{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Parametric plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When looking at Riemann problems, it is common to think about how a *wave* connects a *state* that is known to other states. For example, the Hugoniot curve gives the set of states that can be connected to a known state by a shock. Solutions to Riemann problems can be illustrated by the intersections of such curves in some parametric space.\n", "\n", "Here we will illustrate this by showing how the curves for various problems behave in the pressure-velocity ($P-v$) space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Inert case" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from r3d2 import eos_defns, State, RiemannProblem, utils\n", "from matplotlib import pyplot\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "gamma = 5.0/3.0\n", "eos = eos_defns.eos_gamma_law(gamma)\n", "test_1_U_left = State(10.0, 0.0, 0.0, 2.0, eos, label=\"L\")\n", "test_1_U_right = State(1.0, 0.0, 0.0, 0.5, eos, label=\"R\")\n", "\n", "test_1_rp = RiemannProblem(test_1_U_left, test_1_U_right)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This Riemann problem has a simple rarefaction-shock structure: a left going rarefaction, a contact, and a right going shock." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import display, display_png\n", "display_png(test_1_rp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution in parameter space shows the curves that can connect to the left and right states. Both a shock and a rarefaction can connect to either state. However, the only intersection (for the central, \"star\" state) is when a left going rarefaction connects to the left state, and a right going shock connects to the right state:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/alice/anaconda3/lib/python3.6/site-packages/scipy/integrate/odepack.py:218: ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information.\n", " warnings.warn(warning_msg, ODEintWarning)\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = pyplot.figure(figsize=(10,6))\n", "ax = fig.add_subplot(111)\n", "utils.plot_P_v(test_1_rp, ax, fig)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Varying EOS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As noted previously, it's not necessary for the equation of state to match in the different states. Here is a problem with two inert EOSs. This problem is solved by two rarefactions." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gamma_air = 1.4\n", "eos_air = eos_defns.eos_gamma_law(gamma_air)\n", "U_vary_eos_L = State(1.0, -0.5, 0.0, 2.0, eos, label=\"L\")\n", "U_vary_eos_R = State(1.0, +0.5, 0.0, 2.0, eos_air, label=\"R\")\n", "test_vary_eos_rp = RiemannProblem(U_vary_eos_L, U_vary_eos_R)\n", "display_png(test_vary_eos_rp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parametric solution in this case shows the pressure decreasing across both curves along rarefactions to get to the star state:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig2 = pyplot.figure(figsize=(10,6))\n", "ax2 = fig2.add_subplot(111)\n", "utils.plot_P_v(test_vary_eos_rp, ax2, fig2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Reactive cases" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once reactions start, the behaviour gets more complex, and the parametric pictures can clarify some aspects. An example would be a single deflagration wave that is preceded by a shock to ignite the reaction:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/alice/anaconda3/lib/python3.6/site-packages/scipy/integrate/odepack.py:218: ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information.\n", " warnings.warn(warning_msg, ODEintWarning)\n" ] }, { "data": { "image/png": "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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "eos = eos_defns.eos_gamma_law(5.0/3.0)\n", "eos_reactive = eos_defns.eos_gamma_law_react(5.0/3.0, 0.1, 1.0, 1.0, eos)\n", "U_reactive_right = State(0.5, 0.0, 0.0, 1.0, eos_reactive)\n", "U_reactive_left = State(0.24316548798524526, -0.39922932397353039, 0.0,\n", " 0.61686385086179807, eos)\n", "test_precursor_rp = RiemannProblem(U_reactive_left, U_reactive_right)\n", "display_png(test_precursor_rp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The structure here looks like previous Riemann problems, but there is in fact only one wave. The right state is connected directly to the left state across a compound wave formed from a precursor shock, which raises the temperature until the gas ignites, then a Chapman-Jouget deflagration which is attached to a rarefaction.\n", "\n", "In parameter space we see this behaviour more directly:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAqUAAAF3CAYAAACcxjKLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJzs3XdYlvXix/H3zR6CioLgAFyAimKKI03LlGya7aGdU1mm1bE061SeQ4XtHGULzZYdW1paOUpTK3OkoKkooDgAFRREBWXzfH9/mP7MTFGBh/F5XZfX5T2+9/PhD3k+fu9lGWMQEREREbEnB3sHEBERERFRKRURERERu1MpFRERERG7UykVEREREbtTKRURERERu1MpFRERERG7UykVEREREbtTKRURERERu1MpFRERERG7UykVEREREbtzsneA89W4cWMTHBxs7xgiIiIiZxUfH59tjPG1d47qrMaW0uDgYOLi4uwdQ0REROSsLMtKtXeG6k6n70VERETE7lRKRURERMTuVEpFRERExO5q7DWlIiIiIjVZfHy8n5OT03QgnLoxUWgDEkpLS+/r2rXr/lM3qpSKiIiI2IGTk9N0f3//dr6+vgcdHByMvfNUNpvNZmVlZbXPzMycDgw6dXtdaOUiIiIi1VG4r69vbl0opAAODg7G19f3MMdmhv+6vYrziIiIiFSolStX8swzz9g7xvlwqCuF9Lg/ft7T9s8qKaWWZV1pWVayZVkplmU9eZrtd1uWlWVZ1u9//LmvKnKJiIhIzderVy+ee+65cx43c+ZMgoODcXBwIDg4mJkzZ1ZCOimvSi+llmU5Am8DVwHtgTssy2p/ml2/MMZ0/uPP9MrOJSIiIrXDLbfcwq+//npOY2bOnMnw4cNJTU3FGENqairDhw+vk8X0gQceaB4dHd3k+LLNZsPLy6tzXl5elZ5Rr4oP6w6kGGN2GGOKgc+B66vgc0VERKQOSEhIoGPHjuc0Zty4ceQX5dP0n01xbe4KQH5+PuPGjauMiNVaYmKie+fOnQuOLyclJbn4+PiUenl52aoyR1WU0mZA+knLu/9Yd6qbLMvaaFnWbMuyWlRBLhEREanhCgsLKSkpoX79+uc0Ln1vOoEPB+LTzwfPUM8T69PS0io6YoWJjY31adq0aUcHB4euTZs27RgbG+tTEcdNTk52j4yMzD++HB8f7xEWFlZwpjGVoSpKqXWadade1PsdEGyM6QT8CHx82gNZ1nDLsuIsy4rLysqq4JgiIiJS02zevJn27U93VeDfKygtIOTfIXhf5M3eGXvJWZJzYltgYGBFR6wQsbGxPqNHjw7KyMhwMcaQkZHhMnr06KALLaZZWVmOJSUlVmBgYOnxdRs2bHAPDw/PP9O4ylAVpXQ3cPLMZ3Ng78k7GGMOGGOK/lh8D+h6ugMZY6YZYyKNMZG+vr6VElZERERqjk2bNtGpU6dy759bmMvV71+Nc2tn9s/YT87S/y+kHh4evPDCC5UR84LFxMQ0Kyws/FNvKywsdIiJiTnd2edyi4uLcz91VjQhIcE9IiKiAODyyy9vcyHHPxdVUUrXAm0ty2ppWZYLcDvw7ck7WJYVcNLiICCxCnKJiIhIDXcupfRQ4SGufP9Kspyy6JPXh0n3TiIoKAjLsggKCmLatGkMGTKkkhOfn8zMTJdzWV9eW7ZscQsODj4+MUhZWRnx8fH1oqKijiQnJ7u0aNGi6EzjK1Klv9HJGFNqWdbDwA+AI/CBMWazZVkxQJwx5ltglGVZg4BSIAe4u7JziYiISM03ceLEcu2XnZ/NdTOuI9c1ly7pXXjrmbewLKvaltBT+fv7F2dkZPylgPr7+xdfyHFbtmxZ/P777/vm5+dbHh4e5qmnngro3r37kYCAgNJFixY16NKlS5Wdxq+SW/2NMQuMMSHGmNbGmBf+WBf9RyHFGPOUMaaDMSbCGNPPGJNUFblERESk9ss8msl1/7uOXIdcOu/szIxnZmBZp7vlpfqKjo7e4+bm9qe74d3c3GzR0dF7LuS4N954Y27v3r3z2rZtGx4cHByekpLi+tFHH6UCxMXFefbs2bPKSmmlz5SKiIiI2MueI3sY9v0wjnCEjls78smrn9S4QgowYsSIHDh2bWlmZqaLv79/cXR09J7j6y/Ee++9t5tj9wD9yYYNGzwOHDjg6OTkxG233ZZzzTXXHLnQzzoTlVIRERGplXYd3sV9i+4jvzSf9654j+73dcfBoea+YX3EiBE5FVFCy+uXX37ZVlWfBSqlIiIiUgsl5SRx1zd3UVxczCeDPqFTQPnv0Bf7qLn/XRARERE5jXX71jHk2yHkHswlcEUg7Rq3s3ckKQeVUhEREak1ftn9C8MWDiMvM4/Wv7Xmq+lf4ezsbO9YUg4qpSIiIlIrfL/ze/615F/kpeURtCqIOTPm4OJyQY/xlCqka0pFRESkxvsy+UueX/08IZ4h2BJtzPx8Jq6urvaOJedApVRERERqtOmbpvPGujfo27wvEy+diNvNbvaOJOdBpVRERERqJGMMk9dN5sOED8n9LZeI0gjc+quQ1lQqpSIiIlLjlNnKGL96PF9t+4pDPx3Cb5Mft754q71jyQVQKRUREZEapaisiCd/eZIf037k4MKD+CT6sHjZYho0aGDvaHIBdPe9iIiI1Bi5xbk8sPgBfkz7kZyvcqi/qT5LflyCj4+PvaPVWA888EDz6OjoJseXbTYbXl5enfPy8qq0J2qmVERERGqE/fn7GfnjSHYc3sErfV4h3zOf3r174+vra+9oNVpiYqL7wIEDc48vJyUlufj4+JR6eXnZqjKHZkpFRESk2tt1eBd3LbiLtMNpDGswjKtbXc3NN99MQECAvaNVqdTUVOdu3bqFpqWlVdjEYnJysntkZGT+8eX4+HiPsLCwgoo6fnmplIqIiEi1tilrE/9Y+A+OFB0hfWI6Ux6bQklJib1j2cW4ceMC4uPj640bN65pRRwvKyvLsaSkxAoMDCw9vm7Dhg3u4eHh+WcaVxlUSkVERKTaWrFnBcMWDcMZZ3a+uBPHLEcWLlxYJ18dmpqa6jx79uzGxhhmzZrVuCJmS+Pi4txPnRVNSEhwj4iIKAAIDw9vN2TIkMBevXqFHD58uFJ7o0qpiIiIVEvfbf+Oh5c8TBPXJiRFJ2E7YGPp0qW0bt3a3tHsYty4cQE227HLPG02GxUxW7plyxa34ODgouPLZWVlxMfH14uKijqSkpLiHBkZeWTmzJlpfn5+JRkZGZV6L5JKqYiIiFQ7H2/+mKd/fZqLmlxE2O9hFOUU8eOPPxIaGmrvaHZxfJa0pKTEAigpKbEqYra0ZcuWxb///rtHfn6+BfDUU08FdO/e/UhAQEDpqlWrPLdv3+7Wq1evtiEhIYVhYWHFFfGz/B2VUhEREak2bMbGq2tfZULcBKKCoogdEMsrMa8QHx9PeHi4vePZzcmzpMdVxGzpjTfemNu7d++8tm3bhgcHB4enpKS4fvTRR6kAcXFxHm+88Ub6t99+uyM5ObnSX5WlR0KJiIhItVBUVsRTy59icepiBgcOZvVLq9kduJtWrVoRFBRk73h2FRcX53l8lvS4kpISa+3atZ4Xeuz33ntvN7D71PWJiYnunTp1KnRycqKoqMjKzc118Pb2rrTHRKmUioiIiN0dKjzEqGWjWL9/PSPCRvD2PW+Tnp7O/v37adWqlb3j2V1SUlJiVX/mokWLth//+/fff7+jsj9Pp+9FRETErnbn7eauhXexOXszz3Z5lqn3T2XXrl3Mnz+fnj172jueVBHNlIqIiIjdbM7ezINLHqTUVsqkiycx+tbRbN26lXnz5tG3b197x5MqpFIqIiIidvFz+s88/svj+Lj58M6Ad2hoa0i9evWYM2cOAwYMsHc8qWIqpSIiIlLlvkz+khd+e4EwnzBe7fkqfi5+uLu78/PPP2NZ1tkPILWOSqmIiIhUGWMMU9ZPYfqm6fRp1oeY7jHccv0tuLq6snDhQhXSOkylVERERKpEUVkR0SuiWbBzATe1vYmxncdy4+Ab+fnnn/nf//6nQlrHqZSKiIhIpcspzOHRZY+yfv96HunyCHeF3MVNN93E4sWL+eCDD7jzzjvtHVHsTKVUREREKtWOwzt46MeHyCrIYsKlExgYPJD77ruP+fPn8+6773LPPffYO6JUAyqlIiIiUml+y/iN0T+NxtnBmfcHvk+EbwQAjz76KN27d2f48OF2TijVhR6eLyIiIpVizrY5jFg8Aj93Pz695lM6NurI119/jTGG8PBwFdLzkJqa6tytW7fQtLS0CptYfOCBB5pHR0c3Ob5ss9nw8vLqnJeXV6U9UaVUREREKpTN2Hg9/nWiV0bTzb8bn1z9CQEeATzwwAPcdNNNLF261N4Ra6xx48YFxMfH13v66aebVtQxExMT3Tt37lxwfDkpKcnFx8en1MvLq9Lec386On0vIiIiFaawtJCnf32axamLuTnkZp7u8TROlhMPP/ww06dPZ9y4cfTv39/eMWscV1fXLsXFxSceTzBz5kzfmTNn+rq4uJiioqJ1F3Ls5ORk98jIyPzjy/Hx8R5hYWEFZxpTGTRTKiIiIhUiuyCbe3+4lx9Tf2Rs5Fiie0bjZDnx2GOP8c477zB27FjGjx9v75g10tatWzddd911OW5ubjYANzc326BBg3K2bdu28UKOm5WV5VhSUmIFBgaWHl+3YcMG9/Dw8PwzjasMKqUiIiJywZJzkhkyfwgph1KY3G8y/+zwTyzL4vfff+eNN95g1KhRvPrqq3oW6XkKCgoq8fLyKisqKnL4Y3bUwcvLq+zkMnk+4uLi3E+dFU1ISHCPiIgoAIiPj3ebMmVKo5SUFOeDBw9Wam9UKRUREZELsjRtKXctvItSWykfDvyQ/oH/f3r+oosuYvXq1bz++usqpBcoKyvLeciQIVk//fRT4pAhQ7L279/vfKHH3LJli1twcHDR8eWysjLi4+PrRUVFHQEoLi62pk6d6vf55583rF+/fqVeY6prSkVEROS8GGOYvmk6U9ZPIbxROG9c/gZ+Hn4ATJgwgdDQUK677jq6detm56S1w6JFi7Yf//vFF1+cVhHHbNmyZfH777/vm5+fb3l4eJinnnoqoHv37kcCAgJKAXbt2uUyZMiQ7NatWxcfOnTIwcfHp9KKqUqpiIiInLPC0kKeWfkMC3Yu4OqWV/Ncr+dwc3IDYPLkyTz++OP885//5LrrrrNzUjmTG2+8MXfhwoXebdu2DXd2djZdunQ58tFHH6Ue337HHXccTktLc7rQywTKQ6VUREREzklWfhaPLHuETdmbeKTLIwwLH3bi1Pw777zDmDFjuPnmm5k+fbqdk0p5vPfee7uB3X+3vSoKKaiUioiIyDnYfGAzo5aOIq84jzf6vcHlgZef2Pb+++/z0EMPMWjQID799FOcnFQzpPx0o5OIiIiUy/e7vufuhXfjZDnxyVWf/KmQAmzcuJGrrrqKL7/8EmfnC74HR+oY/RdGREREzshmbLzz+ztM3TiVLn5dmHTZJBq5NzqxvbCwEDc3N15//XVKSkpwcXGxY1qpqTRTKiIiIn8rvySfx356jKkbp3JDmxuYfsX0PxXSOXPmEBYWxvbt27EsS4VUzptmSkVEROS00nLTeGTZI+w4vIPHIx/nrvZ3/elZo/PmzeO2226ja9eu+Pn52TGp1AYqpSIiIvIXv+75lSd+eQIHy4GpUVPpGdDzT9sXLVrETTfdRKdOnVi4cCFeXl52Siq1hUqpiIiInGCM4f2E95mybgohDUN4vd/rNPdq/qd9fvvtNwYPHky7du1YtGgRDRo0sFNaqU10TamIiIgAx64fffyXx3lj3RsMDB7IjKtm/KWQArRv354hQ4awePFifHx87JBUKtoHH3zQsFOnTmEhISHtAwMDwx977LGAl156yffee+9tAfDaa6819vX17RQWFtY+NDS0/VVXXdUqKSnpxAXEJ28PCwtrP3jw4JbnmkGlVEREREjPS2fowqEsTl3MmK5jeLXvq3g4e/xpn02bNnH06FG8vLx477338PX1tVPauik2NtanadOmHR0cHLo2bdq0Y2xsbIX8j+DNN99sNGnSJP85c+Zs37p165ZNmzZt8fDwsG3atMmjU6dO+QAbN270ePLJJ/cmJSVtSU5O3tKvX7+8G264oY3Nduytoxs3bvR4+umn9yYlJW1JSkraMnfu3J3nmkOlVEREpI5buXclt8+7nX1H9/Fu/3e5J/yeP93QBLBu3Tr69OnDyJEj7ZSybouNjfUZPXp0UEZGhosxhoyMDJfRo0cHXWgxzcnJcfjvf//b4ssvv9zeunXrEoD69evbxo8fvy8xMdG9S5cuBQCJiYnuERERBcfHPfHEE1nZ2dlO27dvdzm+PTIyMv9CsqiUioiI1FHGGD5K+IiRP47Ez8OPz6/5nF7Nev1lv40bNxIVFUX9+vUZP368HZJKTExMs8LCwj/1tsLCQoeYmJhmF3LcmTNnNoyIiDjSvn374pPX22w2tm/f7na8lG7btu1EQT3O1dXVZGdnOwKkpKS4Dxs2LDgsLKx9r169Qs4ni250EhERqYPyS/J5duWzLNy1kKigKJ7v/fxfTtcDJCYmMmDAANzd3Vm6dClBQUF2SCuZmZmnfQDs360vr82bN7t37Nix4NT1SUlJLo0aNSqpV6+eSUlJcfb09Czz8fGxHd9eVFRkZWdnO4eFhRWlpKQ4N27cuGTr1q1bLiSLZkpFRETqmF2HdzFkwRC+3/U9j3R5hImXTjxtITXGMGTIEBwcHFiyZAmtW7e2Q1oB8Pf3Lz6X9eXl6elZdvy60JOtW7fOo127dgUAcXFxHm3btv1TcX3zzTcb9ezZM7dhw4a2uLg4j5CQkL8U23OlUioiIlKH/Jj6I7fPv53sgmxio2K5r+N9f7l+9DjLsvjss89YsmQJoaGhVZxUThYdHb3Hzc3tT+3Rzc3NFh0dvedCjjto0KDD3333XcP09HQngIKCAmvixImNN2zY4B4eHl4AsHHjRvd27doVHh/z9ddfe0+ePDlg0qRJu0/aXjNKqWVZV1qWlWxZVoplWU+eYb+bLcsylmVFVkUuERGRuqLUVsqkuEmM/mk0Lb1b8uW1X9Kr6V+vHwVIS0vj5ZdfxhhDaGgoHTp0qOK0cqoRI0bkTJ48OTUgIKDYsiwCAgKKJ0+enDpixIicCznupZdemv/kk0/ujYqKCgkJCWnfoUOH9vv373f6/fffPXr06HEUICEhwf3rr7/26dChQ7v27du3++ijjxotWLBga5cuXQqPb+/QoUPhmT/p7CxjzIUe48wfYFmOwFYgCtgNrAXuMMZsOWU/L2A+4AI8bIyJO9NxIyMjTVzcGXcRERERILsgmyd+eYK1mWu5NeRW/t3937g4nv5SxL1799K3b1+ysrLYuHGjriGtIJZlxRtj/jTptmHDhl0RERHZ9sr0d1JTU5179eoVlpycnFCvXr0KL4obNmxoHBEREXzq+qq40ak7kGKM2QFgWdbnwPXAqRfDjgdeBcZWQSYREZE64ff9v/PYT49xuPgwL1zyAoNaD/rbffft20f//v3Zt28fixcvViGtg6Kjo5vMmjWr0aRJk9Iqo5CeSVWcvm8GpJ+0vPuPdSdYlnUR0MIYM68K8oiIiNR6xhhmJs7knu/vwcXRhZlXzzxjIc3OzmbAgAGkpaWxYMECevbs+bf7Su0VExOzLzExccttt912uKo/uypmSk939fSJ5m1ZlgMwGbj7rAeyrOHAcIDAwMAKiiciIlK75Jfk8+yqZ1m4cyGXNb+MF/q8gLeL9xnHxMfHk5qaynfffUefPn2qKKnI/6uKUrobaHHScnNg70nLXkA48NMfd//5A99aljXo1OtKjTHTgGlw7JrSygwtIiJSE+08vJMxP41hx+EdjLpoFMM6DsPB+vsTo8YYLMti4MCB7Nq1S++yF7upitP3a4G2lmW1tCzLBbgd+Pb4RmPMYWNMY2NMsDEmGFgN/KWQioiIyJkt2LGA2+cde9zTuwPe5f5O95+xkB45coTLL7+cWbNmAaiQil1Veik1xpQCDwM/AInAl8aYzZZlxViW9fcXt4iIiEi5FJUVEbMqhn8v/zehPqHMum7WaR/3NHPmTIKDg3FwcCAwMJDu3buzfPlyHBzKXwdWrlzJM888U5HxRYAqes2oMWYBsOCUddF/s+9lVZFJRESkNkjNTeWxnx4j+WAy94bfy8MXPYyzg/Nf9ps5cybDhw8nPz8fgPT0Y/cgP/jgg9x0003l/rxevXrRq9fpn28qciH0RicREZEa6vud33Prd7eSmZ/J2/3fZnTX0actpADjxo0jPz8fF0cY2un/95k/f/45feYtt9zCr7/+ekG5RU6nSmZKRUREpOIUlRXx2trX+CL5CyJ8I5hw6QT8Pf3POCYtLY3m3hazb/GgR3NHth6wsWZPGWlpaef02QkJCXTs2PFC4ouclkqpiIhIDZKem85jPz9GYk4i93S4h391+dffzo6e7M4eAUy+JBdXJ4sbv8hnzZ4y4NwesVhYWEhJSQn169c/7/xS/cTGxvrMnz+/fk5OjpOvr2+ph4eH7brrrjt0xx13VOmzSlVKRUREaohFuxbxzMpncLAcePPyN7msxWVnH2SzwfIJfDLwKIlZFjd8cZStB2wAeHh48MILL5T78zdv3kz79u3PM71UR0uWLPGMiIgoyMrKcvrmm28azp07d2dycrJLRERE+OWXX76hSZMmZVWVRaVURESkmisuK2ZC3AQ+S/qMTo078dqlr9G0XtOzD8zPga+HQ8pirI63sjH/Yormx2DlpBEYGMgLL7zAkCFDyp1j06ZNdOrU6QJ+EjmT69/6NfTUdQPD/XMevKxN1tGiUoc731vd9tTtgy9qln1P75YH9ucWOt0/I671ydu+efiS5LN9Zv/+/Y8CTJgwock111xzCMDFxcU0atSoxNvb23b+P825UykVERGpxnYe3skTvzxBUk4Sd7W/i9FdRuPsePbT9eyOg1l3w5F9cM0kiLyX2y2L2++697yzbNq0iR49epz3eKmeysrKWLZsWf177703e+rUqT6//fab57fffrvN3d29Sl9UpFIqIiJSDRljmJsyl5fWvISro2v5T9cbA2umwQ/jwDsA7v0BmnWpkEwTJ06skOPI6Z1pZtPT1cl2pu1+3m6l5ZkZPZ1ly5Z5ent7l9WrV8/22muvBbz55pupXbt2Lfy7/bOzsx1feuklv4kTJ2acz+f9HZVSERGRaiavOI/xq8ezcOdCuvl346VLXqKJZ5OzDyzMhW8fhi3fQMiVcEMsuDes/MBSo82dO7fBNddcc/DSSy/NHzNmTMYTTzzR4qqrrkrctm2bS/PmzUvc3d1NTEyM37Jly7yPj0lOTnYPCgoqHjVq1IGKyqHnlIqIiFQjG7M2cst3t7Bo1yL+ddG/eC/qvfIV0oyNMO1SSJwHUTFw+2cqpHJWycnJLrt373aJjo7OBLj//vtzfH19S3r27BmydOnSesdP4UdHR+9ftmxZyrJly1Jmz569s0ePHnlDhw49WJFZNFMqIiJSDdiMjQ8TPuSt9W/h5+HHR1d+RGe/zmcfaAzEfwgLnwSPRnD3fAi6uPIDS60QGhpaPHfu3J3Hl52dnVm6dGnKmcY0atSobMaMGWleXl4VeiOUSqmIiIidZeVn8fSvT7M6YzVRQVE82+tZvF28zz6wMBfmPQoJX0Hr/nDjNPBsXPmBpc6r6EIKKqUiIiJ2tXz3cv6z4j/kl+TzzMXPcFPbm7As6+wDMzYcu7v+4C64/L9wyRhw0FV5UnOplIqIiNhBcVkxr697nU+2fELbhm35YOAHtG7Q+uwDjYG10+GHp8Gj8R+n63tVfmCRSqZSKiIiUsW2H9rOk8ufJCknidtCb2Ns5FjcnNzOPrDgIHz7L0j8DtpEwQ1TwbNR5QcWqQIqpSIiIlXEGMOnSZ8yOX4yHk4evNHvDS4PvLx8g9PXwOxhkLcXosbDxQ/rdL3UKiqlIiIiVSArP4v/rvgvK/au4JJmlzC+93gau5fjpiSbDVZMhqUvQP3mcO8iaN618gOLVDGVUhERkUq2JHUJz656loLSAsb1GMdtobeV72amvMxj767f+TN0uAGuewPc6ld+YBE7UCkVERGpJPkl+byy9hW+3vY17Xza8XKfl2nVoFX5Bm9dBHNHQHE+XDcFuvwDylNkRWoolVIREZFKsCFrA08tf4rdebsZFj6Mhzo/hLOj89kHlhbBj8/C6negSTjc9D74hVV6Xqnb8vLyHJ555hn/zMxM57KyMoYNG5Z9xRVXHK3KDLpCWkREpAKV2kp59/d3+efCf1JqK+WDgR/waNdHy1dIs7bC9P7HCmn3B+C+JSqkUiWuuuqq1gMHDsz99NNPUzt37pw/c+ZMn6rOoJlSERGRCpKWm8ZTy59iY/ZGrm11LU/3eBovF6+zDzz+qtDvnwYXD7jjCwi9svIDS/Ux96EW7N/iUaHH9Gufz+C308uz665du9xatmxZDDBmzJhsm63CX9h0ViqlIiIiF8gYw6yts5gQNwEnByde7fsqV7W8qnyDjx6A70ZB0jxo1Q9uiAUv/8oNLHKK2NjYXYMHD27dqVOn/FdeeWVvUFBQSVVnUCkVERG5AJlHM3lm5TOs3LuSngE9Gd97PP6e5SyV25fBnBGQfwCueB56PqRnj9ZV5ZzRrGglJSU4Oztz7bXX5l199dWJY8aMaRoVFdV269atW07eLzs72/Gll17ymzhxYkZlZVEpFREROQ/GGL7b8R0v//YypaaU//T4D7eG3lq+Rz2VFsGSGFj1FjQOgSGzIKBT5YcWOcWUKVMa33///Tne3t42BwcHXF1dbS1btiwCiImJ8Vu2bJn38X2Tk5Pdg4KCikeNGnWgMrKolIqIiJyj7IJsxq8az9L0pXTx68L43uMJ9A4s3+B9W+Dr+2FfAnS7H6Jijl1HKmIHt95666F77703EKCwsNChWbNmxbNnz94JEB0dvT86Ono/wIEDBxzvu+++FkOHDj1YWVlUSkVERM7B4tTFjF81nqMlRxkbOZah7Ybi6OB49oE2G/wWe+xxT24fGKJEAAAgAElEQVTecOeXEDKw0vOKnEmLFi1KZ8+evets+zVq1KhsxowZaV5eXpV2B5RKqYiISDkcLjrMi7+9yIKdC2jfqD0v9H6BNg3blHPwHvjmQdjxE4RcBYPehHq+lZpXpKJVZiEFlVIREZGz+mX3Lzy78lkOFh7kwc4Pcl/H+3B2KMdzRwESvoJ5Y6CsGK59HbrerTcziZyGSqmIiMjfOFpylNfWvsZX276iTYM2vNX/Ldo3al++wQUHYf5YSJgNzSLhxmnQqHXlBhapwVRKRURETmPl3pU8t/I5MvMzuTf8Xh7q/BAuji7lG7x9Kcx9CI7uh37j4JIx4KivXJEz0b8QERGRk+QW5zIxbiJfb/uaYO9gPr7yYzr7dS7f4OKjsDga1k6HxqFwx6fQ9KLKDSxSS6iUioiI/OHn9J+JWRVDdmE2w8KHMbLzSFwdXcs3OH0NzHkAcnYcewh+//+Cs3vlBhapRVRKRUSkzjtUeIiX177M/B3zaduwLVMun0KHxh3KN7i0CH56CVa8Ad7N4Z/zoGWfyg0sUguplIqISJ22aNciXvjtBXKLchkZMZL7O96Ps2M576zP2ABzRsL+zXDRXTDwxWPPIBWRc6ZSKiIidVJ2QTYv/vYii1MX086nHdOiphHqE1q+wWUlsHwi/PIaeDTWg/ClRvvss8/qf/PNNw0yMzOdGzZsWOrq6mr69OmTN3z48BxnZ2e++uor7zlz5jRIS0tzbdy4cUmDBg3KBgwYkHvnnXcersgcKqUiIlKnGGOYt2Mer6x9hYKSAh7p8gh3d7gbJ4dyfiVmJsDckZC5ETreCle9Ah4+lRtapJIsXrzYs2nTpiVt2rQpTEtLc5kzZ86uzMxMx9tvv73lmjVrPEeNGpXVoEGDsr59++a9+uqrXj/99NO2I0eOOISEhIRfeeWVCT4+PhX2QH2VUhERqTMyj2YyfvV4ftn9CxG+EcT0iqFVg1blG1xWAiteh59eAfcGcNv/oN11lRtYpJJFRUUdBXjllVf8r7/++kMA/v7+ZaNGjdr/+OOPt/j444/TAWbNmtXw2muvPejg4EC9evVsM2fO3F6RhRRUSkVEpA6wGRuzt85mcvxkSm2lPNHtCe4Mu7N876wH2Lf52OxoxgbocCNcPQE8G1VuaKlT/rvivy1SDqZ4VOQx2zRskz++9/j0s+1XUFBgLV++3Pudd95JP3ldw4YNS48vf//99w1at25dcNtttwUNHTo057rrrsuryKygUioiIrXc9kPbeW7Vc6zfv57u/t159uJnaeHdonyDy0rg18nw86vgVh9unQHtr6/cwCJV7LvvvvNq1apVYXBwcMnxdV988YXP4MGDDwLExcW5HThwwCk5OXmHq6urOd0xsrOzHV966SW/iRMnZpxvDpVSERGplYrKipi+aTrTN03H09mT8b3Hc33r67HK+975jI3wzYOQuQnCb4KrXtPsqFSa8sxoVpa5c+c2vOaaaw4B5ObmOjz99NMBGRkZLmPHjt0F8OWXXza88sorD51aSGNiYvyWLVt24nETycnJ7kFBQcWjRo06cD45VEpFRKTWWZu5lphVMezK3cU1ra7h8cjHaeRezkJZWnTsrvpfJ4O7D9w2E9pdW7mBRexkzpw53nPmzPEJDAwsWr58udfhw4cdo6KiDi9dunSbm5ubWbFihfuiRYvqz5w5c+epY6Ojo/dHR0fvBzhw4IDjfffd12Lo0KEHzzeLSqmIiNQah4sOMzl+Ml9t+4pm9ZoROyCW3s16l/8Au+Pgm4cgKwki7jj23FHdWS+12A033JBbUFCw/u+29+7du+D3339POttxGjVqVDZjxow0Ly+v8775SaVURERqPGMMP+z6gZfXvMyhokPcE34PIyNG4u5Uztd8Fh+FZS/C6nfAKwDunAUhV1RuaJFa5kIKKaiUiohIDbf3yF6eX/08y/csp0OjDsRGxRLmE1b+A+z4Cb57BA7ugq73QFSM3sokYgcqpSIiUiOV2kr5NPFT3vr9LQD+3e3f3BF2R/kf81RwEBb9B9b/D3xawd3zIfiSSkwsImeiUioiIjXO5uzNxKyOYcuBLfRt3pf/9PgPAfUCyjfYGEj8FhY8DkezofejcNmT4FzOU/0iUilUSkVEpMY4XHSYN9e/yZfJX9LIvRGv9X2NgcEDy/+Yp9y9MH8sJM8H/04wZBYERFRuaJG/Z7PZbJaDg8Npn/1ZG9lsNgs47bWnKqUiIlLtGWP4bsd3TIybyKGiQwxpN4QHOz+Il4tX+Q5gs0Hc+/Djc2ArOXbdaM+HwFFfg2JXCVlZWe19fX0P14ViarPZrKysrPpAwum261+jiIhUaykHU3j+t+eJ3xdPJ99OTI2aem43Mu3bcuxGpt1roNVlcO3kY9eQithZaWnpfZmZmdMzMzPDAQd756kCNiChtLT0vtNtVCkVEZFqKb8kn9gNsXyy5RM8XTx59uJnuaHtDThY5fzuLik49hD8FW+AqzcMjoWI26G8p/pFKlnXrl33A4PsnaO6UCkVEZFqxRjDkrQlvLzmZfbl7+PGtjfyaJdHaejWsPwH2b4M5o+BnB3HHoJ/xQt6RahINadSKiIi1UZ6bjovrnmRX/f8SkjDECZcOoHOfp3Lf4AjWfDD07Dpy2On6P/xzbFT9iJS7amUioiI3RWVFfFBwgdM3zgdJwcnnuj2BHeE3YGTQzm/pmw2WD8DFkdDcT70fRz6jAVntz/t9vjjj9OkSRPGjh0LHJuVbdiwIXv37sXDw6OifywROQcqpSIiYlfLdy/n5TUvk5aXxpXBVzI2cixNPJuU/wCZCTBv9LEbmYJ6H7uRyTf0tLsmJCQQFRV1Ynnnzp34+vqqkIpUA1VSSi3LuhJ4A3AEphtjXj5l+wjgIaAMOAIMN8ZsqYpsIiJiH2m5aby69lV+3v0zQd5BTI2aSq+mvcp/gKIj8PPLsOodcG8Ag989dv3oGW5k2rRpE506dTqxvHHjxj8ti4j9VHoptSzLEXgbiAJ2A2sty/r2lNL5qTEm9o/9BwGTgCsrO5uIiFS9/JJ8pm2cxowtM3B2cGZM1zEMbTcUZ0fnM47LyMjg9ttv54vPP8f/4Fr4/knI3QNd/gEDngMPnzOOP3jwIMXFxfj7+59Yp1IqUn1UxUxpdyDFGLMDwLKsz4HrgROl1BiTe9L+nkCtf4CsiEhdY4xhwc4FTIqbxP6C/QxqPYhHuzyKr4dvucaPHz+evZtXcGDK5fi77oUm4XDzhxDYo1zjT50lhWOldMiQIQB069aNyMhItm3bxty5c6lXr965/YAickGqopQ2A9JPWt4N/OU3iGVZDwFjABfg8irIJSIiVSTxQCIvrXmJ9fvX075ReyZeNvGc7qrPyMhg//KP2DTCgxLbHnIvfhrvAWPP6Y1MycnJtG7d+sSyzWZjxYoVxMbGkp6ezsUXX8yUKVO46667yMrKUikVqWJV8faA013c85eZUGPM28aY1sC/gf+c9kCWNdyyrDjLsuKysrIqOKaIiFS0g4UHiVkVw23zbiM1N5Xnej3HZ9d8dm6PeeLYLOnq3WV8uqmETlOLeOrb9HN+RWhQUBBr166lsLAQgBdffJG+ffvSuHFj4uPj2bp1K1FRUYSGhtKyZctzOraIXLiqKKW7gRYnLTcH9p5h/8+BwafbYIyZZoyJNMZE+vqW73SPiIhUvVJbKZ8mfso1c67h621fM6TdEL674TtubHtj+d/I9IeMjAw+/PBD9hwqZti3hezKKebDDz8kMzPznI5zxRVX0K9fP8LCwggNDWXbtm3ExsYCEB8fz+TJk5k1axZJSUnndFwRqRhVcfp+LdDWsqyWwB7gduDOk3ewLKutMWbbH4vXANsQEZEaaU3GGl5a8xIph1LoEdCDJ7s9SZuGbc77eOPHj8dms/1pXVlZGePHj+ftt98+p2NNnDiRiRMn/mX95s2bCQkJwdHRkcLCQo4ePYqnp+d5ZxaRc1fppdQYU2pZ1sPADxx7JNQHxpjNlmXFAHHGmG+Bhy3LGgCUAAeBf1Z2LhERqVh7j+xlYtxEFqUuoqlnUyZfNpn+gf2xLvBd86tWraK4uPhP64qLi1m5cuUFHfdkX3/99Ym/z549u8KOKyLlZxlTM290j4yMNHFxcfaOISJS5x0pPsL7Ce8zY/MMLMtiWMdh3NPhHtyc3M4+WKSOsCwr3hgTae8c1Zne6CQiIuel1FbKnJQ5vLX+LXIKc7i21bU80uUR/D39zz5YROQUKqUiInLOVu5dyWtrXyPlUApd/Lrwdv+3CW8cbu9YIlKDqZSKiEi57Ti0gwlxE1i+ZznN6zVn0mWTGBA44IKvGxURUSkVEZGzyinM4d3f32XW1lm4O7nzWNfHuLPdnbg4utg7mojUEiqlIiLyt4rLivk08VOmbZxGfmk+t4TcwsjOI/FxO/N75kVEzpVKqYiI/IUxhsWpi5kUP4k9R/bQp1kfxkaOpVWDVvaOJiK1lEqpiIj8SUJ2Aq+tfY11+9fRpkEbpg6YSq9mvewdS0RqOZVSEREBIC03jSnrp/DDrh/wcfPhmYuf4YY2N+Do4GjvaCJSB6iUiojUcdkF2cRuiOWrrV/h7OjMiIgR3N3hbjyd9ZpNEak6KqUiInXU0ZKjfLz5Yz7a/BHFZcXcHHIzIyJG0Ni9sb2jiUgdpFIqIlLHlNhKmL11NrEbYskpzCEqKIpRF40iuH6wvaOJSB2mUioiUkcYY/gh9QfeXPcmaXlpRDaJ5M3L36STbyd7RxMRUSkVEakL1mSsYVL8JDYf2EybBm14u//b9GnWR29iEpFqQ6VURKQWS85JZvK6yazYswJ/T3+e7/0817a6VnfUi0i1o1IqIlIL7T2yl7fWv8W8HfPwcvHisa6PcUe7O3B1dLV3NBGR01IpFRGpRbLys3hv03vM2joLBxy4O/xuhoUPo75rfXtHExE5I5VSEZFa4FDhIT5I+IDPkj6jxFbC4DaDGRExAn9Pf3tHExEpF5VSEZEaLK84jxlbZvDJlk/IL8nnmlbXMDJiJIHegfaOJiJyTs5aSi3Lugp4FmgAbAAmG2NWVXIuEZEaa9asWUyYMIGCggLy8/O56667aNy4Mdu2beP111+vkM/IL8nn06RP+TDhQ3KLc4kKiuLBiAdp07BNhRxfRKSqlWem9B1gKLAF6Aq8ZlnW28aYzyo1mYhIDfTxxx/z5ptvMnfuXJo3b86RI0d499132bhxIz169Ljg4xeVFTF762ze2/geBwoPcEmzS3j4oofp0KhDBaQXEbEfyxhz5h0sa7UxpudJy57Ab8aY8MoOdyaRkZEmLi7OnhFERP4kNzeXli1bsnbtWlq1avWnbb169WLKlClERkae17FLbCV8k/INUzdOJfNoJt38u/Gvi/7FRX4XVUR0EalklmXFG2PO7xdAHVGemdJdlmU9D8QYY4qBEiCvcmOJiNQ8c+bMoUePHn8ppMYYEhMT6dChfLOZM2fOZNy4caSlpREYFMgdMXewwXMD6XnpdGzckZheMfQM6KkH34tIrVKeUmqAG4H7LcvaBgQCMy3LamuM2Vap6UREapDNmzfTuXPnv6zfuXMnTZo0wd3d/azHmDlzJsOHDyc/Px/vrt443+DMPNs8fPN8efPyN7m0+aUqoyJSK521lBpj7gCwLMsNCAci/vgz3bKsVsaYFpUbUUSkZvD09KSgoOAv6zdt2kSnTuV7v/y4ceMwAeG0GhqER8tEijKKSHs7jbysPC7752UVnFhEpPoo9yOhjDGFQNwff0RE5BRXX301t99+O6NHj6ZJkyYUFRUxY8YMMjMzz1pKjTEsTdpP0WWP4uffluJDm8n9cgPZ328DG+RZumpKRGo3PadURKSCdOvWjWeffZaBAwdSVlZGaWkpQ4cOZd26dYwYMeKMY9/9eTuvfp+Ma72GZC94g6Obl4Kt7MT2wEA9d1REarez3n1fXenuexGpCTIyMrj44otJTEz80zWlxhiWJe/Ht54bHZvXZ++hAn7ZmkXx1uWMfODYNaXHeXh4MG3aNIYMGWKPH0FEKoDuvj87B3sHEBGprSZMmMDVV1/NO++8c6KQGmP4ccs+rn97Bfd+FMcHK3YC0LSBO7d3D+QfQ4cwbdo0goKCsCyLoKAgFVIRqRM0UyoiUkWWJe/nte+T2ZKRSwsfdx7u14YbuzTH2VHzAyK1nWZKz07XlIqIVKIy27H/+Ds6WGzZm0t+cSkTbong+s5NVUZFRE6iUioiUglKy2x8u2Evby9LYVT/tlzfuRnDLmnJA31b4aQyKiLyFyqlIiIVqLjUxpz1u3nnp+2kHsgntIkXDTxcAHBzdrRzOhGR6kulVESkAt370Vp+TckmvJk3U+/qSlS7Jjg46A1MIiJno1IqInIB8gpL+HxNOnf2CMTT1Yn7+7bivj4tuTTEV68DFRE5ByqlIiLnIedoMR+u2MnHK3eRW1iKf303rotoyqUhvvaOJiJSI6mUioicg5IyGy8tSOKzNWkUlJRxZQd/HuzXmk7NG9g7mohIjaZSKiJSDgeOFNGonivOjg5s3ZfH1R0DGHlZK9r4edk7mohIraBSKiJyBhvSD/HuT9tZlryfX57oRxNvNz6+tzuOunlJRKRCqZSKiJzCGMMv27KJ/Wk7q3YcwNvNieF9W+HqdOz5oiqkIiIVT6VUROQUew4VcM+Ha/DzcmPc1e24o0cg9Vz161JEpDLpt6yI1Hn5xaV8sTad7VlHeH5wR5o39OB/9/UgMsgHFye9fUlEpCqolIpInZV9pIiPV+7ik9WpHMovoXuwD0WlZbg6OdKrdWN7xxMRqVNUSkWkTlqatI8R/1tHSZmNK9o3YXjf1nQNamjvWCIidZZKqYjUCcYY1u46iGVBt2AfOrdoyK2Rzbmnd0ta+9azdzwRkTpPpVREarXSMhsLEzKZvnwHG3Yfpm+ILzPu7Y6PpwvPD+5o73giIvIHlVIRqbXmrN/NhB+2sudQAS0bezJ+cDg3d2lu71giInIaKqUiUquk5+TTqJ4LHi5OHC0qo3lDd54d1IH+YX446PmiIiLVlkqpiNR4xhjWpR3k/V938n1CJs8N6sBdFwczpEcgQ3sG2TueiIiUg0qpiNRYxhi+3bCXD1bsYkP6Ieq7OzO8b2sGtG8CgGVpZlREpKZQKRWRGqewpAw3Z0csy2LGqlTyCkoYf30HburaHA8X/VoTEamJ9NtbRGqMpMxcPl65i/kbM1g69jIa13MldmhXGnm66HpREZEaTqVURKq1MpthSeI+Plq5i5XbD+Dm7MANFzWjzGYA8PVytXNCERGpCCqlIlItGWOwLIvdB/N54H/xBHi78eRVYdwW2YKGni72jiciIhVMpVREqpVjp+hTyS8u5Y3bLyKokSdfDL+YLoENcHJ0sHc8ERGpJFVSSi3LuhJ4A3AEphtjXj5l+xjgPqAUyALuNcakVkU2EbG/0jIbi7fs4+NVu1i9IwdXJwdu7NIcm83g4GDRvaWPvSOKiEglq/RSalmWI/A2EAXsBtZalvWtMWbLSbutByKNMfmWZY0EXgVuq+xsIlI9TP91Jy8vTKJZA3edohcRqaOqYqa0O5BijNkBYFnW58D1wIlSaoxZdtL+q4GhVZBLROzg+IPuZ6xK5eqOAQzs4M+NXZrR2rcel4f54ai76EVE6qSqKKXNgPSTlncDPc6w/zBgYaUmEpEqd7SolG9+38snq1NJzMjFy9WJyOBjp+X9vNyIau9m54QiImJPVVFKTzftYU67o2UNBSKBS/9m+3BgOEBgYGBF5RORKnDne6vZsPswYf5evHhDR67v3BRPV91rKSIix1TFN8JuoMVJy82BvafuZFnWAGAccKkxpuh0BzLGTAOmAURGRp622IqI/RWX2vhhcybf/L6Ht+7sgpuzI6OjQqjn6kTXoIZ6/aeIiPxFVZTStUBby7JaAnuA24E7T97BsqyLgKnAlcaY/VWQSUQqwe6D+Xy2Jo0v1u4m+0gRzRu6s+vAUcL8vbks1M/e8UREpBqr9FJqjCm1LOth4AeOPRLqA2PMZsuyYoA4Y8y3wGtAPWDWHzMoacaYQZWdTUQqzvasIwyY9DMWcHmYH0N6BnFpW1+9/lNERMrFMqZmngWPjIw0cXFx9o4hUmdlHC7gi7XplJYZxg4MxRjDRyt3cUUHf5o1cLd3PBGRasWyrHhjTKS9c1RnustARMqttMzGT8lZfLYmjWXJ+zHAlR38T7wS9J7eLe0dUUREaiiVUhEpt0mLt/LOT9vx9XJl5GWtuS0ykMBGHvaOJSIitYBKqYicVkmZjSWJ+/l8bRojL21Nj1aNuCWyBZ2aN6B/Oz+c9R56ERGpQCqlIvInu7KP8vnadGbHH7uD3t/bjZyjxQC0bOxJy8aedk4oIiK1kUqpiJy4JrTMZrg5dhUH84u5PMyPO7q3oG9bX5w0KyoiIpVMpVSkjjLGkLAnly/i0ojbdZD5o/rg6GAx5fbOtParRxNvvfZTRESqjkqpSB1z8Ggxc3/fw5dxu0nMyMXVyYGrOwZwpKiU+u7O9GrT2N4RRUSkDlIpFakDymyGwpIyPF2dWJ9+kOe+20Kn5vUZPzicQRFNqe/ubO+IIiJSx6mUitRi27OO8FX8br5et4ebujbj8YFh9G3ry8JH+tAuwNve8URERE5QKRWphWbH7+bT31JZl3YIRweLS0N86RbsA4CTo4MKqYiIVDsqpSK1QJnN8Hv6QboGHSuePyXvJ6+wlKevDmNw52b46aYlERGp5lRKRWqwlP15zI7fw9z1e8jMLeTHMZfSxq8er9zUCQ8XRyzLsndEERGRclEpFamBUvbn8disjWxI///T8/+9tj3NG7oD4Omqf9oiIlKz6JtLpAYoKi1jWdJ+XJ0d6Rfqd+J0/H+uacf1nZvh6+Vq54QiIiIXRqVUpJoyxrAu7SBfr9vDvI0ZHC4ooV+oL/1C/fB2c+abh3rbO6KIiEiFUSkVqab+9dl65m3MwM3ZgYEd/LmxS3N6t25k71giIiKVQqVUpBrIyiti/sa9fLthL9P/2Q0fTxdu6tqcfqF+DAz3p56uERURkVpO33QidpJfXMr3CZnM/X0vK1KyKbMZ2gd4k3G4AB9PF/qF+tk7ooiISJVRKRWpQsWlNg4VFOPn5caBI8WM+XIDzRq480DfVlzfuRmh/l72jigiImIXKqUilcxmM/y2M4dvN+xlYUIG3YN9mPaPSFr4eDDvX5fQPsAbBwc9T1REROo2lVKRSjR9+Q6mL99JZm4h7s6OXNGhCTdc1OzE9vBm9e2YTkREpPpQKRWpQNv25TF/UwYjL2uNq5MjRaU2wpt58/Q17RjQzg8PF/2TExEROR19Q4pcoNQDR5m3MYPvNuwlKTMPBwt6tW5M95Y+PNSvjb3jiYiI1AgqpSLnocxmcHSwSMzI5ao3lgMQGdSQ5wZ14KqO/vh5udk5oYiISM2iUipSThmHC1iwKZN5G/fSoak3zw/uSJi/FzHXd6B/uyY0a+Bu74giIiI1lkqpyFl8GZfOl2vTiUs9CED7AG9C/b0BsCyLf1wcbMd0IiIitYNKqcgpMg8XsjRpP3d0b4FlWaxPO8SRolLGRIVwbacAWvnWs3dEERGRWkelVATYe6iAhQmZLNyUcWJGNKJFfTo0rc9zgzrg4uRg54QiIiK1m0qp1Fk2m8HBwWLV9gPc8d5qAML8vRgTFcLVHQNo43dsRlSFVEREpPKplEqdsj3rCN8nZPJ9Qib92/nx6IAQLgpswBNXhnJlB3+dmhcREbETlVKpE975KYW56/ewdd8RADq3aECgjwcAbs6OPHiZnicqIiJiTyqlUuvYbIb16YdYn3aQ+/q0AmBj+mEaerjw7HXtuaKDP031+CYREZFqRaVUaoWSMhurdxzgh82ZLNq8j/15RTg7WtzYpTk+ni68PaQLjg6WvWOKiIjI31AplRorv7gUAA8XJ75et5t/f7UJd2dHLgv1ZWAHf/qF+VHf3RlAhVRERKSaUymVGiX7SBFLEvexaPM+fk3J5r/XtmdozyCi2vvT0MOFviG+uDk72jumiIiInCOVUqkRikrLuGv6Gtam5mAMNGvgzp09ArkosAEAPp4uXNHB384pRURE5HyplEq1c/xGpcVb9lFQXMpz14fj6uRIcx93Lm7dlis6NKF9gDeWpVPyIiIitYVKqVQba3bm8FX8bpYk7SP7SDFODhZ9Q3wxxmBZFpNu7WzviCIiIlJJVErFbvblFrIkcT+DL2qKh4sTq7YfYMGmDC4N9SWqfRMuC/GjvoezvWOKiIhIFVAplSpjjGHz3lx+TNzHksT9bNpzGICA+m70C/NjWJ+WjLystV7rKSIiUgeplEqlyi8u5UhRKX5ebmzJyOXa/2vv/oOsKu87jr+/y49F5Meu7AIK7CKIEKSIikhig6GImmnVTGuqBqOhmTJNmjRtlIwzms5UQya/mJgxmaCTOJOkpEmjk8akVo3UH0QhRKtBwSwgIiAiIChEXAH36R97IYi4XNm759ll368Zhvvce/bc737n3t3PPefZ89z6GyLgjBE1zL1wLDPHD2FMaY35ftW+HCVJ6q5MAaq4Ddt382DTFhY9u4Ula1/hr88Yxlf+ZiLjTxzAt66YxLmn1FHXrzp3mZIkqRMxlKrd9v8hEsDVdyzjkVVbARg5qC8fn9rIhye0XqopIrh00rBsdUqSpM7LUKqjsmVXMw81beWhpi38YfMuHviX86iqCqaPrWfamDqmjxvM6Pp+ucuUJEldhKFU78miZ1/mmw+s4pkXdwIwZEA108cOZvfet+hX3ZPZ556cuUJJktQVGUr1rrbsaubhpq08tGornzpvNBOGDaSqKjiuVw/mXjiWD42t9yL2kiSpIgylepvXdu/ltkee4+FVW1mxqfVo6OD+1Vxy+klMGDaQ6WMHM33s4MxVSpKkY42htJvbsL9q4bkAAAzkSURBVH03D6/aSv8+Pbl00jCqe1XxoyUvMP6kAR4NlSRJhTGUdkOLV2/lgZUvs3j1NtZuex2AGeMGc+mkYfTp1YPf3Xg+fXr1yFylJEnqTgylx7iWlsTKl3by1IZXuWpqIwA/XPICi1dvZeqoQcya2siHxtYzqu74A19jIJUkSUUzlB6Dtuxq5qE/bGXxmm08tmYbr7y+B4ALTxtKff9qvvSRCdT07UV1T8OnJEnqHAylR2Hu3LkMGTKE6667Dmi9eHxtbS2bNm2ib9++hdezq3kvS9du5/ThAxk8oA8P/WErX7hrOfX9q5l2aj3TTq3j3FPqqO/fuorSkAF9Cq9RkiSpLYbSo/DMM88wc+bMA+Pnn3+e+vr6wgLpvrdaeHLDq/xm9TYee24bT65/lX0tiS99ZAJXTW3kwtOGMnHEQMYO6e8fKEmSpC6hkFAaERcB3wJ6AN9LKX3lkMenAbcAE4ErUkp3FlHX0Xr66aeZOHHigfHy5cvfNq60lBJNL+9i31uJCcMG8tobe/nogiVEwJ8NG8icaaP48zF1nNVYC8DAvr0Y2LdXh9UjSZJUaVUd/QQR0QP4DvBhYDxwZUSMP2Sz9cAngB93dD3ttWPHDvbs2cPQoUMP3He0oXThwoUMHz6ciGDEiBEsXLjwwGMbtu/mJ8vW80//8SRnz3uAi25ZzPz7mwAY1K+aH/7dFJ784kzGvvALqp75FR8YXUd1zx6klKipqWH37t3t/2YlSZIKUsSR0inAmpTSWoCI+AlwKbBy/wYppXWlx1oKqKddDj1KCq2hdNasWQBcfPHF/PKXvzzifhYuXMicOXMOhMeXdrzOP978bQBmzZrFP//0KZ54YQf1/as595S6A//2m3ZqPZB/KoEkSVIlFBFKhwEbDhpvBM4p4Hk7RFNTE6NHjz4wbmlp4dFHH2XBggWsW7eOkSNHlrWfa/7+U/QecTq1DRPp0ziR3nWNpLf2cvXsK5k1axY3/uX76Ffdk1MG92tzXmjRUwkkSZI6QhGh9HCJKh3VjiLmAHMAGhoa2lPTUWtsbOS73/0uzc3N9OnThy9/+ctMmzaNuro6HnnkEc4888zDft1rb+xl2fPbmXLyCQw8rhfHT7yA2g/NpmVPM29uXMGOpxfR/MLvadn7JgBnNNQesZZKTiWQJEnKqYhQuhEYcdB4OLDpaHaUUroduB1g8uTJRxVs2+uCCy7gvvvuY9y4cVRXVzN16lQWLFgAwBNPPMHll18OwBt73uKx57axdO0rLFn7Cis27SQlWHDVWVw0YSi1O9ew+d/n8uZLq6Fl34H9NzY2ll3LkaYSrFy5kmXLljFjxgxqamro379/e799SZKkDlFEKP0dMCYiTgZeBK4APlbA83aY+fPnM3/+/Lfd99ruvdz/yBJWvbCJITXH8/7z/4oblr5F7x5VnNFQw+dmjOH9owYxqaEGgHk3zOXqq6+Glj9No62qqmLevHll19HWVAKAvXv3cuutt7Jz504++9nPtudbliRJ6lAdHkpTSvsi4jPAfbReEuqOlNKKiLgJeDyldHdEnA38HKgFLo6If0spndbRtbVHSolfr3yZpWu3s3TtKzy7eSfp3GuZPnk4X7vsdFJKjJ64nUkjag67bOf+o5k33HAD69evp6GhgXnz5h24vxxtTSUA2LBhA7Nnz2bUqFHs2rWLAQMGVOablyRJqrBIKctZ8HabPHlyevzxxwt7vi07m/nt89vZ2byXWee0nmL/i288xIuvvsGZDbVMHTWIc0ad8K4htKNce+213HXXXQemEtxyyy3U1v5pPurmzZvfNudUkiQVLyKeSClNzl1HZ2YobcODTVu49+nNLFu3nee3vQ7A8NrjWPyF6UQE67a9zok1fVxDXpIktclQemQuM9qGJc+9wr0rNnP2yBP42JQGppx8AqedNODAJZpG1h2fuUJJkqRjg6G0DZ+bMYbrLxpHVZXrx0uSJHUkQ2kbjq+2PZIkSUWoyl2AJEmSZCiVJElSdoZSSZIkZWcolSRJUnaGUkmSJGVnKJUkSVJ2hlJJkiRlZyiVJElSdoZSSZIkZWcolSRJUnaGUkmSJGVnKJUkSVJ2hlJJkiRlZyiVJElSdoZSSZIkZWcolSRJUnaGUkmSJGVnKJUkSVJ2hlJJkiRlZyiVJElSdoZSSZIkZWcolSRJUnaGUkmSJGVnKJUkSVJ2hlJJkiRlZyiVJElSdoZSSZIkZWcolSRJUnaGUkmSJGVnKJUkSVJ2hlJJkiRlZyiVJElSdoZSSZIkZWcolSRJUnaGUkmSJGVnKJUkSVJ2hlJJkiRlZyiVJElSdoZSSZIkZWcolSRJUnaGUkmSJGVnKJUkSVJ2hlJJkiRlZyiVJElSdoZSSZIkZWcolSRJUnaGUkmSJGVnKJUkSVJ2hlJJkiRlZyiVJElSdoWE0oi4KCKaImJNRFx/mMerI+Knpcd/GxEji6hLkiRJnUOHh9KI6AF8B/gwMB64MiLGH7LZJ4EdKaVTgG8CX+3ouiRJktR5FHGkdAqwJqW0NqW0B/gJcOkh21wK/KB0+05gRkREAbVJkiSpEygilA4DNhw03li677DbpJT2Aa8BgwqoTZIkSZ1AzwKe43BHPNNRbENEzAHmlIZ/jIimdtbWGdQB23IXcYywl5VlPyvHXlaOvaws+1k5R+plY1GFdFVFhNKNwIiDxsOBTe+yzcaI6AkMBLYfuqOU0u3A7R1UZxYR8XhKaXLuOo4F9rKy7Gfl2MvKsZeVZT8rx162XxGn738HjImIkyOiN3AFcPch29wNXFO6fRnwvymldxwplSRJ0rGpw4+UppT2RcRngPuAHsAdKaUVEXET8HhK6W7g+8CPImINrUdIr+jouiRJktR5FHH6npTSPcA9h9z3rwfdbgY+WkQtndAxNR0hM3tZWfazcuxl5djLyrKflWMv2yk8Sy5JkqTcXGZUkiRJ2RlKCxYRJ0TEryNiden/2ja2HRARL0bEt4ussasop5cR0RgRT0TEUxGxIiL+IUetXUGZ/ZwUEUtKvVweEZfnqLWzK/d9HhH3RsSrEfGromvs7FyeunLK6OW0iPi/iNgXEZflqLErKaOfn4+IlaWfkYsiwktBlclQWrzrgUUppTHAotL43dwMPFxIVV1TOb18CfhASmkScA5wfUScVGCNXUk5/dwNXJ1SOg24CLglImoKrLGrKPd9/nXg44VV1UW4PHXllNnL9cAngB8XW13XU2Y/nwQmp5Qm0rpK5deKrbLrMpQW7+AlVX8AfORwG0XEWcAQ4P6C6uqKjtjLlNKelNKbpWE1vubbUk4/V6WUVpdubwK2APWFVdh1lPU+TyktAnYVVVQX4vLUlXPEXqaU1qWUlgMtOQrsYsrp54Mppd2l4VJar8+uMvgLunhDUkovAZT+H3zoBhFRBcwH5hZcW1dzxF4CRMSIiFhO61K2Xy2FKb1TWf3cLyKmAL2B5wqorat5T73UO7g8deWU00uV773285PA/3RoRceQQi4J1d1ExAPA0MM8dEOZu/g0cE9KaUN3/+BfgV6SUtoATCydtv+viLgzpfRypWrsSirRz9J+TgR+BFyTUuqWR1cq1UsdVsWWp5Z9qrCy+xkRVwGTgfM6tKJjiKG0A6SUzn+3xyLi5Yg4MaX0UukX+5bDbPZ+4IMR8WmgH9A7Iv6YUmpr/ukxqQK9PHhfmyJiBfBBWk/3dTuV6GdEDAD+G7gxpbS0g0rt9Cr52tQ7VGx5apXVS5WvrH5GxPm0fkA976ApZDoCT98X7+AlVa8BfnHoBimlWSmlhpTSSOA64IfdMZCW4Yi9jIjhEXFc6XYtcC7QVFiFXUs5/ewN/JzW1+TPCqytqzliL9Uml6eunHJ6qfIdsZ8RcQZwG3BJSskPpO+BobR4XwFmRsRqYGZpTERMjojvZa2s6ymnl+8DfhsRv6f1SgbfSCk9naXazq+cfv4tMA34ROkyW09FxKQ85XZqZb3PI2Ix8DNa/0hnY0RcmKXaTqY0R3T/8tTPAv+5f3nqiLiktNn3gUHRujz152n7SibdVjm9jIizI2IjrSsr3lY6o6TDKPO1+XVaz3L+rPQz0g8BZXJFJ0mSJGXnkVJJkiRlZyiVJElSdoZSSZIkZWcolSRJUnaGUkmSJGVnKJUkSVJ2hlJJkiRlZyiV1O1FxFkR8eBB4wkRsSRnTZLU3RhKJal1ZZZTDxrfBHwxUy2S1C31zF2AJOWWUtodEc0RUQOMAmpTSg/krkuSuhOPlEpSq5XAOOBm4MbMtUhSt2MolaRWK4DZQKSUHs1djCR1N56+l6RWK4AfAGfnLkSSuqNIKeWuQZIkSd2cp+8lSZKUnaFUkiRJ2RlKJUmSlJ2hVJIkSdkZSiVJkpSdoVSSJEnZGUolSZKUnaFUkiRJ2f0/Hs6V5BE5CucAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig3 = pyplot.figure(figsize=(10,6))\n", "ax3 = fig3.add_subplot(111)\n", "utils.plot_P_v(test_precursor_rp, ax3, fig3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The smooth joining of the deflagration and rarefaction curves at the Chapman-Jouget (CJ) point is expected, as the propagation speed of the waves must match there. The ignition point (where the temperature is high enough for the reaction to take place) is illustrated by the \"$i$\"." ] } ], "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 }