{
 "metadata": {
  "name": "",
  "signature": "sha256:50b58a1c001d30f1fe3964195e39b95972186d5bbab1f692ffbd55d9d44715db"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "from IPython.display import display, Image\n",
      "from IPython.display import display_pretty, display_html, display_jpeg, display_png, display_json, display_latex, display_svg\n",
      "from IPython.display import Latex\n",
      "Image(filename='logo3.jpg', width=100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "jpeg": 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5aWiFY8t8DfAb4b+FIEij0K21ZlziXU7S3nfq3fyx/ex+A9K9ItbK1tIvKsrSC2UdFjjC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       "metadata": {
        "jpeg": {
         "width": 100
        }
       },
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<IPython.core.display.Image at 0x7fc80293e710>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href = https://by2pie.wordpress.com/>Visit our website </a>or<a href = https://www.facebook.com/pages/By2Pie/558372994265146> Fanpage!</a>\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href = http://nbviewer.ipython.org/github/by2pie/Fluid-dynamics/blob/master/2.1%20Derivation%20of%20Navier%20-%20Stokes%20equations.ipynb>Project 2.1: Derivation of incompressible Navier - Stokes equations</a><br>\n",
      "<a href = http://nbviewer.ipython.org/github/by2pie/Fluid-dynamics/blob/master/2.2%20Time%20discretization%20of%20Navier-Stokes%20Equations%20in%202D.ipynb>Project 2.2: Time discretization of Navier-Stokes Equations in 2D </a><br>\n",
      "<a href = http://nbviewer.ipython.org/github/by2pie/Fluid-dynamics/blob/master/2.3%20Space%20discratization%20and%20update%20equations.ipynb>Project 2.3: Space discratization and update equations  </a><br>\n",
      "<a href = http://nbviewer.ipython.org/github/by2pie/Fluid-dynamics/blob/master/2.4%20Boundary%20condition%2C%20linear%20equation%20and%20visualization%20of%20N-S%20equations.ipynb>Project 2.4: Project 2.4: Boundary condition, linear equation and visualization of N-S equations</a><br>\n",
      "<a href =http://nbviewer.ipython.org/github/by2pie/Fluid-dynamics/blob/master/Untitled0.ipynb>Project 2.5: Full Code</a><br>\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Project 2.1: Derivation of incompressible Navier - Stokes equations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In following notebook I'm going to derive incompressible version of Navier-Stokes equations governing motion of a fluid. Derivation is first step in our journey to numerical solution and computational simulation of fluid flow. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "1. Mass conservation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We should begin with very fundamental law, namely conservation of mass. It is quite obvious mass of fluid is defined as sum over control volumes multiplied by density."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "\\begin{equation} \n",
      "M = \\int \\rho dV \\quad (1.0)\n",
      "\\end{equation}\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Differentiating both sides with respect to time will result in"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\frac{dM}{dt} = \\int \\frac {d\\rho}{dt} dV     \\quad(1.1)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "We can understand the change of density is equivalent to a flux through enclosed surface:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id ='1.2'></a>\n",
      "\\begin{equation*}\n",
      "\\int \\frac{d\\rho}{dt} dV = \\int \\rho  \\vec{v} \\cdot d\\vec{S}  \\quad(1.2)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Applying divergence theorem yells: "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\int \\frac{d\\rho}{dt} dV = - \\int \\nabla \\cdot (\\rho  \\vec{v}) \\, dV  \\quad(1.3)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Thus:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id ='1.4'></a>\n",
      "\\begin{equation*}\n",
      "\\frac{d\\rho}{dt} + \\nabla \\cdot (\\rho  \\vec{v}) = 0 \\quad(1.4)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "2. Momentum conservation:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we should take into consideration the conservation of momentum, undesrtood as a $\\rho \\vec{v}$. We should start with defining momentum flowing in $i^{th}$ direction:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "    \\pi_i = \\int \\rho \\, v_i \\, dV \\quad(2.1)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One more time we use time derivative:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "    \\frac{d \\pi_i}{dt} = \\int \\frac {d(\\rho \\, v_i)}{dt} dV  \\quad(2.2)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Similarly as in [1.2](#1.2) we use an idea of flow through closed surface:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\int \\frac {d(\\rho \\, v_i)}{dt} dV = \\int (\\rho \\, v_i) \\, v_j \\cdot dS_j \\quad(2.3)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using divergence theorem gives us:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\int \\frac {d(\\rho \\, v_i)}{dt} dV = - \\int \\nabla_j  (\\rho \\, v_i \\, v_j) \\, dV \\quad(2.4)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Thus:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\frac {d(\\rho \\, v_i)}{dt} + \\nabla_j (\\rho \\, v_i \\, v_j) = 0 \\quad(2.5)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The time has come to expand derivatives:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "v_i \\frac {d\\rho}{dt} + \\rho \\frac {dv_i}{dt} + v_i \\nabla_j \\cdot (\\rho \\, v_j) + v_i \\nabla_j  (\\rho \\, v_j) +\n",
      "\\rho \\, v_j \\nabla_j  v_i= 0  \\quad(10)  \\quad(2.6)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Suddenly the conservation of mass [1.4](#1.4) should erect:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "v_i \\overbrace{\\bigg( \\frac {d\\rho}{dt} + \\nabla_j \\cdot (\\rho \\, v_j) \\bigg)}^\\text{mass conservation (1.4)} + \\rho \\frac {dv_i}{dt} +\n",
      "        \\rho \\, v_j \\nabla_j  v_i= 0 \\quad(11)  \\quad(2.7)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally we can simplify formula above by introducing something called material derrivative $\\frac {D}{Dt}$:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "0 + \\rho \\, (\\frac {\\partial}{\\partial t} +\n",
      "    \\, v_j \\nabla_j) \\,  v_i = \\rho \\frac {D \\, v_i}{D \\, t} = 0 \\quad(2.8)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "3. Stress tensor and cauchy momentum equation:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally we should investigate non-relativistic momentum transport. I would like to briefly cover this topic, however if you are interested in farther investigation Wikipedia has some complex information:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import HTML\n",
      "HTML('<iframe src=http://en.wikipedia.org/wiki/Cauchy_momentum_equation?useformat=mobile width=900 height=300></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://en.wikipedia.org/wiki/Cauchy_momentum_equation?useformat=mobile width=900 height=300></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<IPython.core.display.HTML at 0x7fb844232978>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The most important for us part can be summarize in following equation, which is generalization of second law of newton for continuous flow. LHS represent the result of exerted force which is the change of momentum, and RHS its cause, namely stress $\\int_\\omega \\nabla_j \\sigma_{ij} dV$ and external force $ \\int_\\omega \\rho f_i dV$ summed over all control volumes."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "    \\frac {d \\pi_i}{dt} = F_i  \\quad(3.1)\n",
      "\\end{equation*}\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\int \\rho \\frac {D \\, v_i}{D \\, t} dV = \\int_\\omega \\nabla_j \\sigma_{ij} dV + \\int_\\omega \\rho f_i dV \\quad(3.2)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\int \\rho \\frac {D \\, v_i}{D \\, t} dV - \\int_\\omega \\nabla_j \\sigma_{ij} dV - \\int_\\omega \\rho f_i dV = 0 \\quad(3.3)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id ='3.4'></a>\n",
      "\\begin{equation*}\n",
      "\\rho \\frac {D \\, v_i}{D \\, t}  - \\nabla_j \\sigma_{ij}  -\\rho f_i = 0 \\quad(3.4)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Where $\\sigma_{ij}$ is a cauchy stress tensor, which has following significance and form:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "Image(filename='stressedTensor.png', width=400)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": 400
        }
       },
       "output_type": "pyout",
       "png": 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GYD6AbAA31bPFDNNisGCFYZqgLSl32AG69zweaiBAF6rQHeNSV9zj94a1YipBRd4KQTcf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\nyjkiySRPeDvDlGeWm9RQSz8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tFHT+pjlTn2yY1jIuLFhhajIZwG0AjkPrLr0GwDfQZgPV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\nicLNnVKSJHWoOcDLFO8ceoeYKhmK7iSmfmqdTdzX3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       "prompt_number": 7,
       "text": [
        "<IPython.core.display.Image at 0x7fb84422dc18>"
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\sigma_{ij} = \n",
      "\\begin{bmatrix} \n",
      "\\sigma_{11} & \\tau_{12} & \\tau_{13} \\\\ \n",
      "\\tau_{21} & \\sigma_{22} & \\tau_{23} \\\\\n",
      "\\tau_{31} & \\tau_{32} & \\sigma_{33} \n",
      "\\end{bmatrix} = \n",
      "\\begin{bmatrix} \n",
      "P & 0 & 0 \\\\ \n",
      "0 & P & 0 \\\\\n",
      "0 & 0 & P\n",
      "\\end{bmatrix}\n",
      "+\n",
      "\\begin{bmatrix} \n",
      "\\sigma_{11} -P & \\tau_{12} & \\tau_{13} \\\\ \n",
      "\\tau_{21} & \\sigma_{22}-P & \\tau_{23} \\\\\n",
      "\\tau_{31} & \\tau_{32} & \\sigma_{33} - P\n",
      "\\end{bmatrix} = \n",
      "-P {\\bf I} + \\tau_{ij} \\quad(3.5)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Where $P$ is defined as a mean pressure according to the formula:\n",
      "\\begin{equation*}\n",
      "P = -\\frac{1}{3} (\\sigma_{xx} + \\sigma_{yy} + \\sigma_{zz}) \\quad(3.6)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Inserting it into formula [3.4](#3.4) yells our Navier-Stokes equation:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\rho \\frac {D \\, v_i}{D \\, t}  = - \\nabla P + \\nabla \\cdot \\tau  + \\rho f_i  \\quad(3.7)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "4. Stress tensor shape:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For compressible Newtonian fluid the daviatoric stress tensor $\\tau$, which is part of stress tensor responsible for shear stresses, has the following relation:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\tau \\propto \\frac {\\partial v_i}{\\partial x_j} \\quad(4.1)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For incompressible Newtonian fluid, where $\\nabla \\cdot v = 0$, it yells:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\tau_{ij} = \\mu \\bigg( \\frac{\\partial u_i}{\\partial x_j} + \\frac{\\partial u_j}{\\partial x_i} \\bigg) \\quad(4.2)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Where $\\mu$ is proportionality factor called viscosity.\n",
      "We can calculate $\\nabla \\cdot \\tau_{ij}$ for $j = 1$, it would mean for the x component of momentum:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      " \\nabla \\cdot \\tau_{i1}= \\mu \\frac{\\partial}{\\partial x_i} \\bigg(\\frac{\\partial u_i}{\\partial x_1} + \\frac{\\partial u_1}{\\partial x_i} \\bigg) = \\mu \\bigg(\\frac{\\partial^2 v_i}{\\partial x_1 \\partial x_i} + \\frac{\\partial^2 v_1 }{\\partial^2 x_i } \\bigg) = \\mu \\bigg(\\frac{\\partial}{\\partial x_1}\\frac{\\partial v_i}{\\partial x_i} + \\frac{\\partial^2 v_1 }{\\partial^2 x_i } \\bigg) = \\mu \\frac{\\partial^2 v_1 }{\\partial^2 x_i} \\quad(4.3)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since usually the velocity component is defined as $\\vec{v} = (u, v, w)$ and for other component we should expect similar results we might conclude:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " \\begin{equation*}\n",
      "    \\nabla \\cdot \\tau_{ij} = \\mu (\\Delta u + \\Delta v + \\Delta w) = \\mu \\Delta \\vec{v} \\quad(4.4)\n",
      "    \\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally we obtain desired Navier - Stokes equations for inconpressible flow:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id ='4.5'></a>\n",
      "\\begin{equation*}\n",
      "\\rho \\frac {D \\, \\vec{v}}{D \\, t}  = - \\nabla P + \\mu \\Delta \\vec{v}  + \\rho \\vec{f} \\quad(4.5)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "5. Dimensionless form of Navier - Stokes equation:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For computational reasons it is helpful to express N-S equation in dimensionless form and to that end we sould introduce two quantities, characteristic length scale $L$ and characteristic velocity scale $U$. Then our variables change according to following transformation, where variables with tidles are our dimensionless variables:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation*}\n",
      "\\vec{v} = U\u00a0\\vec{\\widetilde{v}}, \\quad t = \\frac {L}{U}\\widetilde{t}, \\quad \\frac {\\partial}{\\partial x} = \\frac{1}{L} \\frac {\\partial}{\\partial \\widetilde{x}}, \\quad P = \\rho U^2 \\widetilde{p}, \\quad \\vec{f} = \\frac {U^2}{L}\\vec{\\widetilde{f}} \\quad \\quad(5.1)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Dropping tildes and substituting equation 5.1 to equation [4.5](#4.5) will result in our final form of Navier - Stokes equation:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id ='5.2'></a>\n",
      "\\begin{equation*}\n",
      "\\frac {D \\, \\vec{v}}{D \\, t}  = - \\nabla P + \\frac {1}{Re} \\Delta \\vec{v}  + \\vec{f} \\quad(5.2)\n",
      "\\end{equation*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Where $Re$ is dimensionless Raynolds number $$Re = \\frac{U L \\rho}{\\mu} $$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "6. What's next?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since we are done with analytical part of the project the times has come to solve equation [5.2](#5.2) numerically in python. If you are looking forward to next notebooks containing proper code visit and follow <a href = http://by2pie.wordpress.com/>by2pie.com </a>:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HTML('<iframe src=http://by2pie.wordpress.com width=900 height=500></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://by2pie.wordpress.com width=900 height=500></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "<IPython.core.display.HTML at 0x7fb844251128>"
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     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "7. References:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[1]<a href = http://fisica.unipv.it/Mihich/FluidiMecc/Navier-Stokes_eqn.pdf>Luigi Mihich, Dipartamento di Fisica Universit\u00e0 degli studi di Pavia<I>Navier-Stokes_eqn.pdf</a><br>\n",
      "[2]<a href = http://en.wikipedia.org/wiki/Derivation_of_the_Navier%E2%80%93Stokes_equations>Many authors, Wikipedia <I>Derivation of the Navier-Stokes equations</a><br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Check other parts:\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2.2 Time discretization of Navier-Stokes Equations in 2D"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {
      "slideshow": {
       "slide_type": "skip"
      }
     },
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      "        },\n",
      "        // Center justify equations in code and markdown cells. Elsewhere\n",
      "        // we use CSS to left justify single line equations in code cells.\n",
      "        displayAlign: 'center',\n",
      "        \"HTML-CSS\": {\n",
      "            styles: {'.MathJax_Display': {\"margin\": 0}},\n",
      "            linebreaks: { automatic: true }\n",
      "        }\n",
      "    });\n",
      "    </script>\n",
      "    <!-- End of mathjax configuration -->\n",
      "{%- endmacro %}"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}