anisotropy/playground/geometry.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c94a76d4-15cb-4628-980e-644c24119b55",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Geometry parameters\n",
    "\n",
    "| Parameter | simple | faceCentered | bodyCentered |\n",
    "| --------- | ------ | ------------ | ------------ |\n",
    "| $\\theta$  | [0.1, 0.28] | [0.1, 0.13] | [0.1, 0.18] |\n",
    "| $r_0$      | 1       | 1              | 1              |\n",
    "| $L$        | $2 r_0$ | $4 r_0 / \\sqrt{2}$ | $4 r_0 / \\sqrt{3}$ |\n",
    "| $r$        | $r_0 / (1 - \\theta)$ | $r_0 / (1 - \\theta)$ | $r_0 / (1 - \\theta)$ |\n",
    "| $r_{fillets}$ | $r_0 (\\sqrt{2} - 1 / (1 - \\theta))$ | $r_0 (2 \\sqrt{3} / 3 - 1 / (1 - \\theta))$ | - |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "60e986af-be50-46ac-b8e6-73e12b0175b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import arange, sqrt\n",
    "\n",
    "thetaMin = 0.01\n",
    "thetaMax = 0.13\n",
    "\n",
    "theta = arange(thetaMin, thetaMax + 0.01, 0.01)\n",
    "\n",
    "r0 = 1\n",
    "L = r0 * 4 / sqrt(2)\n",
    "#L = 1.0\n",
    "#r0 = L * sqrt(2) / 4\n",
    "radius = r0 / (1 - theta)\n",
    "\n",
    "C1, C2 = 0.3, 0.2\n",
    "Cf = C1 + (C2 - C1) / (thetaMax - thetaMin) * (theta - thetaMin)\n",
    "delta = 0.012\n",
    "fillets = (2 * sqrt(3) / 3 - 1 / (1 - theta)) * r0 #Cf * (r0 - radius) #(radius - r0)\n",
    "fillets2 = (sqrt(2) - 1 / (1 - theta)) * r0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "dfa331c2-a2b0-4c81-8113-91ba38c35c42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='theta', ylabel='radius'>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn\n",
    "\n",
    "seaborn.set_style(\"whitegrid\")\n",
    "seaborn.lineplot(\n",
    "    data = {\"theta\": theta, \"radius\": radius}, \n",
    "    x = \"theta\", y = \"radius\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b1ef64d1-ba45-4079-bac6-cbc1468174db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='theta', ylabel='fillets'>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seaborn.lineplot(\n",
    "    data = {\"theta\": theta, \"fillets\": fillets}, \n",
    "    x = \"theta\", y = \"fillets\", legend = \"full\"\n",
    ")\n",
    "seaborn.lineplot(\n",
    "    data = {\"theta\": theta, \"fillets2\": fillets2}, \n",
    "    x = \"theta\", y = \"fillets2\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f587e6da-c921-4533-8077-260f122636da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.14459953, 0.13429238, 0.1237727 , 0.11303387, 0.10206896,\n",
       "        0.09087075, 0.07943172, 0.06774402, 0.05579944, 0.04358943,\n",
       "        0.03110503, 0.0183369 , 0.00527525]),\n",
       " array([0.40411255, 0.3938054 , 0.38328573, 0.3725469 , 0.36158198,\n",
       "        0.35038378, 0.33894475, 0.32725704, 0.31531246, 0.30310245,\n",
       "        0.29061806, 0.27784993, 0.26478828]))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fillets, fillets2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52d9bd9a-b2ed-48aa-8f5c-dd980ea1ff3a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8f04f541-29a8-42cd-99d6-d0d1cd766f7b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}