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guyer/modular_theta.ipynb

Last active November 3, 2023 18:08
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Illustration of modular variables in FiPy
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modular_theta.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "10b2b590-bd38-4e52-96ed-0ee69bf1fb91",
"metadata": {},
"source": [
"# Modular Gradients"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "284593cf-bbe0-4e5d-92c9-9a3c91565dba",
"metadata": {},
"outputs": [],
"source": [
"import fipy as fp\n",
"from matplotlib import pyplot as plt"
]
},
{
"cell_type": "markdown",
"id": "c302529f-d2d7-4fde-bc82-17d10a5ddd7b",
"metadata": {},
"source": [
"## Warren, Kobayashi, Lobkovsky & Carter"
]
},
{
"cell_type": "markdown",
"id": "714f2d02-858f-41a6-9b00-2521f40e79db",
"metadata": {},
"source": [
"The governing equation for orientation in [Warren, Kobayashi, Lobkovsy & Carter](https://www.ctcms.nist.gov/cgi-bin/redirect.py?url=https://doi.org/10.1016/S1359-6454(03)00388-4) is:\n",
"\\begin{align}\n",
"P\\left(\\epsilon\\left\\lvert\\nabla\\theta\\right\\rvert\\right)\n",
"\\tau_\\theta\n",
"\\phi^2\n",
"\\frac{\\partial\\theta}{\\partial t}\n",
"&= \\nabla\\cdot\\left[\n",
" \\phi^2\\left(\\frac{s}{\\left\\lvert\\nabla\\theta\\right\\rvert} + \\epsilon^2\\right) \\nabla\\theta\n",
"\\right]\n",
"\\end{align}"
]
},
{
"cell_type": "markdown",
"id": "88000b0f-7e87-49d1-89a6-a0c655224cb2",
"metadata": {},
"source": [
"## FiPy"
]
},
{
"cell_type": "markdown",
"id": "47d4835f-2ddd-4db8-9318-40c0cf2ba659",
"metadata": {},
"source": [
"As you noted, the discretization in [`examples.phase.polyxtalCoupled`](https://www.ctcms.nist.gov/fipy/examples/phase/generated/examples.phase.polyxtalCoupled.html)\n",
"```python\n",
"thetaEq = (fp.TransientTerm(coeff=tau_theta * phaseMod**2 * Pfunc, var=theta)\n",
" == fp.DiffusionTerm(coeff=D_theta, var=theta)\n",
" + fp.PowerLawConvectionTerm(coeff=v_theta * (theta.faceGrad - theta.faceGradNoMod), var=phase))\n",
"```\n",
"is not the same as in WKLC. FiPy is a Finite Volume code, whereas WKLC presented a Finite Difference discretization. The relevant distinctions are that\n",
"- Finite Volume is weak form, whereas Finite Difference is strong form.\n",
"- Finite Volume works on arbitrary, irregular meshes, whereas Finite Difference generally requires uniform, orthogonal grids."
]
},
{
"cell_type": "markdown",
"id": "61295aef-4dd5-40a4-a4a3-31ab2c24b873",
"metadata": {},
"source": [
"Loosely, \n",
"```python\n",
"fp.DiffusionTerm(coeff=D_theta, var=theta)\n",
"```\n",
"is equivalent to WKLC's\n",
"\\begin{align}\n",
" -\\frac{D_{i-(1/2),j}}{\\delta x^2}\\theta_{i-1,j}\n",
" -\\frac{D_{i+(1/2),j}}{\\delta x^2}\\theta_{i+1,j}\n",
" -\\frac{D_{i,j-(1/2)}}{\\delta y^2}\\theta_{i,j-1}\n",
" -\\frac{D_{i,j+(1/2)}}{\\delta y^2}\\theta_{i,j+1}\n",
" \\\\\n",
" + \\left(\n",
" \\frac{D_{i-(1/2),j} + D_{i+(1/2),j}}{\\delta x^2}\n",
" + \\frac{D_{i,j-(1/2)} + D_{i,j+(1/2)}}{\\delta y^2}\n",
" \\right) \\theta_{i,j}\n",
"\\end{align}\n",
"and\n",
"```python\n",
"fp.PowerLawConvectionTerm(coeff=v_theta * (theta.faceGrad - theta.faceGradNoMod), var=phase)\n",
"```\n",
"is equivalent to WKLC's $-C_{i,j}$."
]
},
{
"attachments": {},
"cell_type": "markdown",
"id": "7a74196c-16b5-4b80-b9dc-d2b7b6750d55",
"metadata": {},
"source": [
"Specifically, the terms in FiPy represent\n",
"\n",
"\\begin{align}\n",
"\\frac{\\partial}{\\partial t}\\left[\n",
" \\tau_\\theta\n",
" \\phi^2\n",
" P\\left(\\epsilon\\left\\lvert\\nabla\\theta\\right\\rvert\\right)\n",
" \\theta\n",
"\\right]\n",
"&= \\nabla\\cdot\\left[\n",
" \\phi^2\\left(\\frac{s}{\\left\\lvert\\nabla\\theta\\right\\rvert} + \\epsilon^2\\right) \\nabla_{?}\\theta\n",
"\\right]\n",
"\\\\\n",
"&\\qquad {} + \\nabla\\cdot\\left[\n",
" \\phi\\left(\\frac{s}{\\left\\lvert\\nabla\\theta\\right\\rvert} + \\epsilon^2\\right)\n",
" \\left(\\nabla_{\\mathrm{mod}}\\theta - \\nabla_{\\cancel{\\mathrm{mod}}}\\theta\\right) \\phi\n",
"\\right]\n",
"\\end{align}\n",
"\n",
"Where\n",
"- $\\nabla_{?}$ is whatever gradient is represented by the discretization of the `DiffusionTerm`.\n",
"- $\\nabla_{\\mathrm{mod}}$ is a gradient that accounts for the branch cut in $\\theta$.\n",
"- $\\nabla_{\\cancel{\\mathrm{mod}}}$ is a gradient that *does not* account for the branch cut in $\\theta$.\n",
"\n",
"I'm going to assert without proof that the discretization of the `DiffusionTerm` also does not account for the branch cut in $\\theta$, such that $\\nabla_{?} \\approx \\nabla_{\\cancel{\\mathrm{mod}}}$.\n",
"\n",
"$\\nabla_{\\mathrm{mod}}\\theta - \\nabla_{\\cancel{\\mathrm{mod}}}\\theta$ will be zero everywhere but at the branch cut."
]
},
{
"cell_type": "markdown",
"id": "3e249d9b-da98-43fc-8758-4af8be88f6a1",
"metadata": {},
"source": [
"Combining terms:\n",
"\\begin{align}\n",
"\\frac{\\partial}{\\partial t}\\left[\n",
" \\tau_\\theta\n",
" \\phi^2\n",
" P\\left(\\epsilon\\left\\lvert\\nabla\\theta\\right\\rvert\\right)\n",
" \\theta\n",
"\\right]\n",
"&\\approx \\nabla\\cdot\\left[\n",
" \\phi^2\\left(\\frac{s}{\\left\\lvert\\nabla\\theta\\right\\rvert} + \\epsilon^2\\right) \\nabla_{\\mathrm{mod}}\\theta\n",
"\\right]\n",
"\\end{align}\n",
"\n",
"(I don't know how close the approximation is; that might actually be an equality.)"
]
},
{
"cell_type": "markdown",
"id": "a0736f2b-6ba2-4eda-a8a2-115d6de9d846",
"metadata": {},
"source": [
"### Illustration of gradient behavior at branch cut"
]
},
{
"cell_type": "markdown",
"id": "de56d4c4-748f-4f78-a5e8-0f6c8b99000e",
"metadata": {},
"source": [
"Consider a 1D field with a couple of \"wraps\" of $\\pi\\to-\\pi$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "61ba311f-38eb-4302-bd3f-615774ea6fc5",
"metadata": {},
"outputs": [],
"source": [
"mesh = fp.Grid1D(nx=100, Lx=6 * fp.numerix.pi)"
]
},
{
"cell_type": "markdown",
"id": "38c57f32-d3bb-43ee-b807-e639180270da",
"metadata": {},
"source": [
"#### Modular Variable"
]
},
{
"cell_type": "code",
"execution_count": 85,
"id": "a8be2a8a-90ea-4c38-a4f9-11f1b360e325",
"metadata": {},
"outputs": [],
"source": [
"theta = fp.ModularVariable(mesh=mesh, name=r\"$\\theta$\")\n",
"theta.value = fp.numerix.mod(mesh.x, 2 * fp.numerix.pi) - fp.numerix.pi"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "37d0f4aa-1aa8-4080-b7e3-34c0e4b3a22f",
"metadata": {},
"outputs": [
{
"data": {
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w5513Tvk14XAY4XDY+DwUCjkVHrEAs15cnJu+Xmwu5XFNwnkSZ/ZYpxf72c3DcVoUato6GcdmTM888wx++9vf4l/+5V+m/Zpdu3ahpKTE+Kivr3cqPGIBVnUvNj8L+SBzFvMZWlbqxdTFnWUgPIZ3z/cAUEsT13EkMX3ta1/DL37xC+zbtw/z5s2b9ut27tyJvr4+46O9vd2J8IgFWNm92M9SnjA+7gjhmg16sZ+6uKMcPNOFSDSGBeX5aKxM7wwtkdhaytM0DV/72tfw5ptvYv/+/Vi4cOGMXx8MBhEMqlULJeNYqRebExP3MjmLPltav9RavZjdxZ2l+VTmZ2iJxNbE9NWvfhU//vGP8fOf/xxFRUW4fv06AKCkpAR5eXl2Xpo4jJV6sbmUR4vLWVpO2bMuQV3cOcaiMew7rVY38cnYWsrbvXs3+vr6sGHDBtTW1hofb7zxhp2XJQ5jtV5slh84Y3IOO/Vi6uLO8cHlm7g5NIrS/Gysmj9HdDhpYXspj7gfq/Vi6uJi0PXiVQ1zUG6xXuzjGpNj6LPeTcuqkJXBGVoiUTNqIhWGlrrCOr2YhwU6j3kcrYalPGfQNC1hxypaxgOYmEiGTNCLLVyXoF7sLGa92I59LyzlOcP5rkFc6hlCTsCP9RmeoSUSJiaSEWa9eE1juWXfl4cFOouuFy+sKEBjZYHl35+dH5xBf0l8oLEchUHH+idYDhMTyQi9bGCbXszM5AgJvbjKFr2YurgzGGcvLVdvU60ZJiaSEXbpxSzlOYdZL7arfY0//qTheNpHz0AYH7RZd4aWSJiYSNp03BrGxx026cX6YjlnTLbzYdst2/VizpjsZ+/pTmgacOfcYtSVqr1PlImJpI3etNUOvZhrTM6hz3o32qgXsyWR/dhVvRABExNJm+b4vhc79WJaXPZi1ovt7BJAXdxeRkajePtMNwAmJuJh+kdG8e55+24EfY2JDzJ7Od81iIvdg7brxdTF7eWd890YHo2itiQXd9QViw4nY5iYSFocPNuN0ahmm17MTgHO4JRe7KMubivNJxPyiopNWyfDxETSInEImT16cYCL5Y7glF7M8bSPWEwz1ns3K66J6zAxkZQZi8awt1XvXlxjyzWoi9uPk3qxrouzlGc9J672obM/jIIcaze5i4SJiaTMB5dv4tbQKObkZ2NlQ6kt16Aubj9O6sWJzg8cT6vRy7EPL6tEMMu6Te4iYWIiKWPoxU0O6MV8jtmGk3oxx9M+jKatLrDxdJiYSEpM0IttvBFocdmL03oxu8XbQ3vvEE5f74ffN74PzS0wMZGUMHcvXmenXsxSnq28e77HUb3YxzVDW9Clh9ULyjCnIEdwNNbBxERSQi//rLFZL2bpx16aTWU8J/Ridhe3B/1wRzurFyJgYiIpYedhcmaoF9uHCL2Y42k9oZFRHL4QP0NL4UMBp4KJiSRNt0kvfsTmBxpLP/bxUUcfboSc1Yupi1vP/tYujMU0NFYWYGGF9ZvcRcLERJLGrBfXltirFycWy229jCfRZ71O6sUs5VmPU9ULETAxkaRpcVBL5UGB9vFrAXoxj72wltFoDPta3bm+BDAxkSQZGY3i4Fnn9GJ2frAHUXoxx9NajlzsRf/IGMoKcnBPgz1naImEiYkkhdPdi6mL24MovdjPfUyWoluVm5qqjLK3m2BiIknhdPdi6uL2IEov5nhah6ZprjoUcCqYmMismPVipxZadb2YFpd1iNSLDZmFmSljztwYQHvvMHKy/Fi3pEJ0OLbAxERmRe9eXBjMwgOLyhy5pj4p40GB1nFAoF5M/d869NnSQ4srUGDjJneRMDGRWTG6Fy91Xi/mC7Z1iCz/BKiLW4Ybm7ZOhomJzIpxI6xwzuJi6cdaRqMx7Dutn6Hl/AONurg1dPaP4Hj7LQDuORRwKpiYyIzoenHA73NUL2bpx1qOXOpFaGQM5YL0Yuri1qC/XNw9rwTVxbmCo7EPJiYyI4ZePH8OSvOd04sD1MUtpSVuVYrSi6mLW4PZjnUzTExkRgy92OHyj9+w8hy9rCvRNA3Np64DENe+hmuGmTMcieLQuS4A7mxDZIaJiUyLWS/e7Pi+l/F/8g07c2TQi7lmmDmHznVjZDSGuaV5aKopEh2OrTAxkWnR9eLFVYWO68VG008mpowx68X5OWL0Yq4ZZo7eq3LLCmc2uYuEiYlMi0i9mKUf65BBL2Z38cyIxTTsOS1+HJ2CiYlMyUS92HktlaUfa5BFL2Ynj8w4fuUWugciKApm4b6FzmxyFwkTE5mSIxcTevEn653Xi1n6sYa9p+TQizmemWE+Qysny/2Pbff/H5K0EN29mAcFWoNejhWxqdaMof9zPNNClnF0CiYmchsTuheL1ouZmdJmKDKWOENL8AONnR/S53LPIM7cGECW34cNS93b7cEMExO5DRn0YpZ+MufQ2W6Ex2KYNycPy6rF6sV+rhmmjb6X8L6FZSjJzxYcjTMwMZHbkEEvDlAXzxizVSlaL+a+tPRpkcCqdBomJnIbMunFfI6lRzSmYY+grh1TQV08PW4NRfD+pV4ATEzEw5j14kcE6sU8Wj0zjrffQs9gBEW5cujF1MXTY39rF6IxDcuqi9BQni86HMdgYiITMPTi+lJUCdSLWfrJDL2Mt2FZFbID4m9zrhmmR/Mp54+ckQHxv7FEKgwtVfBZL+z8kBmJdQk5HmjUxVMnMhbD263xpq0eKuMBTEzExHAkKo1ezM4P6XOpexBnO+N6sYNnaM2En6W8lHnvYg/6w2OoKAzi7nmlosNxFCYmYnDwbJc0ejFLP+mjz3rvX1SGkjw59GJ9PLlmmDzmWa9fwCZ3kTAxEQOZ9GLq4ukjsvnudAR4UGBKjG9y98ahgFPBxEQASKgX+6mLp8OtoQiOXLoJQK4HGtcMU+PUtX5cvTWM3Gw/HlwsZpO7SJiYCACTXhzMwr0LxOvFbEmUHvtaOxGNaWiqKUJ9mTx6McczNRKb3CuRlxMQHI3z2JqY3n77bTz22GOoq6uDz+fDz372MzsvRzLA0IubqqToXqyX1FnKS42Wk3KWf6j/p4Z+P26VoHohAlufQIODg7j77rvxyiuv2HkZYgGy6cXs/JA64bEoDpyJ68WSPdASJxILDkQBrveN4LdX+uDzARub5LgfncbWRmjbtm3Dtm3b7LwEsYAJerEk3YvZ+SF13rvQi4HwGCqLgvjE3BLR4Uwg4Kcuniz6SbX31JeisigoOBoxiOnQOQ3hcBjhcNj4PBQKCYzGO+hlA5m6F7P0kzoJG08+vZi6ePIY1QvJZr1OIn4xwcSuXbtQUlJifNTX14sOyRNIqRfT4koJTdOk7kLNgx+TYzA8ht+c7wEAbJFwHJ1CqsS0c+dO9PX1GR/t7e2iQ3I9Zr1YBk1ch+f3pMbJayF09I1Iqxez80NyHDzbjchYDA1l+VhcVSg6HGFIVcoLBoMIBr1ZUxWF3r1YNr2YnR9SQ7fx1i2pRG62fHpx4tgLjudM6EfObFkhfpO7SKSaMRHnaZawjAew80OqJJrvyjWOOlwznJ1oTMPe03Lej05j64xpYGAA586dMz6/ePEijh8/jrKyMjQ0NNh5aZIEkbEYDrTKrRfzOTY71/qGceKq3Hqxn2tMs/Jh203cHBpFcW4WVi+YIzocodiamI4ePYqNGzcan+/YsQMAsH37drz22mt2XpokwXsXe6TVi6mLJ4/eSkpmvTjRkojjOR26vLKxSY4ztERia2LasGEDFzslRubuxSz9JI9hVUo26zXD8Zwdvawuk4QkCm+nZQ+jaZqx0CpjPZulvOQYDI/hnXPy68WJ87UEByIp57sGcKFrENkBHx5eWik6HOEwMXkU6fVilvKS4uDZLkSiMcwvl1svZilvZvbEZ0sPLCpHUa4cm9xFwsTkUeTXi8f/yQfZzDTHx3Fzk9x6MTs/zIxZEydMTJ5Fdr04wDfsWTHrxbI/0Nj5YXp6BsL44PL4JvfNkt6PTsPE5EGU0IvZkmhWdL24JC8b90quF7OUNz37WrsQ04AVtcWYW5onOhwpYGLyIEroxTyKe1Z0q3JTUxWyJNeLmZimh01bb0fu32ZiC0YZb0WN4Eimx881iVmRtWvHVBhrhhzPCYyMRvH22fFN7rKW1UXAxOQxJujFK+Qs4wHUxWfDrBevXyqfVTkZrjFNzbsXejAUiaK6OIg75xaLDkcamJg8xttnxvXiBeX5aKyUWC+mLj4jevlHFb2YpbypMR9VIrNV6TRMTB5DL/9slvxGoC4+My2KdQmgLn47mqYp0bVDBExMHmIsGsO+0+Pig+wPNOri06OiXpw4Wl1wIBLx0dUQboTCyM8JYM2ictHhSAUTk4f4sO2WoRevni+3XuyjLj4tKurFLOXdjl69WC/pJneRMDF5CL1soIZePP5PPshuR0W92M/ztW5DxXF0CrmfTsRSWhRqexLg0epTYtaLH1kur1U5Gf1FQ9N4vDoAXLk5hJPXQvD7xl8UyUSYmDzC+a4BXOgeRE7Aj/UKdC9m54epMevFd0l2htZM+E2iDcc0scl99fwylBXkCI5GPpiYPIKhFzeWozBo6zFclkBdfGpU1YvN532xPGs+Q4uzpalgYvIIiaatatwIXGO6HbNerEI51oz5HEqvv2yERkZx+ML4JncVunaIgInJAyipF7Pzw23oenFBTgBrGtXSiwOmzOT1MX37TBdGoxoWVRZgkcSb3EXCxOQBdL34jrpi1CmiF/tocd2GoRcvrUQwSy29eOIak7fH1JCQFHlJFAETkwfQbwRVZksAS3lTYV5fUg3zcpiXXzZGozHsjW9ypyY+PUxMLkfV7sXUxSdy9dawoRfLeobWTARMmUmLCQxEMEcv3URoZAxz8rOxskHuTe4iYWJyObpeXFOcq1T3YnZ+mMieeBlPVb3YXMrz8owpscm9esK6G5kIE5PLaT6Z0FJV0osD1MUnYB5HFaEuPtmqVHMcnYKJycXEYprxpq3aukSiU4A3H2Jm3KIXe33d8FznAC73DCEn4Me6JfJvchcJE5OL+aijT1m9mJ0fEhh6cYXaenFi3VBwIILQrcq1i8tRoMAmd5EwMbkY3eJSWS/28nqEjko9DmfC5/EO4ypblU7DxORimuP9uFS8Efzx30yvl/LcpBfrpTwvrht29YdxrP0WAGCzIt1XRMLE5FKu3BzCKRfoxV58iJnR9eKyghzl9WIvd/PYe/oGNA24a24JakvU2OQuEiYml6J692Lq4uOYz9BSXS/2cnm2+aS61QsRMDG5FNW7F3vd4AIm6sVueKDpyrjXxnQ4EsWhc/FN7oqXY52CicmFuEEvZucHk16c5ce6JRWiw8kYr24B+M25boyMxjC3NA/La4tEh6METEwuRNeLGxXuXkxdPKEXP9joDr3YKOV5TBdPzHrV2uQuEiYmF2JoqQqXDYyDAj32dm2m2QXjaMaLpbxYTEPLKXdYlU7CxOQyzHqxSk1bJ+PVso9OZ/8Ijut6cZO642jGi7r4f1+5he6BMAqDWbh/oVqb3EXCxOQyjlzqNfTiexTWiwMeL+XtO90JTQM+Ma8ENSW5osOxBC/q4noZ7+FllcjJ4uM2WfiTchktcS1Vdb3Y5/F9TG7Ui73Y+UG/H1WuXoiAiclFaJqG5lPXAaj/QDPnVK+V89yqFwc8tm7Y1jOE1hv9CPh92LCMTVtTgYnJRZztHEB777Ar9GLzbM9rsyazXtxU4x692GvrhnoZ774FZSjNV2+Tu0iYmFyEbnG5QS82a7Uey0umM3uqXaUXe00XT2xyd8+s1ymYmFyEm26EgEcPlpugFytejp2Ml3TxvqFRvH+xF8D4/iWSGkxMLsFterF5jckLDzIdXS8uCmbhvoVlosOxFKPNlAemwPvPdGIspmFpdSHmlxeIDkc5mJhcgtv0Yr9HS3lu1ou91M3DrbNep3DXb76HcZtebE5MXpIfDL3YBeXYyfg9ootHxmLY75IztETBxOQCzHqxWw4h86IuPkEvXuqOcTSjH/7odl38/Yu96A+PoaIwB5+cVyo6HCVhYnIBh0x68YraYtHhWIIXdfFmk15ckp8tOBrrSXR+cPd46uXYzU3VhvBBUoOJyQXscWH3Yi/q4m5ovjsTPg/o4pqmua75rgiYmBTHrBdvWVEjOBpr0WdNbn/DBuJ68SV368UBD+jip6/34+qtYQSz/Hhosdqb3EXCxKQ4XtCL3b4mAYzrxVGX68Ve6Pygz3rXLalAXk5AcDTqYnti+v73v4+FCxciNzcXq1atwsGDB+2+pKdws17s85BerJd/3Gjj6Xih80PiUED3jqMT2Poke+ONN/Dss8/iG9/4Bo4dO4Z169Zh27ZtaGtrs/OynsLNerFx9IXLM1NkLIYDreNWpZsfaG7XxW+ERvDfV/rg8wGbXTyOTmBrYvrud7+LL37xi/jSl76E5cuX42//9m9RX1+P3bt323lZz+B6vVjvFODSB5lOQi8O4m4X68W6Lu7W8dRnS5+sL0VlUVBwNGpjW2KKRCL44IMPsHXr1gl/vnXrVrzzzjtT/p1wOIxQKDThg0xPi8v1YuN4dZfPmFpMVqWb9WK3z5gMq5KzpYyxLTF1d3cjGo2iunriIFVXV+P69etT/p1du3ahpKTE+Kivr7crPFfgpqatU+GFFjYT9GKXP9DcvMY0GB7Db873AHBnWd1pbF8tn7yvRtO0affa7Ny5E319fcZHe3u73eEpS9/QKN5zefdiL1hcul6cm+3Hgy7Xi92six88243IWAwNZflYUlUoOhzlse3QnoqKCgQCgdtmR52dnbfNonSCwSCCQdZmk8ELerEXTjzVyz8PLa50vV7s5hcNs43nlk3uIrFtxpSTk4NVq1ahubl5wp83Nzdj7dq1dl3WM3hBLzZ0cReWfnSajUMB3TnrNePWzg/RmIa9RtNW94+jE9h6zOmOHTvw1FNPYfXq1VizZg1effVVtLW14emnn7bzsq7HK3pxwOWL5df7RvDbuF68yQVnaM2GW8fzWNtN9A5GUJybhXsXuGuTuyhsTUxPPPEEenp68K1vfQvXrl3DnXfeiV/+8peYP3++nZd1PZ7Ri12ui+857S292K26uD7r3dhUheyAuza5i8LWxAQAX/nKV/CVr3zF7st4Cq/oxW7v/OA1vdjv0g3TXhtHJ2B6Vwwv6cUBF+9j8qJe7Eb9/0LXAM53DSLL78PDyypFh+MamJgUw0t6sZstLl0vnl/uHb3YjaXZPfHO/g8sKkdxrvs2uYuCiUkxPKUXu3jG5EW92O/CfUwJq9Ibs16nYGJSjBYP6cVuLP0Ak/Ril5djzbit88PNwQiOxs/Q2uzSTe6iYGJSCHP3YurF6qLrxSV52Vi9YI7ocBzDbeO593QnYhqwvLYY8+bkiw7HVTAxKYTXuhf7XLgmASQ2R29cVukpvdjQxV0yBTaqF5wtWY537goX4DUt1a2lvGaXN9+dDjeN58hoFAfOxDe5e2wcnYCJSRG8qBcbTT/d8CSLc6FrABe6BpEd8GH9Um/pxW469uLwhR4MRaKoLg7izroS0eG4DiYmRfBi92I36sV6+ceLerGbxlMfx83Lq129yV0UTEyK4GW92E26eMtJ79l4Om7RxTVNM8ZxiwfH0QmYmBTAq92L3bQmAQC9gxEcvexdvdgtuvjHHSFcD40gLzuANY3losNxJUxMCuDV7sVu6/ywz+N6sb5mqPp46lbl+qUVyM129yZ3UTAxKYBucW3yWPdi4w1b8QeZjtf1Yrfo/+ayOrEH7zzlFMbQxD1i4+m4qZRn1ou3rKgRHI0Y3FDK67g1jI87QvD7xl8UiT0wMUmO3r3Yi3qxm3TxCXrx3GLR4QjBDZ0f9sRnSysb5qC80P2b3EXBxCQ5Xu5e7JbSD+BNq3IybtDFm+P3o1f2EoqCiUlymj1czzZmTOo+xwBM1Iu9Vo41o7ou3j8yinfPdwPw9jg6AROTxHi9e7FbTjzV9eL8nADWLPKuXqz6GtPBs90YjWpYVFGAxkpvbHIXBROTxOxr9bZe7IbSD2DSi5dUelovVl0Xb/aohCQCJiaJ8bpe7BZdvMWjTVsno/Ka4Vg05skztETBxCQp4bEoDrR6u3uxG3Txqya9eOMyb1mVk1G5lHf08k30DY9iTn42VjaUig7H9TAxScq753sw6PHuxW7QxakXJ9B1cRVLefpewo1NVcjy0CZ3UfAnLCnsXqx26UdHX5egXpwYT9VKs5qmGXYsm7Y6AxOThLB78Tiql/L6R0Zx+ML4GVpeLceaUVX/P981gMs9Q8gJ+LHOY5vcRcHEJCHsXjyO6qW8t8/E9eJK6sWAugcFNsdfEtc0lqMwmCU4Gm/AxCQh7F48juqlvBaWfyZg6P+KvWjQqnQeJiYJMR5oHm32qRNQWBefoBfzgQZAzc4P3QNhfNh2EwDwiEe3bYiAiUkyOqgXG/gNi0twIGkwUS+eIzocKVBRF997uhOaBtw1twS1JXmiw/EMTEySoevFq+ZTL/bHfztVK/0ACb14U1O1sVbmdVTUxY0jZ1iOdRQmJsnQuxfzRlC388MEvXgFyz86quniI6NRHDyrN23lODoJE5NEsHvxRFTVxc91mvTiJd4ux5pRTRf/zbluDI9GUVeSixW13jxDSxRMTBJh6MXsXgxAXV1cny2tXVyOAurFBn7FSnlmG8+rZ2iJgolJIqilTkRVXVxfl9jMcuwEjFKeAi8asZiGFpbVhcHEJAnsXnw7KuriXf1hHGu/BYB68WQCCuniv73ah67+MAqDWbh/UZnocDwHE5MksHvx7fj96uni+6gXT0vi4EfBgSSBPut9eGklglne3eQuCiYmSWD34tvxKdgpQF9f4qz3dlRqSZQoq3PWKwI+ASWA3YunRrVS3rherJ+hxQfaZFQ5kbi9dwinr/cj4Pdh4zKOowiYmCSA3YunRrXOD785142R0RjmluZRL56CxL40wYHMgj5bunfBHJTm5wiOxpswMUkAuxdPjb7GpILFBZjKP8urqBdPQcCvhi7ewnKscJiYJICa+NSoUvoBJunFHMcpUUEX7xsexXsXegHwcEeRMDEJht2Lp0elzg8T9OKF3j1DayZU6Pxw4EwXxmIallQVYn55gehwPAsTk2D2nhrXi++cW0y9eBIqdX4w9OJllcjJ4m01FQldXN7xNJq2crYkFN5BgknYeN4+e2kqVOr8wEMBZ0f28RyNxrCvlZvcZYCJSSDUi2dGFV3crBdv8PgZWjMRkHwf05GLvegfGUNFYQ4+WV8qOhxPw8QkEF0vZvfiqVFFF9dnS6vnUy+eCb/ka0x69WJTUxXP0BIME5NA2L14ZmQv/egYZTyuS8yIzJ0fNE2jJi4RTEyCYPfi2QkosI+JenHy+CXWxc/cGEB77zCCWX48tKRCdDieh4lJEOxePDsqlPL2t3ZSL06SgMRNefXZ0oOLK5Cfw03uomFiEgS7F8+OCp0fuKk2eWQu5f36JMuxMmFrYnrppZewdu1a5Ofno7S01M5LKQe7F8+O7J0fImMx7KdenDSydn7oDI3gv+NnaG1u4v0oA7Ympkgkgs9//vP4oz/6IzsvoxzsXpwc0uvFl6gXp4KsnR/2xA/ovLu+FFXFuYKjIQBgazH1m9/8JgDgtddes/MyykG9ODlkb0nUfJJ6cSrIWsrTy+pb2BJMGqRa5QuHwwiHw8bnoVBIYDT2Qb04OWTWxakXp46MiWkoMoZD57oBcJ1QJqSSH3bt2oWSkhLjo76+XnRIlkO9OHlk1sVbb/Tjyk3qxakgoy5+6Gw3wmMx1JflYVl1kehwSJyUE9OLL74In88348fRo0fTCmbnzp3o6+szPtrb29P6PjLD7sXJI7Murpd/HqJenDQyjqd51stN7vKQ8h31zDPP4Mknn5zxaxYsWJBWMMFgEMFgMK2/qwrsXpw8MuvizXFNfDPLeEmTkB/kGM9oTMOe+Diy+a5cpJyYKioqUFHB0kU6sHtxasiqi98w6cU8Qyt5ZNPFj7ffQs9gBEW5Wbh3ITe5y4StNYi2tjb09vaira0N0WgUx48fBwAsXrwYhYWFdl5aSt6Pdy8uL6BenAwyln4AGG/Z1ItTQ7bOD3oZb+OyKmQHpFpu9zy2Jqbnn38er7/+uvH5PffcAwDYt28fNmzYYOelpYR6cWr4JT32Qn+gbWU5NiVkG0+9rL6Zs17psPU14bXXXoOmabd9eDEpTdCL+UBLChlLeRP0YpZjU0ImXfxS9yDOdg4gy+/DBm5ylw7OXx3CrBevo16cFDIerX7wbDcicb14abX3ytGZoL9oaNr4i5pI9JfE+xeVoSQvW2gs5HaYmByCenHqyNj5wbAqqRenjN/08xI9ps0nuTlaZpiYHIJ6cerIpotHYxr2nqZenC5+vzkxiRvTm4MRHL18EwATk6wwMTlAJ/XitJBtjel4+030DEZQTL04Lcy+j8iXjf1nOhGNaWiqKUJ9Wb6wOMj0MDE5gN69+JPUi1NCNl28+eT4OG5sol6cDmYTVeSYtsTHkS3B5IV3lwO08BCytJBOL2bT1owwrzGJGtPwWBQHznQB4DjKDBOTzVAvTh+ZSnmXugdxLq4XP7ysUnQ4SmJ2RUSN6XsXejEQHkNVURB3zS0REgOZHSYmmzF3L6ZenBoy6eL6bOmBReUozqVenA4BU2bSYmJi0Mdx8/LqCTIGkQsmJpth9+L08Umkiyf0Ysor6SK6lKdpmqmsznGUGSYmG2H34syQpZRn1oup+6ePaF385LUQOvpGkJcdwNpGbnKXGSYmG9H1YnYvTg9ZSnn7WqkXW4XxsiFgTHUb76ElFcjNDjh+fZI8TEw2YujF7F6cFrJ0ftDLsbQqM0fkmHIc1YFPSxth09bMkEEXD49FcaCVerFV+AUdFnitbxgnrvbB5xvv7k/khonJJi6a9eKl1IvTwR//7RTZ8PPwhV4MRqLUiy1CL+U53fmhJb7Wu7JhDioK3X1KthtgYrKJPSa9mN2L08OYMQms5SXO7KFebAUBQd08Wti0VSmYmGyCenHmiF5jMp+hRb3YGkSUZwfCY3j3fA8AjqMqMDHZAPViaxCti3/cEcI16sWWImKN6eCZLkSiMSwoz0djJTe5qwATkw2we7E1iNbF9dnSOurFliFCF2/mJnflYGKyAXYvtgbRpTzqxdbj9JiORWPYF+/uTztWHZiYLCY8FsX+1viNwDJeRhgHBQoo5V3rG8ZHV0PUiy3G6VLeh223cHNoFKX52Vg9f44j1ySZw8RkMdSLrUMv+4jQxXW9eFXDHJRTL7YMp3Vxfda7aVkVsrjJXRk4UhZDvdg6hHYJOMnN0XbgtC5uvh+JOjAxWQj1YmsRtY/JrBezHGstPgd18fNdA7jQPYicgJ9naCkGE5OFUC+2FvOE08ly3ttxvXhhRQEaKwscu64X0Lt5OLHGpM+WHmgsR2Ewy/brEetgYrIQfba0fin1YisImDKTk7OmFtPmaOrF1pIo5TmQmPTqBTe5KwcTk4WYDwUkmWNOCk7qxXtpVdpGojxr73V6BsL4gJvclYWJySKoF1uPuZTnlF78weWbuBXXi1dRL7Ycp3Txfa1diGnAHXXFqCvNs/VaxHqYmCyCerH1BASceEq92F6c6vzQfPI6AM56VYV3nkVQL7Yev8OlPE3TEs13OY624MQWgJHRKN4+0w2AXTtUhYnJAqgX24M5MTkhP5zvGsSlniHkBPxYzzO0bMGJ7uLvnu/B8GgUNcW5uKOu2LbrEPtgYrIA6sX24LQurpfxqBfbhxO6uNG0dQWtSlVhYrIA6sX24LQuro8j9WL7sFsXj8U045BOVi/UhYkpQ8x68ZYVNYKjcRdO6uI9A2F80Ea92G58NuviH3X04UYojPycANY0lttzEWI7TEwZouvFc/KzsbKhVHQ4rsOpRq57T3dC04A751IvtpOAzbq4Put9eGklglnc5K4qTEwZoq9LbGyiXmwHAYeOvuDmaGewWxdvPsXN0W6AT9IMGG/aGi/j8UawBZ/DejEfaPZi53i29w7h1LUQ/NzkrjxMTBlwvmsQF+Pdi9dRL7YFfbHczg2Zul5cW0K92G6M8bRhBqxLD6sXlGFOQY7l3584BxNTBujlnzXUi23DKP04oRcvr6ZVaTN26uKsXrgHJqYMYLcH+7G7U8AEvZjjaDt+m2ZMoZFRHL4Q3+TOcVQeJqY06TbpxY9w34tt6E0/7drHdOLquF5ckBPAA4vKbLkGSWBXd/EDrV0Yi2lorCzAwgpuclcdJqY0MevFtSXUi+3Cbl1cL8c+vIx6sRPYpYu3cNbrKpiY0iTR7YE3gp3YrYs3cxwdxQ5dfDQaw77TXF9yE0xMaTAyGsXBs9SLncDQi23oFNDeO4TT1/vh9wEbl7Ec6wR26OJHLvYiNDKGsoIc3NPAM7TcABNTGrxzvpt6sUPYaeVRL3YeO3Rx3arcuKxqQn9Foi5MTGnQfDKxu5x6sb3Yue+FerHzWK2Lj29yjzff5fqSa2BiShHqxc5iV6cA6sVi8Fu8YfrMjQG09w4jJ8uPdUsqLPmeRDxMTCly4mofOvupFztFwCZdnHqxGBIHBVrz/fTZ0oON5SjgJnfXwMSUIrrFtZ7dix3BLl2cerEYrB7PZm5ydyW2JaZLly7hi1/8IhYuXIi8vDw0NjbihRdeQCQSseuSjsB6trPYscGWerE4/BbuY+rsH8Hx9lsAaMe6DdvmvqdPn0YsFsMPfvADLF68GB999BG+/OUvY3BwEC+//LJdl7UV6sXOY0dLoiOXxvXicurFjmNl54e9cXnl7nklqC7OzfwbEmmwLTE9+uijePTRR43PFy1ahNbWVuzevVvZxNRCvdhx7CjltcStyk1N1IudxkrLkmdouRdHVwv7+vpQVja9MBAOhxEOh43PQ6GQE2EljVHG443gGInFcuv04uZT1wHwCHURGLp4hlPg4YhpkzvL6q7DMfnh/Pnz+Lu/+zs8/fTT037Nrl27UFJSYnzU19c7Fd6s9A2P4r0LvQB4IziJ1aW8s50JvXj9UurFTmOV/n/oXDfCYzHMLc1DU02RBZERmUg5Mb344ovw+Xwzfhw9enTC3+no6MCjjz6Kz3/+8/jSl7407ffeuXMn+vr6jI/29vbU/49s4sCZcb14cVUh9WIHMZp+WpSZdIvrocUVyM+hXuw0AYtmwHqvyi0ruMndjaR8Zz7zzDN48sknZ/yaBQsWGP/e0dGBjRs3Ys2aNXj11Vdn/HvBYBDBYDDVkByBTVvFYHVLIjZtFYsVa4axmIY9pxPdV4j7SDkxVVRUoKIiuRLI1atXsXHjRqxatQo//OEP4feruW1qNBrDvta4XryCNp6T+HzW6eJmvXgzz9ASghW6+PErt9A9EEZRMAv3LeQmdzdiWy2jo6MDGzZsQENDA15++WV0dXUZ/62mpsauy9rCkYu96I/rxZ+sp17sJInzezL/XtSLxWOFLq5XLx5eVomcLDVfdsnM2JaYfv3rX+PcuXM4d+4c5s2bN+G/2XXom13o3YupFzuPlbo49WLx6PdPJuPJTe7ux7bXjS984QvQNG3KD5Uwdy+mjec8Vuni1IvlQPcU0i3NXu4ZxJkbA8jy+7BhKcuxboXz4FnQuxcH2b1YCFbp4gfPdlEvloBMx1M/quS+hWUoyc+2KiwiGUxMs6DPlqgXi8EqXdxc/qFeLI5MOz80nxzfHM1yrLthYpoFdi8Wi88CXTwW07CXerEUZKL/3xqK4MilmwA4jm6HiWkGJujFTaxni8CKUt6x9lvoHohQL5aATHTx/a1diMY0LKsuQkN5vtWhEYlgYpqBPbpeXF+KKurFQrCilKeX8agXiycTXbzZkJD4kuh2eJfOgNH2hJsxhWFF5wdz+xoilnT1/8hYDAdax/dCsoznfpiYpmEoMoZD56gXiyZTXfxS9yDOdlIvloV0D35872IPBsJjqCwK4u55pTZERmSCiWkaDp0d7148b04ellVTLxZF5nrx+GyJerEcpDue+qx3c1OVkdyIe2FimgZzlwDqxeLQ2yumuzGb3R7kQtfFUxnP8U3ueq9KjqMXYGKagmhMM8QH3ghi8WfQxJV6sXwYnR9SSEynrvXj6q1h5Gb78eBibnL3AkxMU3C8/RZ6BiMoyqVeLJpMSnnUi+Ujnaa8+qx33ZJK5GYH7AiLSAYT0xToN8KGZVXIDvBHJJJMdHHqxfJhvGikMJ5G1w7Oej0Dn7pTQL1YHtLt/EC9WE5S1f+v943gt1f64PMBG7nJ3TMwMU3CrBc/vLRSdDieJ11dXNeLKwqpF8tEqp0f9NnSPfWlqCyS83RrYj1MTJPQb4T7F5WhJI96sWgSFldqf6/FOEKderFMpNr5gUfOeBMmpklQL5YLXRdPZU3CrBdv5jhKRSq6+GB4DO+c6wHA9SWvwcRkgnqxfKRTyjPrxQ9RL5aKVHTxg2e7EInGML88H4urCm2OjMgEE5MJXS9uqilCfRn1YhlIRxc368V5OdSLZSKV8Ww+mTiqhJvcvQUTk4lmlvGkIx1dvPkk9WJZSXY8ozENe0/H2xCxibLnYGKKM0Ev5kKrNKSqi1/rG8aJq9SLZSXZ8fyw7SZuDo2iJC8b9y7gJnevwcQUx9y9+BNzS0SHQ+KkWsrTW0lRL5aTQJK6uG5VblxWyU3uHoQjHod6sZwk+yDToV4sN4nODzN/nV5W37Kixu6QiIQwMWGSXtzEB5pMGKWfJKZM1IvlJzEDnn48z3cN4ELXILIDPqxfSqvSizAxYZJevIQ3gkwEUtDFqRfLjz8JXXxPfLb0wKJyFOVyk7sXYWICuxfLjD+Fzg/Ui+UnmTXDZvaq9DxMTOCNIDPGG3YSevG+Vr3bA208WdHXDKfr/NAzEMYHl8c3ubNrh3fxfGIy68WbqBdLR7JNPz9su4newQhK8rJxH/ViafHN8qKxr7ULMQ1YUVuMuaV5DkZGZMLziUnXi1c2zEFFIfVi2UhWF9etyk1NVciiXiwtsx0UaNixrF54Gs/fwWzaKjfJdgpg1w41mOmgwJHRKN4+O77JnValt/F0YpqgF/OUUylJplMA9WJ1mGk8373Qg6FIFDXFubhzbrHDkRGZ8HRi0vXiBeX5aKykXiwjyeji1IvVYabxTJTxqmhVehxPJybqxfKTjC7eEh9HWpXy4/dPPZ7jm9xZjiXjeDYxmbsXc6FVXmYr5fUORnD0ci8A6sUqMF3nh4+uhnAjFEZBTgBrGstFhEYkwrOJydy9ePX8OaLDIdOgyw/T6cV7T3dSL1aI6fal6fLK+qWVCGZxk7vX8Wxiol6sBrOV8qgXq8V049l8kmU8ksCzT2TqxWrgn2HGRL1YPaaaAV+5OYRT10Lw8wwtEseTiYl6sTr4qRe7iqnWDPVN7qvnl6GsIEdEWEQyPJmY9PLPmsYK6sWSM1PnB30cNy+nXqwKU3V+SJyhxdkSGcebiUk/hIzNPqUnMI3FZdaLqYmrw2QrLzQyisMXxje5s6xOdDyXmNi9WC2m08WpF6vJ5MT09pkujEY1LKoswCJucidxPJeY9O7Fd9QVo456sfRMp4tTL1aTybp4C208MgWeS0y8EdRiOr2Y46gm5vEcjcaw9zS7dpDb8VRimqAX80ZQgqnO77lycwgnqRcriXkGfPTSTYRGxjAnPxsrG7jJnSTwVGJ693xCL76jjnqxCgSmOCiQerG6mNcMdXllU1O1Mc6EAB5LTPq6BPVidZiqlEe9WF3MLxoJq5LjSCbimcQUi2nG8Qgs46mDf9IxCdSL1UYfz9Gohss9Q8jJ8mPdkkrBURHZ8Exi+qijj3qxgkzu/EC9WG0mFyoebCxHQTBLTDBEWjyTmHSLi3qxWkw+Wl0fR/bGU5PApMzE5rtkKjyTmJpPJQ4FJOpgbklk1ov5QFMT/6TEtLmJ40hux9bE9KlPfQoNDQ3Izc1FbW0tnnrqKXR0dNh5ySlh92J1MVtcul5cVpBDvVhR/Cb77hPzSlBTkiswGiIrtiamjRs34l//9V/R2tqKn/70pzh//jw+97nP2XnJKaFerC7mfS8JvbiKerGimIeN1QsyHbauOv7xH/+x8e/z58/H17/+dTz++OMYHR1FdrZzXb2pF6uLubdaC8/QUp4sf+JdmONIpsMxHaa3txc/+tGPsHbt2mmTUjgcRjgcNj4PhUIZX5d6sdroiamtdwgjo7G4XswztFQlLyeA37uvAQCwvLZIcDREVmyXH/7iL/4CBQUFKC8vR1tbG37+859P+7W7du1CSUmJ8VFfX5/x9XW9uJF6sZLopZ+R0RgA6sVuYNdn7sKuz9zFTe5kWlJOTC+++CJ8Pt+MH0ePHjW+/s/+7M9w7Ngx/PrXv0YgEMAf/MEfQJviNFIA2LlzJ/r6+oyP9vb29P/P4hjNPmlxKYnfT72YEK+R8qvnM888gyeffHLGr1mwYIHx7xUVFaioqMDSpUuxfPly1NfX4/Dhw1izZs1tfy8YDCIYDKYa0rRM6F7MMp6SUC8mxHuknJj0RJMO+kzJvI5kJ2NRDf9r8xIcvtCLe6gXK4l5wkS9mBBvYFux/v3338f777+Phx56CHPmzMGFCxfw/PPPo7GxccrZkh3k5QTwpXWL8KV1ixy5HrEesxZOeYUQb2BbYsrLy8O///u/44UXXsDg4CBqa2vx6KOP4ic/+UnS5Tp9hmWFnUfUZGigH7HwEADggXl5/F0gRFH0e3c6x8CMT0vmqwRx5coVS8w8QgghctDe3o558+bN+DVSJ6ZYLIaOjg4UFRWlrJaGQiHU19ejvb0dxcU8FNBO+LN2Dv6snYE/Z+vRNA39/f2oq6uD3z+zEC71hhC/3z9rZp2N4uJi/mI5BH/WzsGftTPw52wtJSUlSX2dZ7qLE0IIUQMmJkIIIVLh2sQUDAbxwgsvWLphl0wNf9bOwZ+1M/DnLBap5QdCCCHew7UzJkIIIWrCxEQIIUQqmJgIIYRIBRMTIYQQqXBtYvr+97+PhQsXIjc3F6tWrcLBgwdFh+Q6pjqbq6amRnRYyvP222/jscceQ11dHXw+H372s59N+O+apuHFF19EXV0d8vLysGHDBnz88cdiglWc2X7WX/jCF277HX/ggQfEBOshXJmY3njjDTz77LP4xje+gWPHjmHdunXYtm0b2traRIfmOu644w5cu3bN+Dhx4oTokJRncHAQd999N1555ZUp//tf//Vf47vf/S5eeeUVHDlyBDU1NdiyZQv6+/sdjlR9ZvtZA8Cjjz464Xf8l7/8pYMRehTNhdx3333a008/PeHPmpqatK9//euCInInL7zwgnb33XeLDsPVANDefPNN4/NYLKbV1NRo3/nOd4w/GxkZ0UpKSrR/+Id/EBChe5j8s9Y0Tdu+fbv26U9/Wkg8XsZ1M6ZIJIIPPvgAW7dunfDnW7duxTvvvCMoKvdy9uxZ1NXVYeHChXjyySdx4cIF0SG5mosXL+L69esTfr+DwSAefvhh/n7bxP79+1FVVYWlS5fiy1/+Mjo7O0WH5Hpcl5i6u7sRjUZRXT3xULnq6mpcv35dUFTu5P7778c///M/41e/+hX+8R//EdevX8fatWvR09MjOjTXov8O8/fbGbZt24Yf/ehH2Lt3L/7mb/4GR44cwaZNmxw7hdurSN1dPBMmH5OhaVrKR2eQmdm2bZvx73fddRfWrFmDxsZGvP7669ixY4fAyNwPf7+d4YknnjD+/c4778Tq1asxf/58/Nd//Rc+85nPCIzM3bhuxlRRUYFAIHDb22NnZ+dtb5nEWgoKCnDXXXfh7NmzokNxLbr1yN9vMdTW1mL+/Pn8HbcZ1yWmnJwcrFq1Cs3NzRP+vLm5GWvXrhUUlTcIh8M4deoUamtrRYfiWhYuXIiampoJv9+RSAQHDhzg77cD9PT0oL29nb/jNuPKUt6OHTvw1FNPYfXq1VizZg1effVVtLW14emnnxYdmqv40z/9Uzz22GNoaGhAZ2cn/vIv/xKhUAjbt28XHZrSDAwM4Ny5c8bnFy9exPHjx1FWVoaGhgY8++yz+Pa3v40lS5ZgyZIl+Pa3v438/Hz8/u//vsCo1WSmn3VZWRlefPFFfPazn0VtbS0uXbqE5557DhUVFfjd3/1dgVF7ANFaoF38/d//vTZ//nwtJydHW7lypXbgwAHRIbmOJ554QqutrdWys7O1uro67TOf+Yz28ccfiw5Lefbt26cBuO1j+/btmqaNK+MvvPCCVlNTowWDQW39+vXaiRMnxAatKDP9rIeGhrStW7dqlZWVWnZ2ttbQ0KBt375da2trEx226+GxF4QQQqTCdWtMhBBC1IaJiRBCiFQwMRFCCJEKJiZCCCFSwcRECCFEKpiYCCGESAUTEyGEEKlgYiKEECIVTEyEEEKkgomJEEKIVDAxEUIIkQomJkIIIVLx/wF5PK4rTGdpxAAAAABJRU5ErkJggg==",
"text/plain": [
"<fipy.viewers.matplotlibViewer.matplotlib1DViewer.Matplotlib1DViewer at 0x29a9e7c50>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 480x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"viewer = fp.Viewer(vars=theta)\n",
"viewer.plot()"
]
},
{
"cell_type": "markdown",
"id": "837b8e01-e3b2-4011-b8be-7e95aa8a9af2",
"metadata": {},
"source": [
"#### Modular vs. Non-Modular Gradient\n",
"\n",
"Because $\\theta$ maps to the circle, (neglecting the boundaries) the slope should uniformly equal one, but there are discontinuities at the branch cut, depending on how the gradient is evaluated.\n",
"\n",
"([FiPy can't plot 1D `FaceVariables`](https://github.com/usnistgov/fipy/issues/133), so use matplotlib directly)"
]
},
{
"cell_type": "code",
"execution_count": 84,
"id": "48a10da5-e48e-41bc-a1d4-afce4ef7cf43",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x29d2d0fd0>"
]
},
"execution_count": 84,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(mesh.faceCenters[0], theta.faceGrad[0], label=\"$\\mathtt{theta.faceGrad}$\")\n",
"plt.plot(mesh.faceCenters[0], theta.faceGradNoMod[0], label=\"$\\mathtt{theta.faceGradNoMod}$\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"id": "43488d3c-90eb-411f-9833-0bc9322f520a",
"metadata": {},
"source": [
"#### Modular vs. Non-Modular Curvature\n",
"\n",
"The curvature $\\nabla^2 \\theta$ should uniformly equal zero, but there are discontinuities at the branch cut, depending on how the gradient is evaluated."
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "925b5401-455b-49d7-81c3-75ad6acce122",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<fipy.viewers.matplotlibViewer.matplotlib1DViewer.Matplotlib1DViewer at 0x29c22afd0>"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 480x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fp.Viewer(vars=theta.faceGrad.divergence)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "b1aef6c4-edb3-4757-bd28-c1b7e6369e8c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<fipy.viewers.matplotlibViewer.matplotlib1DViewer.Matplotlib1DViewer at 0x29c22a4d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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",
"text/plain": [
"<Figure size 480x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fp.Viewer(vars=theta.faceGradNoMod.divergence).plot()"
]
},
{
"cell_type": "markdown",
"id": "163ce0e6-3912-41b0-a86f-f8ecb563e848",
"metadata": {},
"source": [
"These discontinuities in curvature lead to substantial artificial diffusion if not accounted for."
]
},
{
"cell_type": "markdown",
"id": "53e6a9df-a280-4ddd-a519-1d23a2a9f2f4",
"metadata": {},
"source": [
"### Simplified orientation evolution equation"
]
},
{
"cell_type": "markdown",
"id": "a309858e-0550-44a1-9235-d772820fb9a8",
"metadata": {},
"source": [
"Consider a simplified set of equations\n",
"\\begin{align}\n",
"\\frac{\\partial\\theta}{\\partial t} &= \\nabla\\cdot\\left(\\phi\\nabla\\theta\\right)\n",
"\\\\\n",
"\\frac{\\partial\\phi}{\\partial t} &= 0\n",
"\\end{align}"
]
},
{
"cell_type": "markdown",
"id": "08ad479e-3c87-4eba-8858-2c8162efb4c9",
"metadata": {},
"source": [
"#### Naive orientation evolution equation"
]
},
{
"cell_type": "markdown",
"id": "bb2016ff-a63f-44b1-8535-72658e2cac05",
"metadata": {},
"source": [
"A naive implementation in FiPy is"
]
},
{
"cell_type": "code",
"execution_count": 70,
"id": "fb9e0e95-9ba4-4008-8648-eb0b8fcc46f8",
"metadata": {},
"outputs": [],
"source": [
"phi = fp.CellVariable(mesh=mesh, name=r\"$\\phi$\")\n",
"\n",
"theta_eq1 = fp.TransientTerm(var=theta) == fp.DiffusionTerm(coeff=phi, var=theta)\n",
"phi_eq1 = fp.TransientTerm(var=phi) == 0\n",
"\n",
"eq1 = theta_eq1 & phi_eq1"
]
},
{
"cell_type": "code",
"execution_count": 76,
"id": "f5ed034d-7877-4b97-b4eb-fd2c47fdb00e",
"metadata": {},
"outputs": [],
"source": [
"theta.value = fp.numerix.mod(mesh.x, 2 * fp.numerix.pi) - fp.numerix.pi\n",
"phi.value = 1\n",
"eq1.solve(dt=1.)"
]
},
{
"cell_type": "markdown",
"id": "1cd17ab7-e566-40fc-a9f6-c134cf413e91",
"metadata": {},
"source": [
"We observe undesirable smoothing of the orientation due to artificial diffusion at the branch cut."
]
},
{
"cell_type": "code",
"execution_count": 77,
"id": "4ba6220a-92e8-4c5a-b98d-d3fd427e9192",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<fipy.viewers.matplotlibViewer.matplotlib1DViewer.Matplotlib1DViewer at 0x29cda35d0>"
]
},
"execution_count": 77,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 480x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fp.Viewer(vars=(theta, phi))"
]
},
{
"cell_type": "markdown",
"id": "3bfdb177-c22b-4c05-a9b1-daec6463b3fb",
"metadata": {},
"source": [
"#### Orientation evolution equation with branch-cut correction"
]
},
{
"cell_type": "markdown",
"id": "32844d6c-5dfc-4761-832e-b456624a5486",
"metadata": {},
"source": [
"If we apply the $\\nabla_\\mathrm{mod}\\theta-\\nabla_\\mathrm{\\cancel{mod}}\\theta$ correction from above"
]
},
{
"cell_type": "code",
"execution_count": 73,
"id": "da8656b1-3f1d-48ba-90c1-63a1ed57c5e4",
"metadata": {},
"outputs": [],
"source": [
"theta_eq2 = (fp.TransientTerm(var=theta)\n",
" == fp.DiffusionTerm(coeff=phi, var=theta)\n",
" + fp.PowerLawConvectionTerm(coeff=(theta.faceGrad - theta.faceGradNoMod), var=phi))\n",
"phi_eq2 = fp.TransientTerm(var=phi) == 0\n",
"\n",
"eq2 = theta_eq2 & phi_eq2"
]
},
{
"cell_type": "code",
"execution_count": 87,
"id": "555d51c7-4159-4d07-9aa9-cdcced74f331",
"metadata": {},
"outputs": [],
"source": [
"theta.value = fp.numerix.mod(mesh.x, 2 * fp.numerix.pi) - fp.numerix.pi\n",
"phi.value = 1\n",
"eq2.solve(dt=1.)"
]
},
{
"cell_type": "markdown",
"id": "e16481a0-18c7-433d-80da-4c7504fbb8bc",
"metadata": {},
"source": [
"We see that we preserve the profile of theta, representing a smooth gradient with zero curvature at the branch cut."
]
},
{
"cell_type": "code",
"execution_count": 88,
"id": "f5c67c06-0730-441d-a60a-33c199c3c263",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<fipy.viewers.matplotlibViewer.matplotlib1DViewer.Matplotlib1DViewer at 0x29d22cad0>"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 480x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fp.Viewer(vars=(theta, phi))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ae11d261-1573-49af-82de-4607738566fb",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.11.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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