{ "cells": [ { "cell_type": "markdown", "id": "f84d6bba-254e-4060-a54b-76a09ad4d88f", "metadata": {}, "source": [ "## Solving the Mason-Weaver equation\n", "\n", "The Mason-Weaver models the sedimentation of Brownian nanoparticles in a fluid. Here, it is solved by the finite-volume method, which nicely conserves mass in the system.\n", "\n", "Further reading, with other methods of solving the Mason-Weaver equation: \n", "\n", "- Midelet, J.; El-Sagheer, A. H.; Brown, T.; Kanaras, A. G.; Werts, M. H. V. \n", "\"The Sedimentation of Colloidal Nanoparticles in Solution and Its Study Using Quantitative Digital Photography.\" \n", "*Part. Part. Syst. Charact.* **2017**, *34*, 1700095. https://doi.org/10.1002/ppsc.201700095. \n", "Solving the Mason-Weaver equation with a finite-difference scheme.\n", "\n", "\n", "- Barthe, L.; Werts, M. H. V. \n", "\"Sedimentation of colloidal nanoparticles in fluids: efficient and robust numerical evaluation of analytic solutions of the Mason-Weaver equation\". \n", "*ChemRXiv* **2022**. [doi:10.26434/chemrxiv-2022-91vrq](https://doi.org/10.26434/chemrxiv-2022-91vrq) \n", "Exact analytic solutions, requiring specific numerical evaluation." ] }, { "cell_type": "code", "execution_count": 1, "id": "65aae2ae-72f3-41e9-bd03-35a2cf023711", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import pyfvtool as pf" ] }, { "cell_type": "code", "execution_count": 2, "id": "dd71e6f0-307c-4d53-a485-39bca44ca3ae", "metadata": {}, "outputs": [], "source": [ "# physical parameters defining the Mason-Weaver system\n", "z_max = 1.0\n", "D_coeff = 0.015\n", "sg = 0.2" ] }, { "cell_type": "code", "execution_count": 3, "id": "214521c0-cb10-475a-ae71-063a677baa12", "metadata": {}, "outputs": [], "source": [ "# FVM calculation parameters\n", "Nx = 100\n", "Lx = z_max\n", "dt = 0.01\n", "t_simulation = 10.\n", "Nskip = 50 # for plotting" ] }, { "cell_type": "code", "execution_count": 4, "id": "c86f2f4f-a514-4577-af4e-c66fbb350241", "metadata": {}, "outputs": [], "source": [ "msh = pf.Grid1D(Nx, Lx)" ] }, { "cell_type": "code", "execution_count": 5, "id": "6eef21e4-b8f4-4586-9d09-c4f3c59ae025", "metadata": {}, "outputs": [], "source": [ "# Solution variable (default no flux BCs)\n", "c = pf.CellVariable(msh, 1.0)" ] }, { "cell_type": "code", "execution_count": 6, "id": "d94ab818-f1bc-4adb-a26c-99ddbd5ebdf8", "metadata": {}, "outputs": [], "source": [ "# start list, monitoring the total amount of matter in system \n", "# (integral of concentration over full volume)\n", "total_c = [c.domainIntegral()]" ] }, { "cell_type": "code", "execution_count": 7, "id": "dea6150b-a98a-4147-a9e2-321e316b0ef7", "metadata": {}, "outputs": [], "source": [ "# advection field (constant sedimentation)\n", "u = pf.FaceVariable(msh, (sg,))\n", "# closed boundaries: no flow at extremities\n", "u.xvalue[0] = 0.0\n", "u.xvalue[-1] = 0.0" ] }, { "cell_type": "code", "execution_count": 8, "id": "d202f032-e8f9-4abb-8470-719691ca9394", "metadata": {}, "outputs": [], "source": [ "# diffusion field (constant diffusion)\n", "D = pf.FaceVariable(msh, D_coeff)" ] }, { "cell_type": "code", "execution_count": 9, "id": "cd74874b-8ad0-4909-868e-0a40b0131913", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot initial condition\n", "plt.plot(c.cellcenters.x, c.value, 'k:', label = 'initial condition')\n", "\n", "# time loop\n", "it = 0\n", "\n", "while (it*dt < t_simulation):\n", " # In the present implementation, also the 'constant' terms\n", " # (boundaryConditionsTerm, diffusionTerm and convectionTerm)\n", " # are re-constructed every cycle. This is done for clarity.\n", " # Code can be 'optimized' by constructing these terms outside\n", " # of the loop and store their results. The difference in performance is \n", " # probably minimal, since most of the CPU time is in the\n", " # actual solving of the matrix equation\n", " eqnterms = [ pf.transientTerm(c, dt, 1.0),\n", " -pf.diffusionTerm(D),\n", " pf.convectionTerm(u)]\n", "\n", " pf.solvePDE(c, eqnterms)\n", " it+=1\n", " total_c.append(c.domainIntegral())\n", " if (it % Nskip == 0):\n", " plt.plot(c.cellcenters.x, c.value)\n", "\n", "plt.xlabel('depth / a.u.')\n", "plt.ylabel('local concentration / a.u.')\n", "plt.legend(frameon=False)\n", "plt.title('Finite-volume solution to the Mason-Weaver equation');" ] }, { "cell_type": "code", "execution_count": 10, "id": "ef1071b6-cd0d-4f36-8b16-ec2f1328a707", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(total_c)\n", "plt.ylabel('total amount of c')\n", "plt.xlabel('time step')\n", "plt.ylim(0, 1.2*np.max(total_c))\n", "plt.title('mass conservation');" ] }, { "cell_type": "code", "execution_count": 11, "id": "a3472c48-1451-46c4-a06c-d59261c8139c", "metadata": {}, "outputs": [ { "data": { "image/png": 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u3TqcP38eP/74o8l3Ar+T2bNn45tvvsHQoUOxZMkS+Pj44Pfff8e6devw6quvNlrSpq9hw4bh3XffxcKFCxEaGoorV65gyZIl8PPzQ2VlpbbelClTYGtri169esHT0xNqtRorVqyAQqHAI488AqB6+4Nhw4ahY8eOcHZ2xqVLl/Dtt98iODi43v1+lixZgj/++AN9+vTB22+/jaCgIOTm5uLPP//EnDlz0LZtW6O389mzZzFt2jQ8/fTTaNWqFaRSKfbt24ezZ8/irbfeAlC9LH7JkiVYsGAB4uPjMXjwYDg7OyMtLQ3Hjx/X9pTp426fpZCQEDg7O+OVV17BwoULYW1tje+//x5nzpypda9bn5GVK1diyJAhsLS0RMeOHbVDsTWZ+79PMqHGnA1O1FB+++030bFjRyGVSkWLFi3Ee++9JxYuXFjnqpavvvpK9OjRQ8jlcmFraytatmwpXnjhBZ0l3re8/fbbAoDw9vbWWWV1S12r1b766ivRpk0bIZPJhL+/v1ixYoXYsGGDACASEhK09RITE8XAgQOFg4ODdpm7EHWvVhNCiL///lv069dPG3fPnj3Fjh07dOrcabXZ/v37BQCdZdp1qW+1WocOHep8TVJSkhg3bpxwdXUV1tbWok2bNmL16tU67XXrPa1evbrOuH766Se94rjdhAkThFwur1V+p3h9fHzE0KFDtc/LysrEvHnzRLNmzYSNjY3o2rWr2L59u5gwYYL27yGEEF9//bUICwsTHh4eQiqVCi8vLzFmzBhx9uxZbZ233npLdO/eXTg7O2v/9rNnzxaZmZn1vgchqldMTpo0SahUKmFtba29f1pamrbO/bSzEEIAEAsXLhRCCJGWlibCw8NF27ZthVwuF/b29qJjx47iww8/1FmtJYQQ27dvF2FhYcLR0VHIZDLh4+MjnnrqKbFnzx5tnTv9HWq622fpyJEjIjg4WNjZ2Qk3Nzfx4osvipMnT9b6LJSVlYkXX3xRuLm5CYlEovO5un21mrHbjR4cEiFq7DxHRERE9JDjnCMiIiKiGpgcEREREdXA5IiIiIioBrNJjlasWIFHHnkEDg4OcHd3x8iRI2stbRVCYNGiRfDy8tIeWnn7MtqysjJMnz4dSqUScrkcI0aMuOseIkRERPTwMJvkKCoqCq+99hqOHj2KyMhIVFZWYuDAgTonMq9atQpr1qzBJ598ghMnTkClUmHAgAE6G7bNmjUL27Ztw6ZNm3Do0CEUFhZi2LBhqKqqaoy3RURERE2M2a5Wy8jIgLu7O6KiotCnTx8IIeDl5YVZs2bhzTffBFDdS+Th4YGVK1fi5ZdfRl5eHtzc3PDtt99i7NixAKp3QvX29sauXbswaNCgxnxLRERE1ASY7SaQeXl5AP535lJCQgLUarX23CqgeqfU0NBQHDlyBC+//DJiYmJQUVGhU8fLywuBgYE4cuTIHZOjsrIylJWVaZ9rNBpkZ2fD1dW10TbXIyIiIsMIIVBQUAAvLy+dQ65vZ5bJkRACc+bMwWOPPaY9tfnWOVkeHh46dT08PLQnJqvVakilUjg7O9eqU9fZW7esWLFC751eiYiIqGlLSUmp90Bns0yOpk2bhrNnz+LQoUO1rt3ekyOEuGvvzt3qzJ8/H3PmzNE+z8vLQ4sWLZCSklLnKdNERETU9OTn58Pb2xsODg711jO75Gj69On47bffcPDgQZ2sT6VSAajuHfL09NSWp6ena3uTVCoVysvLkZOTo9N7lJ6ejpCQkDv+TplMVufZV46OjkyOiIiIzMzdOk3MZrWaEALTpk3D1q1bsW/fPvj5+elc9/Pzg0qlQmRkpLasvLwcUVFR2sSnW7dusLa21qmTmpqK8+fP15scERER0cPDbHqOXnvtNfzwww/49ddf4eDgoJ0jpFAoYGtrC4lEglmzZmH58uVo1aoVWrVqheXLl8POzg7jxo3T1p08eTLmzp0LV1dXuLi4YN68eQgKCsLjjz/emG+PiIiImgizSY4+++wzAEDfvn11yiMiIhAeHg4AeOONN1BSUoKpU6ciJycHPXr0wO7du3XGFj/88ENYWVlhzJgxKCkpQf/+/bFx40ZYWlo21FshIiKiJsxs9zlqTPn5+VAoFMjLy+OcIyIiIjOh7/e32cw5IiIiImoITI6IiIiIamByRERERFQDkyMiIiKiGpgcEREREdXA5IiIiIioBiZHRERERDUwOSIiIiKqgckRERERUQ1MjoiIiIhqYHJEREREVAOTIyIiIqIamBwRERER1cDkiIiIiKgGJkdERERENTA5IiIiIqqByRERERFRDUyOiIiIiGpgckRERERUA5MjIiIiohqs9KmUn59v8I0dHR0Nfg0RERFRY9MrOXJycoJEItH7phKJBLGxsfD397/nwIiIiIgag17JEQD8/PPPcHFxuWs9IQSeeOKJ+wqKiIiIqLHolRz5+PigT58+cHV11eum/v7+sLa2vq/AiIiIiBqDXslRQkKCQTc9f/78PQVDRERE1Ni4Wo2IiIioBr3nHN2uoqICv//+O65evQpPT0+MGjUKcrncmLERERERNTi9e45CQkKQm5sLAMjIyEC3bt0wduxYfPnll5gyZQrat2+PGzdumCpOIiIiogahd3J09OhRlJeXAwAWLFgAS0tLJCUlITY2FtevX0fz5s3xzjvvmCxQIiIiooZwT3OOoqKisHTpUqhUKgCAq6srli1bhn379hk1OCIiIqKGZlBydGsjyNzcXPj5+elc8/PzQ2pqqvEiIyIiImoEBk3IDg8Ph0wmQ0VFBZKSktC+fXvttdTUVDg5ORk7PiIiIqIGpXdyNGHCBO3P/+///T8UFhbqXP/ll1/QuXNnowVGRERE1BgkQghhjBsVFRXB0tISNjY2xrhdk5afnw+FQoG8vDwesEtERGQm9P3+vud9jm7HPY6IiIjoQWC0HbJTUlIwadIkY92uTgcPHsTw4cPh5eUFiUSC7du361wPDw+HRCLRefTs2VOnTllZGaZPnw6lUgm5XI4RI0bg+vXrJo2biIiIzIfRkqPs7Gx8/fXXxrpdnYqKitCpUyd88sknd6wzePBgpKamah+7du3SuT5r1ixs27YNmzZtwqFDh1BYWIhhw4ahqqrKpLETERGRedB7WO23336r93p8fPx9B3M3Q4YMwZAhQ+qtI5PJtPsv3S4vLw8bNmzAt99+i8cffxwA8N1338Hb2xt79uzBoEGDjB4zERERmRe9k6ORI0dCIpGgvvnbt/ZBakwHDhyAu7s7nJycEBoaimXLlsHd3R0AEBMTg4qKCgwcOFBb38vLC4GBgThy5Mgdk6OysjKUlZVpn+fn55v2TRAREVGj0XtYzdPTE7/88gs0Gk2dj5MnT5oyTr0MGTIE33//Pfbt24cPPvgAJ06cQL9+/bSJjVqthlQqhbOzs87rPDw8oFar73jfFStWQKFQaB/e3t4mfR9ERETUePROjrp161ZvAnS3XqWGMHbsWAwdOhSBgYEYPnw4/vjjD8TGxuL333+v93VCiHp7vebPn4+8vDztIyUlxdihExERUROh97Da66+/jqKiojteDwgIwP79+40SlLF4enrCx8cHV69eBQCoVCqUl5cjJydHp/coPT0dISEhd7yPTCaDTCYzebxERETU+PTuOerduzcGDx58x+tyuRyhoaFGCcpYsrKykJKSAk9PTwDVvV/W1taIjIzU1klNTcX58+frTY6IiIjo4WG0TSAbQmFhIeLi4rTPExIScPr0abi4uMDFxQWLFi3Ck08+CU9PTyQmJuLtt9+GUqnEqFGjAAAKhQKTJ0/G3Llz4erqChcXF8ybNw9BQUHa1WtERET0cDM4Obpy5QratGljilju6p9//kFYWJj2+Zw5cwBUn/v22Wef4dy5c/jmm2+Qm5sLT09PhIWFYfPmzXBwcNC+5sMPP4SVlRXGjBmDkpIS9O/fHxs3boSlpWWDvx8iIiJqegw6W+2ff/7BiBEjcPPmTVPG1OTxbDUiIiLzo+/3t95zjvbu3YsBAwZg5cqVRgmQiIiIqCnSKznaunUrhg8fjhUrVmD8+PGmjomIiIio0eiVHI0dOxYLFizAK6+8Yup4iIiIiBqVXslRy5YtsXv3bpSUlJg6HiIiIqJGpVdydOjQIRQXF2PUqFGoqKgwdUxEREREjUav5EipVGL//v0oLy/HmDFjTB0TERERUaPRe7Wavb09/vjjD1hY6P0SIiIiIrNjUKYjk8nw008/mSoWIiIiokZncDcQe46IiIjoQWbw8SGFhYWIiYmBWq2GRCKBh4cHunXrBnt7e1PER0RERNSg9E6OKisrMXfuXHz55ZcoLS2FVCqFEAIVFRWwsbHBSy+9hNWrV8Pa2tqU8RIRERGZlN5jZHPnzsUvv/yCiIgIZGdno7S0FGVlZcjOzkZERAS2bt2K119/3ZSxEhEREZmc3gfPurm5YfPmzejXr1+d1/fu3YtnnnkGGRkZRg2wKeLBs0RERObH6AfPlpSUQKlU3vG6q6srd9AmIiIis6d3chQWFoY5c+YgLS2t1rW0tDS88cYbd+xVIiIiIjIXek/IXrduHZ544gk0b94cgYGB8PDwgEQigVqtxvnz59G+fXv8/vvvpoyViIiIyOT0nnMEABqNBn/99ReOHj0KtVoNAFCpVAgODsbAgQMfmj2QOOeIiIjI/Oj7/W1QckTVmBwRERGZH6NPyL6boqIiHDx40Fi3IyIiImoURkuO4uLiEBYWZqzbERERETWKh2OSEBEREZGe9F6t5uLiUu/1qqqq+w6GiIiIqLHpnRyVlZXh1VdfRVBQUJ3Xk5KSsHjxYqMFRkRERNQY9E6OOnfuDG9vb0yYMKHO62fOnGFyRERERGZP7zlHQ4cORW5u7h2vu7i44IUXXjBGTERERESNhvsc3QPuc0RERGR+GnyfIyIiIqIHAZMjIiIiohqYHBERERHVwOSIiIiIqAaDkqOqqipERUUhJyfHVPEQERERNSqDkiNLS0sMGjSo3iX9RERERObM4GG1oKAgxMfHmyIWIiIiokZncHK0bNkyzJs3Dzt37kRqairy8/N1HkRERETmzOBNIC0s/pdPSSQS7c9CCEgkkofiAFpuAklERGR+TLYJ5P79+7WPffv2aR+3npvSwYMHMXz4cHh5eUEikWD79u0614UQWLRoEby8vGBra4u+ffviwoULOnXKysowffp0KJVKyOVyjBgxAtevXzdp3ERERGQ+9D549pbQ0FBTxKGXoqIidOrUCRMnTsSTTz5Z6/qqVauwZs0abNy4Ea1bt8bSpUsxYMAAXLlyBQ4ODgCAWbNmYceOHdi0aRNcXV0xd+5cDBs2DDExMbC0tGzot0RERERNzD2drfb333/j888/R3x8PH766Sc0a9YM3377Lfz8/PDYY4+ZIs5aJBIJtm3bhpEjRwKo7jXy8vLCrFmz8OabbwKo7iXy8PDAypUr8fLLLyMvLw9ubm749ttvMXbsWADAzZs34e3tjV27dmHQoEF6/W4OqxEREZkfkw2r/fLLLxg0aBBsbW1x8uRJlJWVAQAKCgqwfPnye4/4PiUkJECtVmPgwIHaMplMhtDQUBw5cgQAEBMTg4qKCp06Xl5eCAwM1NYhIiKihpddVI5rGYX487wav525iSqNwX03RmPwsNrSpUuxfv16vPDCC9i0aZO2PCQkBEuWLDFqcIZQq9UAAA8PD51yDw8PJCUlaetIpVI4OzvXqnPr9XUpKyvTJoEAuCqPiIjoPiVlFeHcjTxcTSvE+Rt52HclHTXHsgZ3UMHSQnLnG5iQwcnRlStX0KdPn1rljo6OTWJzyJor6ID/raKrz93qrFixAosXLzZKfERERA+byioNdl9Mw99XM6HOK0FSVjHiM4tq1bOXWcHNQQaVow3u8tVtUgYnR56enoiLi4Ovr69O+aFDh+Dv72+suAymUqkAVPcOeXp6asvT09O1vUkqlQrl5eXIycnR6T1KT09HSEjIHe89f/58zJkzR/s8Pz8f3t7exn4LREREZk8IgfySShy5lonD1zJxMikXKdnFKCirrFW3g5cjfJVy+LnKMbKLFwLcHRoh4toMTo5efvllzJw5E1999RUkEglu3ryJ6OhozJs3D++8844pYtSLn58fVCoVIiMj0aVLFwBAeXk5oqKisHLlSgBAt27dYG1tjcjISIwZMwYAkJqaivPnz2PVqlV3vLdMJoNMJjP9myAiIjIz6QWliEnMQUxSDmKSc5CSXYzMwvJa9VzlUgwOVKG9lyOcbKXo6uMET4VtI0R8dwYnR2+88Qby8vIQFhaG0tJS9OnTBzKZDPPmzcO0adNMEaNWYWEh4uLitM8TEhJw+vRpuLi4oEWLFpg1axaWL1+OVq1aoVWrVli+fDns7Owwbtw4AIBCocDkyZMxd+5cuLq6wsXFBfPmzUNQUBAef/xxk8ZORERk7oQQiEnKwbkbeUjKKsbey2lIyS6ps67SXobH27mjm48z2qgc0NrDATbW5rFlzj0t5QeA4uJiXLx4ERqNBu3bt4e9vb2xY6vlwIEDCAsLq1U+YcIEbNy4EUIILF68GJ9//jlycnLQo0cPfPrppwgMDNTWLS0txeuvv44ffvgBJSUl6N+/P9atW2fQMBmX8hMR0cOgsKwSx+KzcDA2A+VVAudu5OL8jdqLkrxdbNGthTO6+TijnacjWrk7wNHW6q5zfhuavt/f95wcAUBKSgokEgmaN29+r7cwS0yOiIjoQVRUVonjCdmIvJSGk0k5uKwuqFXHQgL4u9mjvacjBnVQ4RE/Z7g72DRCtIbT9/vb4GG1yspKLF68GB9//DEKCwsBAPb29pg+fToWLlwIa2vre4+aiIiIGkxxeSVOJuXi84PXkFFQhitpBbi9y0RpL0X/th5o7mwLhZ01hnf0grNc2jgBNxCDk6Np06Zh27ZtWLVqFYKDgwEA0dHRWLRoETIzM7F+/XqjB0lERET3p7xSg6yiMlxLL8JvZ26gpEKDfZfSUFSue2C8k501BrTzQE9/V3TzcYaPq12TGx4zNYOH1RQKBTZt2oQhQ4bolP/xxx945plnkJeXZ9QAmyIOqxERkTlIyy/F7gtqxKUX4tczN5FbXFGrjtSq+rCMFx/zw5PdmsNfKX9gkyGTDavZ2NjU2uMIAHx9fSGVPtjdbERERE2NEAIFZZVIzirGyeQcXEotQFJWES6rC5BdpLuk3spCAjupJXoFKOHlZIverZQIbe32wCZD98rg5Oi1117Du+++i4iICO3eP2VlZVi2bJnJl/ITERE97IQQiM8swuG4TFxWF+BwXCaSsorvWL+tygHdfZ3Rq6USAxvxSA5zYnBydOrUKezduxfNmzdHp06dAABnzpxBeXk5+vfvj9GjR2vrbt261XiREhERPYTyiiuQmFWEYwlZ2HryRp0ryADA0kIClaMNfJV2CGmphLuDDH1au8HD0TxWkjUlBidHTk5OePLJJ3XKeJQGERHR/csrqcD1nGKUlFdhz6V0/JOYjdMpuais44T65s626PrfvYX6tXWHp8IGVpYWjRD1g8fg5CgiIsIUcRARET1Uyis1iEuvPpH+rwtq/JOUg7yS2hOmb3nUzwX927rjUT8X+LvZQ2HLrXNMxeDkiIiIiAyXV1yB7OJyRF5UIz6jCDvO3Ky1jB6oXkovtbRAYDMFQlu7oae/K9qomsaBrA8LJkdEREQmoNEIxKYXIOpKBvZeTsfxhOw667X3dKxeNdbGDa09HOAql3L1WCNjckRERGQEpRVV+PX0DRyKy8KZlFwkZ9e9gqyTtxN6+LmgvacjBrT3gFzGr+Kmhn8RIiIiA1VpBM5cz8Wx+GzEphXgzPVcJGYWoY550+jg5Yj+7TzwWIASHZsrzOZk+oeZUZKj3NxcODk5GeNWRERETY5GIxCXUYgDV9JxJiUP0fFZtTZYBAAHmRWGdfJE3zbu8FfKYW9jBU+FbSNETPfD4ORo5cqV8PX1xdixYwEAY8aMwS+//AKVSoVdu3Zp9z4iIiIyR0IIXM8pwYEr6YiKzUBKdglu5pWgoLRSp56VhQR927jBTylH1xbO8HOTo7W7Ayy4yaLZMzg5+vzzz/Hdd98BACIjIxEZGYk//vgDW7Zsweuvv47du3cbPUgiIiJTySupwLH4LMRlFGL3hTRcuJmHiqra42OWFhIENVOgf1t3tFE5ILSNG2RWHCJ7EBmcHKWmpmo3fdy5cyfGjBmDgQMHwtfXFz169DB6gERERMYghEBydjHO3cjDP4k5iEsvREJmEW7kltSqK5EAbTwcMKiDCp28FVDYWqODF+cLPSwMTo6cnZ2RkpICb29v/Pnnn1i6dCmA6n90VVW192sgIiJqDEIInLmeh9PJObieU4K/r2biSlrdR28AQE9/FzzezgO9ApRo4WLHVWQPMYP/8qNHj8a4cePQqlUrZGVlYciQIQCA06dPIyAgwOgBEhER3U1llQZnruchKasIZ1JycTW9EBdT85FbrLvj9K3zx8LausHXVY6W7vbo4OUIB5k1bKXsFaJqBidHH374IXx9fZGSkoJVq1bB3t4eQPVw29SpU40eIBER0e0KyypxMikHV9MLcSo5B1GxGbUmTN/SwsUOj7VSopW7PUZ3aQ6FHY/doPoZnBxFR0dj1qxZsLLSfem0adNw5MgRowVGRER0S2WVBhmFZYi8mIYTiTk4cCW9zmSos7cTWnvYo5O3E3xd5ejs7cThMTKYwf9iwsLCkJqaCnd3d53yvLw8hIWFcd4RERHdlyqNwNnrubiaVoik7CLEZxThcFwm8m9LhlSONvBTytGlhRPaqBzQv50H7JkIkREY/K9ICFHnmS9ZWVmQy+VGCYqIiB4OQgjEZxbhaHwW0vPLcOBKOq5lFKGwrO4hsnaejujTWolgf1f0aeXGPYXIJPROjkaPHg0AkEgkCA8Ph0wm016rqqrC2bNnERISYvwIiYjogVFRpcG5G3k4mZSDfxJzcDI5B+kFZXXW7dhcgQA3e7R0t0d7L0cE+7tyKT01CL2TI4VCAaA6y3dwcICt7f+2Q5dKpejZsyemTJli/AiJiMhsZReVIymrCNtP3cD+Kxl3PIzVS2GDtp6OCGvjhpZu1cmQk520gaMlqqZ3chQREQEhBIQQWLt2LRwcHEwZFxERmaH80grEJOXgWnohtvyTgti0wlp17KSW6Nhcge4+Lujm44yuLZy5goyaFIkQoo4zhOum0WhgY2ODCxcuoFWrVqaMq0nLz8+HQqFAXl4eHB0dGzscIqIGp9EIZBaV4VRyLq6oC3D2eh6uphcgKat2z5DC1hrtPKt3m368nQdUChtYW1o0QtT0sNP3+9ugCdkWFhbazR8f5uSIiOhhUqURyC0uR2JWEU4l52L/lXQcT8iu8/wxALCXWaGztxPC2rrjiSAVT6Uns2PwarVVq1bh9ddfx2effYbAwEBTxERERI2krLIKZ1LycC2jenPFpKxiHEvIvmN9fzc5/Fzl6OrjDBe5FO4OMvRt4w5LriIjM2bQsBpQfbZacXExKisrIZVKdSZmA0B29p0/RA8KDqsR0YNACIGi8irsv5z+32QoFyeTc+6407Sd1BJdWjihtYcDQlu7IbCZAkp7WZ11iZoikwyrAcBHH310P3EREVEjqajS4MCVDETFpuOfxBxkFpYjs7D2MnpnO2v4/Hd36RYudpBZW2B4Jy84yKzq3OeO6EFjcHI0YcIEU8RBRERGpNEIXFLnIyYpB7svpCEhswg3ckvqrKtytMGjfi5oo3JA1xbO6ObjDKkVJ0zTw+u+9lkvKSlBRYXuicccZiIiali3dpmOScpBTGIOYpJzcC2jEHVNmnCRS/GIrzMe8XVBYDMFWrnbw9lOyp2miWowODkqKirCm2++iS1btiArK6vWdZ6tRkRkOlmFZcgtqcDVtEJcuJmH4wnZiE0rQE5xRa26UksLBDZzRJ/WbujSwhmt3O3h7iCDFZfRE9XL4OTojTfewP79+7Fu3Tq88MIL+PTTT3Hjxg18/vnneO+990wRIxHRQ0ejEcgvrcCp5Fycu5GH3OIK7L2cVuc+QgBgIQHaqhzRzad6WKyTtxM8FTY8boPoHhicHO3YsQPffPMN+vbti0mTJqF3794ICAiAj48Pvv/+ezz33HOmiJOI6IF2OC4TMUk5qKjS4GBsBs5cz7tjXVtrS3g62cDXVY5+bd3hp5Sjk7cTT6QnMhKDP0nZ2dnw8/MDUD2/6NbS/cceewyvvvqqcaMz0KJFi7B48WKdMg8PD6jVagDV4/KLFy/GF198gZycHPTo0QOffvopOnTo0BjhEtFDKr2gFCeTchCXXojzN/Lx5wX1Heu6OcjQrYUzVAobdPByRGgbN7g72DRgtEQPH4OTI39/fyQmJsLHxwft27fHli1b8Oijj2LHjh1wcnIyQYiG6dChA/bs2aN9bmn5vy7lVatWYc2aNdi4cSNat26NpUuXYsCAAbhy5QrPiiMio9NoBMr/ewr9qeQcXEotwD9J2UjJrnvV2JBAFZzlUvgr5ejdyg0ejjIevkrUCAxOjiZOnIgzZ84gNDQU8+fPx9ChQ7F27VpUVlZizZo1pojRIFZWVlCpVLXKhRD46KOPsGDBAowePRoA8PXXX8PDwwM//PADXn755YYOlYgeMKUVVdh9MQ0nk3KQW1yOQ3FZde4jBADeLrbo2NwJfq5yPOLngpZucjR3tmvgiImoLgYnR7Nnz9b+HBYWhkuXLiEmJgYtW7ZEp06djBrcvbh69Sq8vLwgk8nQo0cPLF++HP7+/khISIBarcbAgQO1dWUyGUJDQ3HkyBEmR0RkMHVeKeIzC7H7QhrO3chDXHoh8krqWDVmZYE+rZTwdZVXT5j2debQGFETdt+z93x8fODj42OMWO5bjx498M0336B169ZIS0vD0qVLERISggsXLmjnHXl4eOi8xsPDA0lJSfXet6ysDGVl//u/v/z8fOMHT0RNlkYjcFldgN0X1YhLL8TJpByUV2mQWVheq66nwgZ9Wrmhhasd/JRyBPu7wk5mCZkVV40RmYt7So727t2LDz/8EJcuXYJEIkHbtm0xa9YsPP7448aOzyBDhgzR/hwUFITg4GC0bNkSX3/9NXr27AkAtba+F0LcdTv8FStW1JroTUQPJiEETiTmICo2HWUVGlxJK8DJpBwUlde9h5ubgwyP+rngsYDqnqHuvs6w5j5CRGbN4OTok08+wezZs/HUU09h5syZAICjR4/iiSeewJo1azBt2jSjB3mv5HI5goKCcPXqVYwcORIAoFar4enpqa2Tnp5eqzfpdvPnz8ecOXO0z/Pz8+Ht7W2SmImo4eQWlyMhswgnk3ORmFmEfZfTkVtcXmciZG0pwaN+LujawhnNnW3h4WiDoGYKuPLgVaIHjsHJ0YoVK/Dhhx/qJEEzZsxAr169sGzZsiaVHJWVleHSpUvo3bs3/Pz8oFKpEBkZiS5dugAAysvLERUVhZUrV9Z7H5lMBpmM/wEkMldCCGQUluF4QjZOJuXin6RsxGcUobCs7tPnJRLgER8XdPKuTn66+TgjqJmCGyoSPSQMTo7y8/MxePDgWuUDBw7Em2++aZSg7tW8efMwfPhwtGjRAunp6Vi6dCny8/MxYcIESCQSzJo1C8uXL0erVq3QqlUrLF++HHZ2dhg3blyjxk1ExlVaUYXDcZm4rC7AmZRcXEzNx/WcupfP20ktEdRMgXaejnjE1wWtPezh6WTLDRWJHmIGf/pHjBiBbdu24fXXX9cp//XXXzF8+HCjBXYvrl+/jmeffRaZmZlwc3NDz549cfToUe2E8TfeeAMlJSWYOnWqdhPI3bt3c48jIjNVWaVBSk4JsgrLoM4vRWJmEfZcSse5G3mo0tQ+dVVha40OXo541M8FHZsrENhMwVVjRFSLRIi6zm2+s6VLl+L9999Hr169EBwcDKB6ztHhw4cxd+5cODo6auvOmDHDuNE2Efn5+VAoFMjLy9N5v0RkWoVllTiekIW/r2bi7PU8xCTl3LGurbUlVAobyKwsMLprMwzv5AWVo81dF2AQ0YNL3+9vg5OjW0eH3I1EIkF8fLwhtzYbTI6ITC8uvQD/JObganohEjOLkJhVhGsZRXes38bDAQHu9ujkrUDfNu4IcLOHhQUTISL6H32/vw0eVktISLivwIiIbpdVWIbErOrVYlfUhTgcl4mSirqXzjvZWaOtygH923ogJMAVMitLBLjbN3DERPQg44xDImowxeWVuJFTgoNXM5GSXYzMwjL8fTWzzl2lJRLgEV8X+LrawVcpRyt3B7T2sEcLFzsOjRGRSemVHM2ZMwfvvvsu5HK5XjedP38+Xn/9dbi4uNxXcERkvnKKypFfWoHTKbn464Iap5JzkV5QVudEaaB6svSjfi7VJ8+3doO/mz0UttYNHDURkZ5zjiwtLaFWq+Hm5qbXTR0dHXH69Gn4+/vfd4BNEeccEdV2Na0A+6+k43hCDq6k5d/x5HkAkEst0b+dB5o526J3KyVauTvAzYF7iRGRaRl1zpEQAq1bt9a7K7uo6M6TJonI/JVWVOGyugC/nb6JM9dzcSOnBOr80lr1LC0k8HGxQ2gbN/Rp7YaWSns42lrBVsqzxoio6dIrOYqIiDD4xnc7koOIzEdllQaX1QXYeykdxxOzcORaFm7vc7a0kKBTcwUGtFfBT2mHbj4u7A0iIrOkV3I0YcIEU8dBRE1IaUUVTibl4OeY6zhzPRcJmUW4faqQlYUEPfxd0MXbGSEBrghws4e7IzdUJCLzx9VqRA+5iioNEjKLEJOUg32X03EkLrPOg1etLCTo3UqJ7r4uGNDeA35KOU+fJ6IHEpMjoodIfmkF9lxMQ35JBc5cz0NKdjGSsouRUVBWq66jjRX6tXXHsI5e8HOTo5mTLQ9eJaKHApMjogeUEAKJWcU4kZiNyItpSMoqQmxaYZ11bawt4O1sh35t3RHYTIHglq5wsZNyh2kieigxOSJ6AFRUaXAsPhuxaQVIyKzeaVqdX3rHPYW6tHBC1xbO6NhcAYWtNXr6u7JXiIjovwxOjvLy8lBVVVVrg8fs7GxYWVlx3x+iBlBRpcEVdQF2nUvFFXUBouOzUFzHPCGJpPrMsdA2bujU3Amt3O3hp5TDinOFiIjuyODk6JlnnsHw4cMxdepUnfItW7bgt99+w65du4wWHBFVyyuuQHR8JvZfzkBSdhHOpOTVOnvMQgL08HNFaw97dPVxhrOdFB2bK+BkJ22kqImIzJNeO2TX5OLigsOHD6Ndu3Y65ZcvX0avXr2QlZVl1ACbIu6QTaYihEBFlcCN3BIcuJKOqNgMXMsovONu00HNFPh/nb3g4ypHcEtX2Ms4Uk5EdCdG3SG7prKyMlRWVtYqr6ioQEnJnY8LIKK6ZReV41BcJk4m5eDAlXQkZhXfse5jAUoMDlShvZcjgpopuJSeiMgEDE6OHnnkEXzxxRdYu3atTvn69evRrVs3owVG9KDRaASi47NwNa0AV9MLEZdeiMSsIqTl115GbyEB2ns5YnAHFYKaO8FfKUdzZ1ueRk9E1AAMTo6WLVuGxx9/HGfOnEH//v0BAHv37sWJEyewe/duowdIZK4KSitwKjkXJ5NzcDA2A2eu591x9ZjSXoqwNu5oo3JAWFt37ilERNSIDE6OevXqhejoaKxevRpbtmyBra0tOnbsiA0bNqBVq1amiJGoyRNCIDm7GP8k5iAmOQcnk3JwJa2g1vljDjIrdPVxRks3e/i42sHD0QYKW2v08HPhnkJERE2EwROyiROyH3ZZhWU4eDUDp5JzkZRVjLj0QuSXVKCgrPZcPFe5FF19nNFO5YDHWrmhY3MFe4SIiBqJySZkEz1Mbg2NRV5MQ2peCa5lFCEhs+iO9dt4OKCrjzO6/ffh62rHeUJERGaGyRHRf2UUlOFSaj4OxWUiPqMQxeVVOBqfVes0egBQ2svQwcsRvVsp4aeUw9vFDiqFDRxtrBs+cCIiMiomR/TQqazSIL+0ElfTCnApNR97L6fjRk4JkrOLUVlHJuQqlyIkQIkefi5wtpOiu68zPBxtGiFyIiJqCHolR2fPnkVgYCAsLLinCpmfpKwinEzOQX5JJf66oMaRa3feqLS5sy3aqhwQ4O4AR9vqU+nbeDhwaIyI6CGiV3LUpUsXpKamwt3dHf7+/jhx4gRcXV1NHRuRQfJKKnAztwSnU3Jx8WY+krKLcTgu847L590cZPB1tUNrDwc8FqBEKw97BLg7NHDURETU1OiVHDk5OSEhIQHu7u5ITEyERqMxdVxEdySEwLWMIpxKzsGplFxYW0hw+FoW4tIL66x/6/DVFi528HOT49lHWsDVXgoHzg8iIqI66JUcPfnkkwgNDYWnpyckEgm6d+8OS8u6lyPHx8cbNUB6uJVVVuFGTgmuphfiWkYhDsZm4HRKLkor6k7QLS0k8FPK0a+tOxS21ujbxg2+rnLIeeYYERHpSa9vjC+++AKjR49GXFwcZsyYgSlTpsDBgcMPZDwajUBmURlu5JTg76vVq8WSsotx4WY+yitrJ0IWEqCFS/Uy+T6tlGjmbItWHg7oHaCEFc8bIyKi+6D3/04PHjwYABATE4OZM2cyOaJ7VlZZBXVeKa5lFOLCjXztjtL5pbU3UQSqe4N8XO3g42KH1ioH9GqpRDcfZ/YGERGRSRj87RIREaH9+fr165BIJGjWrJlRg6IHg0YjkF1cjtPJubiaXoiLqfm4cDMPKdnFqKiqe5K01MoCfVop0dLdHq3cHdBW5YB2no6w5NEaRETUQAxOjjQaDZYuXYoPPvgAhYXVE2AdHBwwd+5cLFiwgMv9H1LllRokZRXh3I08nEzOQVJWMf6+mlnva/yVcvi42qG7rwu6tnBGlxZOPFqDiIgancHJ0YIFC7Bhwwa899576NWrF4QQOHz4MBYtWoTS0lIsW7bMFHFSEyGEQFx6IS6pC3A0PgtlFRokZBYiMasY2UXldb7GU2GDTs2d4KO0Q7cWzvBVytHSzZ69QURE1CQZfPCsl5cX1q9fjxEjRuiU//rrr5g6dSpu3Lhh1ACboofl4NmS8iqcSs7BtcwiRF3JwNnruUgvKKv3Nd4utujdyg3NnW1hZ22JJzp6wt2Bu0kTEVHjM9nBs9nZ2Wjbtm2t8rZt2yI7O9vQ21ETkV5QipNJOThzPQ+JmUVIzCrGFXV+neeKSS0t4OVkg5Zu9mitcoC3sx383eTo0sIJMisOixERkXkzODnq1KkTPvnkE3z88cc65Z988gk6depktMDINDQagX2X0xGTnIPMgjIkZBbhanoh8koq6qyvsLVGYDNHtPd0RCdvJ/i6yhHgbs+5QURE9MAyODlatWoVhg4dij179iA4OBgSiQRHjhxBSkoKdu3aZYoY6R7klVQgv6QC+6+kIz6jCNcyChGXXojCskoU3GHJvLeLLbr7uMDnv0dqtHK3R0s3e1hwbhARET1EDE6OQkNDERsbi08//RSXL1+GEAKjR4/G1KlT4eXlZYoYTWLdunVYvXo1UlNT0aFDB3z00Ufo3bt3Y4elt4oqDQpLKxGfWYTk7CLcyClBWaUG20/fQEp2Sb2vdbCxwrCOnnC0tUaAmz383ezh42oHpb2sgaInIiJqugyekP0g2Lx5M8aPH49169ahV69e+Pzzz/Gf//wHFy9eRIsWLe76+oaakC2EQElF9YaJiVlFiM8oQnpBGfZfTkdKTvEdj9C4xUICtPZwwKN+Lghwt4ePqxyeCht4O9vBVsphMSIierjo+/39UCZHPXr0QNeuXfHZZ59py9q1a4eRI0dixYoVd329qZKjkvIqHI7LxIWb+dh3OQ03ckuQWVj38vhb5FJLtHS3R4CbPaRWFghspkA3H2e4yqVwd+QqMSIioltMtlrN3JWXlyMmJgZvvfWWTvnAgQNx5MiROl9TVlaGsrL/LWHPz883elzqvFL0/+AAisqral2zkAA+rtV7AznbWSO4pSvaqBzQyt0BVhYSzgkiIiIyoocuOcrMzERVVRU8PDx0yj08PKBWq+t8zYoVK7B48WKTxuXhKIOnky2yi8rh7WwLNwcZerdyw4hOXpDLrCC14s7jREREDeGhS45ukUh0e1uEELXKbpk/fz7mzJmjfZ6fnw9vb2+jx/PDiz3g5iC7YxxERERkegZ3R/Tr1w+5ubm1yvPz89GvXz9jxGRSSqUSlpaWtXqJ0tPTa/Um3SKTyeDo6KjzMAV3RxsmRkRERI3M4OTowIEDKC+vPUm4tLQUf//9t1GCMiWpVIpu3bohMjJSpzwyMhIhISGNFBURERE1FXoPq509e1b788WLF3V6XqqqqvDnn3+iWbNmxo3ORObMmYPx48eje/fuCA4OxhdffIHk5GS88sorjR0aERERNTK9k6POnTtDIpFAIpHUOXxma2uLtWvXGjU4Uxk7diyysrKwZMkSpKamIjAwELt27YKPj09jh0ZERESNTO99jpKSkiCEgL+/P44fPw43NzftNalUCnd3d1haPhwbCzbUJpBERERkPEbf5+hWr4pGU/+uzERERETm7J6W8sfGxuLAgQNIT0+vlSy98847RgmMiIiIqDEYnBx9+eWXePXVV6FUKqFSqXSWnkskEiZHREREZNYMTo6WLl2KZcuW4c033zRFPERERESNyuB9jnJycvD000+bIhYiIiKiRmdwcvT0009j9+7dpoiFiIiIqNEZPKwWEBCA//u//8PRo0cRFBQEa2trneszZswwWnBEREREDU3vfY5u8fPzu/PNJBLEx8ffd1BNHfc5IiIiMj9G3+foloSEhPsKjIiIiKgpM3jOEREREdGDzOCeo0mTJtV7/auvvrrnYIiIiIgam8HJUU5Ojs7ziooKnD9/Hrm5uXUeSEtERERkTgxOjrZt21arTKPRYOrUqfD39zdKUERERESNxShzjiwsLDB79mx8+OGHxrgdERERUaMx2oTsa9euobKy0li3IyIiImoUBg+rzZkzR+e5EAKpqan4/fffMWHCBKMFRkRERNQYDE6OTp06pfPcwsICbm5u+OCDD+66ko2IiIioqTM4Odq/f78p4iAiIiJqEgxOjm7JyMjAlStXIJFI0Lp1a7i5uRkzLiIiIqJGYfCE7KKiIkyaNAmenp7o06cPevfuDS8vL0yePBnFxcWmiJGIiIiowRicHM2ZMwdRUVHYsWMHcnNzkZubi19//RVRUVGYO3euKWIkIiIiajASIYQw5AVKpRI///wz+vbtq1O+f/9+jBkzBhkZGcaMr0nS91RfIiIiajr0/f42uOeouLgYHh4etcrd3d05rEZERERmz+DkKDg4GAsXLkRpaam2rKSkBIsXL0ZwcLBRgyMiIiJqaAavVvv3v/+NwYMHo3nz5ujUqRMkEglOnz4NGxsb/PXXX6aIkYiIiKjBGDznCKjuKfruu+9w+fJlCCHQvn17PPfcc7C1tTVFjE0O5xwRERGZH32/v+9pnyNbW1tMmTLlnoMjIiIiaqruKTm6ceMGDh8+jPT0dGg0Gp1rM2bMMEpgRERERI3B4OQoIiICr7zyCqRSKVxdXSGRSLTXJBIJkyMiIiIyawbPOfL29sYrr7yC+fPnw8LC4MVuDwTOOSIiIjI/Jt3n6JlnnnloEyMiIiJ6sBmc4UyePBk//fSTKWIhIiIianQGD6tVVVVh2LBhKCkpQVBQEKytrXWur1mzxqgBNkUcViMiIjI/JlvKv3z5cvz1119o06YNANSakE1ERERkzgxOjtasWYOvvvoK4eHhJgiHiIiIqHEZPOdIJpOhV69epojlvvn6+kIikeg83nrrLZ06ycnJGD58OORyOZRKJWbMmIHy8vJGipiIiIiaGoN7jmbOnIm1a9fi448/NkU8923JkiU6u3fb29trf66qqsLQoUPh5uaGQ4cOISsrCxMmTIAQAmvXrm2McImIiKiJMTg5On78OPbt24edO3eiQ4cOtSZkb9261WjB3QsHBweoVKo6r+3evRsXL15ESkoKvLy8AAAffPABwsPDsWzZMk6uJiIiIsOH1ZycnDB69GiEhoZCqVRCoVDoPBrbypUr4erqis6dO2PZsmU6Q2bR0dEIDAzUJkYAMGjQIJSVlSEmJuaO9ywrK0N+fr7Og4iIiB5M93R8SFM1c+ZMdO3aFc7Ozjh+/Djmz5+PhIQE/Oc//wEAqNVqeHh46LzG2dkZUqkUarX6jvddsWIFFi9ebNLYiYiIqGlo8ttcL1q0qNYk69sf//zzDwBg9uzZCA0NRceOHfHiiy9i/fr12LBhA7KysrT3q2u7ASFEvdsQzJ8/H3l5edpHSkqK8d8oERERNQkG9xwBwM8//4wtW7YgOTm51kqvkydPGiWwW6ZNm4Znnnmm3jq+vr51lvfs2RMAEBcXB1dXV6hUKhw7dkynTk5ODioqKmr1KNUkk8kgk8kMC5yIiIjMksE9Rx9//DEmTpwId3d3nDp1Co8++ihcXV0RHx+PIUOGGD1ApVKJtm3b1vuwsbGp87WnTp0CAHh6egIAgoODcf78eaSmpmrr7N69GzKZDN26dTN67ERERGR+DD4+pG3btli4cCGeffZZODg44MyZM/D398c777yD7OxsfPLJJ6aKtV7R0dE4evQowsLCoFAocOLECcyePRvdu3fHr7/+CqB6KX/nzp3h4eGB1atXIzs7G+Hh4Rg5cqRBS/l5fAgREZH50ff72+Ceo+TkZISEhAAAbG1tUVBQAAAYP348fvzxx3sM9/7JZDJs3rwZffv2Rfv27fHOO+9gypQpOjFZWlri999/h42NDXr16oUxY8Zg5MiReP/99xstbiIiImpaDJ5zpFKpkJWVBR8fH/j4+ODo0aPo1KkTEhISYGAnlFF17doVR48evWu9Fi1aYOfOnQ0QEREREZkjg3uO+vXrhx07dgAAJk+ejNmzZ2PAgAEYO3YsRo0aZfQAiYiIiBqSwXOONBoNNBoNrKyqO522bNmCQ4cOISAgAK+88gqkUqlJAm1KOOeIiIjI/Oj7/W1wckRMjoiIiMyRySZkExERET3ImBwRERER1cDkiIiIiKgGJkdERERENTA5IiIiIqpBr00gu3TpUu+p9TUZ++BZIiIiooakV3I0cuRIE4dBRERE1DRwn6N7wH2OiIiIzA/3OSIiIiK6BwYfPFtVVYUPP/wQW7ZsQXJyMsrLy3WuZ2dnGy04IiIiooZmcM/R4sWLsWbNGowZMwZ5eXmYM2cORo8eDQsLCyxatMgEIRIRERE1HIOTo++//x5ffvkl5s2bBysrKzz77LP4z3/+g3feeQdHjx41RYxEREREDcbg5EitViMoKAgAYG9vj7y8PADAsGHD8Pvvvxs3OiIiIqIGZnBy1Lx5c6SmpgIAAgICsHv3bgDAiRMnIJPJjBsdERERUQMzODkaNWoU9u7dCwCYOXMm/u///g+tWrXCCy+8gEmTJhk9QCIiIqKGdN/7HB07dgyHDx9GQEAARowYYay4mjTuc0RERGR+9P3+Nngp/8GDBxESEgIrq+qX9ujRAz169EBlZSUOHjyIPn363HvURERERI3M4GG1sLCwOvcyysvLQ1hYmFGCIiIiImosBidHQog6D6HNysqCXC43SlBEREREjUXvYbXRo0cDACQSCcLDw3VWplVVVeHs2bMICQkxfoREREREDUjv5EihUACo7jlycHCAra2t9ppUKkXPnj0xZcoU40dIRERE1ID0To4iIiIAAL6+vpg3bx6H0IiIiOiBdM9L+TMyMnDlyhVIJBK0bt0abm5uxo6tyeJSfiIiIvOj7/e3wROyi4uLMWnSJHh6eqJPnz7o3bs3vLy8MHnyZBQXF99X0ERERESNzeDkaPbs2YiKisKOHTuQm5uL3Nxc/Prrr4iKisLcuXNNESMRERFRgzF4WE2pVOLnn39G3759dcr379+PMWPGICMjw5jxNUkcViMiIjI/Jh1W8/DwqFXu7u7OYTUiIiIyewYnR8HBwVi4cCFKS0u1ZSUlJVi8eDGCg4ONGhwRERFRQzP4bLWPPvoIQ4YMQfPmzdGpUydIJBKcPn0aNjY2+Ouvv0wRIxEREVGDuael/CUlJfjuu+9w+fJlCCHQvn17PPfcczobQz7IOOeIiIjI/Oj7/W1wz9HBgwcREhJSazfsyspKHDx4EH369DE8WiIiIqImwuA5R2FhYcjOzq5VnpeXh7CwMKMERURERNRYDE6OhBCQSCS1yrOyskx6pMiyZcsQEhICOzs7ODk51VknOTkZw4cPh1wuh1KpxIwZM1BeXq5T59y5cwgNDYWtrS2aNWuGJUuW4B43CSciIqIHkN7DaqNHjwYASCQShIeHQyaTaa9VVVXh7NmzCAkJMX6E/1VeXo6nn34awcHB2LBhQ63rVVVVGDp0KNzc3HDo0CFkZWVhwoQJEEJg7dq1AKrHGgcMGICwsDCcOHECsbGxCA8Ph1wu5waWREREBMCA5EihUACo7jlycHDQmXwtlUrRs2fPWvOQjGnx4sUAgI0bN9Z5fffu3bh48SJSUlLg5eUFAPjggw8QHh6OZcuWwdHREd9//z1KS0uxceNGyGQyBAYGIjY2FmvWrMGcOXPq7BEjIiKih4veyVFERAQAwNfXF/PmzTPpENq9iI6ORmBgoDYxAoBBgwahrKwMMTExCAsLQ3R0NEJDQ3V6vQYNGoT58+cjMTERfn5+dd67rKwMZWVl2uf5+fmmeyNERETUqAyec7Rw4cImlxgBgFqtrrVzt7OzM6RSKdRq9R3r3Hp+q05dVqxYAYVCoX14e3sbOXoiIiJqKgxOjoxp0aJFkEgk9T7++ecfve9X17DY7RPIb69zazJ2fUNq8+fPR15envaRkpKid0xERERkXgze58iYpk2bhmeeeabeOr6+vnrdS6VS4dixYzplOTk5qKio0PYOqVSqWj1E6enpAFDneXG3yGQynaE4IiIienA1anKkVCqhVCqNcq/g4GAsW7YMqamp8PT0BFA9SVsmk6Fbt27aOm+//TbKy8shlUq1dby8vPROwoiIiOjB1qjDaoZITk7G6dOnkZycjKqqKpw+fRqnT59GYWEhAGDgwIFo3749xo8fj1OnTmHv3r2YN28epkyZot0ifNy4cZDJZAgPD8f58+exbds2LF++nCvViIiISOuezlbbu3cv9u7di/T0dGg0Gp1rX331ldGCqyk8PBxff/11rfL9+/ejb9++AKoTqKlTp2Lfvn2wtbXFuHHj8P777+sMiZ07dw6vvfYajh8/DmdnZ7zyyit45513DEqOeLYaERGR+dH3+9vg5Gjx4sVYsmQJunfvDk9Pz1pJxbZt2+4tYjPC5IiIiMj8mOzg2fXr12Pjxo0YP378fQVIRERE1BQZPOeovLzcpMeEEBERETUmg5OjF198ET/88IMpYiEiIiJqdAYPq5WWluKLL77Anj170LFjR1hbW+tcX7NmjdGCIyIiImpoBidHZ8+eRefOnQEA58+f17nG5fBERERk7gxOjvbv32+KOIiIiIiahPvaBPL69eu4ceOGsWIhIiIianQGJ0cajQZLliyBQqGAj48PWrRoAScnJ7z77ru1NoQkIiIiMjcGD6stWLAAGzZswHvvvYdevXpBCIHDhw9j0aJFKC0txbJly0wRJxEREVGDMHiHbC8vL6xfvx4jRozQKf/1118xderUh2KYjTtkExERmR99v78NHlbLzs5G27Zta5W3bdsW2dnZht6OiIiIqEkxODnq1KkTPvnkk1rln3zyCTp16mSUoIiIiIgai8FzjlatWoWhQ4diz549CA4OhkQiwZEjR5CSkoJdu3aZIkYiIiKiBmNwz1FoaChiY2MxatQo5ObmIjs7G6NHj8aVK1fQu3dvU8RIRERE1GAMnpBNnJBNRERkjvT9/tZrWO3s2bMIDAyEhYUFzp49W2/djh07GhYpERERUROiV3LUuXNnqNVquLu7o3PnzpBIJKirw0kikaCqqsroQRIRERE1FL2So4SEBLi5uWl/JiIiInpQ6ZUc+fj4aH9OSkpCSEgIrKx0X1pZWYkjR47o1CUiIiIyNwavVgsLC6tzs8e8vDyEhYUZJSgiIiKixmJwciSEgEQiqVWelZUFuVxulKCIiIiIGovem0COHj0aQPWk6/DwcMhkMu21qqoqnD17FiEhIcaPkIiIiKgB6Z0cKRQKANU9Rw4ODrC1tdVek0ql6NmzJ6ZMmWL8CImIiIgakN7JUUREBADA19cX8+bN4xAaERERPZC4Q/Y94A7ZRERE5seoO2Tf7ueff8aWLVuQnJyM8vJynWsnT568l1sSERERNQkGr1b7+OOPMXHiRLi7u+PUqVN49NFH4erqivj4eAwZMsQUMRIRERE1GIOTo3Xr1uGLL77AJ598AqlUijfeeAORkZGYMWMG8vLyTBEjERERUYMxODlKTk7WLtm3tbVFQUEBAGD8+PH48ccfjRsdERERUQMzODlSqVTIysoCUH2syNGjRwFUn7nGud1ERERk7gxOjvr164cdO3YAACZPnozZs2djwIABGDt2LEaNGmX0AImIiIgaksFL+TUaDTQajfbg2S1btuDQoUMICAjAK6+8AqlUapJAmxIu5SciIjI/+n5/c5+je8DkiIiIyPwYdZ+js2fPIjAwEBYWFjh79my9dTt27GhYpERERERNiF7JUefOnaFWq+Hu7o7OnTtDIpHUOflaIpGgqqrK6EESERERNRS9JmQnJCTAzc1N+3N8fDwSEhJqPeLj400W6LJlyxASEgI7Ozs4OTnVWUcikdR6rF+/XqfOuXPnEBoaCltbWzRr1gxLlizhKjsiIiLS0qvnyMfHR/uzm5sb7OzsTBbQnZSXl+Ppp59GcHAwNmzYcMd6ERERGDx4sPa5QqHQ/pyfn48BAwYgLCwMJ06cQGxsLMLDwyGXyzF37lyTxk9ERETmweCz1dzd3TFy5EiMHz8eAwYMgIWFwbsB3JPFixcDADZu3FhvPScnJ6hUqjqvff/99ygtLcXGjRshk8kQGBiI2NhYrFmzBnPmzIFEIjF22ERERGRmDM5svvnmG5SVlWHUqFHw8vLCzJkzceLECVPEdk+mTZsGpVKJRx55BOvXr4dGo9Fei46ORmhoKGQymbZs0KBBuHnzJhITExshWiIiImpqDE6ORo8ejZ9++glpaWlYsWIFLl26hJCQELRu3RpLliwxRYx6e/fdd/HTTz9hz549eOaZZzB37lwsX75ce12tVsPDw0PnNbeeq9XqO963rKwM+fn5Og8iIiJ6MN3zmJiDgwMmTpyI3bt348yZM5DL5dqhL30tWrSozknUNR///POP3vf717/+heDgYHTu3Blz587FkiVLsHr1ap06tw+d3ZqMXd+Q2ooVK6BQKLQPb29vA94lERERmROD5xzdUlpait9++w0//PAD/vzzT7i7u2PevHkG3WPatGl45pln6q3j6+t7ryGiZ8+eyM/PR1paGjw8PKBSqWr1EKWnpwNArR6lmubPn485c+Zon+fn5zNBIiIiekAZnBzt3r0b33//PbZv3w5LS0s89dRT+OuvvxAaGmrwL1cqlVAqlQa/Tl+nTp2CjY2Ndul/cHAw3n77bZSXl2uPOdm9eze8vLzqTcJkMpnOPCUiIiJ6cBmcHI0cORJDhw7F119/jaFDh8La2toUcdWSnJyM7OxsJCcno6qqCqdPnwYABAQEwN7eHjt27IBarUZwcDBsbW2xf/9+LFiwAC+99JI2sRk3bhwWL16M8PBwvP3227h69SqWL1+Od955hyvViIiICMA9nK2Wn5/fKOeJhYeH4+uvv65Vvn//fvTt2xd//vkn5s+fj7i4OGg0Gvj7++PFF1/Ea6+9pj0kF6jeBPK1117D8ePH4ezsjFdeecXg5IhnqxEREZkfkx48e+3aNURERODatWv497//DXd3d/z555/w9vZGhw4d7itwc8DkiIiIyPzo+/1t8Gq1qKgoBAUF4dixY9i6dSsKCwsBVB9Ou3DhwnuPmIiIiKgJMDg5euutt7B06VJERkZqJzUDQFhYGKKjo40aHBEREVFDMzg5OnfuHEaNGlWr3M3NDVlZWUYJioiIiKixGJwcOTk5ITU1tVb5qVOn0KxZM6MERURERNRYDE6Oxo0bhzfffBNqtRoSiQQajQaHDx/GvHnz8MILL5giRiIiIqIGY3BytGzZMrRo0QLNmjVDYWEh2rdvjz59+iAkJAT/+te/TBEjERERUYO5p6X8QPVy/lOnTkGj0aBLly5o1aqVsWNrsriUn4iIyPzo+/19z2ertWzZEi1btrzXlxMRERE1SXolRzUPXb2bNWvW3HMwRERERI1Nr+To1KlTOs9jYmJQVVWFNm3aAABiY2NhaWmJbt26GT9CIiIiogakV3K0f/9+7c9r1qyBg4MDvv76azg7OwMAcnJyMHHiRPTu3ds0URIRERE1EIMnZDdr1gy7d++udYba+fPnMXDgQNy8edOoATZFnJBNRERkfkx2tlp+fj7S0tJqlaenp6OgoMDQ2xERERE1KQYnR6NGjcLEiRPx888/4/r167h+/Tp+/vlnTJ48GaNHjzZFjEREREQNxuCl/OvXr8e8efPw/PPPo6KiovomVlaYPHkyVq9ebfQAiYiIiBrSPW8CWVRUhGvXrkEIgYCAAMjlcmPH1mRxzhEREZH5MfkmkHK5HB07drzXlxMRERE1SQbPOSIiIiJ6kDE5IiIiIqqByRERERFRDUyOiIiIiGpgckRERERUA5MjIiIiohqYHBERERHVwOSIiIiIqAYmR0REREQ1MDkiIiIiqoHJEREREVENTI6IiIiIamByRERERFQDkyMiIiKiGpgcEREREdXA5IiIiIioBiZHRERERDUwOSIiIiKqwSySo8TEREyePBl+fn6wtbVFy5YtsXDhQpSXl+vUS05OxvDhwyGXy6FUKjFjxoxadc6dO4fQ0FDY2tqiWbNmWLJkCYQQDfl2iIiIqAmzauwA9HH58mVoNBp8/vnnCAgIwPnz5zFlyhQUFRXh/fffBwBUVVVh6NChcHNzw6FDh5CVlYUJEyZACIG1a9cCAPLz8zFgwACEhYXhxIkTiI2NRXh4OORyOebOnduYb5GIiIiaCIkw026T1atX47PPPkN8fDwA4I8//sCwYcOQkpICLy8vAMCmTZsQHh6O9PR0ODo64rPPPsP8+fORlpYGmUwGAHjvvfewdu1aXL9+HRKJRK/fnZ+fD4VCgby8PDg6OprmDRIREZFR6fv9bRbDanXJy8uDi4uL9nl0dDQCAwO1iREADBo0CGVlZYiJidHWCQ0N1SZGt+rcvHkTiYmJDRY7ERERNV1mMax2u2vXrmHt2rX44IMPtGVqtRoeHh469ZydnSGVSqFWq7V1fH19derceo1arYafn1+dv6+srAxlZWXa53l5eQCqM1AiIiIyD7e+t+82aNaoydGiRYuwePHieuucOHEC3bt31z6/efMmBg8ejKeffhovvviiTt26hsWEEDrlt9e51UD1DamtWLGizji9vb3rjZ2IiIianoKCAigUijteb9TkaNq0aXjmmWfqrVOzp+fmzZsICwtDcHAwvvjiC516KpUKx44d0ynLyclBRUWFtndIpVJpe5FuSU9PB4BavU41zZ8/H3PmzNE+12g0yM7Ohqurq97zlPSRn58Pb29vpKSkcC6TCbGdGwbbueGwrRsG27lhmLKdhRAoKCjQmYJTl0ZNjpRKJZRKpV51b9y4gbCwMHTr1g0RERGwsNCdLhUcHIxly5YhNTUVnp6eAIDdu3dDJpOhW7du2jpvv/02ysvLIZVKtXW8vLxqDbfVJJPJdOYpAYCTk5Oe79Jwjo6O/OA1ALZzw2A7Nxy2dcNgOzcMU7VzfT1Gt5jFhOybN2+ib9++8Pb2xvvvv4+MjAyo1WqdXqCBAweiffv2GD9+PE6dOoW9e/di3rx5mDJlirZxx40bB5lMhvDwcJw/fx7btm3D8uXLMWfOHKP2ABEREZH5MosJ2bt370ZcXBzi4uLQvHlznWu35gxZWlri999/x9SpU9GrVy/Y2tpi3Lhx2n2QgOpsMTIyEq+99hq6d+8OZ2dnzJkzR2fIjIiIiB5uZpEchYeHIzw8/K71WrRogZ07d9ZbJygoCAcPHjRSZMYlk8mwcOHCWkN4ZFxs54bBdm44bOuGwXZuGE2hnc12E0giIiIiUzCLOUdEREREDYXJEREREVENTI6IiIiIamByRERERFQDk6MmZN26dfDz84ONjQ26deuGv//+u7FDMhsrVqzAI488AgcHB7i7u2PkyJG4cuWKTh0hBBYtWgQvLy/Y2tqib9++uHDhgk6dsrIyTJ8+HUqlEnK5HCNGjMD169cb8q2YlRUrVkAikWDWrFnaMrazcdy4cQPPP/88XF1dYWdnh86dO2sP0QbYzsZQWVmJf/3rX/Dz84OtrS38/f2xZMkSaDQabR228705ePAghg8fDi8vL0gkEmzfvl3nurHaNScnB+PHj4dCoYBCocD48eORm5t7/29AUJOwadMmYW1tLb788ktx8eJFMXPmTCGXy0VSUlJjh2YWBg0aJCIiIsT58+fF6dOnxdChQ0WLFi1EYWGhts57770nHBwcxC+//CLOnTsnxo4dKzw9PUV+fr62ziuvvCKaNWsmIiMjxcmTJ0VYWJjo1KmTqKysbIy31aQdP35c+Pr6io4dO4qZM2dqy9nO9y87O1v4+PiI8PBwcezYMZGQkCD27Nkj4uLitHXYzvdv6dKlwtXVVezcuVMkJCSIn376Sdjb24uPPvpIW4ftfG927dolFixYIH755RcBQGzbtk3nurHadfDgwSIwMFAcOXJEHDlyRAQGBophw4bdd/xMjpqIRx99VLzyyis6ZW3bthVvvfVWI0Vk3tLT0wUAERUVJYQQQqPRCJVKJd577z1tndLSUqFQKMT69euFEELk5uYKa2trsWnTJm2dGzduCAsLC/Hnn3827Bto4goKCkSrVq1EZGSkCA0N1SZHbGfjePPNN8Vjjz12x+tsZ+MYOnSomDRpkk7Z6NGjxfPPPy+EYDsby+3JkbHa9eLFiwKAOHr0qLZOdHS0ACAuX758XzFzWK0JKC8vR0xMDAYOHKhTPnDgQBw5cqSRojJveXl5AAAXFxcAQEJCAtRqtU4by2QyhIaGats4JiYGFRUVOnW8vLwQGBjIv8NtXnvtNQwdOhSPP/64Tjnb2Th+++03dO/eHU8//TTc3d3RpUsXfPnll9rrbGfjeOyxx7B3717ExsYCAM6cOYNDhw7hiSeeAMB2NhVjtWt0dDQUCgV69OihrdOzZ08oFIr7bnuz2CH7QZeZmYmqqip4eHjolHt4eOicH0f6EUJgzpw5eOyxxxAYGAgA2nasq42TkpK0daRSKZydnWvV4d/hfzZt2oSTJ0/ixIkTta6xnY0jPj4en332GebMmYO3334bx48fx4wZMyCTyfDCCy+wnY3kzTffRF5eHtq2bQtLS0tUVVVh2bJlePbZZwHw37OpGKtd1Wo13N3da93f3d39vtueyVETcvvht0IIHoh7D6ZNm4azZ8/i0KFDta7dSxvz7/A/KSkpmDlzJnbv3g0bG5s71mM73x+NRoPu3btj+fLlAIAuXbrgwoUL+Oyzz/DCCy9o67Gd78/mzZvx3Xff4YcffkCHDh1w+vRpzJo1C15eXpgwYYK2HtvZNIzRrnXVN0bbc1itCVAqlbC0tKyV6aanp9fKrKl+06dPx2+//Yb9+/frHFKsUqkAoN42VqlUKC8vR05Ozh3rPOxiYmKQnp6Obt26wcrKClZWVoiKisLHH38MKysrbTuxne+Pp6cn2rdvr1PWrl07JCcnA+C/Z2N5/fXX8dZbb+GZZ55BUFAQxo8fj9mzZ2PFihUA2M6mYqx2ValUSEtLq3X/jIyM+257JkdNgFQqRbdu3RAZGalTHhkZiZCQkEaKyrwIITBt2jRs3boV+/btg5+fn851Pz8/qFQqnTYuLy9HVFSUto27desGa2trnTqpqak4f/48/w7/1b9/f5w7dw6nT5/WPrp3747nnnsOp0+fhr+/P9vZCHr16lVrK4rY2Fj4+PgA4L9nYykuLoaFhe7XoKWlpXYpP9vZNIzVrsHBwcjLy8Px48e1dY4dO4a8vLz7b/v7ms5NRnNrKf+GDRvExYsXxaxZs4RcLheJiYmNHZpZePXVV4VCoRAHDhwQqamp2kdxcbG2znvvvScUCoXYunWrOHfunHj22WfrXDravHlzsWfPHnHy5EnRr1+/h35J7t3UXK0mBNvZGI4fPy6srKzEsmXLxNWrV8X3338v7OzsxHfffaetw3a+fxMmTBDNmjXTLuXfunWrUCqV4o033tDWYTvfm4KCAnHq1Clx6tQpAUCsWbNGnDp1Srs9jbHadfDgwaJjx44iOjpaREdHi6CgIC7lf9B8+umnwsfHR0ilUtG1a1ftMnS6OwB1PiIiIrR1NBqNWLhwoVCpVEImk4k+ffqIc+fO6dynpKRETJs2Tbi4uAhbW1sxbNgwkZyc3MDvxrzcnhyxnY1jx44dIjAwUMhkMtG2bVvxxRdf6FxnO9+//Px8MXPmTNGiRQthY2Mj/P39xYIFC0RZWZm2Dtv53uzfv7/O/yZPmDBBCGG8ds3KyhLPPfeccHBwEA4ODuK5554TOTk59x2/RAgh7q/viYiIiOjBwTlHRERERDUwOSIiIiKqgckRERERUQ1MjoiIiIhqYHJEREREVAOTIyIiIqIamBwRERER1cDkiIjMwoEDByCRSJCbm9vYoRDRA47JERE1OX379sWsWbN0ykJCQpCamgqFQtE4Qd2Br68vPvroo8YOg4iMyKqxAyAi0odUKtWe5k1EZErsOSKiJiU8PBxRUVH497//DYlEAolEgsTExFrDahs3boSTkxN27tyJNm3awM7ODk899RSKiorw9ddfw9fXF87Ozpg+fTqqqqq09y8vL8cbb7yBZs2aQS6Xo0ePHjhw4EC9MS1atAgtWrSATCaDl5cXZsyYAaC6hyspKQmzZ8/WxnrLkSNH0KdPH9ja2sLb2xszZsxAUVGR9rqvry/effddjBs3Dvb29vDy8sLatWuN15BEdM+YHBFRk/Lvf/8bwcHBmDJlClJTU5Gamgpvb+866xYXF+Pjjz/Gpk2b8Oeff+LAgQMYPXo0du3ahV27duHbb7/FF198gZ9//ln7mokTJ+Lw4cPYtGkTzp49i6effhqDBw/G1atX6/wdP//8Mz788EN8/vnnuHr1KrZv346goCAAwNatW9G8eXMsWbJEGysAnDt3DoMGDcLo0aNx9uxZbN68GYcOHcK0adN07r169Wp07NgRJ0+exPz58zF79mxERkYaoxmJ6H7c99G1RERGFhoaKmbOnKlTduuU71snbkdERAgAIi4uTlvn5ZdfFnZ2dqKgoEBbNmjQIPHyyy8LIYSIi4sTEolE3LhxQ+fe/fv3F/Pnz68zlg8++EC0bt1alJeX13ndx8dHfPjhhzpl48ePFy+99JJO2d9//y0sLCxESUmJ9nWDBw/WqTN27FgxZMiQOn8PETUc9hwRkdmys7NDy5Yttc89PDzg6+sLe3t7nbL09HQAwMmTJyGEQOvWrWFvb699REVF4dq1a3X+jqeffholJSXw9/fHlClTsG3bNlRWVtYbV0xMDDZu3KjzOwYNGgSNRoOEhARtveDgYJ3XBQcH49KlSwa3AxEZFydkE5HZsra21nkukUjqLNNoNAAAjUYDS0tLxMTEwNLSUqdezYSqJm9vb1y5cgWRkZHYs2cPpk6ditWrVyMqKqrW77pFo9Hg5Zdf1s5NqqlFixb1vqea85aIqHEwOSKiJkcqlepMojaWLl26oKqqCunp6ejdu7fer7O1tcWIESMwYsQIvPbaa2jbti3OnTuHrl271hlr165dceHCBQQEBNR736NHj9Z63rZtW/3fEBGZBIfViKjJ8fX1xbFjx5CYmIjMzExtz8/9at26NZ577jm88MIL2Lp1KxI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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "total_dev = np.array(1e15*(total_c-total_c[0])/total_c[0])\n", "plt.plot(total_dev)\n", "plt.ylabel('deviation total amount of c [parts per 10^15]')\n", "plt.ylim(-200, 200)\n", "plt.xlabel('time step')\n", "plt.title('deviation from mass conservation');" ] }, { "cell_type": "code", "execution_count": 12, "id": "8d89372a-bb1a-4b29-86e0-a0d5155da5d3", "metadata": {}, "outputs": [], "source": [ "# deviation from mass conservation should be less than 1 part in 1e12\n", "# in this case\n", "\n", "maxdev_ppq = 1000. # max rel deviation in parts per 10^15\n", "assert np.max(np.abs(total_dev)) < maxdev_ppq" ] }, { "cell_type": "code", "execution_count": 13, "id": "9049e5ed-3c9f-4e0c-be75-09e651ac1291", "metadata": {}, "outputs": [], "source": [ "# amplitude of steady-state solution\n", "z0 = D_coeff/sg\n", "B = z_max/(z0*(1.0-np.exp(-z_max/z0)))\n", "\n", "# simulation should have reached at least 90% of steady-state value\n", "# \n", "assert np.max(c.value) > 0.9*B" ] } ], "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": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 5 }