4DlXg9DN8lwOPEPKhRcndLzMMm0enShYJmaOPgGFUieoNZEuAks9Mp3ezGsZOan1HoJy+3aHuB7Khicp3oHnqTmEzyQmacZISK2AoepLxgkbUJunSytUUS8RL2MJy1M1C/3INVN/nRmfjKt7KzrEREfUJsXzU34ymFYdjv1qeCOzPypnTsL7MzMZ2ZY3xeoQLE7M//tks6S1oGhQFpHEXEOOAgs/dPLecbP/QJYyMyFEWUfAy5k5va2s+NR4CxwODMvz6g+89RSzmcy89Qs7ilp9hw+kNbXi8CHwN4Nfu4eYOy4/S4gI+IG8B212+GhWQWC5n7gLWo3RUmblD0F0n9Q25L5UmauZcMjSf9zhgJJkgQ4fCBJkhpDgSRJAgwFkiSpMRRIkiTAUCBJkhpDgSRJAgwFkiSpMRRIkiTAUCBJkhpDgSRJAgwFkiSpMRRIkiTAUCBJkhpDgSRJAgwFkiSpMRRIkiTAUCBJkpo/AEmCcGSEitYwAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "v_inds = [200, 245]\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(3.25, 2.))\n", "im1 = ax.imshow(F2,extent=(np.amin(X[0,:]), np.amax(X[0,:]),\n", " np.amin(V[:,0]), np.amax(V[:,0])),\n", " origin='bottom',\n", " aspect='auto')\n", "cb1 = plt.colorbar(im1, ax=ax)\n", "ax.axhline(rateeq.profile['Fx'].V[0, v_inds[0], 0], color='w', linestyle='-', linewidth=0.5)\n", "ax.axhline(rateeq.profile['Fx'].V[0, v_inds[1], 0], color='w', linestyle='--', linewidth=0.5)\n", "cb1.set_label('$f/(\\hbar k \\Gamma)$')\n", "ax.set_xlabel('$x/(\\hbar \\Gamma/\\mu_B B\\')$')\n", "ax.set_ylabel('$v/(\\Gamma/k)$')\n", "ax.set_ylim((np.amin(v), np.amax(v)))\n", "fig.subplots_adjust(left=0.15, bottom=0.2, right=0.95)" ] }, { "cell_type": "code", "execution_count": 171, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(2, 1, figsize=(3.25, 3))\n", "ax_twin = np.array([ax_i.twinx() for ax_i in ax])\n", "\n", "for jj, v_ind in enumerate(v_inds):\n", " [ax[jj].plot(x, np.concatenate((rateeq.profile['Fx'].Neq[v_ind, x<0, ii],\n", " rateeq.profile['Fx'].Neq[v_ind, x>=0, 2-ii])),\n", " '-', color='C%d'%ii, linewidth=0.75) for ii in range(3)];\n", " [ax_twin[jj].plot(x, np.concatenate((np.sum(rateeq.profile['Fx'].Rijl['g->e'][v_ind, x<0, 0, ii, :], axis=1),\n", " np.sum(rateeq.profile['Fx'].Rijl['g->e'][v_ind, x>=0, 0, 2-ii, :], axis=1))),\n", " '--', color='C%d'%ii, linewidth=0.75) for ii in range(3)];\n", " [ax_twin[jj].plot(x, np.concatenate((np.sum(rateeq.profile['Fx'].Rijl['g->e'][v_ind, x<0, 1, ii, :], axis=1),\n", " np.sum(rateeq.profile['Fx'].Rijl['g->e'][v_ind, x>=0, 1, 2-ii, :], axis=1))),\n", " '-.', color='C%d'%ii, linewidth=0.75) for ii in range(3)];\n", "\n", " #ax[jj].axvline(-rateeq.profile['Fx'].V[0, v_ind, 0]-det, color='k', linewidth=0.5, linestyle='--')\n", " #ax[jj].axvline(-rateeq.profile['Fx'].V[0, v_ind, 0]+det, color='k', linewidth=0.5, linestyle='--')\n", "\n", " ax[jj].set_xlim(-15, 15)\n", "\n", "[ax[ii].set_ylabel('$N_{eq}$') for ii in range(2)]\n", "[ax_twin[ii].set_ylabel('$R_{i,l}/\\Gamma$') for ii in range(2)]\n", "ax[1].set_xlabel('$x/(\\mu_B B\\'/\\hbar \\Gamma)$')\n", "\n", "ax[0].xaxis.set_ticklabels('');\n", "fig.subplots_adjust(left=0.155, bottom=0.13, hspace=0.08, right=0.86)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Look along the line of resonance\n", "\n", "Firt, compute the line where the rightward going beam is always supposed to be resonant:" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(3.25, 2.))\n", "im1 = ax.imshow(F2,extent=(np.amin(X[0,:]), np.amax(X[0,:]),\n", " np.amin(V[:,0]), np.amax(V[:,0])),\n", " origin='bottom',\n", " aspect='auto')\n", "cb1 = plt.colorbar(im1, ax=ax)\n", "ax.plot(x, det - x, 'w--', linewidth=0.75)\n", "cb1.set_label('$f/\\hbar k \\Gamma$')\n", "ax.set_xlabel('$x/(\\hbar \\Gamma/\\mu_B B\\')$')\n", "ax.set_ylabel('$v/(\\Gamma/k)$')\n", "ax.set_ylim((np.amin(v), np.amax(v)))\n", "fig.subplots_adjust(bottom=0.2, right=0.85)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, compute the parameters along that line: " ] }, { "cell_type": "code", "execution_count": 172, "metadata": {}, "outputs": [], "source": [ "# Along the line v = delta - alpha x, we\n", "v_path = det - alpha*x\n", "\n", "rateeq.generate_force_profile([x, np.zeros(x.shape), np.zeros(x.shape)],\n", " [v_path, np.zeros(x.shape), np.zeros(x.shape)],\n", " name='res_path', default_axis=np.array([1., 0., 0.]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, plot up the scattering rate and populations along that line:" ] }, { "cell_type": "code", "execution_count": 173, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(2, 1, figsize=(3.25, 2.5))\n", "\n", "for ii in range(2*Fl+1):\n", " ax[0].plot(x, np.concatenate((rateeq.profile['res_path'].Rijl['g->e'][x<0, 0, ii, ii],\n", " rateeq.profile['res_path'].Rijl['g->e'][x>=0, 0, -1-ii, -1-ii])),\n", " color='C{0:d}'.format(ii+1), linewidth=0.5,\n", " label='$m_F= {0:d}\\\\rightarrow {1:d}$'.format(ii-1,ii-2))\n", "\n", "for ii in range(2*Fl+1):\n", " ax[0].plot(x, np.concatenate((rateeq.profile['res_path'].Rijl['g->e'][x<0, 1, ii, ii+2],\n", " rateeq.profile['res_path'].Rijl['g->e'][x>=0, 1, -1-ii, -1-ii-2])),\n", " '--', color='C{0:d}'.format(ii+1), linewidth=0.5,\n", " label='$m_F= {0:d}\\\\rightarrow {1:d}$'.format(ii-1,ii))\n", " \n", "for ii in range(2*Fl+1):\n", " ax[1].plot(x, np.concatenate((rateeq.profile['res_path'].Neq[x<0, ii],\n", " rateeq.profile['res_path'].Neq[x>=0, ham.ns[0]-ii-1])),\n", " color='C{0:d}'.format(ii+1), linewidth=0.5)\n", "\n", "for ii in range(2*(Fl+1)+1):\n", " ax[1].plot(x, np.concatenate((rateeq.profile['res_path'].Neq[x<0, ham.ns[0]+ii],\n", " rateeq.profile['res_path'].Neq[x>=0, -1-ii])),\n", " '--', color='C{0:d}'.format(ii), linewidth=0.5)\n", "\n", "[ax_i.set_xlim(-20, 20) for ax_i in ax];\n", "ax_twin = [ax[ii].twiny() for ii in range(2)]\n", "[ax_twin[ii].set_xlim(det - alpha*np.array(ax[ii].get_xlim())) for ii in range(2)];\n", "ax_twin[1].xaxis.set_ticklabels('')\n", "ax[0].xaxis.set_ticklabels('')\n", "ax[1].set_xlabel('$x/(\\hbar\\Gamma/\\mu_B B\\')$')\n", "ax_twin[0].set_xlabel('$v/(\\Gamma/k)$')\n", "ax[0].set_ylabel('$R/\\Gamma$')\n", "ax[1].set_ylabel('$N_{m_F}$')\n", "fig.subplots_adjust(left=0.135, top=0.85)" ] } ], "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }