{ "cells": [ { "cell_type": "markdown", "id": "bdb38ce8", "metadata": {}, "source": [ "# SAFT-VR-Mie\n", "\n", "The SAFT-VR-Mie EOS of Lafitte et al. (https://doi.org/10.1063/1.4819786) is based on the use of a Mie potential of the form\n", "\n", "$$\n", "u(r) = C\\epsilon \\left((\\sigma/r)^{\\lambda_r}-(\\sigma/r)^{\\lambda_a}\\right)\n", "$$\n", "with \n", "$$\n", "C = \\frac{\\lambda_r}{\\lambda_r-\\lambda_a}\\left(\\frac{\\lambda_r}{\\lambda_a}\\right)^{\\lambda_a/(\\lambda_r-\\lambda_a)}\n", "$$\n", "\n", "which allows for a better representation of thermodynamic properties in general, but not always." ] }, { "cell_type": "code", "execution_count": 1, "id": "d1842386", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:40:05.276868Z", "iopub.status.busy": "2024-03-15T22:40:05.276707Z", "iopub.status.idle": "2024-03-15T22:40:05.290605Z", "shell.execute_reply": "2024-03-15T22:40:05.290178Z" } }, "outputs": [ { "data": { "text/plain": [ "'0.19.1'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import teqp\n", "teqp.__version__" ] }, { "cell_type": "code", "execution_count": 2, "id": "16f05ec8", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:40:05.292517Z", "iopub.status.busy": "2024-03-15T22:40:05.292355Z", "iopub.status.idle": "2024-03-15T22:40:05.939527Z", "shell.execute_reply": "2024-03-15T22:40:05.939068Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import pandas\n", "import matplotlib.pyplot as plt\n", "import CoolProp.CoolProp as CP\n", "import scipy.integrate" ] }, { "cell_type": "code", "execution_count": 3, "id": "be8268a7", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:40:05.942046Z", "iopub.status.busy": "2024-03-15T22:40:05.941619Z", "iopub.status.idle": "2024-03-15T22:40:05.949764Z", "shell.execute_reply": "2024-03-15T22:40:05.949327Z" } }, "outputs": [ { "data": { "text/plain": [ "-0.04926724350863724" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "-0.04926724350863724" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Show two ways to instantiate a SAFT-VR-Mie model, the\n", "# first by providing the coefficients, and the second\n", "# by providing the name of the species. Only a very small\n", "# number of molecules are provided for testing, you should\n", "# plan on providing your own parameters.\n", "# \n", "# Show that both give the same result for the residual pressure\n", "\n", "z = np.array([1.0])\n", "model = teqp.make_model({\n", " \"kind\": 'SAFT-VR-Mie',\n", " \"model\": {\n", " \"coeffs\": [{\n", " \"name\": \"Ethane\",\n", " \"BibTeXKey\": \"Lafitte\",\n", " \"m\": 1.4373,\n", " \"epsilon_over_k\": 206.12, # [K]\n", " \"sigma_m\": 3.7257e-10,\n", " \"lambda_r\": 12.4,\n", " \"lambda_a\": 6.0\n", " }]\n", " }\n", "})\n", "display(model.get_Ar01(300, 300, z))\n", "\n", "model = teqp.make_model({\n", " \"kind\": 'SAFT-VR-Mie',\n", " \"model\": {\n", " \"names\": [\"Ethane\"]\n", " }\n", "})\n", "display(model.get_Ar01(300, 300, z))" ] }, { "cell_type": "code", "execution_count": 4, "id": "d3d42d81", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:40:05.951857Z", "iopub.status.busy": "2024-03-15T22:40:05.951525Z", "iopub.status.idle": "2024-03-15T22:40:07.071578Z", "shell.execute_reply": "2024-03-15T22:40:07.070973Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Here is an example of using teqp to trace VLE for propane\n", "# with the default parameters of PC-SAFT and SAFT-VR-Mie\n", "# models\n", "for kind in ['SAFT-VR-Mie', 'PCSAFT']:\n", " j = {\n", " \"kind\": kind,\n", " \"model\": {\n", " \"names\": [\"Propane\"]\n", " }\n", " }\n", " model = teqp.make_model(j)\n", "\n", " z = np.array([1.0])\n", " Tc, rhoc = model.solve_pure_critical(300, 10000)\n", "\n", " # Extrapolate away from the critical point\n", " Ti = Tc*0.9997\n", " rhoL, rhoV = model.extrapolate_from_critical(Tc, rhoc, Ti)\n", "\n", " o = []\n", " T = Ti\n", " while T > 88:\n", " rhoL, rhoV = model.pure_VLE_T(T, rhoL, rhoV, 10)\n", " T -= 0.1\n", " o.append({'rhoL': rhoL, 'rhoV': rhoV, 'T': T})\n", "\n", " df = pandas.DataFrame(o)\n", " line, = plt.plot(df['rhoL'], df['T'], label=kind)\n", " plt.plot(df['rhoV'], df['T'], color=line.get_color())\n", "\n", "# From the reference EOS of Lemmon et al. via CoolProp\n", "name = 'Propane'\n", "Tc = CP.PropsSI(name, 'Tcrit')\n", "Ts = np.linspace(88, Tc, 1000)\n", "rhoL = CP.PropsSI('Dmolar','T',Ts,'Q',0,name)\n", "rhoV = CP.PropsSI('Dmolar','T',Ts,'Q',1,name)\n", "line, = plt.plot(rhoL, Ts, label='Reference EOS')\n", "plt.plot(rhoV, Ts, line.get_color())\n", "\n", "plt.gca().set(xlabel=r'$\\rho$ / mol/m$^3$', ylabel=r'$T$ / K')\n", "plt.legend()\n", "plt.tight_layout(pad=0.2)\n", "plt.savefig('SAFTVRMIE_PCSAFT.pdf')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "id": "5c617489", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:40:07.074195Z", "iopub.status.busy": "2024-03-15T22:40:07.073707Z", "iopub.status.idle": "2024-03-15T22:40:18.954693Z", "shell.execute_reply": "2024-03-15T22:40:18.954218Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.25 ms ± 6.94 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "215 µs ± 188 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n" ] } ], "source": [ "# Time calculation of critical points\n", "for kind in ['SAFT-VR-Mie', 'PCSAFT']:\n", " j = {\n", " \"kind\": kind,\n", " \"model\": {\n", " \"names\": [\"Propane\"]\n", " }\n", " }\n", " model = teqp.make_model(j)\n", "\n", " z = np.array([1.0])\n", " %timeit model.solve_pure_critical(300, 10000)" ] }, { "cell_type": "code", "execution_count": 6, "id": "c34aaf8b", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:40:18.956927Z", "iopub.status.busy": "2024-03-15T22:40:18.956494Z", "iopub.status.idle": "2024-03-15T22:40:19.718094Z", "shell.execute_reply": "2024-03-15T22:40:19.717505Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Checking the effective hardness of interaction,\n", "# the neff parameter defined in https://doi.org/10.1063/5.0007583\n", "# SAFT-VR-Mie comes closest to the right behavior\n", "modelVR = teqp.make_model({\n", " \"kind\": 'SAFT-VR-Mie',\n", " \"model\": { \"names\": [\"Methane\"] }\n", "})\n", "modelPCSAFT = teqp.make_model({\n", " \"kind\": 'PCSAFT',\n", " \"model\": { \"names\": [\"Methane\"] }\n", "})\n", "modelMF = teqp.build_multifluid_model([\"Methane\"], teqp.get_datapath())\n", "\n", "for model, label in [(modelVR, 'SAFT-VR-Mie'), \n", " (modelPCSAFT, 'PC-SAFT'), \n", " (modelMF, 'reference EOS')]:\n", " z = np.array([1.0])\n", " rho = 1e-5\n", " T = np.geomspace(8, 10000, 10000)\n", " neff = []\n", " for T_ in T:\n", " neff.append(model.get_neff(T_, rho, z))\n", " plt.plot(T, neff, label=label)\n", "plt.xscale('log')\n", "plt.ylim(0, 30)\n", "plt.gca().set(xlabel=r'$T$ / K', ylabel=r'$n_{\\rm eff}$')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "ab669adc", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:40:19.720323Z", "iopub.status.busy": "2024-03-15T22:40:19.720005Z", "iopub.status.idle": "2024-03-15T22:40:20.516083Z", "shell.execute_reply": "2024-03-15T22:40:20.515541Z" } }, "outputs": [ { "data": { "image/png": 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IiYmhc+fORfazt7e3wp+O7ZJAZCO0Gi1TQ6cy4X8T+O70dwy/YziBboFqlyWEEBWnKFBw69aTSmXnBBpNmQ650YIDMHHiRFavXs26deto0qQJ33zzDWvWrOHBBx8s3D8oKIgHHniA9PT0m54vNTWVnTt3sm3bNnr06AFAw4YN6dy5c7F9MzMzWblyJQcPHiQuLo6lS5fy2muvFdvPy8ursMabyc3NLdV+tYkEIhvS1b8rd/nfxa6ru/jk0CfM6DFD7ZKEEKLiCrLh/eKtHFXitatg71yhUzg6OpKUlMQ333xDixYtioShGzQaDe7u7jc93sXFBRcXF9asWUOXLl0wGAy3vNb333/PHXfcQYsWLRgxYgRTpkzh1VdfRVPGUCeKkz5ENub50OfRoOHXS79y9PpRtcsRQohaS1EUNm/ezG+//Ubv3r05e/YsLVq0KPN59Ho9S5cuZdmyZXh4eHDXXXfx2muvceTIkWL7Llq0iBEjRgCWW3dpaWls37692H533nlnYdBycXHh0KFDZX+DtYy0ENmYFp4teKDJA6w9v5ZZkbNY0neJ/MtACGHb7JwsLTVqXbuM1q9fj4uLCwUFBZjNZoYPH87bb7/N+vUlzxW3c+dO+vfvX7j+xRdf8NhjjzFkyBAGDBjAzp072bt3Lxs3buSjjz7iyy+/ZPTo0QCcPn2a/fv3s3r1asASpIYNG8aiRYuKdYheuXIlLVu2LFwPDJQuFiWRQFSC8PBwwsPDMZmqzyzRz7R/hl8v/UpkfCTbY7fTM7Cn2iUJIUT5aTQVvm1VlXr16sXnn3+Ovb09/v7+6PWWr9LmzZtz6tTtH8bdsWNHoqOjC9d9fX0Lf3dwcODee+/l3nvv5c033+SJJ55g+vTphYFo0aJFGI3GIp2oFUXBYDAwb968IrfkAgMDadq0qRXebe0ht8xKoPbEjDfj5+zHiJaWJtM5kXMwmo0qVySEELWHs7MzTZs2pUGDBoVhCGD48OGcOXOGtWvXFjtGURTS0tJwdHSkadOmhYurq+str9OqVSuysrIAMBqNLF++nFmzZhEdHV24HD58GH9/f7799lvrv9FaRgKRjRrXdhweBg8upF1g9bnVapcjhBC13r///W+GDRvGo48+yvvvv8/Bgwf5448/WL9+PX369GHr1q03PS4pKYnevXvz9ddfc+TIES5evMgPP/zARx99VNhBe/369aSkpDBu3DjatGlTZBkyZAiLFi2qyrdaI0kgslGu9q48FfwUAJ9Ff0a2WkNWhRBCAJaRZCtWrGD27NmsWbOGHj160K5dO95++20efPBB+vbte9PjXFxcCAsLY86cOdx99920adOGN998k/HjxzNv3jzAcrusT58+Nx2pNmTIEA4ePHjTTtii9DSKoihqF2EL0tPTcXd3Jy0tDTc3N7XLAaDAVMADax4gNjOWp0OeZmLwRLVLEkKIEuXm5nLx4kUaNWqEg4OD2uWIGuB2n6nSfn9LC5ENs9PZ8VzocwAsObaExJxElSsSQgghbJMEIhvXt2Ff2nq3JceYw+fRn6tdjhBCCGGTJBDZOI1Gw9TQqQCsOruKC2kXVK5ICCGEsD0SiGqAjn4d6RnYE5Ni4uPIj9UuRwghhLA5EohqiOc7PI9Oo2NLzBYi4yPVLkcIIYSwKRKIaojGHo0Z3GwwALMPzkYGDwohhBClV6sC0aBBg6hTpw5Dhw5Vu5RK8XTI0zjqHTmSeIT//fE/tcsRQgghbEatCkTPPfccy5cvV7uMSuPt6M3o1qMBmBs1lwJTgboFCSGEEDaiVgWinj173va5MTXB6Naj8XLwIiYjhu/PfK92OUIIIYRNsJlAtGPHDgYOHIi/vz8ajYY1a9YU2yc8PJygoCAcHBwICwtj//79VV+oypzsnHg65GkAvjj8BRn5GSpXJIQQtZuiKEyYMAFPT080Gk2Rp92L6sNmAlFWVhbBwcGEh4ff9PWVK1cydepUpk+fTlRUFMHBwfTt25eEhIRyXS8vL4/09PQii60Y3GwwQW5BpOSlsOTYErXLEUKIWu3XX39l6dKlrF+/nmvXrtGmTRu1S7K6oKAgNBpNseW///1vkf2WLVtGp06dcHJywtXVlR49erB+/fpi51u4cCHBwcG4uLjg4eFB+/bt+eCDDyr1PdhMIOrfvz/vvfcegwYNuunrs2fPZvz48YwZM4ZWrVoxf/58nJycWLx4cbmu98EHH+Du7l64BAYGVqT8KqXX6nk+9HkAlp9YTlxWnMoVCSFEzZOfn1+q/c6fP0+9evW488478fPzQ6/Xl/laiqJgNBrLfFxVevfdd7l27VqRZfLkyYWvT5s2jSeffJJhw4Zx5MgR9u/fT7du3XjwwQcLH2ILsHjxYqZMmcKzzz5LdHQ0u3bt4qWXXiIzM7Ny34BigwBl9erVhet5eXmKTqcrsk1RFOXxxx9XHnjggSLbtm7dqgwZMqTEa+Tm5ippaWmFS0xMjAIoaWlp1ngLlc5sNiuPb3hcabO0jfLG72+oXY4QQhTKyclRTpw4oeTk5CiKYvn7Kis/S5XFbDaXuu4ePXookyZNUp577jnFy8tL6dmzp6IoinL06FGlX79+irOzs1K3bl1lxIgRyvXr1xVFUZRRo0YpQOHSsGFDRVEUxWQyKe+//74SFBSkODg4KO3atVN++OGHwmtt3bpVAZQNGzYoHTp0UOzs7JStW7eW+rjNmzcroaGhiqOjo9K1a1fl1KlTRd7LunXrlI4dOyoGg0Hx8vJSHnroocLXcnNzlRdeeEHx9/dXnJyclM6dOytbt2697Z9Nw4YNlTlz5tzy9T179iiA8sknnxR7berUqYqdnZ1y+fJlRVEU5cEHH1RGjx592+v90z8/U3+XlpZWqu/vssfUaigxMRGTyYSvr2+R7b6+vpw6dapwvU+fPhw+fJisrCzq16/PDz/8QNeuXW96ToPBgMFgqNS6K5NGo+GFji/w2IbHWHtuLSNbjaR5neZqlyWEEMXkGHMIWxGmyrX3Dd+Hk51TqfdftmwZEydOZNeuXQCkpqbSu3dvnnjiCebMmUNOTg4vv/wy//73v9myZQsff/wxTZo0YcGCBRw4cACdTgdY7kJ8/fXXzJ8/n2bNmrFjxw5GjBiBj48PPXr0KLzeK6+8wsyZM2ncuDF16tQp9XGvv/46s2bNwsfHh6eeeoqxY8cW1vzLL78waNAgXn/9dZYvX05+fj4bNmwoPPaZZ57hxIkTfPfdd/j7+7N69Wr69evH0aNHadasWbn+nL/99ltcXFx48skni732wgsvMHv2bFatWsWUKVPw8/Nj+/bt/PHHHzRs2LBc1yuPGhGISmvz5s1lPiY8PJzw8HBMJlMlVFS52vm0476G97Hpj03MiZzD533k4a9CCFERzZo146OPPipcf++992jfvj3vv/9+4bbFixcTGBjImTNnaN68Oa6uruh0Ovz8/ABLH9X333+fzZs3F/6jvHHjxvz+++988cUXRYLNu+++y7333lvm4/7v//6vcP2VV15hwIAB5Obm4uDgwP/93//xyCOP8M477xTuHxwcDMDly5dZsmQJly9fxt/fH7Dc6vr1119ZsmRJkff5Ty+//DJvvPFGkW0bN26ke/funDlzhiZNmmBvb1/sOH9/f9zc3Dhz5gwA06dPZ/DgwQQFBdG8eXO6du3Kv/71L4YOHYpWW3k9fWpEIPL29kan0xEfH19ke3x8fOEHsLwmTZrEpEmTSE9Px93dvULnUsNzHZ5jS8wWfr/yO3uv7aVLvS5qlySEEEU46h3ZN3yfatcui9DQ0CLrhw8fZuvWrbi4uBTb9/z58zRvXrxl/ty5c2RnZxcGnRvy8/Np3759kW0dO3Ys13Ht2rUr/L1evXoAJCQk0KBBA6Kjoxk/fvxN39/Ro0cxmUzF6s7Ly8PLy+umx9zw4osvMnr06CLbAgICCn9XSvkEhXr16rFnzx6OHTvGjh072L17N6NGjeLLL7/k119/rbRQVCMCkb29PaGhoURERPDQQw8BYDabiYiI4JlnnqnQuW25hQiggVsDhrUYxjcnv2H2wdl8d/93aDU205deCFELaDSaMt22UpOzs3OR9czMTAYOHMiHH35YbN8bQeSfbnQO/uWXX4oEBqBYV42/X68sx9nZ2RX+rtFoAMv3IoCj461DYGZmJjqdjsjIyMLbezfcLPT9nbe3N02bNr3pa82bN+f3338nPz+/WCvR1atXSU9PLxbC2rRpQ5s2bXj66ad56qmn6N69O9u3b6dXr163raO8bCYQZWZmcu7cucL1ixcvEh0djaenJw0aNGDq1KmMGjWKjh070rlzZ+bOnUtWVhZjxoyp0HVtvYUIYEK7Caw9t5aTySfZcHED9ze+X+2ShBCiRujQoQOrVq0iKCio1KPHWrVqhcFg4PLly0Vuc1XWcf/Url07IiIibvr92L59e0wmEwkJCXTv3r3c1/inRx55hE8++YQvvviiyMgzgJkzZ2JnZ8eQIUNueXyrVq0AyxQ8lcVmAtHBgweLpMKpU6cCMGrUKJYuXcqwYcO4fv06b731FnFxcYSEhPDrr78W62hdG3k6eDKu7Tg+jvqYT6I+4d6G92LQ2W6HcSGEqC4mTZrEwoULefTRR3nppZfw9PTk3LlzfPfdd3z55ZfFWlkAXF1dmTZtGs8//zxms5lu3bqRlpbGrl27cHNzY9SoUTe9VnmP+6fp06dzzz330KRJEx555BGMRiMbNmzg5Zdfpnnz5jz22GM8/vjjzJo1i/bt23P9+nUiIiJo164dAwYMuOV5MzIyiIsrOs2Lk5MTbm5udO3aleeee44XX3yR/Px8HnroIQoKCvj666/5+OOPmTt3buH0NhMnTsTf35/evXtTv359rl27xnvvvYePj88tB0JZRZnGtdVC8+bNU1q2bKk0b97cpobd/1NOQY5yz/f3KG2WtlGWHF2idjlCiFrsdkOkq7MePXoozz33XLHtZ86cUQYNGqR4eHgojo6Oyh133KFMmTKlcEj/nDlzCofb32A2m5W5c+cqLVq0UOzs7BQfHx+lb9++yvbt2xVF+Wv4fEpKSoWPO3TokAIoFy9eLNy2atUqJSQkRLG3t1e8vb2VwYMHF76Wn5+vvPXWW0pQUJBiZ2en1KtXTxk0aJBy5MiRW/7ZNGzYsMj0AjeWJ598ssh+ixYtUkJDQxUHBwfF2dlZ6d69u7Ju3boi+/z444/Kv/71L6VevXqKvb294u/vrwwZMuS217fGsHuNopSyl1Mtd+OWWVpaGm5ubmqXUy5rzq3hzV1v4mrvysbBG3E32OYtQCGEbcvNzeXixYs0atQIBwcHtcsRNcDtPlOl/f6W3rW1yMDGA2lWpxkZ+RksPLJQ7XKEEEKIakMCUS2i0+qYGmrpe7Xi1ApiM2JVrkgIIYSoHiQQlSA8PJxWrVrRqVMntUuxirv876JLvS4UmAv49NCnapcjhBBCVAsSiEowadIkTpw4wYEDB9QuxSo0Gk1hK9GGixs4nnRc5YqEEEII9UkgqoVaerUsnIto9sHZpZ49VAghrEn+7hHWcmPSyYqwmXmIhHVNbj+ZTZc2sT9uPzuv7OTu+nerXZIQopaws7NDo9Fw/fp1fHx8CmdSFqKsFEUhPz+f69evo9Vqb/qstNKSQFQCW390x634u/jzWMvHWHJ8CXMi53CX/13otMUnEBNCCGvT6XTUr1+f2NhYLl26pHY5ogZwcnKiQYMGFXrOmcxDVEo1YR6if0rLS+NfP/2L9Px03r3zXQY1G6R2SUKIWsRkMlFQUKB2GcLG6XQ69Hr9LVsaS/v9LS1EtZi7wZ0J7SYw8+BM5h2aR9+gvjbzgEUhhO3T6XQ3fbSFEGqQTtW13KN3PEqASwAJOQl8ffJrtcsRQgghVCGBqJaz19nzbPtnAVh8bDFJOUkqVySEEEJUPQlEJahpEzPeTL9G/Wjl1Yqsgiy+OPKF2uUIIYQQVU46VZdSTexU/Xf7r+1n3KZx6DV6Vj+4miD3ILVLEkIIISpMHu4qyqRzvc7cXf9ujIqRTw59onY5QgghRJWSQCQKTekwBa1Gy//++B/RCdFqlyOEEEJUGQlEolCzOs14qOlDAMw6OEum1RdCCFFrSCASRTwd/DQOOgeir0ez5fIWtcsRQgghqoQEIlGEr7Mvj7d+HIC5UXMpMMssskIIIWo+CUQlqA3D7v9pTOsxeDp4cin9Ej+d+UntcoQQQohKJ8PuS6mmD7v/p29Pfcv7+97H08GTDYM34GznrHZJQgghRJnJsHtRIUObD6WhW0OSc5NZcmyJ2uUIIYQQlUoCkbgpO60dUzpMAWD5ieUkZCeoW5AQQghRiSQQiVu6p8E9BPsEk2PM4bPoz9QuRwghhKg0EojELWk0GqZ1nAbA6nOrOZdyTuWKhBBCiMohgUjcVkjdEPo06INZMTM3aq7a5QghhBCVQgKRKNFzHZ5Dp9GxPXY7B+IOqF2OEEIIYXUSiESJgtyDGNp8KGB5pIdZMatckRBCCGFdEohKUBsnZryZicETcdI7cTzpOL9d+k3tcoQQQgirkkBUgkmTJnHixAkOHKjdt4q8HL0Y22YsAB9HfUy+KV/lioQQQgjrkUAkSm1kq5H4OPpwJfMK3536Tu1yhBBCCKuRQCRKzcnOiUkhkwD44sgXpOWlqVyREEIIYR0SiESZPNj0QZp6NCU9P51FxxapXY4QQghhFRKIRJnotXqeD30egG9OfMO1zGsqVySEEEJUnAQiUWbdA7rTya8T+eZ8Pj30qdrlCCGEEBUmgUiUmUaj4YXQFwBYf2E9J5NOqlyREEIIUTESiES5tPZuTf9G/VFQmBM5R+1yhBBCiAqRQCTK7dn2z6LX6tlzbQ+7r+xWuxwhhBCi3CQQiXKr71qfR+94FIBZkbMwmU0qVySEEEKUT60KROvXr6dFixY0a9aML7/8Uu1yaoQn2z2Jq70rZ1LOsP7CerXLEUIIIcql1gQio9HI1KlT2bJlC4cOHWLGjBkkJSWpXZbNcze4M77teAA+PfQpucZclSsSQgghyq7WBKL9+/fTunVrAgICcHFxoX///mzatEntsmqE4S2HU8+5HvHZ8Xx98mu1yxFCCCHKzGYC0Y4dOxg4cCD+/v5oNBrWrFlTbJ/w8HCCgoJwcHAgLCyM/fv3F7529epVAgICCtcDAgK4cuVKVZRe4xl0Bia3nwzAoqOLSMlNUbkiIYQQomxsJhBlZWURHBxMeHj4TV9fuXIlU6dOZfr06URFRREcHEzfvn1JSEgo1/Xy8vJIT08vsohbG9B4AHd43kFmQSYLjixQuxwhhBCiTGwmEPXv35/33nuPQYMG3fT12bNnM378eMaMGUOrVq2YP38+Tk5OLF68GAB/f/8iLUJXrlzB39//ltf74IMPcHd3L1wCAwOt+4ZqGK1Gy9TQqQB8d/o7YtJjVK5ICCGEKD2bCUS3k5+fT2RkJH369CncptVq6dOnD3v27AGgc+fOHDt2jCtXrpCZmcnGjRvp27fvLc/56quvkpaWVrjExMgXfEm6+nflLv+7MJqNfHzoY7XLEUIIIUqtRgSixMRETCYTvr6+Rbb7+voSFxcHgF6vZ9asWfTq1YuQkBBeeOEFvLy8bnlOg8GAm5tbkUWU7PnQ59Gg4bdLv3Hk+hG1yxFCCCFKpUYEotJ64IEHOHPmDOfOnWPChAmlOiY8PJxWrVrRqVOnSq6uZmjh2YIHmjwAwOzI2SiKonJFQgghRMlqRCDy9vZGp9MRHx9fZHt8fDx+fn4VOvekSZM4ceIEBw4cqNB5apNn2j+DQWcgMj6SbTHb1C5HCCGEKFGNCET29vaEhoYSERFRuM1sNhMREUHXrl1VrKx28nP2Y0TLEQDMiZqD0WxUuSIhhBDi9mwmEGVmZhIdHU10dDQAFy9eJDo6msuXLwMwdepUFi5cyLJlyzh58iQTJ04kKyuLMWPGVOi6csusfMa1HYeHwYOLaRdZfW612uUIIYQQt6VRbKSTx7Zt2+jVq1ex7aNGjWLp0qUAzJs3jxkzZhAXF0dISAiffPIJYWFhVrl+eno67u7upKWlSQfrUvrm5Df8d/9/8Xb05pdBv+Bk56R2SUIIIWqZ0n5/20wgUpsEorIrMBXwwJoHiM2M5engp5kYMlHtkoQQQtQypf3+tplbZmqRW2blZ6ez47nQ5wBYcnwJiTmJKlckhBBC3JwEohLIKLOK6duwL22925JjzOHz6M/VLkcIIYS4KQlEolJpNJrCR3qsOruKC2kXVK5ICCGEKE4CUQnkllnFdfTrSM/AnpgUE3Mj56pdjhBCCFGMdKouJelUXTEXUi8weN1gTIqJpf2WEuobqnZJQgghagHpVC2qlcYejRncbDAAsw/KIz2EEEJULxKIRJV5OuRpHPWOHEk8wqY/NqldjhBCCFFIAlEJpA+R9Xg7ejO69WgAPo76mAJTgboFCSGEEH+SQFQCGXZvXaNbj8bLwYuYjBi+P/O92uUIIYQQgAQiUcWc7Jx4OuRpAL44/AUZ+RkqVySEEEJIIBIqGNxsMEFuQaTkpbD42GK1yxFCCCEkEImqp9fqeT70eQC+OvEVcVlxKlckhBCitpNAJFTRK7AXHep2IM+UR3h0uNrlCCGEqOUkEJVARplVDo1GwwsdXwBg7bm1nE4+rXJFQgghajMJRCWQUWaVp51PO+5reB8KCnOi5qhdjhBCiFpMApFQ1XMdnkOv1bPryi72XN2jdjlCCCFqKQlEQlUN3BowrMUwAOZEzsGsmFWuSAghRG0kgUiobkK7CbjYuXAy+SS/XPhF7XKEEELUQhKIhOo8HTwZ13YcAJ8e+pQ8U57KFQkhhKhtJBCVQEaZVY0RLUfg6+TLtaxrfHvyW7XLEUIIUctoFEVR1C7CFqSnp+Pu7k5aWhpubm5ql1MjrTm3hjd3vYmrvSsbB2/E3eCudklCCCFsXGm/v8vcQrR582YkQ4nKMLDxQJrVaUZGfgYLjixQuxwhhBC1SJkDUd++fbl+/Xpl1CJqOZ1Wx9TQqQB8e+pbYjNiVa5ICCFEbVHmQCStQ6Iy3eV/F13qdaHAXMCnhz5VuxwhhBC1hHSqFtWKRqMpbCXacHEDxxOPq1yREEKI2qBcgejzzz8nIiKClJQUa9cjBC29WnJ/4/sBmBU5S1olhRBCVLoyjzLTarV4eXmRlJSERqMhMDCQDh06FFn8/Pwqq17VyCizqnUt8xr3r76ffHM+n/b+lJ6BPdUuSQghhA2qtFFmAMePHyc2NpZ169Yxbtw4FEVh4cKF3H///QQEBBAQEFDuwoUAqOdSj5GtRgIw6+AsCswFKlckhBCiJtOX9QCNRgOAv78//v7+DBgwoPC1pKQkIiMjiY6OtlqBovYa13YcP539iUvpl/jpzE8Mu2OY2iUJIYSooaw6yszLy4v77ruPl156qUJFVScyU7V6XO1dmRgyEYDPDn9GZn6myhUJIYSoqcociH799Vfc3WvPDMKTJk3ixIkTHDhwQO1SaqWhzYcS5BZEcm4yi48tVrscIYQQNVSZOlVPnTq11CeePXt2uQqqrqRTtXoiLkcwZesUDDoD6wetx8+55nXaF0IIUTlK+/1dpj5Ehw4dKrIeFRWF0WikRYsWAJw5cwadTkdoaGg5Shbi5noH9qZD3Q5EJUTx6aFP+b9u/6d2SUIIIWqYMt0y27p1a+EycOBAevToQWxsLFFRUURFRRETE0OvXr2KdLQWoqI0Gg3TOk4D4OfzP3My6aTKFQkhhKhpyv20+4CAADZt2kTr1q2LbD927Bj33XcfV69etUqB1YXcMlPfSzteYuPFjYTVC2PhvQsLRzwKIYQQt1Kp8xDduMDNHvJ6/fp1MjIyyntaIW7puQ7PYae1Y9+1ffx+5Xe1yxFCCFGDlDsQDRo0iDFjxvDTTz8RGxtLbGwsq1atYty4cQwePNiaNQoBQIBLAI+1fAywTNZoNBtVrkgIIURNUe5ANH/+fPr378/w4cNp2LAhDRs2ZPjw4fTr14/PPvvMmjUKUeiJtk/gbnDnfNp51pxbo3Y5Qgghaohy9yG6ISsri/PnzwPQpEkTnJ2drVJYdSN9iKqPr098zYcHPsTLwYsNgzfgZOekdklCCCGqqUrrQ/TWW28RGRlZuO7s7Ey7du1o165dtQ9DgwYNok6dOgwdOlTtUkQFDGsxjEDXQJJyk1hyfIna5QghhKgByhyIYmNj6d+/P/Xr12fixIls3LiR/Pz8yqjN6p577jmWL1+udhmigux0djwf+jwAy44vIyE7QeWKhBBC2LoyB6LFixcTFxfHt99+i6urK1OmTMHb25shQ4awfPlykpOTK6NOq+jZsyeurq5qlyGsoE+DPoT4hJBjzCE8OlztcoQQQti4cnWq1mq1dO/enY8++ojTp0+zb98+wsLC+OKLL/D39+fuu+9m5syZXLlypdTn3LFjBwMHDsTf3x+NRsOaNWuK7RMeHk5QUBAODg6EhYWxf//+8pQvagCNRsMLHV8AYPXZ1ZxOPq1yRUIIIWxZuUeZ/V3Lli156aWX2LVrFzExMYwaNYqdO3fy7bfflvocWVlZBAcHEx5+83/tr1y5kqlTpzJ9+nSioqIIDg6mb9++JCT8dbskJCSENm3aFFtq2iSRwiKkbgj3NbwPBYU5kXPULkcIIYQNq/Aos8qg0WhYvXo1Dz30UOG2sLAwOnXqxLx58wAwm80EBgYyefJkXnnllVKfe9u2bcybN48ff/zxtvvl5eWRl5dXuJ6enk5gYKCMMqtmYtJjeGDtAxjNRub3mc9dAXepXZIQQohqpNJGmSUlJTFt2jSefvppjhw5Urg9NjaWzMzM8lVbgvz8fCIjI+nTp0/hNq1WS58+fdizZ0+lXPODDz7A3d29cAkMDKyU64iKCXQL5NE7HgVgVuQsTGaTyhUJIYSwRWUORE888QQLFixg7969dO/enX379hESEkLDhg3x8vLi+eeft3qRiYmJmEwmfH19i2z39fUlLi6u1Ofp06cPDz/8MBs2bKB+/fq3DVOvvvoqaWlphUtMTEy56xeV68l2T+Jq78rZlLOsO79O7XKEEELYoDIHoh07drBq1SqioqKYOXMmgwYNwsPDg9WrV/PBBx+wdOlSvvrqq8qotcI2b97M9evXyc7OJjY2lq5du95yX4PBgJubG1999RVdunThnnvuqcJKRVm4G9x5st2TAMw7NI/sgmyVKxJCCGFryhyIUlJSaNu2LQCjRo0iPj6eDz/8kAceeICpU6cye/Zsqz+6w9vbG51OR3x8fJHt8fHx+Pn5WfVa/zRp0iROnDjBgQMHKvU6omIeveNRAlwCSMhJYPkJmWtKCCFE2ZR72D2Avb09Tk5O+Pj4FL7Wo0cPzp49a53q/mRvb09oaCgRERGF28xmMxEREbdt5RG1h73OnikdpgCw+NhiEnMS1S1ICCGETSlXIFqxYgXR0dEYjcWfNu7s7ExKSkqZz5mZmUl0dDTR0dEAXLx4kejoaC5fvgzA1KlTWbhwIcuWLePkyZNMnDiRrKwsxowZU563UGrh4eG0atWKTp06Vep1RMX1DepLO+92MlmjEEKIMivzsPsePXoQHR1NZmYm9vb25OfnM3z4cLp160aHDh3w9vamadOmmExlG+2zbds2evXqVWz7qFGjWLp0KQDz5s1jxowZxMXFERISwieffEJYWFiZrlNe8nBX2xAVH8WoX0eh1WhZNXAVTes0VbskIYQQKirt93e55yE6c+YMkZGRHDp0iKioKKKiokhNTUWj0QCUORBVdxKIbMeUrVOIuBzB3fXvJvweaSkSQojarLTf3/ryXqB58+Y0b96cRx99tHDbxYsXiYyMJCoqqrynrXbCw8MJDw+v1IBnMivotJpKO39tM6XDFLbHbGdH7A72XttLl3pd1C5JCCFENVemFqKpU6eW+sSzZ88uV0HVVWW1EG06HseczWdZPrYzPq4Gq523tvtg3wesOLWCOzzvYOX9K9FqrPKUGiGEEDamUlqIDh06VGQ9KioKo9FIixYtAMttNJ1OR2hoaDlKrn3yjWbe++Ukl5OzGb5wLyvGd5FQZCVPBT/FuvPrOJV8ivUX1vNAkwfULkkIIUQ1VqZ/Nm/durVwGThwID169CA2NrawD1FMTAy9evViwIABlVVvlavMUWb2ei3Lx3bGz82BswmZDF+4l8TMvJIPFCWq41CH8e3GA/BJ1CfkGnNVrkgIIUR1Vu5O1QEBAWzatInWrVsX2X7s2DHuu+++GveE+crsVH0pMYtHFuwlLj2XZnVd+HZCF7xdpKWoovJMeQxcPZBrWdd4rsNzPNH2CbVLEkIIUcUq7eGuf7/A9evXi22/fv06GRkZ5T1trRTk7cy3E7rg62aQliIrMugMPNvhWQC+PPolSTlJKlckhBCiuip3IBo0aBBjxozhp59+IjY2ltjYWFatWsW4ceMYPHiwNWusFRp5O/PdhK74uhk4E5/JYwv3kSShqML+1ehftPJqRVZBFp8f/lztcoQQQlRT5Q5E8+fPp3///gwfPpyGDRvSsGFDhg8fTr9+/az+LLPaopG3M9+O70JdVwOn4zMYLqGowrQaLdM6TgPgxzM/ciHtgsoVCSGEqI7K3YfohqysLM6fPw9AkyZNcHZ2tkph1cXf5yE6c+ZMlUzMeOF6Jo8s2EtCRh53+LnyzRNheEmfogqZvGUy22K20TOwJ5/2/lTtcoQQQlSRSp+purap6pmqz1/P5NG/haIV47vg6Wxf6detqS6kXWDw2sGYFBOL+y6mk588m04IIWqDSu9ULSpXEx/LaDMfVwOn4jIYvnAvyVn5apdlsxq7N2Zo86EAzDo4C7NiVrkiIYQQ1YkEomqsiY8L347/KxQ99uU+UiQUldvE4Ik42zlzPOk4Gy5uULscIYQQ1YgEomquaV1LKPJ2MXDyWjrDJRSVm5ejF+PajAPg46iPyTHmqFyREEKI6kICUQkqc6bq0mpa14XvJoQVhiJpKSq/ka1GUs+5HnFZcXx14iu1yxFCCFFNlCsQJSQkMHPmzJu+9vHHH9eoWaonTZrEiRMnOHDggKp1NK3ryrfjw/B2sefEtXRGLNpHaraEorJy0DswpcMUwDJZY2JOoroFCSGEqBbKFYiSkpKYNWsWkyZNKrL9xRdf5L333rvpDNai4pr5uv55+8ye41ctLUUSisquf6P+tPNuR44xh08PyRB8IYQQ5QxELVu2ZNu2baxdu5axY8diNpt59tln+eqrr4iIiCA4ONjadYo/NfO1DMH3craEImkpKjuNRsOLnV4EYPXZ1ZxOPq1yRUIIIdRW7j5ELVq0YPv27WzZsoUWLVqwatUqtm7dSrt27axZn7iJ5r6ufDvBEoqOXbGEorTsArXLsikhdUPoF9QPBYUZB2Yg03EJIUTtVqFO1U2aNKFr166cP3+eTp060aJFC2vVJUrQ/G8tRTdCkbQUlc2U0CnYa+3ZF7eP7bHb1S5HCCGEisodiBRFYcSIEezdu5ft27dz+vRp/v3vf2M0Gq1Zn7iNFn+bwfrolTQZfVZGAS4BjGg1ArBM1lhgllY2IYSorcoViIxGI8OGDWPfvn3s2LGD7t27s23bNk6fPs3gwYPJz685X8rVYdj97bTwK9rR+tGFe+WBsGUwvu14PB08uZR+ie9Pf692OUIIIVRSrkC0f/9+zp49y86dOwkMDATA19eXrVu3EhcXx86dO61apJqqy7D722nh58p3RR7zsY9ECUWl4mLvwqQQy2jJzw9/TlpemsoVCSGEUEO5H+6qKAoajabU221dpT3c1WyC7GRw8anwqf7+QNhmdV34ZnwYdV0drFBkzWY0G3n454c5l3qOka1G8lKnl9QuSQghhJVU+sNdbxV6amIYqlQ7ZsDnXeHs/yp8qiY+Lqx8sit+bg6cTcjkkQV7iU/PtUKRNZteq2dax2kAfHvqW/5I/0PlioQQQlQ1eXSHmoz5cOoXyLoO3wyF314HY8VudTXydmblk10I8HDkwvUsHlmwl7g0CUUluSvgLroFdMNoNjL74Gy1yxFCCFHFyhyINm/eLHO2WIveHsb9DzpPsKzvmQeL7oXEcxU6bUMvZ76b0IX6dRy5mJjFsAV7uJoqDzItybSO09BpdGyJ2cKBuOrbZ0wIIYT1lTkQ9e3bVx7NYU12DvCvGfDICnCsA9cOwxd3Q/S3UIHgGejpxHcTutDA04k/krIZtmAPMcnZViy85mni0YShzYcCMOPADMyKWeWKhBBCVJUyByJpHaokdwyAp3ZBw25QkAVrnoKfJkBuerlPWb+OJRQFeTkRk5zDIwv2cjlJQtHtPB3yNC52LpxMPsnP539WuxwhhBBVRPoQVSfuATBqHfR6AzQ6OPo9fNEdYiPLfUp/D0e+m9CVxt7OXEnN4ZEFe7iUmGXFomsWTwdPJrSz3ML8JOoTsgskQAohRG1QrkD0+eefExERQUpKirXrqXaqfGJGrQ56vAhjNoB7IKRcgsX3we9zwVy+Wzh+7g58N6ELTeu6cDUtl0cW7OXC9Uyrll2TDG85nACXABJyElh6fKna5QghhKgCZZ6HSKvV4uXlRVJSEhqNhsDAQDp06FBk8fPzq6x6VVNp8xDdTk4q/PwcnFhjWW/cEwZ9Aa7l+/O9npHHY1/u5Ux8JnVdDawYbwlJorjfLv3GtO3TcNA5sH7QenydfdUuSQghRDlU6jxEx48fJzY2lnXr1jFu3DgURWHhwoXcf//9BAQEEBAQUO7Cxd84esDDS2HgJ6B3hAvb4PO7yj1nkY+rgW/Hd+EOP1cSMvJ4ZMFezsZnWLPiGuO+hvfRvm57ck25fHLoE7XLEUIIUcnK3EKk0+m4du0adevWLfZaUlISkZGRREdH89JLNWu2X1VaiP7u+mn4cSzEH7Osd5kEfaaD3lDmUyVn5TPiy32cuJaOl7M9K8Z3oYWfq5ULtn1Hrx9l+IbhAHw34Dtae7dWuSIhhBBlVWktRLfLT15eXtx33301LgxVCz4t4IkI6PykZX1vOHzZp1xzFnk627NifBhtAtxIysrnkQV7OH5VnuH1T2192jKg8QAAZhycISMshRCiBitzIPr1119xd3evjFpESewc4F8fwaPfgaMnxB2xzFl06Jsyz1nk4WTPN+O6EFzfnZTsAoYv3MfhmNTKqduGTekwBYPOQGR8JBGXI9QuRwghRCUpcyC67777MBjKfptGWFGL/jBxFwR1t8xZtPZpWPVEmecscney46snwghtWIe0nAIe+3IfBy4lV1LRtsnP2Y9RrUcBMDtyNvmmfJUrEkIIURlkHiJb5eYPj6+F3n/OWXTsR5jfDWIPlu00DnYsH9uZLo09ycwz8vii/ew+l1hJRdumcW3G4e3oTUxGDN+c/EbtcoQQQlQCCUS2TKuDu1+EMRvBvQGk/gGL+8Lvc8o0Z5GzQc/SMZ3p0dyHnAITo5ceYOuphEos3LY42TnxbPtnAfjiyBck5khgFEKImsYqgSg2NhZzOScNFFbQIAye2gmtB4HZCJvfhq8HQUZcqU/hYKdjweOh3NvKl3yjmQlfHeTXY6U/vqZ7sOmDtPJqRVZBFvMOzVO7HCGEEFZmlUDUqlUrLl26ZI1TifJy9IChS+CBT8HO6c85i+6EM5tKfQqDXsdnj3Xg/nb1KDApTFoRxdroK5VWsi3RarS82vlVAH46+xMnkk6oXJEQQghrskogsoXhyDExMfTs2ZNWrVrRrl07fvjhB7VLsj6NBjo8DhO2gW9byE6CFQ/Dr6+CMa9Up7DTafn4kfYMDa2PyawwZWU03x+Iqdy6bURI3RD6N+qPgsKH+z+0ic+9EEKI0qk1fYj0ej1z587lxIkTbNq0iSlTppCVVUMfcurTAp7YDGFPWdb3fgZf3gOJZ0t1uE6r4aMh7RjRpQGKAi+tOsLyPZcqr14bMjV0Kg46B6ISovjt0m9qlyOEEMJK9OU5aPny5UXWjUYjP/30U5HZqx9//PGKVWZl9erVo169egD4+fnh7e1NcnIyzs7OKldWSewcoP+HluefrXka4o5a5iz61wwIeczSmnQbWq2G/zzYBoNex6LfL/LW2uPkFpiYcHeTqqm/mvJz9mNs27F8Fv0ZsyJn0SOwB456R7XLEkIIUUHlaiFasmRJkaWgoIAff/yxcH3p0qVlPueOHTsYOHAg/v7+aDQa1qxZU2yf8PBwgoKCcHBwICwsjP3795enfCIjIzGZTAQGBpbreJvSoj9M3P3nnEXZsHYSrBoHuSXPTK3RaHhjQEsm9bKEoPc3nOLjzWdr/a2i0a1HU8+5HnFZcSw9vlTtcoQQQlhBmZ9ldjOurq4cPnyYxo0bl/scGzduZNeuXYSGhjJ48GBWr17NQw89VPj6ypUrefzxx5k/fz5hYWHMnTuXH374gdOnTxe2TIWEhGA0Goude9OmTfj7+wOQnJxM9+7dWbhwIXfeeect68nLyyMv769+N+np6QQGBqr3LLOKMptg11zY8n+gmMCjAQxZDIGdSnX4vC1nmbnpDAATezbhpb4t0JTQylST/XrpV17c/iIOOgd+HvQzfs5+apckhBDiJkr7LLNqE4j+TqPRFAtEYWFhdOrUiXnzLEOezWYzgYGBTJ48mVdeeaVU583Ly+Pee+9l/PjxjBw58rb7vv3227zzzjvFtttsILoh5gCsGguply0TOvZ+He56HrQlNxZ+ufMC7/1yEoDRdwYxfWCrWhuKFEVh9K+jiUqIon+j/nx090dqlySEEOImKu3hrmrIz88nMjKSPn36FG7TarX06dOHPXv2lOociqIwevRoevfuXWIYAnj11VdJS0srXGJiashIq8BO8NTv0HqwpaUo4l346iFIv1bioU90b8x/HmoDwNLdl3ht9VHM5tp5+0yj0fBK51fQoGHjxY0cSjikdklCCCEqwCqB6LXXXsPT09Map7qpxMRETCYTvr6+Rbb7+voSF1e6yQN37drFypUrWbNmDSEhIYSEhHD06NFb7m8wGHBzc+Orr76iS5cu3HPPPRV6D9WKgzsMXQwPzLPMWXRxO8y/C86UPGpqZJeGzBjaDq0Gvt0fwws/HMZoqp2Tcrb0asngZoMB+O/+/2JWauefgxBC1ARWCUSvvvoqHh4e1jhVpenWrRtms5no6OjCpW3btiUeN2nSJE6cOMGBAweqoMoqpNFAh5Hw5A7wuzFn0b9h4yslzln0cMdA5j7SHp1Ww+pDV3j6myjyjKYqKrx6eab9M7jYuXAi6QRrz61VuxwhhBDlZBO3zLy9vdHpdMTHxxfZHh8fj5+fdGatEO9m8EQEhE20rO/73DJn0fUztz3sgWB/5o8IxV6vZdOJeMYtPUh2fvEO7TWdt6M3TwVb5nv6OOpjMvMzVa5ICCFEedhEILK3tyc0NJSIiIjCbWazmYiICLp27Vqp1w4PD6dVq1Z06lS60Vg2SW+A/v+FR1eCk5dlzqIFPSDqK7hNn/t7W/myZHQnnOx1/H4ukRFf7iMtu6AKC68eht8xnIZuDUnKTWLB0QVqlyOEEKIcqk0gyszMLLyVBXDx4kWio6O5fPkyAFOnTmXhwoUsW7aMkydPMnHiRLKyshgzZkyl1lVjb5ndTIt+8NQuaNTDMmfRumfgx7G3nbPorqbefP1EGG4OeqIup/LIwr1czyjdY0JqCjudHS92fBGAr058xeX0yypXJIQQoqzKHIiSkpKYNm0aTz/9NEeOHCncHhsbS2Zm+W8XHDx4kPbt29O+fXvAEoDat2/PW2+9BcCwYcOYOXMmb731FiEhIURHR/Prr78W62gtKsitHoxcA/dMtwzLP/4TzO9mGa5/Cx0a1GHlk13xdjFw8lo6//5iD1dSc6qu5mrg7vp3c5f/XRjNRmYenKl2OUIIIcqozPMQDRo0iIiICJo2bcr58+fZtGkTTz75JEePHkWv1/P0008zZ86cyqq3yoWHhxMeHo7JZOLMmTO2Pw9RWcQcsMxqnfqHJRz1eg26PQ9a3U13v5iYxYgv93ElNQd/dwe+fiKMxj4uVVy0ei6kXmDwusGYFBNf3PsFd/rfeuJPIYQQVaPS5iHasWMHq1atIioqipkzZzJo0CA8PDxYvXo1H3zwAUuXLuWrr76qUPHVSa26ZfZPgZ3gqZ3QZohlzqIt/4HlD0L61Zvu3sjbmR+e6kpjH2eupuXy7y/2cOJqehUXrZ7GHo159I5HAcsw/AJT7etPJYQQtqrMLURarZarV6/i5+dHfn4+jo6O7N69m7CwMMDynLMFCxaUesJEW1HahFkjKQpEr4ANL0JBFjh6wkOfW/oc3URiZh6PL9rPiWvpuDnoWTKmE6ENK2+equokPT+dgasHkpybzLSO0xjVepTaJQkhRK1WqTNVa/98zIO9vT1OTk74+PgUvtajRw/Onj1bntOK6kqjgfaPwZPbwa8d5CTDt8Ng48tQkFtsd28XA99O6ELHhnVIzzUy4sv9/H42UYXCq56bvRtTOkwB4LPoz0jITlC3ICGEEKVSrkC0YsUKoqOjb/ogVWdnZ1JSUipcWHVRK4bdl5Z3M3hiM3SZZFnfNx++7HPTOYvcHe1YPq4z3Zt5k1NgYuzSA/x2vHSzitu6B5s+SDvvdmQbs5kdOVvtcoQQQpRCmW+Z9ejRg+joaDIzM7G3tyc/P5/hw4fTrVs3OnTogLe3N02bNsVkqlkzF9fqW2Y3c2YTrJkI2YmWx3/0/xDaj7S0Jv1NntHElO+i2XgsDp1Ww4yh7Rjcob5KRVed44nHefSXR1FQWNJ3CR39OqpdkhBC1EqV/rT7s2fPEhkZSVRUVOGSmpqKVqtFURQJRLVBRhz8NMHyLDSA1oPg/rng6FFkN6PJzCs/HeXHyFgA3n2wNY93DarSUtXw7p53+eHMDzSr04zv7/8evVavdklCCFHrVHogupmLFy9y8OBBDh06xPvvv2+t01YLEohuwWyG3R/DlvfAbAT3QBi8EBp2/cduCv/55QRLdl0C4Pk+zXn2nqZo/tGiVJOk5qZy/5r7SctL45XOr/BYy8fULkkIIWodVQJRTVSr5yEqi9hIWDUWUi6BRgt3vwh3vwS6v1pFFEVh7uazfBxh6XQ/qmtDpg9sjVZbc0PR96e/5z97/4OLnQs/D/oZb0dvtUsSQohaRQKRlUkLUSnkZcCGl+DwCst6/c4wZCHUCSqy27Ldl3j75+MoCgwM9mfWw8HY66vNU2SsymQ28egvj3Iy+SQPNnmQ97q9p3ZJQghRq1TqsHshbsrgCoM+hyGLwOAGsfthfnc48kOR3UbdGcTHj7THTqfh58NXGbfsAFl5xUcs1gQ6rY7Xu7wOwNrza4lOiFa3ICGEEDclgUhYX9uh8NTvENgF8tLhpycsna9z/5q1+oFgfxaN6oSjnY6dZxMZ/uU+krPyVSy68gT7BPNQ04cAeH/f+5jMNWvAgRBC1AQSiETlqNMQRv8CPV+19Ck6srLYQ2Lvbu7DivFheDjZcTgmlYfn7+ZqDX0o7JQOU3C1c+Vk8klWnV2ldjlCCCH+QQJRCWRixgrQ6aHnKzBmI7g3sDwkdnFf2D4D/mwlad+gDj8+1ZV67g6cv57FkM93cy4hQ+XCrc/L0YtJ7S0TWn5y6BNSc1PVLUgIIUQR0qm6lKRTdQXlpsH6qXDsR8t6gzth8ALwCATgSmoOjy/ax/nrWXg42bFkdCfaN6ijYsHWZzQbGbZ+GGdSzjC0+VCmd52udklCCFHjSadqUb04uMOQL2HQF2DvApd3w/y74NhPAAR4OPLDU3cSHOhBanYBwxfuY/uZ6yoXbV16rZ7Xwl4DYNWZVRy+fljlioQQQtwggUhUHY0Ggh+Bp3ZCQEdLq9GPY2DNJMjLxNPZnhVPhBU+/+yJZQdYd/iq2lVbVahvKA80eQAFhXf3vIvRXDNH1wkhhK2RQCSqnmdjGPsrdJ8GaCD6a/jibrgShbNBz6JRnbi/XT0KTArPfXeIZbsvqV2xVb3Q8QXcDe6cSTnDNye/UbscIYQQSCASatHZwT1vwuj14BYAyedh0b3w+xzstfDJI+15vGtDFAWmrzvOrE2nqSnd3TwdPJkaOhWA8Ohw4rLiVK5ICCGEBCKhrqBuMHEXtHrQ8iy0zW/DVw+izbzGOw+05vk+zQH4dMs5Xl51hAKTWd16reShpg/Rvm57cow5/Hf/f9UuRwghaj0JRCWQYfdVwLEOPLwMHpgHdk5wcQd8fieaU+t5rk8z3h/UFq0Gvj8Yy/jlB2vErNZajZY3uryBXqMn4nIE22K2qV2SEELUajLsvpRk2H0VSTwHq8bBtWjLeuho6Ps+/zuXyeRvo8gtMNOuvjuLR3fC28WgZqVWMTtyNkuOLcHf2Z/VD67Gyc5J7ZKEEKJGkWH3wjZ5N4Vx/4O7ngM0ELkUFvTk3jpxrBjfhTpOdhyJTWPI57u5lJildrUV9lS7p6jnXI+rWVf54sgXapcjhBC1lgQiUf3o7eHed+HxNeBaDxLPwMJ76BD7Daue6kKgpyN/JGUz5PPdRMekql1thTjZORXOTbT8+HLOppxVuSIhhKidJBCJ6qtxT5i4G+64H8wFsOl1Gv82itUjm9AmwI2krHweXbCXLafi1a60QnoG9qR3YG+MipH/7P0PZqVmdBwXQghbIoFIVG9OnjDsa7h/Dugd4fwWvL/qxQ+90ri7uQ85BSbGL4/ku/2X1a60Ql4NexVHvSOHEg6x+uxqtcsRQohaRwKRqP40Gug4Fp7cDr5tITsJxx8fY4nPCh4J8cRkVnjlp6PM3XzGZucq8nP2Y1KI5eGvsyNnk5iTqHJFQghRu0ggErbDpwWMj4AuluCgi1zCB9ef4T+d8gGYu/ksr/50FKONzlX0WMvHaOnZkvT8dD7Y94Ha5QghRK0igUjYFr0B+r0PI9eAaz00SecYefwJ1rTdjV5j5rsDMUz4KpLsfNubq0iv1fPOne+g0+jY9McmtlzeonZJQghRa0ggKoFMzFhNNell6XD95wzXIWfnccB/Nk30iWw5lcCwL/aSkJ6rdpVl1tKrJaNbjwbg//b+Hxn5GeoWJIQQtYRMzFhKMjFjNaUocPg72PAi5GdgsnPhHeNolud0JcDDicWjO9HCz1XtKssk15jL0J+H8kf6HwxtPpTpXaerXZIQQtgsmZhR1A4aDYQ8ChN/h8Au6AoyeVeZxzLncLJSExj6+W52nLmudpVl4qB34O2ubwPw45kfORB3QN2ChBCiFpBAJGqGOkEwZgP0fhO0enqYdrPF6TWCCw4xZukBmxuW39GvIw83fxiAt3e/Ta7R9m7/CSGELZFAJGoOrQ7ungZPbAavZniak/ja/gNe0y5n+k+RfPjrKcxm27lD/Hzo89R1rMvljMt8fvhztcsRQogaTQKRqHn828OTO6DTEwCM029krf2bbN2+lWe/O0RugUnlAkvH1d6VN7q8AcCy48s4kXRC5YqEEKLmkkAkaiZ7JxgwC4Z/D84+3KGNYZ39G/ge/5IRC/eQlJmndoWl0qtBL/oG9cWkmHhr11sUmArULkkIIWokCUSiZmveFybugeb9sdcYedPuG56/9hJPhq/j/PVMtasrlVc6v4KHwYPTKadZcHSB2uUIIUSNJIFI1HwuPvDot3D/XMx6R+7SHWdR9rPMD5/JvgtJaldXIm9Hb17v8joAC48s5HjicZUrEkKImkcCkagdNBroOAbtU79T4Nced002M5jD1aWjWL2n+vfN6RfUr/DW2eu/v06eyTZu+QkhhK2QQCRqF++m2I3/H8Zu0zCjZZB2J51+Hcg3332NqZqPQHs97HW8HLw4n3ae8EPhapcjhBA1Sq0JRKmpqXTs2JGQkBDatGnDwoUL1S5JqEVnh77PmzBmI6mGAOprEnns1CS2zhlDRkaa2tXdUh2HOoWzVi89vpTohGh1CxJCiBqk1jy6w2QykZeXh5OTE1lZWbRp04aDBw/i5eVVquPl0R01VF4ml76bStDFlQDEaAOwH7oQ31Z3qVzYrb3+++usO7+OBq4N+GHgDzjZOaldkhBCVFvy6I5/0Ol0ODlZvjjy8vJQFIVakgXF7RhcCBq1gPN9l5GAJ4HmK3h9fz9XVr8Bxny1q7uplzu/TF0ny4SNH0d9rHY5QghRI1SbQLRjxw4GDhyIv78/Go2GNWvWFNsnPDycoKAgHBwcCAsLY//+/WW6RmpqKsHBwdSvX58XX3wRb29vK1UvbF2Trg9hnriLbfY90GMm4PCnpHxyN8RXvw7XbvZuvHvnuwCsOLWCPVf3qFyREELYvmoTiLKysggODiY8/OadRVeuXMnUqVOZPn06UVFRBAcH07dvXxISEgr3udE/6J/L1atXAfDw8ODw4cNcvHiRFStWEB8ff8t68vLySE9PL7KIms3P15/O037iS7+3SFFcqJN+EuP8uzH//jGYq9fs1ncF3MW/m/8bsNxCS8lNUbkiIYSwbdWyD5FGo2H16tU89NBDhdvCwsLo1KkT8+bNA8BsNhMYGMjkyZN55ZVXynyNp59+mt69ezN06NCbvv7222/zzjvvFNsufYhqPrNZYeHGPTTd+xr36A4BYKzfBf3g+eDZSOXq/pJjzGHY+mFcTLtIr8BefNzrYzQajdplCSFEtVKj+hDl5+cTGRlJnz59CrdptVr69OnDnj2lu10QHx9PRkYGYAk1O3bsoEWLFrfc/9VXXyUtLa1wiYmJqdibEDZDq9Xw5IA7yRryDa+bJpCpOKCP3Yv58zvh4BKoJv+GcNQ78mH3D9Fr9WyN2coPZ35QuyQhhLBZNhGIEhMTMZlM+Pr6Ftnu6+tLXFxcqc7xxx9/0L17d4KDg+nevTuTJ0+mbdu2t9zfYDDg5uZWZBG1ywMhATw84XVG2M1mn/kOtAXZsH4KfPMwpF9TuzwAWnq1ZEqHKQDMODCDC6kX1C1ICCFslE0EImvo3Lkz0dHRHD58mCNHjvDkk0+W6rjw8HBatWpFp06dKrlCUR2FBHrwxbND+Mh3Jv8peIw8xQ7O/Q/lsy5w9Mdq0Vo0stVIutbrSq4pl5d3vky+qXqOjhNCiOrMJgKRt7c3Op2uWCfo+Ph4/Pz8KvXakyZN4sSJExw4cKBSryOqL183B1Y8eSfZoU8xIP//OGJuhCY3FVaNg+8fh8yEEs9RmbQaLe91ew8Pgwenkk/xSdQnqtYjhBC2yCYCkb29PaGhoURERBRuM5vNRERE0LVr10q9trQQCQCDXscHg9sx5qF+DDO9y1zjYIzo4OQ6CA9TvbWorlPdwqH4y04sY2fsTtVqEUIIW1RtAlFmZibR0dFER0cDcPHiRaKjo7l8+TIAU6dOZeHChSxbtoyTJ08yceJEsrKyGDNmTKXWJS1E4u8eC2vIV+O78Y3jYzyQ9x9O0RByki2tRStHQMatp3KobL0a9GJYi2EAvPb7a8Rlla5/nRBCiGo07H7btm306tWr2PZRo0axdOlSAObNm8eMGTOIi4sjJCSETz75hLCwsCqpTx7dIf4uLi2Xp76O5FhMIpP063jWbg06xQgOHvCvGdD2YVBhCHy+KZ+RG0dyIukE7XzasbTvUux0dlVehxBCVBel/f6uNoGougoPDyc8PByTycSZM2ckEIlCeUYTb605zsqDMdyhucwCt0U0yDtrebF5f7h/DrjVq/K6YjJiGPbzMDIKMni81eO82OnFKq9BCCGqCwlEViYtROJmFEXh632XeWfdcTAX8Jr7JsYUrERjLgAHd+j3IQQ/UuWtRVsub+G5rc8BMLfnXO5peE+VXl8IIaqLGjUxoxDVlUajYWSXhnw3oQtebs68m/YvHjS+T6pHa8hNgzVPwYphkH61Suvq3aA3o1qNAuDNXW8Sky4TiwohxO1IIBLCCjoGefLLs925s4kXR/IDCI17hc31nkTR2cPZ3yC8Cxz6ukpHoj0X+hzBPsFkFGQwdftUcow5VXZtIYSwNRKISiDD7kVpebsY+GpcGM/0aooJHU9c7MGzbh+T7xsCeWmwdhJ8NQiSL1ZJPXZaO2b2mImngyenkk8xfdd05A65EELcnPQhKiXpQyTKYsupeJ5feZi0nAK8HbV8HxxF42OfgDEX9I7Q6zXo8jTo9JVey8G4g4zfNB6jYuT50OcZ22ZspV9TCCGqC+lDJISKet/hy/rJ3Wgb4E5ijpl79oWwuN03KEHdwZgD/3sTvuwNV6MrvZaOfh15ufPLAMyNnCuTNgohxE1IIBKikgR6OvHDU115LKwBigLv7s7jsfzXSb9vjmUE2rXDsLA3bHoT8rMrtZZhLYYxpNkQFBRe3vEyl9IuVer1hBDC1kggKoH0IRIV4WCn4/8GtWX2v4NxtNOx+0IyvSIC2dVvI7QeBIoJdn8Cn3eF81srrQ6NRsPrYa8T4hNCRkEGz259loz8jEq7nhBC2BrpQ1RK0odIVNT565k8s+IQJ6+lAzDh7sa8GHQBu19fhPQrlp2Ch0Pf/wMnz0qpITEnkWHrh5GQnUBYvTA+v+dzmclaCFGjSR8iIaqZJj4urH76TkbfGQTAgh0XGLrFnZhHt0LnCYAGDq+AeZ3gyPeVMkTf29Gbeb3n4ah3ZN+1fbyz5x0ZeSaEEEggEqJKOdjpePuB1iwYGYq7ox2HY9PoPz+adQHPw7hN4HMHZCfCT+Nh+QNw/YzVa2jp1ZKZPWai0+hYe34t84/Mt/o1hBDC1kggEkIF97X2Y+Nz3ekUVIfMPCPPfnuIl/YZyB67FXq9AXoHuLgDPr8TIt61eqfru+vfzWthrwHwWfRnrDu/zqrnF0IIWyOBqATSqVpUFn8PR74d34Vn72mGRgPfH4zlX/P2cajRE/D0Xmh2H5gLYOcs+CwMTv9q1ev/u8W/GdNmDADTd09nz9U9Vj2/EELYEulUXUrSqVpUpt3nE3nh+8NcS8tFp9UwqVdTJvdqgt3ZDbDx5b86Xd9xP/T7L3gEWuW6ZsXMSzte4rdLv+God2ThfQsJ9gm2yrmFEKI6kKfdW5kEIlHZ0nIKmL72GGuiLQ+CDa7vzuxhITRxA7Z/CHs/A7MR7Jygx0vQZRLo7St83XxTPs9EPMOea3twtXdlab+lNK/TvMLnFUKI6kACkZVJIBJV5efDV3l99VHSc4042Gl5/V8tGdGlIZqEk/DLVLj8560t7xbQ/0No0qvC18wuyGbC/yZw+PphvB29WdZvGQ3cGlT4vEIIoTYJRFYmgUhUpWtpObz4wxF+P5cIQI/mPnw0tB2+rgaIXmF59Ed2kmXnO+6H+94Dz0YVumZaXhpjfxvLmZQz+Dv7s6z/Mvyc/Sr6VoQQQlUSiKxMApGoamazwrI9l/jvxlPkGc24Oeh5a2BrhnQIQJOTAtv+Cwe+tMx2rTPAnc9At6lgcCn3NRNzEhm1cRSXMy4T6BrI4r6LJRQJIWyaBCIrk0Ak1HI2PoOp3x/m6JU0AHq18OH9wW2p5+4I8Sfg11fg4nbLzq714N53oe3DoNGU63pXM68y9rexXMm8Qn2X+izuu5h6LvWs9XaEEKJKSSCykvDwcMLDwzGZTJw5c0YCkVCF0WRmwc4LzP3fWfJNZlwNel4f0JJhnQLRAJz6BX57DVL/sBwQGGbpX+TfvlzXu5Z5jbG/jSU2M5YAlwAW9V1EgEuA1d6PEEJUFQlEViYtRKI6OJeQwYs/HuHQ5VQAujX15oPBbQn0dIKCXNgzzzJvUUE2oIH2j0Gv18HNv8zXisuKY9xv47iccZl6zvVYdN8iAt2sM9xfCCGqigQiK5NAJKoLk1lhya6LzPjtNHlGM872Ol7qdwcjujREp9VA+lX433Q4+r3lAL2jpX/RXc+BwbVM10rITmDcb+O4lH4JLwcv5t87nzs876iEdyWEEJVDApGVSSAS1c3FxCxe/vEI+y8lA9CuvjvvD2pLmwB3yw4xB2DTGxCz17Lu7AM9X4EOo6AMT7hPzEnkqf89xemU07jYufBJ70/o5CcztwshbIMEIiuTQCSqI7NZ4Zv9l/no11Nk5BrRauDxrkG8cF9zXB3sQFHg5M+w+W1IPm85yKsZ9Hkb7hhQ6o7XGfkZPLvlWQ7GH8ROa8eHd3/IvQ3vrbT3JYQQ1iKByMokEInqLCEjl/fWn2TdYcss175uBqYPbE3/Nn5oNBowFcDBJbD9v3/NX9TgTrjvP1C/Y6mukWfK4+UdLxNxOQINGl7u/DLD7xhuOb8QQlRTEoisTAKRsAU7z17nzTXHuJSUDUDPFj68PbA1Qd7Olh1y0+D3uZbHgBhzLdtaDIDer4Nv6xLPbzKbeG/fe/x45kcAhjYfymthr2GnLf0tOCGEqEoSiKxMApGwFbkFJj7bdp75286TbzJjr9MytlsjnundFBeD3rJTWixsfR8OfwuKGdBAmyHQ6zXwanLb8yuKwrLjy5gdORsFhc5+nZnVYxYeDh6V/t6EEKKsJBBZmQQiYWvOX8/k7XXH2XnW8vgPH1cDL/VtwZAO9dFq/7zNdf20JRidWGNZ1+gg5FHo8TJ43P5ZZttjtvPSjpfINmYT6BrIJ70+oWmdppX4joQQouwkEFmJTMwobJmiKGw5lcB/1p8ovI0WXN+dtwa2JrRhnb92vHYYtvwfnP3Nsq6zh9DR0P0FcL31ozvOpJzh2S3PciXzCo56R97s8iYDmwysxHckhBBlI4HIyqSFSNiyPKOJpbsu8emWc2TmGQF4MMSfafe1sEzqeEPMfoh4Fy7ttKzrHSzB6M5nwf3mM1Un5ybzyo5X2HNtDwBDmg3h1bBXMegMlfmWhBCiVCQQWZkEIlETJGTkMvO30/wQGYuigJ1Ow2NhDZncuyleLn8LMBe2w5b3IHa/ZV1rZ5n1utvzUCeo2HlNZhMLjizg88Ofo6Bwh+cdzLh7BkHuxfcVQoiqJIHIyiQQiZrk2JU0Pvz1VGH/IheDngl3N2Zct0Y43+h4rShwYRvsmAl//G7ZptFBu2GWW2nexfsL7b66m1d2vEJKXgoOOgde6PgCw1oMk6H5QgjVSCCyMglEoib6/WwiH/56iqNX0gDwdjHw7D1NGdYpEINe99eOf+yGHTPg/BbLukYLrQdBt6ng16bIOeOz4nlj1xvsvWaZIfsu/7t49653qetUt0rekxBC/J0EIiuTQCRqKrNZ4Zej15i56TR//Nnxup67A0/3bMK//xmMYg9aWozObPxrW5N74M7J0Lhn4czXZsXMt6e+ZU7kHPJMebgb3Hm508vc3/h+aS0SQlQpCURWJoFI1HT5RjMrD1wmfOt54tItkzb6uTkwsWcThnUKxMHub8Ho2hHYOQtOrvtzHiPAt60lGLUZXPistAupF3j191c5kXQCgK71uvJmlzcJdAus0vcmhKi9JBBZmQQiUVvkFpj4/mAMn/0tGPm6GZjYownDOjXA0f5vwSjlEuz9HKKWQ4GldQm3AAh7CkJHgYM7BeYClh1fxvzD88kz5WHQGXgq+ClGtR4lM1wLISqdBCIrk0Akaps8o4nvD8Tw2bbzXEuzBKM6TnaM7BrEqK4Ni45Ky06GyCWw7wvIjLdss3eFkOHQeTx4N+Ny+mXe3fsu+67tA6CReyNe7Pgi3et3r+q3JoSoRSQQWZkEIlFb5RlN/HAwli92nCcmOQcAg17L0ND6PNG9MY1uPCcNwJgHR76H3Z9C4um/tjfuBZ0noDS7j/WXNjLz4EySc5MBS6fraR2nySzXQohKIYHIyiQQidrOaDLz6/E4Fuy4wJFYy6g0jQb6tvJj1J1BdGns+VeHabMZLm6D/Qvh9Ebgz79m3BtAp3FktB3MwrM/8tXJrzCajeg0OoY2H8qEdhNkNJoQwqokEN1CdnY2LVu25OGHH2bmzJmlPk4CkRAWiqKw72IyC3ZcYMuphMLtzeq6MLJrQwa1D8DV4W99g1L+gIOLIWoZ5KRYtukM0HoQl1v2Y3bcdiIuRwBg0BkY1mIYY9uMxcvRqyrflhCihpJAdAuvv/46586dIzAwUAKREBV0Jj6DpbsvsebQFbLzTQA42+sY1CGAkV2CaOHn+tfOBTlw7CfY/4Xl2Wk3eDbhQMs+fJJ7mejk4wA46h15rOVjjGo1Cg8Hjyp8R0KImkYC0U2cPXuWV155hYEDB3Ls2DEJREJYSXpuAT9FxvLV3j84fz2rcHv7Bh4MDa3PwGB/3G60GikKXIm0jEw7tgryMy2bNTp2Nb2LeQYjx7NiAUswGtR0EI+3fpwAl5s/S00IIW6ntN/f2iqs6bZ27NjBwIED8ff3R6PRsGbNmmL7hIeHExQUhIODA2FhYezfv79M15g2bRoffPCBlSoWQtzg5mDH6LsasXlqD1Y8EUa/1n7otBoOXU7l9dXH6PTeZp799hA7z17HpAD1O8IDn8ALp+GBeRAYhkYx0e3sDr49tpuP0wpoqXcnx5jDilMrGPDTAF7a8RInk06q/VaFEDWUXu0CbsjKyiI4OJixY8cyePDgYq+vXLmSqVOnMn/+fMLCwpg7dy59+/bl9OnT1K1r6YQZEhKC0WgsduymTZs4cOAAzZs3p3nz5uzevbvEevLy8sjLyytcT09Pr8C7E6J20Gg03NnUmzubepOQkcuaQ1f44WAsZxMyWXf4KusOX8Xf3YGBwf7c386fNgFuaDqMhA4jIeEUHPoKzeFv6Z18jV7J19jrYGCJTz326E1svLiRjRc30qFuB4a1GEafhn2w19mr/ZaFEDVEtbxlptFoWL16NQ899FDhtrCwMDp16sS8efMAMJvNBAYGMnnyZF555ZUSz/nqq6/y9ddfo9PpyMzMpKCggBdeeIG33nrrpvu//fbbvPPOO8W2yy0zIcpGURSOXknjh4OxrI2+QnruX/9oCfJyYkC7etzfzp87/Fwto9SM+XDuf5bh+6c3gimPk/Z2LHV34zdnZ0x/DmTzdPBkUNNBPNziYbmdJoS4JZvuQ/TPQJSfn4+TkxM//vhjkZA0atQoUlNTWbt2bZnOv3Tp0hL7EN2shSgwMFACkRAVkFtgYuupBNYfuUbEqXhyC8yFrzXxcaZ/m3rc07IuwfU90Go1kJsGJ3+GIyvh4k7idVp+cnXmR1dXEv58xpoGDWH1wnigyQPc0+AenOyc1Hp7QohqqLSBqNrcMrudxMRETCYTvr6+Rbb7+vpy6tSpSrmmwWDAYDCUvKMQotQc7HT0b1uP/m3rkZVnJOJUAusPX2Xbmeucv57FvK3nmLf1HN4uBu65oy59WvnSrfWjOLYfAelX8T36IxOP/sD4mCNsd3LkOzcX9jo6svfaXvZe24ujzoE+De9lYJOBdPbrjE6rK7koIYTARgKRtY0ePbrU+4aHhxMeHo7JZKq8goSohZwNeh4I9ueBYH8ycgvYfDKezScS2H7mOomZeaw8GMPKgzEY9FrubOJF92Y+dG82hqZ3Tkafcol7Tq7jnhPriI05xHoXZ352ceYy8POFn/n5ws942btzT9B99Gl4L538OqHX1sq/7oQQpVQrb5mVhwy7F6Jq5BvN7LuYRMTJBDafjCc2JafI63VdDXRr6k23Zt7c1dQbXyURTq5HObGGI/FR/OzixEZnJ9J1f7UOeeid6BXYmz6N+xNWLwyDTlp/hagtalQfIrB0qu7cuTOffvopYOlU3aBBA5555plSdaquKAlEQlQ9RVE4HZ/BttPX2XUukf0Xk8kzmovs08THmc6NPOnY0JMwHyMB17djPPMr+67uYbNBwxYnR1L+Fo4cNDo6ebWlW6N+dK9/N4FugVX9toQQVcjmAlFmZibnzp0DoH379syePZtevXrh6elJgwYNWLlyJaNGjeKLL76gc+fOzJ07l++//55Tp04V61tkTX+/ZXbmzBkJREKoKLfAROQfKfx+LpHfzyZy7Goa//wbrK6rgU5BnnRu4Ex3uzP4J23nyKX/8T9zGlucHEnQF7111tDeg24B3egSdB8d/EJxs5f/v4WoSWwuEG3bto1evXoV2z5q1CiWLl0KwLx585gxYwZxcXGEhITwySefEBYWViX1SQuRENVPSlY+B/9I4eClZA5cSubolTQKTEX/SrPXabnDz4Ve3un00EShzd5LZOYpdtlrOeRgwHjjgbSABrjDwZeO9cLoFHQPHXxDcTe4V/G7EqJ2MZqNJOYkEpcVR/M6za0+UtTmAlF1J4FIiOovt8DE4ZhUDv6RwoFLyUTHpJKaXVBsP2e9mQe9r3Gn4Ri5SiTHzNeINNhzyd6uyH4aoJm9J22929Iu8G7a+XagkXsjGb0mRCnlGHNIyE4gITuBuKw4ErITiM+OJz4rvvD3xJxEFCxRZFm/ZXTw7WDVGiQQWYncMhPCdimKQmxKDkdi0zhyJZUjMWkcu5JGRl7RGe0dyaWz9jRhzscxOJ0lxi6JSINdsYAE4KzR08a5Pm19Q2ld/05aeLYkwDUArabaPAlJiEqXY8whMTuR6znXSchJKPz9evZ1rudcJzEnkYTsBNLzS/eUB71GT12nuky/czp3+t9p1VolEFmZtBAJUTOYzQqXkrI4eiWNU3EZnLqWzum4DK6m5RbuY08BbTQXaWN3FHen0+Q7xnPGoOG4wZ4cbfHg46zR08ypHi28W9PCryMtvFrS1KOpTBIpbIqiKGQVZJGYUzTc/D3k3FjPLMgs9Xkd9Y74Ovni6+RLXae6+DoX/93TwbPS/lEhgcjKJBAJUbOl5RRwJj6DU3EZnI6zhKTz17NIzspHg5nGmmu00ZwjwOEUOscYkh3SOWvQc97Ojnyt5qbnrKd3oZFLAI28WhLk1YpGHo1p5N4IH0cfy2NKhKhkRrORlNwUknOTScpNsvzMsfy8sfx9Pc+UV/JJ/+Sgc8DHyQcfRx+8Hb3xcbL8rOtU17Lu6IOvsy+udq6qft4lEFmJ3DITonZLzc7nQmIWF69ncSExk4uJWVy4nsXlxHQamGJooz1LgOE09g6xZBoyuGCv5bS9PUn6W/czckRPfYM3ge4NCPRsRoB7QwJcAghwCcDfxR9HvWMVvkNhKxRFIduYTWpeKql5qaTlpv31e14aKXkpxQJOal5qma/jbOdcJOT4OP4Zepy8qetYF28nS9hxsXOxiWAvgcjKpIVICPF3ZrPCldQcYpKziUnJJiY5h9jkDPKvX8Ql7Qwe+adxd/gDnX0CGfbZXLbTc9Hejli9HlMJXyJuGkd8DD74ONfD36MB9d3qUdepLj5OPvg6+eLj5KP6v7pF+ZkVM5kFmWTmZ5KRn0FGfgZp+Wmk5aUVhpsbv99Yv/G70Wws+QL/oNVoqWOog6ejJ54OlsXLwQsvR6/CdU8HT7wcvahjqFPjbvVKILIyCURCiLLILTARm5JDTEo2164nkxt3Cm3yeezTz1NQcAGzNg6zPo0kOzNX9HrLYqcn8yZ9lG7GDj2uOjdc7evg4eiNt5M3fi5eeDvVoY6hDh4OHng6eOJh8MDN3g0XexeZobuCFEUhx5hDtjGbnALLz2xjNtkF2UUDTkFGYdDJzM8kPT+dzILMwvXMgszCUVXlYa+1x8PggbuDOx4GD8vvBnfqGOrg5eiFl8Pfgo6jJ+727rV6ZKQEIiuTQCSEsCZFUUjJyich/gqZV0+TH38GTcof5Gf9QWbBVXJJIlebTZJeS4JOx3WdjgS9jgSdrshjScpChx5HvRPOdq642rvgbnDFzeCKq70rznbOuNhZQpOD3gEHnQMG/d9+1xlw1DsWvm7QGdBr9eg0OvRafeGi0+jQaXSV1nqlKApGxYjJbMJoNmJS/vp5Y1ueKY88cx75pnzyTH/9zDXmFtt24/dcUy65xtzCkFMYeAr+Cj05xpwKBZl/stPa4Wrvipu9G672rrgbigacW/3uqHeU1sEyqFFPu1eTPNxVCFEZNBoNni4GPF0aQ5PGQP/iO5kKyEuOJS3uPDkJlyhIvoSSfo2CtGtk5V8nx5RCviaLdK2GFJ2WVK3O8lOnI0WrJUWnJUWnK2x1MmEk05hOpjGd+Jzil7MmveZvIUlrCUllZVbMlpCjGAtDj1kxl3xgFXDSO+Fk51Tkp6u9JVy62LkU/u5q74qLvQtudm6Fv9/YLi121Yu0EJWStBAJIaolswmyElEyrpGTcpWsxFjyUq5hzExCyU5Cm5OMNi8JkzEdzBkUaPLI1GrI1Gr/XCy/Z2i1ZGu05Go05Gk15GosS96fP3O1f63naLTka8Co0ZTYH6qq3GiZ0ml1GHQG7HX2OOgcsNfZY9AZbrqt8DW9AXutPY56x2Ihp/Cn3glHO0ec9E446B1k3ikbIi1EQghRG2h14OqLxtUXJ/8QSuwOa8yD7GSU7CRyUuPJTEsmOzOFvIxUCrJTMWano+SmoclLR5+fgd6YhcGUiZM5CxeycSQfreavf0crgAlLODICJo2Ggj9/GjVg4q+fZaEAOhR0iuWnXgEdoFeUIus6RUGPZVZxNFrQ6v+26G69rtGBVms5UqO9zaL5c7nF69zudU3x32/8ORQGSU3R363yGrd47SbnuN1rpbr2P91i+00332Rj26FQJ+gW565cEoiEEKI20RvArR4at3o4+bUpOUD9TYHJTFJWPmkZGaSnp5ORmU5WZhrZWZnkZGWQn5NJQU4mBblZmPKzMOdlQ0E29koedhixx4iBAuw1RuwpwB7LTzuM2Gv+fO3PbYX7aYwYMKLHjA4TWsxob9WPRzGDKd+yCNsU0EECkRBCiOrNTqfFx80BHzcHCPAp1TGKopCVbyIlK5/U7AJSc/JJyS4gNTuflKwCUrLzLb/f2JZt2ZaRe+vh5RrM6P5c9JjQYSoMTHrMOOjMeDho8XTQ4uGgxcNBg7uDDneDBneDBjd7Da72GlwNWlwMWlzstTjb67DTYglVxRalhPVbbOcf6+Yb/Z+UG384//i9gq/ddD+K72eta//TLXvg3GT7rfZ1rXeLc1Q+CURCCCEqjUajwcWgx8WgJ9Cz9McZTWbScgqKBaW/wtON7ZaglfLn9nyj2XIPL+vPpdTMONvr8HBypI6zHXWc7PFwsqeOkx0eTvZ4ONpRx9nuz21/bXc16NHeYqZyYVskEJVARpkJIUTV0+u0eLkY8HIp/UgsRVHIKTAVBqS/B6XUrHxSc4puv/EzLacARYGsfBNZ+TlcSS39EDydVoO7ox0eTnZFglJhkHK6Ea5uvG753cGu9s4LVF3JKLNSklFmQghRM5nNCum5BUVbobL+Cksp2UVv891opcopKP8/lB3stEVaoW4Epb8CVPFw5e5oh05ao8pMRpkJIYQQpaDVav5szbGnEc6lPi63wPRXYPpbUErN+bP1KevvfaNu9KEqwGRWyC0wcy0tl2tpuaW+nkYDbg52RYJSHSd73Iu1Tv0Vrjyd7XG0q7yJMmsSCURCCCFEOTjY6XCw0+Hr5lDqYxRFISPPSGrWjZan/L/1h/pnf6k/W6myC8jIM6IokJZTQFpOASRll/qaBr0WT2dL4PP8s3+Up7P9Xz+d7fF0si/sO+XpbF8rb+lJIBJCCCGqiEajwc3BDjcHOxp4lX7SgwKTuUhwunFrzxKa/mqFuvF76p8dz/NNZvKMZW+NcrTT/RmWigaoOjdCVWGIsv8zbNlh0Nt2iJJAJIQQQlRzdjotPq4GfFzL1sn8xpQHKdn5JP/580b/qOS/b88qIDk7n5SsfIxmS+f0K6ll62DuYtAX3qYr2gr1V4DyKGyVsgQtO131mfFbAlEJZJSZEEIIW1R0yoPStUb9/ZbejYCU/I9Alfxn36gbQSsl29IvKjPPSGaekdiU0ocoVwd9kQD17D3NCAn0KOc7rhgZZVZKMspMCCGEKM5sVsjINZJc2NqUX9g/KjnLEpwKw9WfP1P/nOrgn1Y8EcadTb2tWp+MMhNCCCFEpdNqNbg72eHuZEcj79KN0jOZFdJzirdCNfN1reRqb00CkRBCCCGqlE6roc6fI9wo3VNgKl316c0khBBCCKESCURCCCGEqPUkEAkhhBCi1pNAJIQQQohaTwKREEIIIWo9CURCCCGEqPUkEJUgPDycVq1a0alTJ7VLEUIIIUQlkZmqS0lmqhZCCCFsT2m/v6WFSAghhBC1ngQiIYQQQtR6EoiEEEIIUetJIBJCCCFErSeBSAghhBC1njztvpRuDMZLT09XuRIhhBBClNaN7+2SBtVLICqljIwMAAIDA1WuRAghhBBllZGRgbu7+y1fl3mISslsNnP16lVcXV3RaDQAdOrUiQMHDpR4bEn7lef19PR0AgMDiYmJsZl5kUr751VdrlPe85T1uNLsX9F9bvWafI4q/xpV8Tmy1t9FJe1TUz5H8ndRxfa3te80RVHIyMjA398frfbWPYWkhaiUtFot9evXL7JNp9OV6j9cSftV5HU3Nzeb+AsISv/nVV2uU97zlPW40uxf0X1KOl4+R5V3jar4HFnr76KS9qkpnyP5u6hi+9vid9rtWoZukE7VFTBp0iSr7FfR121FVb0Pa12nvOcp63Gl2b+i+9SUzxBUzXux5jWq4nNkrb+LStqnpnyO5O+iiu1fU7/T5JaZjZJHiQhrkM+RsAb5HImKqg6fIWkhslEGg4Hp06djMBjULkXYMPkcCWuQz5GoqOrwGZIWIiGEEELUetJCJIQQQohaTwKREEIIIWo9CURCCCGEqPUkEAkhhBCi1pNAJIQQQohaTwJRDTVo0CDq1KnD0KFD1S5F2KiYmBh69uxJq1ataNeuHT/88IPaJQkbk5qaSseOHQkJCaFNmzYsXLhQ7ZKEDcvOzqZhw4ZMmzatUs4vw+5rqG3btpGRkcGyZcv48ccf1S5H2KBr164RHx9PSEgIcXFxhIaGcubMGZydndUuTdgIk8lEXl4eTk5OZGVl0aZNGw4ePIiXl5fapQkb9Prrr3Pu3DkCAwOZOXOm1c8vLUQ1VM+ePXF1dVW7DGHD6tWrR0hICAB+fn54e3uTnJysblHCpuh0OpycnADIy8tDURTk3+CiPM6ePcupU6fo379/pV1DAlE1tGPHDgYOHIi/vz8ajYY1a9YU2yc8PJygoCAcHBwICwtj//79VV+oqNas+TmKjIzEZDIRGBhYyVWL6sQan6HU1FSCg4OpX78+L774It7e3lVUvagurPE5mjZtGh988EGl1imBqBrKysoiODiY8PDwm76+cuVKpk6dyvTp04mKiiI4OJi+ffuSkJBQxZWK6sxan6Pk5GQef/xxFixYUBVli2rEGp8hDw8PDh8+zMWLF1mxYgXx8fFVVb6oJir6OVq7di3NmzenefPmlVuoIqo1QFm9enWRbZ07d1YmTZpUuG4ymRR/f3/lgw8+KLLf1q1blSFDhlRFmaKaK+/nKDc3V+nevbuyfPnyqipVVFMV+bvohokTJyo//PBDZZYpqrnyfI5eeeUVpX79+krDhg0VLy8vxc3NTXnnnXesXpu0ENmY/Px8IiMj6dOnT+E2rVZLnz592LNnj4qVCVtSms+RoiiMHj2a3r17M3LkSLVKFdVUaT5D8fHxZGRkAJCWlsaOHTto0aKFKvWK6qk0n6MPPviAmJgYLl26xMyZMxk/fjxvvfWW1WuRQGRjEhMTMZlM+Pr6Ftnu6+tLXFxc4XqfPn14+OGH2bBhA/Xr15ewJIoozedo165drFy5kjVr1hASEkJISAhHjx5Vo1xRDZXmM/THH3/QvXt3goOD6d69O5MnT6Zt27ZqlCuqqdJ+p1UFfZVeTVSZzZs3q12CsHHdunXDbDarXYawYZ07dyY6OlrtMkQNMnr06Eo7t7QQ2Rhvb290Ol2xjonx8fH4+fmpVJWwNfI5EhUlnyFhDdXpcySByMbY29sTGhpKRERE4Taz2UxERARdu3ZVsTJhS+RzJCpKPkPCGqrT50humVVDmZmZnDt3rnD94sWLREdH4+npSYMGDZg6dSqjRo2iY8eOdO7cmblz55KVlcWYMWNUrFpUN/I5EhUlnyFhDTbzObL6uDVRYVu3blWAYsuoUaMK9/n000+VBg0aKPb29krnzp2VvXv3qlewqJbkcyQqSj5Dwhps5XMkzzITQgghRK0nfYiEEEIIUetJIBJCCCFErSeBSAghhBC1ngQiIYQQQtR6EoiEEEIIUetJIBJCCCFErSeBSAghhBC1ngQiIYQQQtR6EoiEEEIIUetJIBJCCCFErSeBSAghhBC1ngQiIUSN8Ntvv6HRaG67bNq06abHjhkzhjfeeOOmr40ePZqHHnqoyLYff/wRBwcHZs2aZe23IYRQiV7tAoQQwhruvvturl27Vrjepk0bnn76aZ5++unCbT4+PsWOM5lMrF+/nl9++aVU1/nyyy+ZNGkS8+fPZ8yYMRUvXAhRLUggEkLUCI6Ojjg6OgJw5coVkpKS6N69O35+frc9bvfu3djZ2dGpU6cSr/HRRx8xffp0vvvuOwYNGmSVuoUQ1YMEIiFEjXPo0CEAOnToUOK+69atY+DAgWg0mtvu9/LLL/PZZ5+xfv167rnnHqvUKYSoPiQQCSFqnKioKAIDA/Hy8ipx37Vr1zJnzpzb7rNx40bWrl1LREQEvXv3tlaZQohqRDpVCyFqnKioqFK1Dp08eZKrV6+W2OLTrl07goKCmD59OpmZmdYqUwhRjUggEkLUOKUNROvWrePee+/FwcHhtvsFBASwbds2rly5Qr9+/cjIyLBWqUKIakICkRCiRklMTCQmJqZUgWjt2rU8+OCDpTpvw4YN2b59O3FxcRKKhKiBJBAJIWqUqKgooOQO1QkJCRw8eJD777+/1OcODAxk27ZtJCQk0LdvX9LT0ytUqxCi+pBAJISoUQ4dOoSvry/+/v633e/nn3+mc+fOeHt7l+n89evXZ9u2bSQmJkooEqIG0SiKoqhdhBBCVLUHHniAbt268dJLL6ldihCiGpAWIiFErdStWzceffRRtcsQQlQT0kIkhBBCiFpPWoiEEEIIUetJIBJCCCFErSeBSAghhBC1ngQiIYQQQtR6EoiEEEIIUetJIBJCCCFErSeBSAghhBC1ngQiIYQQQtR6EoiEEEIIUev9P0k7ut7bP9wfAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Checking the temperature derivative of the virial coefficient\n", "name = 'Methane'\n", "modelVR = teqp.make_model({\n", " \"kind\": 'SAFT-VR-Mie',\n", " \"model\": { \"names\": [name] }\n", "})\n", "modelPCSAFT = teqp.make_model({\n", " \"kind\": 'PCSAFT',\n", " \"model\": { \"names\": [name] }\n", "})\n", "modelMF = teqp.build_multifluid_model([name], teqp.get_datapath())\n", "\n", "for model, label in [(modelVR, 'SAFT-VR-Mie'), \n", " (modelPCSAFT, 'PC-SAFT'), \n", " (modelMF, 'reference EOS')]:\n", " z = np.array([1.0])\n", " T = np.geomspace(8, 10000, 10000)\n", " n = 2\n", " B, TdBdT, thetan = [],[],[]\n", " for T_ in T:\n", " TdBdT.append(model.get_dmBnvirdTm(n, 1, T_, z)*T_)\n", " B.append(model.get_dmBnvirdTm(n, 0, T_, z))\n", " thetan.append(B[-1]+TdBdT[-1])\n", " plt.plot(T, thetan, label=label)\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.gca().set(xlabel=r'$T$ / K', ylabel=r'$B+T\\times$d$B$/d$T$')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "id": "f89b0433", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:40:20.518161Z", "iopub.status.busy": "2024-03-15T22:40:20.517987Z", "iopub.status.idle": "2024-03-15T22:40:29.812211Z", "shell.execute_reply": "2024-03-15T22:40:29.811646Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "795 µs ± 2.5 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "331 µs ± 2.23 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n" ] } ], "source": [ "# Time model instantiation\n", "for kind in ['SAFT-VR-Mie', 'PCSAFT']:\n", " j = {\n", " \"kind\": kind,\n", " \"model\": {\n", " \"names\": [\"Propane\"]\n", " }\n", " }\n", " %timeit teqp.make_model(j)" ] }, { "cell_type": "markdown", "id": "95237e68", "metadata": {}, "source": [ "## Calculation of diameter\n", "\n", "The calculation of the diameter is based upon\n", "$$\n", "d_{ii} = \\int_0^{\\sigma_{ii}}(1-\\exp(-\\beta u_{ii}^{\\rm Mie}(r)){\\rm d}r\n", "$$\n", "but the integrand is basically constant from 0 to some cutoff value of $r$, which we'll call $r_{\\rm cut}$. So first we need to find the value of $r_{\\rm cut}$ that makes the integrand take its constant value, which is explained well in the paper from Aasen (https://github.com/ClapeyronThermo/Clapeyron.jl/issues/152#issuecomment-1480324192). Finding the cutoff value is obtained when \n", "$$\n", "\\exp(-\\beta u_{ii}^{\\rm Mie}(r)) = EPS\n", "$$\n", "where EPS is the numerical precision of the floating point type. Taking the logs of both sides, \n", "$$\n", "-\\beta u_{ii}^{\\rm Mie} = \\ln(EPS)\n", "$$\n", "\n", "To get a starting value, it is first assumed that only the repulsive contribution contributes to the potential, yielding $u^{\\rm rep} = C\\epsilon(\\sigma/r)^{\\lambda_r}$ which yields\n", "$$\n", "-\\beta C\\epsilon(\\sigma/r)^{\\lambda_r} = \\ln(EPS)\n", "$$\n", "and \n", "$$\n", "(\\sigma/r)_{\\rm guess} = (-\\ln(EPS)/(\\beta C \\epsilon))^{1/\\lambda_r}\n", "$$\n", "\n", "Then we solve for the residual $R(r)=0$, where $R_0=\\exp(-u/T)-EPS$. Equivalently we can write the residual in logarithmic terms as $R=-u/T-\\ln(EPS)$. This simplifies the rootfinding as you need $R$, $R'$ and $R''$ to apply Halley's method, which are themselves quite straightforward to obtain because $R'=-u'/T$, $R''=-u''/T$, where the primes are derivatives taken with respect to $\\sigma/r$." ] }, { "cell_type": "code", "execution_count": 9, "id": "79563001", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:40:29.814982Z", "iopub.status.busy": "2024-03-15T22:40:29.814802Z", "iopub.status.idle": "2024-03-15T22:40:30.280112Z", "shell.execute_reply": "2024-03-15T22:40:30.279561Z" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\kappa \\left(- \\frac{j^{\\lambda_{a}} \\lambda_{a}}{j} + \\frac{j^{\\lambda_{r}} \\lambda_{r}}{j}\\right)$" ], "text/plain": [ "kappa*(-j**lambda_a*lambda_a/j + j**lambda_r*lambda_r/j)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\frac{\\kappa \\left(- j^{\\lambda_{a}} \\lambda_{a}^{2} + j^{\\lambda_{a}} \\lambda_{a} + j^{\\lambda_{r}} \\lambda_{r}^{2} - j^{\\lambda_{r}} \\lambda_{r}\\right)}{j^{2}}$" ], "text/plain": [ "kappa*(-j**lambda_a*lambda_a**2 + j**lambda_a*lambda_a + j**lambda_r*lambda_r**2 - j**lambda_r*lambda_r)/j**2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculation of the residual function (needed for Halley's method)\n", "import sympy as sy\n", "kappa, j, lambda_r, lambda_a = sy.symbols('kappa, j, lambda_r, lambda_a')\n", "u = kappa*(j**lambda_r - j**lambda_a)\n", "display(sy.diff(u, j))\n", "display(sy.simplify(sy.diff(u, j, 2)))" ] }, { "cell_type": "code", "execution_count": 10, "id": "8e1e5746", "metadata": { "execution": { "iopub.execute_input": "2024-03-15T22:40:30.282377Z", "iopub.status.busy": "2024-03-15T22:40:30.281959Z", "iopub.status.idle": "2024-03-15T22:40:30.288730Z", "shell.execute_reply": "2024-03-15T22:40:30.288207Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "quasi-exact; (value, error estimate):\n", "3.597838592720949 3.228005612223332e-12\n", "teqp; (value, error from quasi-exact in %)\n", "3.597838640613809 1.331156429529301e-06\n" ] } ], "source": [ "# Here is a small example of using adaptive quadrature \n", "# to obtain the quasi-exact value of d for ethane\n", "# according to the pure-fluid parameters given in \n", "# Lafitte et al.\n", "\n", "epskB = 206.12 # [K]\n", "sigma_m = 3.7257e-10 # [m]\n", "lambda_r = 12.4 \n", "lambda_a = 6.0\n", "C = lambda_r/(lambda_r-lambda_a)*(lambda_r/lambda_a)**(lambda_a/(lambda_r-lambda_a))\n", "T = 300.0 # [K]\n", "\n", "# The classical method based on adaptive quadrature\n", "def integrand(r_m):\n", " u = C*epskB*((sigma_m/r_m)**(lambda_r) - (sigma_m/r_m)**(lambda_a))\n", " return 1.0 - np.exp(-u/T)\n", "\n", "print('quasi-exact; (value, error estimate):')\n", "exact, exact_error = scipy.integrate.quad(integrand, 0.0, sigma_m, epsrel=1e-16, epsabs=1e-16)\n", "print(exact*1e10, exact_error*1e10)\n", "\n", "j = {\"kind\": 'SAFT-VR-Mie', \"model\": {\"names\": [\"Ethane\"]}}\n", "model = teqp.make_model(j)\n", "d = model.get_core_calcs(T, -1, z)[\"dmat\"][0][0]\n", "print('teqp; (value, error from quasi-exact in %)')\n", "print(d, abs(d/(exact*1e10)-1)*100)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.0" } }, "nbformat": 4, "nbformat_minor": 5 }