anisotropy/playground/geometry.ipynb

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    "# Geometry parameters\n",
    "\n",
    "## Simple structure\n",
    "\n",
    "$$ \\theta \\in \\left[ 0.01, 0.28 \\right] $$\n",
    "$$ r_0 = 1 $$\n",
    "$$ L = 2 r_0 $$\n",
    "$$ r = \\frac{r_0}{1 - \\theta} $$\n",
    "$$ r_{fillet} = r_0 \\left (\\sqrt{2} - \\frac{1}{1 - \\theta} \\right) $$\n",
    "\n",
    "## Face centered structure\n",
    "\n",
    "$$ \\theta \\in \\left[ 0.01, 0.13 \\right] $$\n",
    "$$ r_0 = 1 $$\n",
    "$$ L = \\frac{4 r_0}{\\sqrt{2}} $$\n",
    "$$ r = \\frac{r_0}{1 - \\theta} $$\n",
    "$$ r_{fillet} = r_0 \\left( \\frac{2 \\sqrt{3}}{3} - \\frac{1}{1 - \\theta} \\right) $$\n",
    "\n",
    "## Body centered structure\n",
    "\n",
    "$$ \\theta \\in \\left[ 0.01, 0.18 \\right] $$\n",
    "$$ r_0 = 1 $$\n",
    "$$ L = \\frac{4 r_0}{\\sqrt{3}} $$\n",
    "$$ r = \\frac{r_0}{1 - \\theta} $$\n",
    "$$ r_{fillet} = r_0 \\left( \\frac{\\sqrt{2}}{\\sqrt{1 - \\cos \\left(\\pi - 2 \\arccos \\left(\\sqrt{\\frac{2}{3}} \\right) \\right)}} - \n",
    "            \\frac{1}{1 - \\theta} \\right) $$\n"
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