report-coupled-3Domains_Anthony_May8_8pm.ipynb

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    "**Engy-5050** Reactor Physics, UMass Lowell, Chem. Eng. Nuclear Program Spring 2022; Prof. V. F. de Almeida\n",
    "\n",
    "# 1-D Point Source Neutron Transport\n",
    "$  \n",
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    "  \\newcommand{\\Lmtrx}{\\boldsymbol{\\mathsf{L}}}\n",
    "  \\newcommand{\\Umtrx}{\\boldsymbol{\\mathsf{U}}}\n",
    "  \\newcommand{\\Smtrx}{\\boldsymbol{\\mathsf{S}}}\n",
    "  \\newcommand{\\xvec}{\\boldsymbol{\\mathsf{x}}}\n",
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    "  \\newcommand{\\bvec}{\\boldsymbol{\\mathsf{b}}}\n",
    "  \\newcommand{\\cvec}{\\boldsymbol{\\mathsf{c}}}\n",
    "  \\newcommand{\\rvec}{\\boldsymbol{\\mathsf{r}}}\n",
    "  \\newcommand{\\mvec}{\\boldsymbol{\\mathsf{m}}}\n",
    "  \\newcommand{\\gvec}{\\boldsymbol{\\mathsf{g}}}\n",
    "  \\newcommand{\\zerovec}{\\boldsymbol{\\mathsf{0}}}\n",
    "  \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n",
    "  \\newcommand{\\transpose}[1]{{#1}^\\top}\n",
    "  \\DeclareMathOperator{\\rank}{rank}\n",
    "  \\newcommand{\\Power}{\\mathcal{P}}\n",
    "$"
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   "source": [
    "**Student(s):** Anthony Bowers, Andrew Hamel <br>\n",
    "**Course:** Engy-5050 Reactor Physics  <br>\n",
    "\n",
    "\n",
    "UMass Lowell, Dept. of Chemical Engineering, Nuclear Energy Program \n",
    "<br>\n",
    "**7March2022**"
   ]
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    "---\n",
    "## Table of Contents<a id=\"toc\"></a>\n",
    "* [Introduction](#intro)\n",
    "* [Problem Statement](#problem)\n",
    "* [Objectives](#obj)\n",
    "* [FEM Approach](#app)\n",
    " + [Analytical Solution](#analyticalsol)\n",
    " + [Weak Form of Problem Statement](#weakform)\n",
    " + [MOOSE Kernels](#kernels)\n",
    " + [Setup](#setup)\n",
    "    - [One-Group Energy](#onegroupenergy)\n",
    "    - [Two-Group Energy](#twogroupenergy)\n",
    "* [FDM Approach](#appFDM)\n",
    " + [Discretization](#setupFDM)\n",
    "    - [One-Group Energy](#onegroupenergyFDM)\n",
    "    - [Two-Group Energy](#twogroupenergyFDM)\n",
    "* [Results and Analysis](#ranalysis)\n",
    "* [Conclusions](#conclusions)\n",
    "* [References](#refs)\n",
    "---"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "## [Introduction](#toc)<a id=\"intro\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Problem Statement](#toc)<a id=\"problem\"></a>"
   ]
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    "This investigation looks to determine how Finite Element Method (FEM) computation of the neutron diffusion equation compare to that of the Finite Difference Method (FDM) computation given standard assumptions about the definition of the diffusion coefficient in homogenous mediums far from and close to voids. Defining diffusion coefficients for neutron transport is an active field of research and includes approximations such as isotropic scattering, linear in angle, nonlocal weighting of nearby average transport properties, Monte Carlo study and experiment.\n",
    "\n",
    "Here we will compare the analytic linear transport result for non-absorbing and moderately absorbing mediums given a point source in spherical geometry. As well as, comaprison of the two computational methods of FEM and FDM. \n",
    "\n",
    "For a monoenergetic group time independent neutron diffusion equation (NDE) in written assuming azimuthal symmetry as\n",
    "\n",
    "Compute $\\Phi_g:[r_\\text{i},r_\\text{o}]\\subset\\Reals\\rightarrow\\Reals$ such that:\n",
    "\n",
    "\\begin{align*}\n",
    "  \\nabla \\cdot D_g \\nabla \\Phi_g(r) - \\Sigma_{g,r} \\Phi_g(r) + S_{g'\\rightarrow g} &= 0 \\\\\n",
    "   q_{n,g}(r_\\text{i}) &= A_g, \\\\\n",
    "   q_{n,g}(r_\\text{o}) &= \\frac{\\alpha}{2}\\Phi_g(r_\\text{o}).\n",
    "\\end{align*}\n",
    "\n",
    "where the source term $S_{g'\\rightarrow g} := \\sum_{g'=1}^{G} \\int_\\Omega \\Sigma_{s,g'\\rightarrow g}\\, f_{s,g'\\rightarrow g}(\\mu)\\,d\\Omega$ is the group down-scattering contribution for each group $g$.\n",
    "\n",
    "The neutron scalar flux is: $\\Phi(r)\\ [n/cm^2 s]$ \n",
    "\n",
    "The total macroscopic cross section is: $\\Sigma_{tot} = \\Sigma_{non-el} + \\Sigma_{el} \\approx \\Sigma_{abs} + \\Sigma_{el}$\n",
    "\n",
    "And the removal cross section for the multi group cross section is $ \\Sigma_{r} = \\Sigma_{tot} - \\bar{\\mu}\\Sigma_{s} $\n",
    "\n",
    "For brevity, $S' = Q^{fis}_{ext} + Q^{sc}_{in}$, is written as the combined source for exterior sources and fission sources or scatter in from out of group (up and down scatter). The full _scatter in term_ requires a _group averaged scatter cross section_ that further requires a _transfer function_ differential in post collision direction $\\Omega \\cdot \\Omega '$. \n",
    "\n",
    "Here for the free surface (vacuum) boundary condition. The neutron density at the outer boundary $\\Phi(r) = |v| n(r) = 0$ if $ n_b\\cdot \\Omega < 0 $."
   ]
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   "source": [
    "### Domain\n",
    "The domain utilized in the simulation is spherical geometry containt a point source. Surronding the point source is light-water."
   ]
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    "### [Analytic Solution](#toc)<a id=\"analyticalsol\"></a> \n",
    "\n",
    "A general solution is commonly given without the asymptotic condition as:\n",
    "\n",
    "\\begin{align*}\n",
    "    \\Phi(r) =  \\frac{S_0 e^{-\\kappa r}}{4\\pi Dr} \\ \\ \\ (2)\n",
    "\\end{align*}\n",
    "\n"
   ]
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   "source": [
    "## [FEM Approach](#toc)<a id=\"app\"></a>"
   ]
  },
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   "source": [
    "### [Strong Form of Problem Statement BARE REACTOR](#toc)<a id=\"dbcstrong\"></a>\n",
    "\n",
    " Find $\\Phi_1:[a,b]\\subset \\mathbb{R} \\rightarrow\\mathbb{R}$ and $\\Phi_2:[a,b]\\subset\\mathbb{R}\\rightarrow\\mathbb{R}$ for $D_1 > 0$ and $D_2 > 0$ such that:\n",
    "\n",
    "\\begin{align*}\n",
    " 0= -div_{x}(-D_1\\, \\nabla_{x}\\Phi_1)- \\Sigma_{1,a} \\Phi_1(x)+ S(\\Phi_1, \\Phi_2) + \\chi(E_{1}) \\frac{v}{k}\\Sigma_{1,f}\\Phi_1(x)  \\quad \\forall \\quad x\\in [a,b], \\\\\n",
    "-D_1 \\nabla \\Phi_1(a) &= 0, \\\\\n",
    " -D_1 \\nabla \\Phi_1(b) &= ( \\frac{1}{2} \\Phi_1).\n",
    "\\end{align*}\n",
    "\n",
    "and\n",
    "\n",
    "\\begin{align*}\n",
    "  0= -div_{x}(-D_2\\,\\nabla_{x}\\Phi_2) -\\Sigma_{2,a} \\Phi_2(x) - S(\\Phi_1, \\Phi_2) + \\chi(E_{2}) \\frac{v}{k}\\Sigma_{2,f}\\Phi_2(x)  \\quad \\forall \\quad x\\in [a,b], \\\\\n",
    " -D_2 \\nabla \\Phi_2(a) &= 0, \\\\\n",
    " -D_2 \\nabla \\Phi_2(b) &= ( \\frac{1}{2} \\Phi_2).\n",
    "\\end{align*}\n",
    "\n",
    "The *diffusion flux* associated to the quantity $\\Phi_i, \\, \\ i=1,2$ is denoted $q_i := -D_i\\,\\Phi_i'$, and it is often of interest as a derived quantity of the neutron spatial transport theory. "
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    "### [Source Coupling](#toc)<a id=\"sourcecoupling\"></a>\n",
    "\n",
    "Consider the following source coupling:\n",
    "\n",
    "\\begin{align*}\n",
    " S(\\Phi_1, \\Phi_2) = S_1 - h_1\\,\\bigl(\\Phi_1-\\Phi_1^*\\bigr) - \\Bigl( S_2 - h_2\\, \\bigl(\\Phi_2 - \\Phi_2^*\\bigr) \\Bigr)\n",
    "\\end{align*}\n",
    "\n",
    "where $S_i$ is a fixed source (sink) for each Neutron group, $h_i$ is a transfer coefficient, and $\\Phi_i^*$ is a saturation value.\n",
    "\n",
    "Moreover, for this particular problem:\n",
    "\n",
    "\\begin{align*}\n",
    " S_1=0 \\\\\n",
    " S_2=0 \\\\\n",
    " \\Phi_2=0 \\\\\n",
    " \\Phi_1^*=0 \\\\\n",
    " \\Phi_2^*=0 \\\\\n",
    " h_1=\\Sigma_{s,1 \\rightarrow 2} \\\\\n",
    " h_2=0\n",
    "\\end{align*}\n",
    "\n",
    "Enstating these values reduces the source coupling to \n",
    "\\begin{align*}\n",
    " S(\\Phi_1, \\Phi_2) = -\\Sigma_{s,1 \\rightarrow 2} \\Phi_1 \n",
    "\\end{align*}\n",
    "\n",
    "Where the conceptual reads this means that group one neutrons looses neutrons due to the downscattering into group two. Conversely this means group two has a source term. Moreover, if upscattering was to be taken into account $h_2 = \\Sigma_{s,2 \\rightarrow 1}$ and $\\Phi_2$ would exist for a combined source term of, \n",
    "\n",
    "\\begin{align*}\n",
    " S(\\Phi_1, \\Phi_2) = -\\Sigma_{s,1 \\rightarrow 2} \\Phi_1 + \\Sigma_{s,2 \\rightarrow 1} \\Phi_2\n",
    "\\end{align*}"
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    "### [Weak Form of Problem Statement](#toc)<a id=\"weakform\"></a> \n",
    "\n",
    "The Galerkin weak formulation of the strong form is as follows. Find $\\Phi_1 \\in H^1\\!\\bigl([a,b]\\bigr)$ and $\\Phi_2 \\in H^1\\!\\bigl([a,b]\\bigr)$\n",
    "so that \n",
    "\n",
    "\\begin{align*}\n",
    " \\int\\limits_a^b \\Sigma_{1,a}  \\Phi_1(x)\\, w(x)\\,dx + \\int\\limits_a^b D\\, \\Phi_1'(x)\\,w'(x)\\,dx - \\int\\limits_a^b S(\\Phi_1, \\Phi_2)\\,w(x)\\,dx &= 0 \\quad \\forall \\quad w \\in H^1_0\\!\\bigl([a,b]\\bigr), \\text{and}\n",
    " \\\\\n",
    "  \\int\\limits_a^b \\Sigma_{2,a}  \\Phi_2(x)\\, w(x)\\,dx + \\int\\limits_a^b D\\, \\Phi_2'(x)\\,w'(x)\\,dx + \\int\\limits_a^b S(\\Phi_1, \\Phi_2)\\,w(x)\\,dx &= 0 \\quad \\forall \\quad w \\in H^1_0\\!\\bigl([a,b]\\bigr),\n",
    "\\end{align*}\n",
    "\n",
    "where $H^1\\!\\bigl([a,b]\\bigr) := \\bigl\\{ \\Phi:[a,b]\\subset\\mathbb{R}\\rightarrow\\mathbb{R} \\mid \\int_a^b \\Phi'^2\\,dx < \\infty\\bigr\\}$ and $H^1_0\\!\\bigl([a,b]\\bigr) := \\bigl\\{ w \\mid w \\in H^1(a,b), w(a) = 0, w(b) =0 \\bigr\\}$. Both function sets as just defined are Hilbert spaces. The function $w$ is called a test function. Because $w$, $\\Phi_1$, $\\Phi_2$ are sought in very similar sets of functions, this weak form is called Galerkin's weak form.\n",
    "\n",
    "The new form of the source term is the key term to be computed here. Since the MOOSE framework performs the integration, and provides the implementation of the test function, we need to provide the integrand of the integral, that is, the kernel. Therefore the kernel needed is an expansion of what has been covered so far in the course:\n",
    "\n",
    " 1. $\\pm S(\\Phi_1, \\Phi_2)\\,w(x)$.\n",
    " \n",
    "The kernels are to be evaluated at quadrature points provided by the MOOSE framework.\n",
    "1. Multiply NDE by a test function $\\phi$.\n",
    "2. Integrate over spatial and angular domain.\n",
    "3. Use divergence theorem to set the boundary condition across the domain surface.\n",
    "\n",
    "The weak form becomes:\n",
    "\n",
    "\\begin{align*}\n",
    "    ( \\nabla \\phi, D_1 \\nabla \\Phi_1  )\\ - < \\phi, D_1 \\nabla \\Phi_1 \\cdot \\bar{n_b} > +\\ (\\phi , \\Sigma_{a,1} \\Phi_1) = (\\phi,S(\\Phi_1, \\Phi_2)) \\ \\ \\ (G1)\\\\\n",
    "      ( \\nabla \\phi, D_2 \\nabla \\Phi_2  )\\ - < \\phi, D_2 \\nabla \\Phi_2 \\cdot \\bar{n_b} > +\\ (\\phi , \\Sigma_{a,2} \\Phi_2) = - (\\phi,S(\\Phi_1, \\Phi_2)) \\ \\ \\ (G2)\n",
    "\\end{align*}\n",
    "\n",
    "This weak form contains the volume and surface integral as written with parenthesis and brackets respectively. \n",
    "\n",
    "Then boundary conition at the center, $a$, is implemented and descritized as such: \n",
    "\\begin{align*}\n",
    "\\\\\n",
    " 4\\pi r^{2} \\lim_{r\\rightarrow 0}(-D_1\\Phi_1'(a)) &= S_0 \\\\\n",
    "  -D_2 \\nabla \\Phi_2'(a) &= 0 \\\\\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Then the boundary conditions for the partial currents at the surface, $b$, given as $\\Gamma^{\\pm}$ must be solved for:\n",
    "\n",
    "\\begin{align*}\n",
    "    \\Gamma^{+} = J^{out}({R_S}) = \\nabla \\Phi \\cdot \\bar{n_b}\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "    \\Gamma^{-} = J^{in}({R_S}) = 0\n",
    "\\end{align*}\n",
    "\n",
    "Here we will use the Robin Vacuum boundary condition, at position $b$, such that the reflectivity at the boundary is 0 as:\n",
    "\n",
    "\\begin{align*}\n",
    "    \\frac{1}{4} \\Phi + \\frac{1}{2} D \\nabla \\Phi \\cdot \\bar{n_b} = J^{-} = \\frac{\\Phi}{4} - \\frac{J}{2} = \\frac{\\Phi}{4} - \\frac{D \\nabla \\Phi}{2}\n",
    "\\end{align*}\n",
    "\n",
    "Solving for the weak form boundary condition and multiplying our test function $\\phi$:\n",
    "\n",
    "\\begin{align*}\n",
    "     \\phi (D_1 \\nabla \\Phi_1(b) \\cdot \\bar{n_b}) = \\phi( \\frac{1}{2} D_1 \\nabla \\Phi_1) \\\\\n",
    "     \\phi (D_2 \\nabla \\Phi_2(b) \\cdot \\bar{n_b}) = \\phi( \\frac{1}{2} D_2 \\nabla \\Phi_2)\n",
    "\\end{align*}\n",
    "\n",
    "#### 2 Group NDE  Weak Form:\n",
    "\n",
    "Assuming no upscattering from group 2 to group 1:\n",
    "\n",
    "\\begin{align*}\n",
    "    -\\nabla \\cdot D_1 \\nabla \\Phi_1(r)  + \\Sigma_{a,1} \\Phi_1(r) =  -\\Sigma_{s,1 \\rightarrow 2} \\Phi_1(r) \\ \\ \\ \n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "    -\\nabla \\cdot D_2 \\nabla \\Phi_2(r)  + \\Sigma_{a,2} \\Phi_2(r) =  \\Sigma_{s,1 \\rightarrow 2} \\Phi_1(r) \\ \\ \\  \n",
    "\\end{align*}\n"
   ]
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    "This report will examine bare and reflected spherical core geometries for the case of a plutonium core and a beryllium reflector. This configuration is somewhat similar to the \"demon core\", a weapon core which was the cause of two criticality accidents at Los Alamos in the mid 1940's. While the core itself was subcritical, it briefly became supercritical when it was encased in two hemispheres of reflective beryllium. A model of the neutron flux in the fuel and reflector for a spherical reactor has been developed using a two group approximation. This approximation assumes an energy cutoff of 1 eV between the slow and fast neutron energy bins. Some key assumptions are made, firstly that no slow neutrons upscatter into the fast energy bin. Continuity of flux and neutron density is assumed at the interface between the fuel and reflective regions. A Neumann boundary condition of zero flux is assumed at the center of the sphere, and a vacuum condition is assumed at the outer edge of the reflector. "
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   "source": []
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   "cell_type": "code",
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
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   "source": []
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     "text": [
      "Diffusion Coefficent for group-1 [cm] =  1.4453177854041355\n",
      "Diffusion Coefficent for group-2 [cm]= 0.9033236158775847\n",
      "Downscattering Macroscopic cross section [cm^-1]= 0.7687659574468086\n",
      "Macroscopic cross section for Fission (group-1) [cm^-1]= 0.06611387234042554\n",
      "Macroscopic cross section for Fission (group-2) [cm^-1]= 0.07380153191489362\n",
      "Macroscopic cross section for Absorption (group-1) [cm^-1]= 0.0041000851063829795\n",
      "Macroscopic cross section for Absorption (group-2) [cm^-1]= 0.014350297872340427\n"
     ]
    }
   ],
   "source": [
    "# Parameters of fissioning u-235\n",
    "#Mircoscopic cross section for transport, fission, and absorption\n",
    "eta_tr=[4.5e-24, 7.2e-24]\n",
    "eta_f=[1.29e-24, 1.44e-24]\n",
    "eta_a=[.08e-24, .28e-24]\n",
    "eta_12=1.5*10e-24\n",
    "\n",
    "#Parameters for atomic density\n",
    "Na=6.022*10e23\n",
    "molar_mass=235\n",
    "mass_of_fuel=2 # 2 grams of fuel\n",
    "N_density= Na*mass_of_fuel/molar_mass\n",
    "\n",
    "#Macroscopic cross section for transport, fission, and absorption\n",
    "sigma_tr=[N_density*eta_tr[0], N_density*eta_tr[1]] \n",
    "sigma_f=[N_density*eta_f[0], N_density*eta_f[1]]\n",
    "sigma_a=[N_density*eta_a[0], N_density*eta_a[1]]\n",
    "#Macroscopic cross section for group-1 downscattering into group-2\n",
    "sigma_12=N_density*eta_12\n",
    "\n",
    "#Fission emission\n",
    "v=[2.7 ,2.5]\n",
    "\n",
    "#Fission Spectrum\n",
    "chi=[.575, .425]\n",
    "\n",
    "#Diffusion Coefficent\n",
    "D1=1/(3*sigma_tr[0])\n",
    "D2=1/(3*sigma_tr[1])\n",
    "\n",
    "print('Diffusion Coefficent for group-1 [cm] = ',D1)\n",
    "print('Diffusion Coefficent for group-2 [cm]=',D2)\n",
    "print('Downscattering Macroscopic cross section [cm^-1]=',sigma_12)\n",
    "print('Macroscopic cross section for Fission (group-1) [cm^-1]=',sigma_f [0])\n",
    "print('Macroscopic cross section for Fission (group-2) [cm^-1]=',sigma_f [1])\n",
    "\n",
    "print('Macroscopic cross section for Absorption (group-1) [cm^-1]=',sigma_a[0])\n",
    "print('Macroscopic cross section for Absorption (group-2) [cm^-1]=',sigma_a[1])"
   ]
  },
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   "source": [
    "#### [One-Group Energy](#toc)<a id=\"onegroupenergy\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   "source": [
    "!cat inputEigenProblem.hit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!rm inputEigenProblem_out_eigenvalue-data_0001*.csv\n",
    "!./neutron__transport-opt -i inputEigenProblem.hit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'.' is not recognized as an internal or external command,\n",
      "operable program or batch file.\n"
     ]
    }
   ],
   "source": [
    "#!rm output1G*.csv\n",
    "!./neutron__transport-opt -i input_test.hit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_csv('output1G_x-data_0002.csv')\n",
    "#plot_solution(df, title='Dirichlet BC FEM Solution', basis_functions_type='Linear Lagrange', flux_basis_functions_type='Constant Monomial')\n",
    "#print(df)\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "plt.plot(df[\"x\"],df[\"u1\"],\"r-\")\n",
    "plt.yscale(\"log\")\n",
    "#plt.xlim(0,100)\n",
    "plt.xlabel(\"Radius [cm]\")\n",
    "plt.ylabel(\"Neutron flux [N/cm^2]\")\n",
    "font = {'family' : 'DejaVu Sans',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 15}\n",
    "plt.rc('font', **font)\n",
    "plt.title(\"1-Group FEM Solution\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### [Two-Group Energy](#toc)<a id=\"twogroupenergy\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'.' is not recognized as an internal or external command,\n",
      "operable program or batch file.\n"
     ]
    }
   ],
   "source": [
    "#!rm output2G*.csv\n",
    "!./neutron__transport-opt -i input2G.hit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Zkunx55xzDjNmzGDUqFG88sor7N27l7Zt2x6QTL766qvMmjWL8ePHc8899/DWW28xaNCgHMd5MPPmzcM5x6mnnpqt951//vmcddZZvP3225x11lksX76c008/nTJlyvD6668zbNgwXnrppf1aWbNj4cKFjBkzhtGjR/PUU0/x1Vdfcc455+ToXAcT692p9wOrnHM9zX99KRd0QCIiCeH66+GLL4K59rHHwoMPZvttf/zxBwUKFNhv3/vvv7/f5IbRo0czevTo/Y5p06YNc+bM2W9fUlIS3bp1Y+LEiVx88cVMnDiRRo0acfTRR4cVy4QJE+jRowddunQhKSmJxo0b06NHD/r06UPBggUBeOaZZ1i7di2rVq2ibNmylChRghYtWlCjRg3GjRvHwIEDs/0zAL8yQN26dQFo3LhxlpMJ3n33XRYsWMCcOXNo06YNAO3ataNatWrcd999jBs3bt+xBQoUYOrUqfsmgixfvpyJEyfy2GOP5SjOg1m/fj0AVapU2W//nj179kvO005MAejTpw99+/bd97xHjx5UrVqVN998k3z58gFw+OGH0717dxYuXMjxxx+frbg2btzIRx99RNWqVQGoWrUqrVq14t133+X000/P1rkOJs+TODOrBdwMtAQaAPOccykZHFcPGAMcD2wCngSGOef2hF4vAZwDVAFw/o7F9zQUERHJseTkZGbOnLnfvtRkJtVFF12033/wQKZj3Hr06LGvVSzcrtRU7dq147vvvmP69OnMmjWLmTNncvPNNzN16lTmzp1LUlISixYtokmTJtSoUWNfa13lypU58cQTmT9/ftjXOhSLFi2ibNmy+xI4gGLFinHWWWcdEEPbtm33S5jq1avHxo0b2blz577ENCf27t3L3r179z3Ply8fZrYvUUvfBX3MMcewbNmyfc+3bNmy32STDh06HPAZu3btui+BA+jSpQv58+dn/vz52U7imjRpsi+BAzjxxBMpV64cixYtiv0kDqgPnAl8DGR4V82sFDATWA50AmriW92SgMGhw2oAvwEPmVlL4Cegr3NuTSSDFxERctQSFrT8+fPTtGnTLI8pX778QY9Jdfzxx1OxYkVGjBjB559/zuuvv56teEqUKEGPHj3o0aMHzjmGDBnC8OHDmTZtGp06deKXX36hfPnyGcb4448/ZutaOZVVDOm7dNPOcgUoWLAgzrlDTuIuu+wynn322X3Pn3nmGXr27EmlSpUA+Pnnn6lRo8a+11955RW2bdvGW2+9xbBhwzKMPa2MPmO+fPkoXbp0jrqty5U7sFOwXLly/PLLL9k+18EEMSZumnOuinOuG7Ask2OuBooAnZ1z7zvnxgLDgBvNLHWF2AL4lrw3nHNNgDeAZzM8m4iISAR0796dBx54gBYtWlC9evUcn8fM9s1UXblyJeBnymZUcmPDhg0cfvjhmZ6rcOHC7Ny5c799OR1Dl9MYctPQoUP59NNP922pkzJat26NmfHee+/td3z9+vVp2rRppt3E6VvuMvqMe/bs4Y8//tj3GVNnsKb/uWY0cSOjn9fGjRupUKFC5h8yh/I8iXPO7T34UZwBzHDO/Z1m30R8YpfapvsTsNk5NyPN68flWqAiIiIHcckll9CxY0duvPHGsN+za9euDP/z//bbb4H/WopatGjBkiVL+OGHH/Yds27dOj766CNatWqV6fkrV67MihUr9tv3/vvv7/c8tWVs+/btWcbaokULNm7cyNy5c/ft27p1K9OnT88yhtxUrVo1mjZtum8rXbr0vv2dOnXizjvvPKRWrhYtWjBlypT9JrBMnjyZ3bt37/uMlStXBtjv5/rJJ5/w999/k95nn33G2rVr9z1fsGABGzdupHnz5jmOMTPROrHhKGB22h3OubVmtjX02jTn3AYz+8rMmjnnPgVOAb4OINYDnX461K8P998fdCQiIpINv/zyCx9//PEB+5s0aZJhl2C9evX2zVAN1+bNm6lTpw6XXHIJbdu2JTk5mW+++YaRI0dSqVIlzj33XAB69uzJPffcwxlnnMHAgQMpXrw4Q4cOpUyZMlx11VWZnv/cc8/luuuuY8SIETRr1ozJkyfvN0YM/hsLOG7cOHr06EHRokVp2LDhAec67bTTOPHEE+nevTt33303pUuXZtSoUWzbtm2/GneHIrU23KpVq9i6deu+523atDlozbqxY8eSkpJCkyZN6Nu3L82aNSMpKYk1a9YwduxYihQpst9Yt4wMHjyYxo0bc84553DNNdfw888/079/f0477bR94+GaN29OpUqV6NOnD8OHD+fPP//k3nvvpWTJkgecr1y5cpx11lkMHTqU7du3079/f5o0aZLr4+EgepO4UvjJDOn9FXot1dXAk2ZWPHT8ZZmd0Mx6Ab3Af8tJP9PoUKTW3Ul13Pffs2PLFpbm4jUk+9LfF4keujfRKbP7kpycnGkZjFixY8cOnHNZfg7nHC+99FKGBWJXrFhBpUqV9rVcbdmyJdPCvHv37mXXrl2ZXsvM6Nu3L++99x4vvvgiW7ZsoUKFCrRr146bb76ZpKSkfe+dOnUqgwYNonfv3jjnaNWqFc899xwFChTY7/zbt2/f9/z8889nxYoVPPTQQ+zcuZMePXrQr18/+vbtuy/uww8/nLvuuouxY8cyZswYKlWqxNKlSzP8fM8//zyDBg3i+uuvZ/v27Rx33HFMmzaN8uXL77tm6ti39DEd7GcF0K1btwyfT58+ndatW2f6PoCiRYsyc+ZMxowZw3PPPccdd9yBc47q1avTvn17nn76aXbv3s2WLVsyjefII4/cV1qkc+fOlChRgi5dujB8+PD9Ps8LL7zAjTfeSNeuXalduzb3338/l19++X6fe8+ePTRr1oyUlBT69u3L77//TqtWrXj44Yez/Lu3ffv2HP1OtCCrQ5vZJKBM+tmpZrYL6Oeceyjd/nXABOfcrYdy3aZNm7r0hQoPxZw5c0hJSflvx6mnwj//wEcf5do1JPsOuC8SNXRvolNm92XFihVhl86QyNiyZctBV4KQvJf+vqSkpFCmTJlsrzxxsH9jZrbEOXfAjJtoLfb7F3BYBvuTybiFLrqUKQO//x50FCIiIhLHojWJW4kf+7aPmVUBioVei26lSyuJExERkYiK1jFx7wA3m1kJ51xqJ3J3YBvwYXBhhalMGfjrL9i9G/JH649YREREclNej/XN85Y4MytqZl3NrCtQCSib+tzMioYOGwvsACab2cmhSQlDgdHpyo5EpzJl/OMhrG0nIiIikpUgmonKAa+l25f6vDqwxjn3l5m1Bx4BpuHHwT2AT+SiX2oS98cfkEHlZhEREZFDledJXGhZLAvjuOVAu4gHFAmpSZzGxYmIiEiEROvEhogws45mNn7z5s2RvZCSOBEREYmwhErinHPTnHO9kpOTI3uh0JIgSuJEREQkUhIqicszSuJEREQkwpTERUKRIlCsmJI4EZEoMXToUMzsgO3kk0/ed0y1atUyPCZ/mlJREyZMwMwoWbIk27ZtO+A67du3x8zo2bNnlvHs2rWL0aNH06BBA4oWLUqZMmVo0aIFd999d7Y/m5nxyCOPZOs9q1atYujQoWzatGm//amf759//sl2HDkxc+ZMunfvTtWqVSlatCgNGjTgkUce2W8x+oP5+++/GTp0KA0bNqRo0aIULVqU+vXrM2TIEDZs2BDB6IOnImaRolUbRESiSnJyMu++++4B+9K64IILuO666/bbZ3bgXDznHNOnT6dr16779m3YsIEPP/yQ4sWLHzSW3r178+KLL3LrrbfSokULNm3axMcff8y0adMYMGBAdj5WjqxatYphw4bRs2dPDjvssH37O3TowMKFCylatGjmb85F48ePZ+vWrdx5551UqVKF+fPnc9NNN/HDDz9w//33H/T9GzZsICUlhU2bNtGnTx+aNWuGmbF48WLGjh3L7NmzmTdvXh58kmAoiYuUMmV8iREREYkK+fPnp2XLllkeU6FChYMeA9CxY0cmTpy4XxL36quvUrNmzYOucbp161aeeeYZ7rrrLm6++eZ9+zt37pzlQvF5oWzZspQtWzbPrvfYY49RJnUyIH7t0a1bt/LAAw8wYsQIChUqlOX7r776ajZv3sySJUuoWLHivv3t27fn+uuv56WXXsry/du3b6dw4cKH9iECpO7USFFLnIhI3OrRowfTp09ny5Yt+/ZNnDiRHj16HPS9//77L7t27eKII4444LX0rX4//PAD55xzDpUqVaJEiRJ07NiR1atXZ3n+atWq0a9fv/32pe0mnTNnDh07dgSgevXqmBnVqlU74LhUv//+O5dccgmlS5emaNGipKSksHjx4gyv+cADD1C5cmVKlSpFjx49DuiuTS9tApeqcePGbN++nb//zrq2/5o1a3jjjTcYPHjwfglcqkKFCnHppZce8DNYtGgRKSkpFClShPvuuw+A2bNn06JFCwoXLkz58uW59tpr9/sZZNbN3KBBg/1+1ikpKXTt2pXx48dTrVo1ihQpQocOHVi3bl2WnyWnlMRFStmyEOd98SIisWb37t37belbvpxzBxyT0fislJQUSpUqxdSpUwFYu3YtCxcuDCuJK1u2LFWqVGHo0KFMnjx5v0QwrR07dtC+fXtWrFjBww8/zIQJE/jhhx9o06YNfx7CikBNmjRh1KhRAEyePJmFCxcyZcqUTI8/55xzmDFjBqNGjeKVV15h7969tG3b9oBk8tVXX2XWrFmMHz+ee+65h7feeotBgwZlO76PPvqIMmXKHLRFcN68eTjnOPXUU7N1/vPPP5+zzjqLt99+m7POOovly5dz+umnU6ZMGV5//XWGDRvGSy+9tF8ra3YsXLiQMWPGMHr0aJ566im++uorzjnnnByd62ASqjvVzDoCHWvVqhX5ix1xhE/inIMMxlOIiEje+uOPPyhQoMB++95///39JjeMHj2a0aNH73dMmzZtDlgTMykpiW7dujFx4kQuvvhiJk6cSKNGjTj66KPDimXChAn06NGDLl26kJSUROPGjenRowd9+vShYMGCADzzzDOsXbuWVatWUbZsWUqUKEGLFi2oUaMG48aNY+DAgTn4KUDJkiWpW7cu4Fu9UlvhMvLuu++yYMEC5syZQ5s2bQBo164d1apV47777mPcuHH7ji1QoABTp07dNxFk+fLlTJw4kcceeyzs2JYvX87YsWPp37//QY9dv349AFWqVNlv/549e/ZLzvOnW8O8T58+9O3bd9/zHj16ULVqVd58803y5csHwOGHH0737t1ZuHAhxx9/fNjxA2zcuJGPPvqIqlWrAlC1alVatWrFu+++y+mnn56tcx1MQiVxzrlpwLSmTZteGfGLHXEEbNsGW7ZAyZIRv5yISF66/nr44otgrn3ssfDgg9l/X3JyMjNnztxvX2oyk+qiiy7a7z94INMxbj169NjXKhZuV2qqdu3a8d133zF9+nRmzZrFzJkzufnmm5k6dSpz584lKSmJRYsW0aRJE2rUqLGvta5y5cqceOKJzJ8/P+xrHYpFixZRtmzZfQkcQLFixTjrrLMOiKFt27b7JUz16tVj48aN7Ny5c19impW//vqLLl260KhRo/1a8Pbu3cvevXv3Pc+XLx9mti9RS98Ffcwxx7Bs2bJ9z7ds2bLfZJMOHToc8Bm7du26L4ED6NKlC/nz52f+/PnZTuKaNGmyL4EDOPHEEylXrhyLFi3K9SRO3amRkjrW4ddfg41DREQA3yLTtGnT/bb0CVr58uUPOCZ9opfq+OOPp2LFiowYMYLPP/+c7t27ZyueEiVK0KNHD5544gm+//57brvtNhYsWMC0adMA+OWXXyhfvvwB7ytfvvwhdadmR3ZiSDvLFaBgwYI459i5c+dBr7N9+3Y6derEjh07ePPNN/dL+i677DIKFCiwb3v22WcBqFSpEgA///zzfud65ZVX+PTTTxkyZEiG10r/eTL6jPny5aN06dI5+jmXy2DN9HLlyvHLL79k+1wHk1AtcXkqbRJXp06wsYiI5LKctITFo+7duzNq1ChatGhB9erVc3weM+Pmm29m+PDhrFy5kk6dOlGhQoX9WpRSbdiwgcMPPzzTcxUuXPiAxCmnSV+FChXYuHFjtmPIjj179nDBBRewbNkyPvroowMSqqFDh9K7d+99z1N/zq1bt8bMeO+997j66qv3vV6/fn0Ali5dmuH10rfcZfQZ9+zZwx9//LHvM6bOYE3/c81o4kZGP6+NGzdSoUKFDOM5FGqJixS1xImIxL1LLrmEjh07cuONN4b9nl27dmX4n/+3334L/NdS1KJFC5YsWcIPP/yw75h169bx0Ucf0apVq0zPX7lyZVasWLHfvvfff3+/56ktXdu3b88y1hYtWrBx40bmzp27b9/WrVuZPn16ljFkx7XXXsu7777LtGnTMmz1rFat2n4to6VDqyJVq1aNTp06ceeddx5SK1eLFi2YMmXKfhNYJk+ezO7du/d9xsqVKwPs93P95JNPMpxB+9lnn7F27dp9zxcsWMDGjRtp3rx5jmPMjFriIkVJnIhIzPnll1/4+OOPD9jfpEmTDMd11atXb98M1XBt3ryZOnXqcMkll9C2bVuSk5P55ptvGDlyJJUqVeLcc88FoGfPntxzzz2cccYZDBw4kOLFizN06FDKlCnDVVddlen5zz33XK677jpGjBhBs2bNmDx58gEteqnJ0rhx4+jRowdFixalYcOGB5zrtNNO48QTT6R79+7cfffdlC5dmlGjRrFt27b9atzl1IgRIxg/fjwDBw4kKSlpv599vXr1KHmQMeVjx44lJSWFJk2a0LdvX5o1a0ZSUhJr1qxh7NixFClSZL+xbhkZPHgwjRs35pxzzuGaa67h559/pn///px22mn7xsM1b96cSpUq0adPH4YPH86ff/7Jvffem2F85cqV46yzzmLo0KFs376d/v3706RJk1wfDwf46dSJth133HEuN33wwQcH7tyzx7kCBZwbODBXryXhy/C+SFTQvYlOmd2X5cuX520gETBkyBBXunTpLI+pWrWqAzLcfvrpJ+ecc88884wD3JYtWzI9z3HHHecuueSSTF/fsWOHGzlypGvdurUrV66cK1y4sKtZs6a76qqr9l0n1Xfffec6derkihcv7ooVK+Y6dOjgVq1atd8xgBszZsy+5zt37nQ33HCDK1++vDvssMNcnz593Lhx4w6Ie9SoUe7II490+fLlc1WrVs30823cuNFdfPHF7rDDDnOFCxd2J510klu0aNEBP7ubbrppv33h/KzatGmT6c883N8TmzdvdrfffrurX7++K1KkiCtcuLCrX7++u/HGG92aNWvCimfmzJmuefPmrlChQq5s2bLummuuOeC4RYsWuaZNm7oiRYq4Y4891s2fP98deeSR+33uNm3auC5durjHH3/cValSxRUuXNidfvrpbu3atVl+hoP9GwMWuwzyGXMBV4cOQtOmTV36QoWHYs6cOaSkpBz4QpUqcMop8PTTuXYtCV+m90UCp3sTnTK7LytWrAi7dIZExpYtWw66EoTkvfT3JSUlhTJlyjBp0qRsnedg/8bMbIlzrmn6/RoTF0lHHKHuVBEREYkIJXGRpCROREREIiShJjbk6YoN4JO4JUvy5loiIiISqPQre0RaQrXEOeemOed6JScn580FjzgCNm6EDNbdExERETkUCZXE5bkjjvAJ3O+/Bx2JiIiIxBklcZEUWhKEdEuCiIjEmkSsZCCSFw7l35aSuEgKVXhWEicisaxAgQJs27Yt6DBE4tK2bdsoUKBAjt6rJC6SqlTxjz/9FGwcIiKHoFy5cqxbt46tW7eqRU4klzjn2Lp1K+vWraNcuXI5OkdCzU7Nc2XLQoECaokTkZiWurTQ+vXr2bVrV8DRJKbt27fvW4Rdoseh3pcCBQpQvnz5gy4vlhklcZGUlOS7VNUSJyIxrmTJkjn+j0YO3Zw5c2jcuHHQYUg6Qd8XdadGWpUqaokTERGRXKckLtLUEiciIiIRoCQu0qpUgXXrYO/eoCMRERGROJJQSZyZdTSz8Zs3b867i1auDDt3wm+/5d01RUREJO4lVBKX58tugcqMiIiISEQkVBIXCBX8FRERkQhQEhdpaokTERGRCFASF2llykChQkriREREJFcpiYu0pCSoWhV++CHoSERERCSOKInLCzVqKIkTERGRXKUkLi9Urw7ffx90FCIiIhJHlMTlhRo14K+/YNOmoCMRERGROKEkLi9Ur+4f1aUqIiIiuURJXF6oUcM/KokTERGRXKIkLi+ktsRpXJyIiIjkEiVxeeGww6BUKbXEiYiISK5JqCTOzDqa2fjNmzfn/cU1Q1VERERyUUIlcc65ac65XsnJyXl/cdWKExERkVyUUElcoFKTuL17g45ERERE4oCSuLxSsybs3Ak//xx0JCIiIhIHlMTllTp1/OM33wQbh4iIiMQFJXF5JTWJW7Uq2DhEREQkLiiJyysVKkDx4mqJExERkVyhJC6vmEHdukriREREJFcoictLSuJEREQklyiJy0t16sDatbBtW9CRiIiISIxTEpeX6tYF52D16qAjERERkRinJC4v1a3rH9WlKiIiIodISVxeql3bPyqJExERkUOkJC4vFS8OlSopiRMREZFDpiQur9WrB8uXBx2FiIiIxDglcXmtYUNYtgz27Ak6EhEREYlhCZXEmVlHMxu/efPm4IJo0AC2b4fvvw8uBhEREYl5CZXEOeemOed6JScnBxdEgwb+cenS4GIQERGRmJdQSVxUqFfPL8H19ddBRyIiIiIxTElcXitWDGrUUEuciIiIHBIlcUFo0EBJnIiIiBwSJXFBaNAAVq2CHTuCjkRERERilJK4IDRo4EuMrFwZdCQiIiISo5TEBaFhQ/+oyQ0iIiKSQ0riglCnDhQsCF9+GXQkIiIiEqOUxAWhQAFo1Ag++yzoSERERCRGKYkLSpMmPolzLuhIREREJAYpiQtKkyawaROsWRN0JCIiIhKDlMQFpUkT/6guVREREckBJXFBadgQ8udXEiciIiI5oiQuKIULQ/36SuJEREQkR5TEBalJE1iyRJMbREREJNuUxAWpSRP47TdYty7oSERERCTGKIkLUurkhsWLg41DREREYo6SuCA1buwnN3zySdCRiIiISIxREhekIkV8Ivfxx0FHIiIiIjFGSVzQWraERYtg9+6gIxEREZEYklBJnJl1NLPxmzdvDjqU/7RsCVu3wtKlQUciIiIiMSShkjjn3DTnXK/k5OSgQ/nP8cf7R3WpioiISDYkVBIXlapVg3LlYOHCoCMRERGRGKIkLmhmvjVOLXEiIiKSDUriokHLlrBqFfzxR9CRiIiISIxQEhcNWrb0j2qNExERkTApiYuAzZth165svKF5cyhQAObNi1hMIiIiEl/yBx1APGrZElauhOLFoUYNqFsX6tWDpk2hWTMoXz7dG4oW9S/MmRNEuCIiIhKDlMRFwC23+DXtf/8dVq+Gzz+H11+HvXv960ce6XO244+H1q39og0F2rSBe++Ff/7x2Z+IiIhIFpTERcCllx64759/fDK3aBF8+ql/fP11/1qxYtCy9k203lOAkx5bQYvezShaNG9jFhERkdiiJC6PFC/uW91at/5v3y+/+GFw8+bBvA8PYxhDcP2TKDAYjjvOH5uS4h9LlAgsdBEREYlCSuICVKECnHee3yAfm5qezEdbj2Vep1HMnQsPPgj33Qf58vnxdG3b+u3EE33rnYiIiCQuzU6NIoe1P44zVz/MyNu2smABbNoEM2fCgAE+kRs1Ck47DUqVglat4LbbYPZs2LYt6MhFREQkrymJiyZt2vjaJKEluIoWhfbt4c47YcEC+OsvePdduPFGf9iIEf71ww7zbx06FD78EHbsCPRTiIiISB5QEhdNWrWCpKRMS40UL+5b4u6+Gz75xCd1b70F113nJ07ccYcfQ3fYYfsnf9mqWSciIiIxQWPioknJkr7w78yZMHx4WId36OA38End3LnwwQd+u+02v794cTjpJJ/YtW8PDRv6XFFERERil5K4aHPqqb4J7a+//OC3bChVCjp18hv4OnUffgizZvnt7bf9/rJl/QSJ9u3h5JN9QWIRERGJLWqPiTannuqrAs+adcinKlMGunSBxx6Db76Bn36CCRPg9NNh/ny46iqoWROqV4crroCXX4YNGw79I4iIiEjkKYmLNs2b+37S997L9VNXrgyXXALPPQc//wzLl8OYMXDssb7w8AUXwBFH+O7W66+HadPg779zPQwRERHJBepOjTYFCkC7dj6Jcw7MInIZMzj6aL/17g179sBnn/3X9TpuHDz0kC9t0rz5f+Ppjj8eChWKSEgiIiKSDWqJi0annQY//gjffptnl8yXz6/nOmAAvP++H5I3e7Z/vnevL2fStq0fd3fqqXDPPbB4sU/+REREJO+pJS4anXqqf3zvPahTJ5AQChf+b4WIO++EzZv3nyQxYIA/rlQpX9bk5JN9S12dOhFrPBQREZE0lMRFoxo1/IyDGTN8X2cUSE6Gs8/2G8Cvv/qWulmzfEWUKVP8/kqVfEKXuh1xRHAxi4iIxDMlcdHq9NPhmWf8mlpFigQdzQGOOMJPhLjgAj9077vv/mule+stePZZf1zDhnDKKX476SS/CoWIiIgcOo2Ji1YdO8LWrb65K8qZQa1avmTJq6/Cxo1+vNzIkb4m3SOPwBln+K7Xdu38fo2nExEROTRK4qJVSopfamHatKAjybakJDjuOD9ubtas/9Z8ve46+OMPGDTIT6IoVw66dYPx4+GHH4KOWkREJLaoOzVaFSrkZ6lOmwaPPx7TswWKFvUf5bTT/PMNG3xy9/77fps0ye+vWfO/rtd27fwasCIiIpIxtcRFs44dYf16X8AtjpQv78fSPfOMX0Vi+XJfk+7oo+GFF/wqE6VLQ8uWfv3XuXNh586goxYREYkuSuKi2Zln+r7JGOxSDVdq0eE+ffzH/PNPn7Tdeqt/bcQIaNMGDj8cOnSABx+EZcv8ZAoREZFEllBJnJl1NLPxmzdvDjqU8JQt65dIePPNoCPJMwUKQOvWcMcdsHChH0M3eTL83//BqlVwww3QoMF/S4i98IIvdyIiIpJoEiqJc85Nc871Sk5ODjqU8HXsCJ9/7hc7TUCHHQbnnguPPeYXsPjhB3jiCWjVCqZPh4svhgoVoFEjuOkmP4Fi69agoxYREYm8hEriYlKnTv4xtZpugqtWDa64Al555eClTF5+uQpffKGuVxERiU9K4qLdUUf5/sPXXgs6kqiTVSmT33+H8eNr0rixb6n7v//zXa8bNwYdtYiISO5QiZFY0K0bDB0Kv/ziMxLJUPpSJpMmfcQ//5zAe+/BO+/A88/7/Y0b++VpTzsNTjwRChYMLmYREZGcUktcLOjWzfcJvv560JHElDJldtKzJ7z0kq9N9+mncOedUKIE3H+/73I9/HA/7HDMGD9xQl2vIiISK5TExYKjj4b69dWlegiSkqBpU1+65MMP/azXqVN9N+uKFb7ESd26UKMGXH21nxEbK5OYRUQkMSmJixXnnQfz5vkuVTlkJUv6OSOPPQarV/vt0UfhmGN8y11qweFWrXy5k08+0VqvIiISXZTExQp1qUZUzZpw7bW+de6PP3xrXf/+sGOHH47YsqVf67V7d3jqqYSt+CIiIlFESVysUJdqnilQAE46Ce66y4+j27DBt86dfbZvDL3iCqhSxd+OG2/0M2K3bQs6ahERSTRK4mJJ9+5+Taq1a4OOJKGULQvnn+/Xel23Dr76Cu67DypV8t2xqbXpTj3VT5j4+mtNkBARkchTEhdLLrrIP774YrBxJDAzaNgQ+vWD997za72+8w5cc41P8Pr186tHVKniW+xef10TJEREJDKUxMWS6tX9SPvnn1dTT5QoWhROPx0eeACWLfONpE884cfQvfYadO3qJ0icdJJfWUIrSIiISG5REhdrLr7Y18T47LOgI5EMpLbATZrkV42YOxduuQW2bIFBg3yh4YoV4dJL4dVX/SoTIiIiOaEkLtZ06+aXGEhdfkCiVoEC0Lo1jBgBn38O69f7cXUnneRnwXbvDmXK+FUj7rwTliyBvXuDjlpERGKFkrhYU6qUX2Lg5Zdh9+6go5FsqFABevaEV16B336DBQt869yOHXDbbb4Yceo6ry+/7EudiIiIZEZJXCy6+GK/kvt77wUdieRQ/vxwwgkwfDgsXuzLmDz3HLRvD9OnwwUX+Lp0xx8Pw4bBokUqNiwiIvtTEheLzjjDj5afMCHoSCSXlCvnc/OXXvL5+ccf+9Y553wS16IFHHEEXHghvPCCb8kTEZHEpiQuFhUs6P/HnzpV/5vHoXz5fNI2dKhP5jZu9FVlTj8d3n/f3/ry5aFZM7j9dli4UK10IiKJSElcrLrySti1C559NuhIJMLKlPHdq88/D7/+6leRGDbM5/J33eW7ZVMLEj//vJ8VKyIi8U9JXKyqV89Pa3ziCRUeSyBJSX4CxG23+YkRv/0GEyf6JcFmz/aTIlLH0t15p58Vq78eIiLxSUlcLLvySli1yhcjk4R0+OG+VMmECfDLL34CxJAhvnv1ttugSROoXNn/VZkyxderExGR+KAkLpZ16wbJyb41ThJeUpIfJzdkiE/mfv3V16U74QRfWLhzZz8f5pRT4MEH4dtvg45YREQOhZK4WFa0qF9PddIkv4inSBrly/u6dK+95sfJffAB9O3r13i94QaoUwdq14brr/cTJnbsCDpiERHJDiVxse7KK/3/vs89F3QkEsUKFICUFLjvPli+HL7/Hh55xCdxY8fCqaf6CRTnngtPPulXlxARkeimJC7WHXOM7y979FGt2SRhq14d/vc/ePtt34g7bZpv1F2yxH8vqFTJr/M6eLBKmIiIRCslcfHguutg9Wp4992gI5EYVLQonHUWPP44/PgjfPUV3H03lCjhH084wRcavvhiPxNWPfciItFBSVw86NIFKlaEhx8OOhKJcWbQsCH07+8nPf/2m1/H9fTT4Z13fC26smWhdWu45x5YsUIlTEREgqIkLh4UKADXXAMzZsDKlUFHI3GkVCno0cMXEd6wwXetDhoE//4LAwb4coW1a/uJErNn+/rTIiKSN5TExYtevXwJ/0ceCToSiVP58kHLljB8OHz2Gfz0k++CrVPHP7Zv71vpevTwy4Sp21VEJLKUxMWLcuX8/54TJsDmzUFHIwmgcmW4+mo/OeKPP3wx4S5dfCmTiy7yfyVTUuD++31NahERyV1K4uJJnz6+n+vpp4OORBJMsWJwzjnw1FN+5YiPP/bdrX/9Bf36Qd26fuvXDz78EPbssaBDFhGJeUri4slxx/kR5w88oMFJEpikJGjRwq/d+uWXsGaN7+WvVg3GjPGtc+eeewIXXQSvvKKGYxGRnFISF29uucUPVpo4MehIRACoWtXXpJsxw68cMWkSnHDCH8yY4UcAlCnjx9M9+CB8913Q0YqIxA4lcfHmzDOhfn24917VfpCoU6KEHzc3YMBKfv0VFizwXay//upnuNaq5We89u/vX1ORYRGRzCmJizdJSb41bulSX9hLJErly+cLCY8cCcuW+Va4Bx/0JQ9Hj4ZWrXyR4UsvhTfegK1bg45YRCS6KImLR+efD1Wq+GqsIjGiRg3o2xdmzvTdrq+84td0nTLFT5ooU8Y/TpjgXxcRSXRK4uJRgQK+b2ruXD9NUCTGJCfDeef5enO//eYTu8sv92u7XnoplC8Pbdr4Frvvvw86WhGRYCiJi1dXXunL7d99d9CRiBySAgX8xIcxY2DtWp/I3XorbNoEN90ENWtCo0Zw223+NQ0FFZFEoSQuXhUv7vum3ngDvvgi6GhEcoUZNGkCd9zhy5d8951vjTv8cBgxApo2hSOPhN69feudKu2ISDxTEhfP+vb1/VJ33BF0JCIRUaOGHzkwZ45f23XCBJ/IPf00nHKKXwbswgvh1Vfh77+DjlZEJHcpiYtnhx3m/4ebMkWtcRL3ypSBSy7xf91//903QnfuDO+9B927+4TuzDNh3Di/qoSISKxTEhfv1BonCahoUTj7bN8i9+uvfo7Pddf5NVyvvtqXMWnZ0g8Z1bquIhKrYj6JM7M1ZrbczL4IbfWCjimqHHYYXH+9WuMkYeXL51ejGzUKvv0Wvv7aLwm2Zw8MHOjXdG3YEIYM8ePsNDFCRGJFzCdxIWc6544NbcuDDibqXH+9WuNE8BMjGjTws1s//RR+/BEeeghKl/aJ3bHHQu3avl72xx/D3r1BRywikrlAkjgzq2Vm48zsSzPbY2ZzMjmunpnNMrOtZrbezO4ws3x5HG7sS9sat2RJ0NGIRI0jj4Q+ffzEiF9+gfHjfRL34INw/PG+Znbv3vDBB7B7d9DRiojsL6iWuPrAmcCq0HYAMysFzAQc0Am4A7gJGJbB4VNDCeFdZlYgMiHHuBtu8M0NAwYEHYlIVCpXzpdXfOcd2LgRXngBWrTw4+ratfNLgF1+OUyfDjt2BB2tiEhwSdw051wV51w3YFkmx1wNFAE6O+fed86NxSdwN5pZyTTHtXLOHQucCNQD+kUw7tiVnOz7kGbO9JuIZOqww3xpksmT/YoRr78Op58OkybBWWf5ma4XXOCf//NP0NGKSKLKNIkzs4052DaYWcODXdQ5F85IkzOAGc65tNWdJuITuzZpzvVz6PEf4CnghDDOnZiuucb3Hw0YoME+ImEqVsyXKnnhBd9C9/bbvmTJ++9Dt24+oTvnHHj+efjrr6CjFZFEkj+L18rgk6KfwzxXPuBWILe6M48CZqfd4Zxba2ZbQ69NM7NiQD7n3N9mlh/oAnyVS9ePP4ULw/DhvpjWpEl+cUoRCVuhQnDGGX57/HGYP9+31k2e7OvS5c/vu147d4Zzz/VdtCIikWIuk/n0ZrYXaOmcWxTWifyEg11AU+fcZ2EHYDYJKOOcS0m3fxdws3PuwXT7fwaec84NMrMawGR8i2I+YCHQxzm3NYPr9AJ6AZQvX/64iRMnhhviQf3zzz8UL148184XUXv20PTKK0nauZNPJ0zA5c8qj49tMXVfEky83Zu9e2HlyhLMm1eWuXPLsn59EZKSHMccs4mUlN9o3fo3SpWK/jXA4u2+xBPdm+iUV/elbdu2S5xzTdPvzyqJawMsCXVThiX0nsXOuX+z8Z6skrh+zrmH0u1fB0xwzt0a7jXSa9q0qVu8eHFO336AOXPmkJKSkmvni7i33oKOHeGxx3wXa5yKufuSQOL53jgHX30Fr73mt1WrICkJ2rTx3a+dO0P58kFHmbF4vi+xTvcmOuXVfTGzDJO4TMfEOec+zE4Cl+Y9YSdwB/EXcFgG+5OBTbl0jcTUoQOcdJKvbrp5c9DRiMQVMzjmGF93buVKX0B40CBYvx6uvdavFtG2rf8O9euvQUcrIrEsmov9rsSPfdvHzKoAxUKvSU6ZwQMP+AUmhw8POhqRuGUGjRr5f2YrVvgWultv9cnb//7nE7qUFHj0USV0IpJ9WSZxZtbYzJ4ys2lmdreZ1c7gmGPN7PsIxPYOcJqZlUizrzuwDfgwAtdLLE2awGWXwcMP+7WIRCSizPzyXnfcAcuX++W/brvNz3jt3dsndG3awCOP+MLDIiIHk1WJkab4iQLtAAMuAb4ys+vSHVoIqJqdi5pZUTPramZdgUpA2dTnZlY0dNhYYAcw2cxODk1MGAqMTld2RHLqrrv8jNWbbgo6EpGEkrr817BhPqFbuhRuv903jl93HVSq5Ec8jBnju2FFRDKSVUvcXfgVE+o4587CJ2r3AQ+Y2Rgzs0O4bjngtdDWEl+kN/V5OQDn3F9Ae/ys02n4Qr8PAEMO4bqSVvnyMHgwTJsG770XdDQiCat+fRg6FJYt89uQIfDnn35JsMqVoXVrn9Cpy1VE0soqiTsOGOOc2wXgnNvpnLsdvwRWT+B1Myuck4s659Y45yyTbU2a45Y759o554o45yo4525zzu3JyTUlE337Qs2aflkuLQ4pErh69XwSt3Spb6UbOhQ2bfIJXaVKcPLJ8OSTPskTkcR2sIkNB7S2Oeem47tYT8S31B0egbgiwsw6mtn4zZqR+Z9ChWDUKP+/xWOPBR2NiKRx9NG+m/Xrr31Sd+ut8OOPfo3X8uX9EmAvvABbtgQdqYgEIaskbjm+O/MAzrlPgdZAReDFCMQVEc65ac65XsnJyUGHEl06dYJTT/WjrDWiWiQq1a/vJ0WsWgVLlvjG86++gosv9itDdO3q13jdti3oSEUkr2SVxE0HLjezDDMe59wqfGvc2kgEJnnIzNc42LEDbrwx6GhEJAtmfnL5vffCmjWwYIFvmZs/3ydy5cr5xG76dNi5M+hoRSSSskri7gOqAJk21DvnfsFPTKiRy3FJXqtVCwYOhIkT/creIhL1kpLghBN8paCff4aZM6FHD5/AnXUWHHGET/BmzYI9Gk0sEneyWrFhr3PuX+fc3qxO4Jzb7pz7MfdDkzzXv79P5q69FrZvDzoaEcmG/PmhfXt44gk/i/Wtt/ziLBMn+skQlSr5yREffeTXehWR2BfNKzZIXitc2E9uWL0a7rkn6GhEJIcKFvQJ3PPP+2LCkyb5MiVPPAEnngjVq8OAAX7ChIjErrCSODMraGYvRToYiQKnnOL7Y0aO1EoOInGgSBHo0gVee80ndC+84AsN33+/XxKsUSM/vu6nn4KOVESy66BJnJmVBN4FakU+HIkKo0f7VrlevdTvIhJHSpSACy/0Y+bWr/dLfBUv7kdSVK0K119/LE8+6evSiUj0O9jaqZWA+UBJ4NQ8iSiCVCcuTBUq+K/pc+bA+PFBRyMiEVC2LPzvf36M3OrVfgmwP/8suK8GXefOMHmyhseKRLOs1k6tj187dS9wqnNuU14FFSmqE5cNl13mR0PffDOsVRUZkXhWs6YvE/nss4v49FM/t+mjj3w3bOoM1zlz1DAvEm2yaonril+N4XTnnBZ4STRmvhXOOd+t6lzQEYlIhJlB06bwwAO+ZMmMGXD22X6Ga9u2vsu1f39fZFhEgpdVEjc/9PqjZpYvj+KRaFK9Otx9t/9N/uyzQUcjInkof36/kMtzz8GGDfDyy3DMMX7I7DHHQMOG/teDJkSIBCerOnGzgJOBk4CJZqZyJIno2muhVSu/xo+W5BJJSEWL+knrb73134SIEiV8ffCqVf3Ii+efh3//DTpSkcSSZWLmnPsIv7RWE+DlPIlIoktSEjz1lB/dfNVV6lYVSXDpJ0Tcfjt8/z383//58XOXXgoffKDxcyJ54aCta6E1Uk8Aqkc+HIlKderAiBEwbZpP6ERE8BMihg71ydzcudC9O7z+OrRrBzVq+MkSKjcpEjlhdZE65zYAKZENRaJa377+N/P118N33wUdjYhEkaQkvyLEk0/6Jb9efBHq1vXf/erU8atEjB+v+nMiuS3scW7Oua2RDESiXFISTJjgRztffDHs3h10RCIShYoWhQsu8POh1q71K/ht2uRHYxxxhG+te/tt/QoRyQ2arCDhq1LFr626cKHWVhWRg6pUCW65BZYuhU8/9fXmZs3y67pWqQL9+mn9VpFDEXYSZ2bnmdnLZjbXzBal3yIZZG7Rig254IIL/DS1oUNhyZKgoxGRGJBaf27MGD+7dfJkaNECHnrIr9163HHw6KPw119BRyoSW8JK4szsbmAiUAP4CViWwRb1tGJDLnn0Ub8uz0UXqaaAiGRLwYJw7rkwdaqvWvTww34ma+/efsW/Cy7wrXWa3SpycOG2xF0G3Oqca+Gcu9A5d2n6LZJBSpQ5/HBf/Pebb/yEBxGRHChTBq67Dj7/HD77DK64At55x9edq1kT7rhDq/6JZCXcJG4XoL4z+U/79jBokC858tJLQUcjIjGucWNfRPiXX/yvlFq1YMgQqFYNTjsNXn0VduwIOkqR6BJuEvcQcIWZWSSDkRgzdKhfzeGqq1QMSkRyReHCcP758P778MMPvtbcihV+VmvFir7xX2u3injh1om7F1gLrDSz8WZ2b7pNUxUTUf78/itzwYL+N6y+JotILqpWDYYN88ncjBlwyikwdqxfu7VpU3j8cdWek8QW7sSGC4Hr8as2dAC6ZbBJIqpSxdeP+/xzuPnmoKMRkTiULx+ceipMnOhntz78sK8zd+21fjLERRf5FSO0KqAkmnC7U+8GXgFKO+cqOeeqp9tqRDBGiXYdO8INN/j6AVOmBB2NiMSx0qX/mwyxeLFfq/Wtt6BNG6hfHx58EP78M+goRfJGuElcSeBp59yWSAYjMezuu6FZM+jZU+PjRCTizHx9ucceg3Xr4OmnITnZf5+sWNEvLDNvnlrnJL6Fm8S9DrSNZCAS4woWhNdegwIFoHNn1Y8TkTxTrJhvkVu4EL74wpcqefNNOOkktc5JfAs3iZsBXGhmT5rZBWZ2ZvotkkFKjKhaFV5+GZYt8+vr6CuwiOSxY47xpUrWr/etcyVL7t86N3++fjVJ/Ag3iXsZqIov+vsC8Fa6bVpEostlWnYrD5xyCtx5p0/mHn446GhEJEGlts59/LFvnbv8ct8617o1NGjgl/zSMl8S68JN4qofZIuJiQ1adiuPDBgAnTr51a3nzQs6GhFJcMcc41cLXL/e1ycvUQKuv963zv3f//lET61zEovCrRP348G2SAcqMSQpyS/LVb06nHeeL8EuIhKwYsXgsst80vb55/7PU6fC8cf7unNPPw1btwYdpUj4wq0T18PMMiwCZmb9zOy83A1LYl5yMkyeDH//7Sc6bN8edEQiIvsce6xvnVu3zs9w3bHDd7lWrgw33QSrVwcdocjBhdudOhDI7H/hraHXRfbXoAE895z/2turl/orRCTqlCgB11wDX38Nc+bAySf74by1a8MZZ/gadHv2BB2lSMbCTeJqAUszeW0FUDt3wpG406UL3HEHPP883Hdf0NGIiGTIzBcMfvVV+PFHvzT0l1/6Wua1asG998Lvvwcdpcj+wk3itgKVM3mtCqBFMyVzgwf7tVUHDIBpMTGRWUQSWMWKMGSIT+ZefdVXT+rf33e1XnIJLFoUdIQiXrhJ3EzgNjMrl3anmZUFbgXey+3AJI6YwTPP+PLqF1wASzNr1BURiR4FCkC3br6b9euv/USIyZOhRQu/QM1zz/mxdCJBCTeJ6w8UB74zs9fM7GEzew34DigC3BKpACVOFCnip4GVKOH7J377LeiIRETC1qDBf0t8jRkD//zjW+WqVoVhw2DDhqAjlEQUbomRtcAxwCP47tMzQo9jgCbOuZ8iFqHEj0qVfCL366+asSoiMalkSejdG5YvhxkzoEkTP37uyCP90tGffx50hJJIMk3izKxu2ufOud+ccwOdcy2dc7VDj7c65zTUU8LXvLmvITd/vv8au3dv0BGJiGSbGZx6Krz9Nqxc6ddrnTTJJ3Vt2vhuV81qlUjLqiVuuZmtNrOHzOxUMyuYZ1FJfDvvPD/V69VX/WQHEZEYVreurzn3888wapSfENGli5/Vev/9sGlT0BFKvMoqiasA3AlUBF4F/jCzqWZ2pZlVypPoJH716wfXXuvLjjz6aNDRiIgcssMO+69Q8OuvQ5Uq/ldd5cq+C3bVqqAjlHiTaRLnnNvonJvgnOsGlAE6AauBG4G1Zva5md1pZsebmeVRvIfEzDqa2fjNmzcHHYqY+YqaHTtCnz5+ZWoRkTiQP78f9jt3Lnz2GXTtCk884VvszjrLz3ZV7XPJDeFObNjtnJvtnOvnnDsaqAM8DTQFZgMbzey5CMaZK5xz05xzvZKTk4MORQDy5YOXX/alR3r0UPElEYk7jRvDhAmwdq2fALFoEbRt60uUTJwIu3cHHaHEsnBLjOzHOfedc26Mc+50oDRwBbAtVyOTxFCsmC8AfMQR/ivqd98FHZGISK4rX/6/AsLjxsGWLXD++X7c3EMP+eci2ZWjJC4t59xW59wbzrmrciMgSUDly8M77/iZqqecAr/8EnREIiIRUaSIX0p6xQp44w1fmuT66/3jwIGwfn3QEUosyarEyOxsbLPyMmiJQ3Xr+rn6GzfCaafBX38FHZGISMQkJcHZZ/txcx9/7L+/3nsvVKsGl14Ky5YFHaHEgqxa4v4IYysIpIQ2kUPTvLkvBvzNN75rdevWoCMSEYm4Fi18xaVvv4WrrvJ/btAAzjwTZs/WJAjJXFazU7tltgE3ARuB44DfgcF5FK/Eu5NPhpde8l9Nu3aFXbuCjkhEJE/UqOGX9Fq7Fu68089sbd/eT4KYO7eMaqPLAbI1Js7MapnZU8C3wNnAQKCqc25kJIKTBNWlC4wd68fJ9eypVR1EJKGULg233gpr1sD48bB5MwwZ0oD69f1MV323lVRhJXFmVt/MXgJWAG2BvkBN59yDzjnNSpXcd+WVMHKkb5Xr00f9CSKScAoX9r8KV66E225bRqFCfrxcrVq+xU4jTiTLJM7MjjOzycBXQGN8KZHazrmxzrmdeRGgJLD+/X3580cf9ctzKZETkQSULx+0a/cbn38O06f7max9+vhJEHfdpWW9EllWs1PfARYB1YEezrmjnXPPOue0pK/kDTO/LNc11/hpW0OHBh2RiEhgzPxkh3nz/KzWpk1h8GCf1A0YABs2BB2h5LWsWuJOAwyoAjxqZhuz2vImXEk4ZvDII3DZZXDHHTBiRNARiYgErnVrX5Xps8/gjDP899yqVeF///MFhSUx5M/itWF5FoVIVpKS/OjenTv9aN9ChXw3q4hIgmvcGF55BYYP94ncE0/4rWdPGDTId7lK/Mo0iXPOKYmT6JEvHzzzDOzYAf36+USud++goxIRiQp16sCTT/qlve6+2//5mWfgkkt8MlejRtARSiQc8rJbInkmf3548UXo1Amuu863zomIyD5Vqvi5YN9954cTv/CCT/Auu0xLU8ejrCY2jDazKuGeyLzRZlYpd0ITyUCBAr7v4MwzfWnzJ54IOiIRkahTuTI8/DB8/73vtHj5Zb+6Yc+efmUIiQ9ZtcT1BY7I5rn6AuUPKaIIMrOOZjZ+8+bNQYcih6JQIXj9dT+at1cveOyxoCMSEYlKFSvCgw/6ZK5PH7+k11FHwf/9H6xaFXR0cqiySuIMmGBmi8LZgIV5FHOOOeemOed6JScnBx2KHKrChWHKFOjY0U/HevjhoCMSEYlaFSrA6NHwww9www3+e/DRR8PFF8Pq1UFHJzmVVRL3LL5O3LJsbM/h11IVibxChWDSJOjcGfr2hfvvDzoiEZGoVr48jBrlk7mbbvLJ3FFH+U6Nn34KOjrJrqxmp16al4GI5EjBgjBxIlx4oZ+1umuXr3opIiKZKlfOlyS58UZffnPcOHj2WT8ZYuBAn+xJ9NPsVIl9BQr4NVYvuMD/9hk+POiIRERiwhFH+NEo337ru1YfecSXIxk4EP78M+jo5GCUxEl8yJ8fnnvOj9a9/XZfFFhrrYqIhOXII31tuRUrfBWne+6B6tX9d+ItW4KOTjKjJE7iR2pB4F69YMQIaj/8MOzdG3RUIiIxo3Zt37Hx5ZfQrp3/Tlyjhh9yvG1b0NFJekriJL4kJcHYsXDLLVSaOtW3zO3aFXRUIiIxpWFDXwBg0SJo0sQPOa5TByZMgD17go5OUimJk/hjBvfcw/dXXulXeOjSRV8hRURyoFkzmDEDPvjAlym59FI49lh4+22NWIkGYSVxZnZZFq8VNLP7ci8kkdyx9oILfCHgt97yhYH//jvokEREYlJKCnzyiS8WvH07dOjgu1s//TToyBJbuC1x48xsmpntN+nYzJoCXwCZJnkigbrmGt8at2ABtG8Pv6uMoYhITphBt26wbBmMGeMfmzeH7t1VMDgo4SZxJwK1gGVm1sPM8pvZXfhVGtYADSMUn8ihO/98mDoVli6F1q1V0VJE5BAULOjXY129Gm67zXd2HH00XHcdbNwYdHSJJawkzjm3CDgWvyLD88A64H/ANc65M51z6yMWoUhu6NAB3n0X1q+H44/3CZ2IiORYyZJwxx0+mbv8cnj8cahZ0xcP1jDkvJGdiQ27gD+BvcBhwEbgywjEJBIZbdrA3Lm+7EirVvDhh0FHJCIS8ypU8EUBli71o1ZuvdW3zL36qiY/RFq4ExuOwned3gJcDxwJLAcWmNmdZpbp8l0iUeWYY2DhQqhYEU49FV57LeiIRETiwlFH+ZErs2ZBcrIfK9e6NSxeHHRk8SvclrjPgR1AY+fc4865Dc65c4ArgGsB3SKJHVWrwvz5fu589+7w0ENBRyQiEjfatYPPPoMnnvDLeTVrBj17+tEskrvCTeJuA9o4575Lu9M59xzQCPgltwMTiajDD4f334dzzoHrr4ebb9bqDiIiuSRfPrjiCp/E9e8PL7/sV4O4806Nl8tN4U5sGOVcxj3bzrmfnXNn5G5YInmgSBHfnXrttTBqlF/9eefOoKMSEYkbJUvC3Xf7NVnPOMPPZq1bFyZO1Hi53BDumLh6B9siHahIROTLB4884qdTvfSSHyf3559BRyUiEldq1IBJk2DOHChTxld+attWhQIOVbjdqUuBrw+yicQmMxg4EF54wU96OP54Va4UEYmANm38Kg/jxsHXX/slvG64ATZvDjqy2BRuEtcWaJdu6wqMxxf77RSJ4ETy1IUX+mlVf/wBLVrAvHlBRyQiEnfy5YNevWDVKj9u7qGHfBfrCy+oizW7wh0T92EG2xTn3DXAy8B5kQ0zd5hZRzMbv1kpv2SmVSu/QGDZsr7g0fPPBx2RiEhcKl3a15dbtMgXDbj4Yt9S99VXQUcWO7JT7DczHxAjLXHOuWnOuV7JyclBhyLRrGZN363aqhX83//B7bfr66GISIQ0bep/5T7xBCxfDk2aQN++sGlT0JFFv9xI4joAm3LhPCLRo1Qpv0zXZZfB8OG+q3X79qCjEhGJS0lJvmt11Srf1TpmjC8e/PLL+g6dlbBWWjCzVzPYXRA4CqgNDMrNoESiQsGC8OSTUKcODBgAa9bAlClQvnzQkYmIxKXDD4fHHvMJ3dVXwwUXwLPP+nVZq1cPOrroE25LXNkMtkLAPKCjc+6eyIQnEjAzX6nytdfgiy98u/+SJUFHJSIS15o08V2sDz8MCxZA/fpw772wa1fQkUWXcCc2tM1gO8M5d6Vz7u1IBykSuK5d/W8SMz9W7uWXg45IRCSu5csH113nCwWfdpr/Pt20qZ97Jl5ujIkTSQyNG/uVnJs29W38AwfCnj1BRyUiEtcqV/YjWaZM8RWgjj8eeveGv/8OOrLgZTomzszuzcZ5nHOufy7EIxLdypXzteSuu86vJfP11/Dii6AZzyIiEXXOOb7y0+DBfuLDlCnw6KN+f6LKamLDeUC4c0IcoCROEkPBgr7c+LHHQp8+0LIlvPGGnwAhIiIRU6KELw580UVw5ZVw7rnQo4dP6sqUCTq6vJdpd6pzrppzrnqYW428DFokKlxzDcycCb//Ds2b+5IkIiIScc2a+eW7hg+H11+HevX8/LNEk2kSZ2Z7zKxZ6M9Pm5km94qkl7oQYNWqcOaZMGIE7N0bdFQiInGvQAHftfrZZ/5X8Hnn+TloGzYEHVneyWpiw058GRGAnviyIiKSXrVq8NFH0L073HordO6s1ZxFRPJIgwa+HMnIkTBtmm+Ve+mlxCgSnNWYuOXAUDObGnre1cyaZnKsc849nquRicSSYsX8b42WLaFfPz+DdcoU/9tFREQiKn9+X5O9Uye/0M6FF8Irr/i1WStUCDq6yMmqJe46oDzwAH7iQj/gkSw2kcRm5hf8mz0b/vkHWrRQPTkRkTx09NEwfz6MGgXvvee/R8fzWLmsJjZ85Jxr6JwrABjQ0jmXlMmWL+9CFolyrVv7QRpNmvh6ctdfrzLjIiJ5JF8+uOkmv8hOzZp+rNzFF8OmTUFHlvvCLfbbFt+9KiLhqFDBt8j17evnw7dtC7/8EnRUIiIJo25dv9DOkCG+U6RRI5gzJ+iocle4y2596Jz7J9LBiMSVAgXgwQf9WLnPP/ctc3PnBh2ViEjCKFAAhg71yVzhwtCunW+l27496Mhyh5bdEom088/3i/2VKOF/g4wcqTIkIiJ5qEUL/1366qth9Gg/9+yLL4KO6tApiRPJCw0a+HVXu3aFQYOgQwf47begoxIRSRjFisFjj8Hbb/s1WJs39wldLH+nVhInkldKlvQDMx5/HD74ABo39tOoREQkz5xxhl/2ukMH37V61lmwcWPQUeWMkjiRvGTm2/MXLoQiRSAlBe6+O7a/CoqIxJgyZWDyZHjkET8H7ZhjYNasoKPKvmwlcWZWx8zamdmZ6bdIBSgSlxo3hiVLfPfqwIHqXhURyWNm8L//+SHLhx0Gp5ziF92JpYpQWa3YsI+Z1QNeAerha8al5wDVihPJjtTu1ZQUX0uucWOYOBFatQo6MhGRhHHMMX7Ict++fvnrDz7wRQWqVQs6soMLtyVuHFAQ6AzUBaqn22pEJDqReJdR9+rIkbBnT9CRiYgkjGLF4Mkn/ffqpUvh2GP9yonRLtwkrjFwk3PuDefct865H9NvkQxSJO6l7V4dNMi3669bF3RUIiIJpUcPX3qkTh3o3Bluvhl27w46qsyFm8R9BxSOZCAiCS+1e/Xpp2HRIl9e/I03go5KRCSh1KgB8+bBtdf6NVjbt4/eBXfCTeJuAgaZmbpNRSLJDC691K+9Wq0anHOO/02ybVvQkYmIJIxCheDRR+H55+HTT6N3wZ1wk7iRQCVgpZmtMrNF6bcIxiiSeOrU8ePk+vXzdeWaNvWFjUREJM9cdJHvGClZ0i+4M2oUOBd0VP8JN4lbCrwNvAgsAJZlsIlIbipYEO67D2bM8OXFmzXzRY2i6TeIiEica9DAt8adc44fI9elC/z9d9BReWGVGHHOXRrpQPKCmXUEOtaqVSvoUETCd+qp8NVXcNllcN11Pql7+mkoWzboyEREEkLJkvDaa/Dggz6Ra94cpk4NOqocrNhgZmXMrLaZlY5EQJHknJvmnOuVnJwcdCgi2VOuHEybBg8/DO+/7yc9zJgRdFQiIgnDDG64wa/s8OefPpFbsCDYVCjsJM7MupvZCmADsBLYaGYrzKxbxKITkf+Y+Za4RYvg8MPh9NOhd2/YujXoyEREEkabNr44cJ06cO+9RwXatRpWEmdm5wMvA98DlwJnhh6/ByaaWY+IRSgi+2vUyNeUu+EGP32qcWM/YENERPLEkUf6MiT33/8lJUsGF0e4LXG3AuOdcx2cc88552aEHjsATwCDIxeiiBygcGEYPdq362/bBscfD8OGxdaifyIiMaxIEahV659AYwg3iasFvJ7Ja6+HXheRvNaunZ/0cP75MHSoX3d11aqgoxIRkTwQbhK3AWiayWtNQ6+LSBAOO8xXpHz1VVi92i/69/jjKkUiIhLnwk3ingGGmtlgMzvKzEqZWV0zGwwMAZ6OXIgiEpZu3XxB4JNO8qs8nHkmrF8fdFQiIhIh4SZxdwCjgAH4wr6/A8tDz0eFXheRoFWsCO+84yc8fPghNGzoW+hERCTuHDSJM7MkoAJwN1AFSAHODz1Wcc4Ndk79NiJRw8y3xH3+OdSqBd27+1a6jRuDjkxERHJROC1xScAa4ETn3F/OuXnOuVdDj39FNjwRybG6dWHBAhg5Et58E+rX9yXHRUQkLhw0iXPO7QZ+BIpGPhwRyVX588OAAfDZZ1CtGpx3nm+Z++23oCMTEZFDFO6YuHuAW81MizWKxKL69WHhQrjrLpgyxT9/PbOqQSIiEgvCTeJOxY+LW2Nmc83sNTN7Nc32SgRjFJHckD8/DBrkW+WOPBK6doUePeD334OOTEREciDcJK4M8A2wCNgTel42zVYuItGJSO5r0MC3yg0fDpMn+1a5KVOCjkpERLIpfzgHOefaRjoQEclDBQrA4MFw9tnQsyd07uxXfRgzBkqXDjo6EREJQ1gtcWZ2u5lVzOS1CmZ2e+6GJSJ5olEj+OQTv+7qa6/B0UfDK69otQcRkRgQbnfqEKByJq9VDL0uIrGoQAG4/XZYssTPYO3RAzp1gp9/DjoyERHJQrhJnAGZfTWvDKhenEisa9TIj5W7/36YORPq1YOxY2Hv3qAjExGRDGSaxJnZJWY228xm4xO4x1Ofp9k+Al4APsyrgEUkgvLlgxtv9GuwNmsG11wDbdvCqlVBRyYiIulk1RK3FfgjtBmwOc3z1O0H4F6gV2TDFJE8VbOmb4178kn48kvfSnfPPbB7d9CRiYhISKazU51zrwGvAZjZM8Bw59z3eRWYiATMDC6/HM48E3r39is/vPIKPPUUNG4cdHQiIgkvrDFxzrlLlcCJJKgKFfzqDpMmwfr1vpt14EDYti3oyEREElpYdeLM7NWDHeOcO+/QwxGRqNWlC7RrB/36wd13+8Ru3Dg/Zk5ERPJcuLNTy2aw1QXOBk7Er+AgIvGuVCnfnfr++7Bnj0/qevbU0l0iIgEItzu1bQbbMUBt4BfggYhGKSLR5eSTYelSvxbriy/CUUfBhAkqEiwikofCbYnLkHPuJ2AkfoaqiCSSIkXgrrvgiy98Enfppb5rdeXKoCMTEUkIh5TEhewh89UcRCTe1a8Pc+fC+PG+HMkxx8CQIbB9e9CRiYjEtXDXTq2XwXasmZ0PjAI+jWyYIhLVkpLgyit9K1y3bnDHHb623OzZQUcmIhK3wm2JWwp8nW5bAryIL/p7RUSiE5HYUr48vPACvPeeX66rfXu45BL47begIxMRiTthlRgBMqohsB342Tm3LhfjEZF4cMopfumuu+6Ce++Ft96CUaP8TFazoKMTEYkL4c5O/TCD7RMlcCKSqSJF4M474fPPoV49uOwyaNPGJ3ciInLIwp7YYGaFzOwaM3vKzN4zs9qh/d3N7OjIhSgiMa1+ffjwQ78O6/Ll0LgxNR97DLZsCToyEZGYFu7EhjrAKnw5kWpAe6BE6OXWwMBIBCcicSIpya/D+s03cNllVJ40yZclmThRteVERHIo3Ja4h4G1+ATuNCDtoJYPgVa5G5aIxKXSpWH8eD575BE44gg4/3w/fk615UREsi3cJK41MNI5twlI/7V5A1AhN4MSkfi2pV49WLQIHn0Ulizx5UgGDoR//w06NBGRmBFuErcdKJLJa5WATbkSjYgkjnz54NprfRfrBRfA3Xf7CRBTpqiLVUQkDOEmce8Dg8wsOc0+Z2aFgOuAt3M9MhFJDOXK+XVX582D5GTo3Bk6dIDVq4OOTEQkqoWbxN0MlAVWA8/ju1Rvxxf9rQjcGpHoRCRxtGoFn30Go0fD/PnQoIFfvmvbtqAjExGJSuHWifsJOAYYi5/c8B1+HNxrwHHOuV8jFaCIJJD8+eGGG/xEh86d/fJd9evDm2+qi1VEJJ2w68Q55/5yzt3mnDvBOVfHOdfSOXerc+6PSAYoIgmoYkV46SWYNQsKF4ZOneCMMzSLVUQkjbCTOBGRPNeuHXz5JTzwACxcCA0bws03w99/Bx2ZiEjgMl071cxmZ+M8zjnXPhfiERHZX4ECcP31fgbroEFw//3w/PNwzz1w8cW+kLCISALK6rffH2FsBYGU0BYYM3vMzDRgRiSelSvnl+765BOoVg169oQTT4TFi4OOTEQkEJm2xDnnumX2mpkdCfQHzgJ+Bx7I/dDCY2atgWJBXV9E8lizZvDRR741rn9/aN4cLrsMRozwiZ6ISILIVj+EmdUys6eAb4Gz8WumVnXOjczmOcaZ2ZdmtsfM5mRyXD0zm2VmW81svZndYWb50h1TCLgb6JedzyEiMS4pCS65xBcKvvFGePZZqFMHHn4Ydu0KOjoRkTwRVhJnZvXN7CVgBdAW6AvUdM496JzLbhGn+sCZwKrQltH1SgEz8fXoOgF3ADcBw9IdejvwlHPut2zGICLxIDkZRo2Cr7+GFi2gb19o3BhmZ2dIr4hIbMoyiTOz48xsMvAV0Bi4AqjtnBvrnNuZw2tOc85VCXXXLsvkmKvxy3x1ds6975wbi0/gbjSzkqHYGgEtgGdyGIeIxIujjoJ334U33vDFgdu3h65d4ccfg45MRCRiMk3izOwdYBFQHejhnDvaOfesc27PoVzQObc3jMPOAGY459LWEZiIT+zahJ6fCNQDfjCzNaGY15hZ2UOJT0RilBmcfTYsWwZ33gnvvOOTu9tug3/+CTo6EZFcl1VL3GmAAVWAR81sY1ZbLsd1FLBfVU/n3Fpga+g1nHOPO+cqOueqOeeqhfZVU9eqSIIrXBhuvdUXBu7SxSd0der4cXN7w/kOKSISG8xlspSNmQ3Jzomcc+nHqx384maTgDLOuZR0+3cBNzvnHky3/2fgOefcoAzO5ZxzlsW1egG9AMqXL3/cxIkTsxtupv755x+KFy+ea+eT3KH7Er3y8t6UXL6cWo88QskVK/i7bl2++9//2NywYZ5cO9bo30z00r2JTnl1X9q2bbvEOdc0/f5Mk7i8cJAkrp9z7qF0+9cBE5xztx7KdZs2beoW52JtqTlz5pCSkpJr55PcofsSvfL83uzdCy+/7EuSrFsH550H994LVavmXQwxQP9mopfuTXTKq/tiZhkmcdFa6vwv4LAM9icDm/I0EhGJfUlJcOGFviTJ0KEwbRrUrQuDB2u8nIjErGhN4lYSGvuWysyq4Iv6agVsEcmZYsVgyBBYtQq6dYO77oLatWHCBI2XE5GYE61J3DvAaWZWIs2+7sA24MNgQhKRuFG5sl/x4eOP/RJel17qV4KYNy/oyEREwpbnSZyZFTWzrmbWFagElE19bmZFQ4eNBXYAk83s5NCkhKHA6HRlR0REcq5FC7+E10svwcaNcNJJfrzcDz8EHZmIyEEF0RJXDngttLXE13pLfV4OwDn3F9AeyAdMwxf6fQDI1oxZEZGDMoPzz/fj5YYNg+nT4eijYdAg2LIl6OhERDKV50mcc26Nc84y2dakOW65c66dc66Ic66Cc+62Qy00LCKSqaJF4fbb/Xi57t1h5Eg/Xu6JJ2CPfvWISPSJ1jFxEWFmHc1s/ObNm4MORUSiVaVKvjDwJ59ArVrQqxcce6xf1ktEJIokVBLnnJvmnOuVnJwcdCgiEu2aN/cTHV5/HbZvhzPOgNNOg6++CjoyEREgwZI4EZFsMYPOnf16rA8+CIsX+1a5yy+H9euDjk5EEpySOBGRgylYEPr2hdWr4cYb4YUX/Hi5oUNVLFhEAqMkTkQkXKVKwahRsGIFdOzoZ7PWqQNPPaXJDyKS55TEiYhkV40aMHEiLFwI1avDFVf4btYZM4KOTEQSiJI4EZGcatkS5s+H116DrVvh9NP99vXXQUcmIglASZyIyKEwg65dYflyGD0aFi3yrXJXXgm//BJ0dCISxxIqiVOdOBGJmEKF4IYb/OSH66/3teZq1/bj5v79N+joRCQOJVQSpzpxIhJxhx8O99/vJz+ceaafwZq68sPu3UFHJyJxJKGSOBGRPFOzJrz6KixYANWq+ZUfGjWCN94A54KOTkTigJI4EZFIOuEEn8hNngx798I558BJJ8HHHwcdmYjEOCVxIiKRZgbnngtLl8LYsX7c3PHHQ5cusGpV0NGJSIxSEiciklfy54erroJvv4U77oD33oN69eDaa2HDhqCjE5EYoyRORCSvFS8Ot90G330HV1/tJz3UrOknQWzZEnR0IhIjlMSJiASlXDl45BFfY+7MM305klq14LHHYNeuoKMTkSinJE5EJGi1a/uZrJ98AkcfDf/7H9SvD5MmaSariGRKSZyISLRo3hw++ADeegsKFoRu3fzs1nnzgo5MRKJQQiVxWrFBRKKeGXToAF9+CU89BT/95EuSnH2273YVEQlJqCROKzaISMzIlw8uu8yXIBkxAj78EBo2hCuugHXrgo5ORKJAQiVxIiIxp2hRGDjQz2Tt0weee86PoRs0CNSrIJLQlMSJiMSCMmXggQfgm2984eCRI6FGDb9O6/btQUcnIgFQEiciEkuqV4cXX4TPPoNmzaBfP98y9/TTsHt30NGJSB5SEiciEosaN4Z334XZs6FiRbj8cmjUCKZMUVkSkQShJE5EJJa1bQsffwyvvw5790Lnzn5d1jlzgo5MRCJMSZyISKwz88nb0qXw5JPw888+uTvjDPjii6CjE5EIURInIhIv8uf33arffgv33edXgGjcGC64wM9uFZG4oiRORCTeFCniJzx8/70vTzJ1Khx1FPTuDb/+GnR0IpJLlMSJiMSrww7zhYK/+84XCR47FmrVgttuU405kTiQUEmclt0SkYRUoQI8/jisWAFnnQV33gk1a8Lo0aoxJxLDEiqJ07JbIpLQateGiRNh8WI47ji46SaoUweeeQb27Ak6OhHJpoRK4kREBJ/AzZgBs2bBEUf4NVobNaL0/PmqMScSQ5TEiYgkqnbt/AzWSZNgzx4a3nYbnHgizJ0bdGQiEgYlcSIiicwMunSBpUv5pl8/WLsW2rSBM8+EL78MOjoRyYKSOBERgfz5+aVDB19j7p57YOFCX2Puoot8qRIRiTpK4kRE5D9FisAtt/jErX9/mDzZ15i77jrYsCHo6EQkDSVxIiJyoFKlYORIWL3aT3x4/HFflkQ15kSihpI4ERHJXMWKvkhw2hpzNWrA/ferxpxIwJTEiYjIwaXWmFuyBJo188t61a4NTz8Nu3cHHZ1IQlISJyIi4WvSBN59F2bP9q10l18ODRv6sXOqMSeSp5TEiYhI9rVtCx9/7JO31DIlLVv65E5E8oSSOBERyRkzOPdc+Oor3636yy/Qvj2cdprvdhWRiEqoJM7MOprZ+M2aWSUiknvy54dLL4VVq/yEhyVLoGlT6N7d7xORiEioJM45N8051ys5OTnoUERE4k/hwnDjjfDdd74UyfTpUK8eXHUVrFsXdHQicSehkjgREckDyclwxx0+mbv2WnjmGahVCwYMgL/+Cjo6kbihJE5ERCKjfHl4+GH45hvo1g3uvdfXmLv7bti6NejoRGKekjgREYms6tXhuefgiy+gVSsYONC3zI0dC7t2BR2dSMxSEiciInmjUSOYNg3mzfMtctdc48fMTZwIe/cGHZ1IzFESJyIieatVK5/IvfUWFCkC55/vZ7POmKGCwSLZoCRORETynhl06ACffw4vvACbNsHpp0O7dr6IsIgclJI4EREJTr58cOGFsHIljBkDy5fD8cf7IsLLlwcdnUhUUxInIiLBK1gQevf2ZUmGD4dZs/yarJdeCmvXBh2dSFRSEiciItGjeHEYPBi+/x5uuAFefhlq1/ZFhH/7LejoRKKKkjgREYk+ZcrAqFHw7bdw0UXw0ENQs6YvIrxlS9DRiUQFJXEiIhK9qlSBp56CpUvhlFNgyBCfzD38MOzYEXR0IoFSEiciItHv6KPh9df9zNUGDaBvXzjqKHj+edizJ+joRAKhJE5ERGJHixZ+0sN778Hhh8P//R8ce6wvIqwac5JglMSJiEhsMfNdq59+Cq+84rtVzz77vyLCIgkioZI4M+toZuM3b94cdCgiInKokpLgvPNg2TIYNw7WrIGTTvJFhL/8MujoRCIuoZI459w051yv5OTkoEMREZHcUqAA9OrlZ7Lecw989BE0buyLCH//fdDRiURMQiVxIiISx4oWhVtu8Ylb//4wZQrUreuLCP/6a9DRieQ6JXEiIhJfSpWCkSNh9Wq44goYO9aXJRk8GDScRuKIkjgREYlPFSvC44/DihV+4sNdd0GNGr6I8LZtQUcncsiUxImISHyrXdsv37VkCTRrBjffDHXq+CLCu3cHHZ1IjimJExGRxNCkCbz7LsyeDZUq+a7WBg18EWHVmJMYpCROREQSS9u2sHChn/iQlARdu/5XRFgkhiiJExGRxGMG55wDX38NzzzjZ6+efDKceiosXhx0dCJhURInIiKJK18+6NkTVq2C0aPhs8/8uLnzzoNvvgk6OpEsKYkTEREpXBhuuMHXmLv9dnj7bahf3xcRXrcu6OhEMqQkTkREJFXJkjBsmE/m/vc/mDABatXyRYT//DPo6ET2oyROREQkvXLl4KGHfJdqt26+tlyNGr6I8L//Bh2dCKAkTkREJHPVq8Nzz8GXX8JJJ8GgQb5l7vHHYdeuoKOTBKckTkRE5GAaNoQ334T5830Sd+21cPTRvojw3r1BRycJSkmciIhIuE48EebOhenToVgxuOACOO44eP/9oCOTBKQkTkREJDvM4Mwz4fPP4YUXYNMmX1/utNN8t6tIHlESJyIikhNJSXDhhbByJdx/P3z6KTRu7OvO/fxz0NFJAlASJyIicigKFYIbb4TvvoObbvLj5GrX9pMgNm8OOjqJY0riREREckOpUnDffb4sSZcuvhxJrVowZgzs3Bl0dBKHlMSJiIjkpmrV/Fi5xYuhUSPo08ev/jBpEjgXdHQSRxIqiTOzjmY2frOat0VEJNKOOw5mzvRLeBUu7IsGn3ACLFgQdGQSJxIqiXPOTXPO9UpOTg46FBERSQRmcMYZ8MUX8OST8OOP0KoVdO7su11FDkFCJXEiIiKByJcPLr8cvv0Whg/3deXq1/frs27cGHR0EqOUxImIiOSVYsVg8GA/k/Wqq2DcOKhZE+68U2uySrYpiRMREclr5crBo4/CsmW+UPBtt0GdOvDUU7BnT9DRSYxQEiciIhKUunXh9df9mqxVq8IVV8Cxx8J77wUdmcQAJXEiIiJBO/FEP2v1tddg61a/hFeHDrBiRdCRSRRTEiciIhINzKBrV1i+3BcNnj8fGjaE3r0poNJYkgElcSIiItGkUCHo1w9Wr/aTH8aOpcWFF/r1WXfsCDo6iSJK4kRERKJR2bJ+8sNXX7G5QQOf2NWvD5Mna+UHAZTEiYiIRLd69fj67rthxgy/8kOXLpCSAkuWBB2ZBExJnIiISCw49VS/8sO4cbByJTRtCpdcAuvWBR2ZBERJnIiISKzInx969fIrPwwYAK+8ArVrw9ChKhacgJTEiYiIxJqSJWHkSF+C5OyzYdgwXyz42Wdh796go5M8oiROREQkVlWvDhMn+hpzlStDz57QrJkvTyJxT0mciIhIrDvhBFi4EF56CX77DVq3hvPPh59+CjoyiSAlcSIiIvEgKcknbitXwu23w9SpcNRRMHw4bNsWdHQSAUriRERE4knRon6M3MqVfumu22+Ho4+GSZNUXy7OKIkTERGJR1WrwquvwgcfQHIydOsG7dvDV18FHZnkEiVxIiIi8Sy1MPBjj8GXX0LjxvC//8EffwQdmRwiJXEiIiLxLn9+uOYaX1/u2mt9weDateGRR2D37qCjkxxSEiciIpIoDj8cxozxKz80bgzXXecfZ88OOjLJASVxIiIiiaZBA5g5EyZP9is9tG/v12T94YegI5NsUBInIiKSiMzg3HNh+XK48054912oV8+XJNm+PejoJAxK4kRERBJZ4cJw663wzTd+Ca/bb/ctdW+/HXRkchBK4kRERMQv2/XKK/D++34iRIcOcM45sGZN0JFJJpTEiYiIyH9OPtnXkrv7bp/QHX20725VF2vUURInIiIi+ytYEPr396s+dOwIt93mu1jfeSfoyCQNJXEiIiKSsSpV/KoP770H+fLBmWf6yRDqYo0KCZXEmVlHMxu/efPmoEMRERGJHaec4rtYR470CV29enDXXbBjR9CRJbSESuKcc9Occ72Sk5ODDkVERCS2FCoEAwbAihW+RW7wYN/FOmNG0JElrIRK4kREROQQHXkkTJrkkzczOP10OP98+PXXoCNLOEriREREJPtOPdV3sQ4d6ld+OOooGDsW9u4NOrKEoSROREREcqZwYRgyxCdzTZrANdfAiSf65xJxSuJERETk0NStC7NmwXPPwerVPqG75Ra/LqtEjJI4EREROXRmcPHFvrZcz55w331Qvz5Mnx50ZHFLSZyIiIjkntKl4cknYe5cKFoUzjoLunWD9euDjizuKIkTERGR3Ne6NXzxha8n99ZbfuLDmDGwZ0/QkcUNJXEiIiISGQULwqBBsHQpHH889OnjJz4sWxZ0ZHFBSZyIiIhEVs2a8O678OKL8N130LgxDBsGO3cGHVlMUxInIiIikWcGF1wAy5f7MXJDh8Jxx8EnnwQdWcxSEiciIiJ5p2xZ3yL31luwaZPvZr3xRpUjyQElcSIiIpL3OnTwY+OuvhoeeAAaNoSZM4OOKqYoiRMREZFglCwJjz0GH34IBQrAKafA5ZfDX38FHVlMUBInIiIiwTrpJPjySxg4EJ59FurV8+uxSpaUxImIiEjwCheGESPg00+hQgXo0gV69IDffw86sqilJE5ERESiR+PGsGiRLxI8ebJfumvq1KCjikpK4kRERCS65M/viwQvXgyVKsG55/p1Wf/8M+jIooqSOBEREYlOjRr5OnJDh8LEidCgAUyfHnRUUUNJnIiIiESvAgVgyBCfzJUpA2edBZdd5mvMJTglcSIiIhL9mjTxkx5uvRWee87XlZsxI+ioAqUkTkRERGJDoUJw552wcCGUKAGnnw69esGWLUFHFgglcSIiIhJbmjWDzz6Dm2+GJ5+EY4/1iV2CURInIiIisadwYbj3Xr/aw5490KoV3H477NoVdGR5RkmciIiIxK7WreGrr3wJkuHD4cQTYdWqoKPKE0riREREJLaVLAkTJsBrr8Hq1b5g8Pjx4FzQkUWUkjgRERGJD127wtdf+9a4q66Cs8+GjRuDjipilMSJiIhI/KhUCd59Fx58EN5/35cieeutoKOKCCVxIiIiEl+SkqBvX1iyBCpUgI4doXdv2L496MhylZI4ERERiU/16/uVHm68ER59FFq0gBUrgo4q1yiJExERkfhVqBDcfz+8/TasXw9Nm8Izz8TFpAclcSIiIhL/zjgDvvwSWrb0a69eeCH8/XfQUR0SJXEiIiKSGCpWhPfe80t3vfrqf+uxxiglcSIiIpI48uWDW2/1Kz3s2gUnnOC7W/fuDTqybFMSJyIiIonnxBPhiy98Lbl+/eCss+D334OOKluUxImIiEhiKlUKJk2Cxx6DWbN89+onnwQdVdiUxImIiEjiMoNrroGPPvJdra1bw5gxMTF7VUmciIiIyHHHwWefwWmnQZ8+cP75sGVL0FFlSUmciIiICPju1TfegJEj4bXXoFkzWLYs6KgypSROREREJFVSEgwY4MfIbdoEzZvDCy8EHVWGlMSJiIiIpJeSAp9/7rtZL74Yrr4aduwIOqr9KIkTERERyUiFCjB7Ntx8M4wb5xO79euDjmqfmE7izOxDM/vSzL4ys0lmVjLomERERCSO5M8P997rV3j4+mvfMrdgQdBRATGexAFnO+eOcc41AtYCNwcdkIiIiMShbt3g44+hWDFo2xbGjg28DEmeJ3FmVsvMxoVa0PaY2ZxMjqtnZrPMbKuZrTezO8wsX9pjnHObQ8cmAcWA6C/qIiIiIrGpQQO/1urJJ8M111B31KhAx8kF0RJXHzgTWBXaDmBmpYCZ+KSsE3AHcBMwLINj3wY2AHWBeyMTsoiIiAi+DMm0aTB4MEXXrAk0lCCSuGnOuSrOuW5AZsVXrgaKAJ2dc+8758biE7gb0497c86dCRwBLAKujWDcIiIiIn5lh+HD+eLBB6FQocDCyPMkzjm3N4zDzgBmOOf+TrNvIj6xa5PBOfcAzwL/lytBioiIiByEK1Ag0OtH68SGo4CVaXc459YCW0OvYWalzKx8mkO6AEvzLEIRERGRAOUPOoBMlAI2ZbD/r9Brqce8amYFAQNWANdldkIz6wX0Aihfvjxz5szJtWD/+eefXD2f5A7dl+ilexOddF+il+5NdAr6vkRrEgcZzzS11P3Oue+BpmGfzLnxwHiApk2bupSUlFwI0ZszZw65eT7JHbov0Uv3JjrpvkQv3ZvoFPR9idbu1L+AwzLYn0zGLXQiIiIiCSVak7iVhMa+pTKzKvhacCszfIeIiIhIAonWJO4d4DQzK5FmX3dgG/BhMCGJiIiIRI88HxNnZkXxxX4BKgElzaxr6PnbzrmtwFigDzDZzO4BagBDgdHpyo6IiIiIJKQgJjaUA15Lty/1eXVgjXPuLzNrDzwCTMOPg3sAn8iJiIiIJLw8T+Kcc2vws0wPdtxyoF3EAxIRERGJQdE6Ji4izKyjmY3fvHlz0KGIiIiIHJKESuKcc9Occ72Sk5ODDkVERETkkCRUEiciIiISL5TEiYiIiMQgJXEiIiIiMUhJnIiIiEgMUhInIiIiEoOUxImIiIjEICVxIiIiIjEooZI4FfsVERGReJFQSZyK/YqIiEi8SKgkTkRERCReKIkTERERiUHmnAs6hjxnZr8BP+biKcsAv+fi+SR36L5EL92b6KT7Er10b6JTXt2Xqs65sul3JmQSl9vMbLFzrmnQccj+dF+il+5NdNJ9iV66N9Ep6Pui7lQRERGRGKQkTkRERCQGKYnLHeODDkAypPsSvXRvopPuS/TSvYlOgd4XjYkTERERiUFqiRMRERGJQUricsjM6pnZLDPbambrzewOM8sXdFyJzsy6mdmbZrbOzP4xsyVmdn7Qccn+zKxS6P44MysedDyJzMzym9kAM/vWzHaY2c9m9kDQcQmYWQ8z+yz0b2WdmT1nZhWDjiuRmFktMxtnZl+a2R4zm5PBMWZmg8zsJzPbZmZzzezYvIhPSVwOmFkpYCbggE7AHcBNwLAg4xIAbgT+AW4AzgY+AF4ys+sCjUrSuw9/nyR4zwB9gFHAqcAAYFugEQlmdjbwMvAR/v+Z/sBJwFtmpv+780594ExgVWjLyADgNuAeoCP+d9tMMzsi0sFpTFwOmNlA4BZ88b2/Q/tuAYYCR6Tuk7xnZmWcc7+n2/cScLxzrnpAYUkaZtYaeAMYgU/mSjjnlNAFwMxOB6YBxzjnlgcdj/zHzCYCtZ1zx6XZdzb+304959yKwIJLIGaW5JzbG/rzJKCMcy4lzeuFgQ3A/c65O0L7igFrgHHOucGRjE/ZfM6cAcxIl6xNBIoAbYIJSQDSJ3AhnwPl8joWOVBoyMEYfOu1qs8H7zJgthK4qFQA2Jxu36bQo+VtKIkrNYHLwglASeDVNO/5F//l6IwIhgYoicupo4CVaXc459YCW0OvSXQ5AdB/UtHhaqAw8GjQgQgALYBVZvaImf0dGuM7WeOuosLTQGsz+z8zK2lmdYA7gQ+UdEeVo4A9wLfp9q8gD/IBJXE5U4r/vhGl9VfoNYkSZtYeP55ESUPAzKw0MBy40Tm3K+h4BIAjgJ7AsUAP4FLgOGCKmam1J0DOuen4ezMe3yL3DZAP6BxgWHKgUsA/zrk96fb/BRQ1s4KRvHj+SJ48zmU0mNAy2S8BMLNqwEvAG865CcFGI8BdwCfOubeDDkT2sdDWyTn3B4CZ/QJ8CLQDZgUYW0Izs7bAWOAh4B2gPH7c9RQzOzmDpEGCk1k+kNlruUZJXM78BRyWwf5kMm6hkzxmZofjf/GtBS4KOJyEZ2b18eOvTjKzw0K7i4Yek81sj3NOMyLz3l/A96kJXMh8YCdQDyVxQbofeNM51z91h5l9gR/K0wmYHFBcsr+/gBJmli9dYn0YsDXSvQ7qTs2ZlaTr6zazKkAx0o2Vk7xnZkWBt4CCQIfQIFMJVm38QO2F+F96f/FfF/fP+MkOkvcym+FowMEGdEtkHQV8kXaHc+4bfPmXmkEEJBlaie/mrpVu/wFj5yNBSVzOvAOcZmYl0uzrjv/H9WEwIQn4wqXAa/ik4Qzn3MaAQxJvPtA23XZP6LUz8aVGJO+9BTQyszJp9p2ET7i/DCYkCfkRaJJ2h5kdja+CsCaIgCRDHwF/A91Sd4QaEjric4WIUndqzozFF8ecbGb3ADXwYxVGq0Zc4B7DJwV9gcPNrGWa1z53zu0IJqzEFir9MiftvtCYRYB5qhMXmPH432XTzGwEUAKfXM90zs0PNDIZCzxgZuv5b0zc7fgETuNK80goITsz9LQSUNLMuoaev+2c22pmdwO3mdlf+Na3G/GNZBHvYVCx3xwys3rAI8Dx+HFwTwJDNdg0WGa2BqiaycvVnXNr8i4ayYqZ9cSvFqBivwEys1rAw/galzvxxWRvcM79FWhgCS40O/hq4Bp89+kmfIv2QOfc9wGGllBCXzZ/yOTl6s65NaF7NQh/r0oDi4E+zrnPIx6fkjgRERGR2KMxcSIiIiIxSEmciIiISAxSEiciIiISg5TEiYiIiMQgJXEiIiIiMUhJnIiIiEgMUhInIlHLzIaamUuz/Wpmb5lZo1y8xu9mNjTN8zlmNim3zp/FddN+tqmRvl4G14z4ZxSRyNKKDSIS7TYDp4f+XA24A3jfzI52zv0ZgetdC0R00eo0Uj9bJD5HRp4E3sWvbCIiMU5JnIhEu93OuY9Df/44tCrHQnzy81JuX8w5tzy3z5mFtJ8t4pxzPwM/m5mWBxSJA+pOFZFYk7owe5XUHWZ2vJm9aWbrzexfM/vCzC5M/0YzO8nMvjSz7Wa2xMxOyOCY/bpTzWyCmS1Od0y1UJfkWWn2XW5my8xsW6iL9kMzq5+TD2hmjcxsmpltMrN/zGyRmZ0Sei0ldO32ZvZG6PN+a2anmlk+M7svdP11ZnZjTq4vIrFBLXEiEmuODD2mXc+wKrAAv2j4duBE4Bkz2+ucexnAzCriFxJfBHQFKgIvAkUPNSAzOyl07dvxrYQl8esqJ+fgXEeFPss3+LUz/wCakiZpDRkX2h4FbgEm4T+PARcAHYD7zeyjvGztE5G8oyRORKKemaX+rqoKPAJ8gV+oHQDn3MQ0xxowF6gMXAm8HHrpenyC18E5tzV07L/AC7kQYnPgK+fcyDT73szhuYbgx8q1ds5tC+17P4PjnnfO3QdgZj8Dy4C6zrl2oX0zge7AuYCSOJE4pO5UEYl2pfETDXYBq4HGQGfn3I7UA8yslJk9bGY/pjm2F1AnzXmaA++nJnAhk3Mpxi+Axmb2QKjLtuAhnKsd8EqaBC4zs9L8eXXocXbqDufcXuB7oNIhxCIiUUxJnIhEu81AM6AlcBVQEHjJzNL+/pqAb3W6Dzg1dPzTQOE0xxwBbEx74lCi9M+hBuicmwlcCpwEzAF+N7PHzKxYDk5XGvgljOM2pbn+zvT7Qnay/89AROKIulNFJNrtds6lTiz4xMy2Ac8B3YBXzKwwfvxXb+fc2NQ3pUvyAH4FyqXdYWZFgOIHuf52fOKY1uHpD3LOPQs8a2Zlgc7AA8DfwICDnD+9P4AK2XyPiCQgtcSJSKx5AT/+q3/oeSEgH5C2e7UEcHa6930KnGJmaScydA7jej8D1ULJYqpTMjvYOfebc24cMA+oF8b505sFnJfueiIiB1BLnIjEFOecM7MRwItm1t45N8vMPgVuD9U/24tv/dqMnyWa6kHgf8BbZjYaPzt1IHCwsWdT8QWGnzSzCfgxeZemPcDMhuFb5+YAv4eOaUP2W+EAhuETzrlmdj++Za4x8Idz7ukcnE9E4pRa4kQkFr0CfIsvrQG+pMYP+G7Wh4DXQ3/exzm3DjgTKBN6/VrgIiDtRIcDOOeWApfhS4a8iU/OLkt32Kf4VrexwAzgGmBoKJZscc59A7TCJ4NPAlPwJVF+zO65RCS+mXMu6BhERBJOaL3W3vgJF3tDs0kjfc0k/Jf3WcBvzrmukb6miESOWuJERIKTWj4lt0qdHMztoeudlEfXE5EIUkuciEgAQitIVAw9/cs5910eX/NP59z3kb6miESOkjgRERGRGKTuVBEREZEYpCROREREJAYpiRMRERGJQUriRERERGKQkjgRERGRGKQkTkRERCQG/T8w9Q4ET9jRaQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_csv('output2G_x-data_0002.csv')\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "plt.plot(df[\"x\"],df[\"u1\"],\"r-\",label=\"FEM Solution 1-Group\")\n",
    "plt.plot(df[\"x\"],df[\"u2\"],\"b-\",label=\"FEM Solution 2-Group\")\n",
    "plt.yscale(\"log\")\n",
    "#plt.xlim(0,100)\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.xlabel(\"Radius [cm]\")\n",
    "plt.ylabel(\"Neutron flux [N/cm^2]\")\n",
    "font = {'family' : 'DejaVu Sans',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 15}\n",
    "plt.rc('font', **font)\n",
    "plt.title(\"2-Group FEM Solution\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [FDM Approach](#toc)<a id=\"appFDM\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Discretization](#toc)<a id=\"setupFDM\"></a> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similary to the FEM descretiation we are implementing the idea that group-1 is the fast neutrons that scatter into group-2 the thermal neutrons. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taking our NDE's and expanding to spherical coordinates:\n",
    "\n",
    "For Group-1\n",
    "\\begin{align*}\n",
    "    -\\nabla \\cdot D_1 \\nabla \\Phi_1(r)  + \\Sigma_{a,1} \\Phi_1(r) =  -\\Sigma_{s,1 \\rightarrow 2} \\Phi_1(r) \\ \\ \\ \n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "   -D_{fast} \\left [ \\frac{d\\Phi(r)_{fast}^{2}}{d^{2}r}+\\frac{2}{r}\\frac{d\\Phi(r)_{fast}}{dr} \\right ] +\\Sigma_{a,fast}\\Phi(r)_{fast} + \\Sigma_{s,fast \\rightarrow thermal}\\Phi(r)_{fast} = 0\\ \\ \\ \n",
    "\\end{align*}\n",
    "\n",
    "Then Group-2\n",
    "\\begin{align*}\n",
    "    -\\nabla \\cdot D_2 \\nabla \\Phi_2(r)  + \\Sigma_{a,2} \\Phi_2(r) =  \\Sigma_{s,1 \\rightarrow 2} \\Phi_1(r) \\ \\ \\  \n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    " -D_{thermal} \\left [ \\frac{d\\Phi(r)_{thermal}^{2}}{d^{2}r}+\\frac{2}{r}\\frac{d\\Phi(r)_{thermal}}{dr} \\right ] +\\Sigma_{a,thermal}\\Phi(r)_{thermal} -  \\Sigma_{s,fast \\rightarrow thermal} \\Phi(r)_{fast} =0 \\ \\ \\  \n",
    "\\end{align*}\n",
    "\n",
    "Re-organizing results in the fast neutron (1eV>) equation:\n",
    "\\begin{align*}\n",
    "\\frac{d\\Phi(r)_{fast}^{2}}{d^{2}r}+\\frac{2}{r}\\frac{d\\Phi(r)_{fast}}{dr}-\\frac{\\Sigma_{a,fast}}{D_{fast}}\\Phi(r)_{fast}= \\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}\\Phi(r)_{fast}\n",
    "\\end{align*}\n",
    "\n",
    "Likewise for thermal neutrons (1eV<)\n",
    "\\begin{align*}\n",
    "\\frac{d\\Phi(r)_{thermal}^{2}}{d^{2}r}+\\frac{2}{r}\\frac{d\\Phi(r)_{thermal}}{dr}-\\frac{\\Sigma_{a,thermal}}{D_{thermal}}\\Phi(r)_{thermal}= -\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{thermal}}\\Phi(r)_{fast}\n",
    "\\end{align*}\n",
    "\n",
    "As depicted from the equation above the coupling of the two groups is done by the source term. This conceptually makes sense *need to look over interaction cross section for thermalcase*\n",
    "\n",
    "\n",
    "Now that the differentials are expanded into their respected spherical coordinates a Talyor series expansion using a central approximation for each each derivative can be implemented. \n",
    "\n",
    "Where for a second order derivative the central approximation: \n",
    "\\begin{align*}\n",
    "\\frac{d\\Phi(r)_{fast}^{2}}{d^{2}r}= \\frac {\\Phi(r)_{i+1,fast}-2\\Phi(r)_{i,fast}+\\Phi(r)_{i,fast}}{h^2}\n",
    "\\end{align*}\n",
    "\n",
    "Then for the first order central approximation:\n",
    "\\begin{align*}\n",
    "\\frac{d\\Phi(r)_{fast}}{dr}= \\frac{2}{r_{i}}\\frac {\\Phi(r)_{i+1,fast}-\\Phi(r)_{i-1,fast}}{2h}\n",
    "\\end{align*}\n",
    "\n",
    "Next for the zeroth order central approximation for both absorption and downscattering, respectively:\n",
    "\\begin{align*}\n",
    "-\\frac{\\Sigma_{a,fast}}{D}\\Phi(r)_{fast}=-\\frac{\\Sigma_{a,fast}}{D_{fast}}\\Phi(r)_{i,fast} \\\\\n",
    "\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}\\Phi(r)_{fast}=\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}\\Phi(r)_{i,fast}\n",
    "\\end{align*}\n",
    "\n",
    "Then combining all terms results in: \n",
    "\\begin{align*}\n",
    "\\frac {\\Phi(r)_{i+1,fast}-2\\Phi(r)_{i,fast}+\\Phi(r)_{i,fast}}{h^2}+\\frac{2}{r_{i}}\\frac {\\Phi(r)_{i+1,fast}-\\Phi(r)_{i-1,fast}}{2h}-\\frac{\\Sigma_{a,fast}}{D_{fast}}\\Phi(r)_{i,fast}=\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}\\Phi(r)_{i,fast}\n",
    "\\end{align*}\n",
    "\n",
    "Now we simplify: \n",
    "\\begin{align*}\n",
    " \\Phi(r)_{i+1,fast}-2\\Phi(r)_{i,fast}+\\Phi(r)_{i,fast}+h\\frac{\\Phi(r)_{i+1,fast}-\\Phi(r)_{i-1,fast}}{r_{i}}-h^2\\frac{\\Sigma_{a,fast}}{D_{fast}}\\Phi(r)_{i,fast}=h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}\\Phi(r)_{i,fast}\n",
    " \\end{align*}\n",
    " \n",
    " Repeating the same process thermal: \n",
    " \\begin{align*}\n",
    " \\Phi(r)_{i+1,thermal}-2\\Phi(r)_{i,thermal}+\\Phi(r)_{i,thermal}+h\\frac{\\Phi(r)_{i+1,thermal}-\\Phi(r)_{i-1,thermal}}{r_{i}}-h^2\\frac{\\Sigma_{a,thermal}}{D_{thermal}}\\Phi(r)_{i,thermal}=-h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{thermal}} \\Phi(r)_{i,fast}\n",
    " \\end{align*}\n",
    " \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have both groups descritized as such:\n",
    "\n",
    "\n",
    "\\begin{align*}\n",
    " \\Phi(r)_{i+1,fast}-2\\Phi(r)_{i,fast}+\\Phi(r)_{i,fast}+h\\frac{\\Phi(r)_{i+1,fast}-\\Phi(r)_{i-1,fast}}{r_{i}}-h^2\\frac{\\Sigma_{a,fast}}{D_{fast}}\\Phi(r)_{i,fast}=h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}\\Phi(r)_{i,fast}\n",
    " \\end{align*}\n",
    " \n",
    " \\begin{align*}\n",
    " \\Phi(r)_{i+1,thermal}-2\\Phi(r)_{i,thermal}+\\Phi(r)_{i,thermal}+h\\frac{\\Phi(r)_{i+1,thermal}-\\Phi(r)_{i-1,thermal}}{r_{i}}-h^2\\frac{\\Sigma_{s,thermal}}{D_{thermal}}\\Phi(r)_{i,thermal}=-\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{thermal}} \\Phi(r)_{i,fast}\n",
    " \\end{align*}\n",
    " \n",
    " We must now describe the domain and boundary conditions. First we describe some domain $\\Omega [a,b] $ that has a step size equal to the difference in the boundaries length divided by the number of node , $N$: \n",
    " \n",
    " \\begin{gather*}\n",
    " h=\\frac{b-a}{N}\n",
    "\\end{gather*}\n",
    "  \n",
    "  Then as for the boundary condition of the $first \\ group$, fast neutrons, a Dirichlet and RobinVacuum boundary condition apply. \n",
    " \\begin{gather*}\n",
    " \\Phi(r\\rightarrow a)_{fast}=S_{0} \\\\\n",
    " \\frac{d\\Phi(r=b)_{fast}}{dr}=\\frac{\\Phi_{fast}}{2}\n",
    " \\end{gather*}\n",
    " \n",
    "These boundary conditions must be descritized similarly to the the differential but at that specific location in the domain. Where in terms of the matrix b is located at the Nth node of the matrix so b is located at $i = N  $ and vice versa for a located in $ i=0 $.   \n",
    " \n",
    "\\begin{gather*}\n",
    "\\Phi_{i=0,fast}=S_{0}  \\\\\n",
    "\\frac{\\Phi(r)_{N+1,fast}-\\Phi(r)_{N-1}}{2h}=\\frac{\\Phi_{N,fast}}{2}\n",
    "\\end{gather*}\n",
    "\n",
    "These are the closure relations for first matrix cell i=1 and last matrix cell i=N. Now we set up the first cell of the matrix by enstating i=1  in the differential. \n",
    "\\begin{gather*}\n",
    "\\Phi(r)_{2,fast}-2\\Phi(r)_{1,fast}+\\Phi(r)_{0,fast}+h\\frac{\\Phi(r)_{2,fast}-\\Phi(r)_{0,fast}}{r_{i}}-h^2\\frac{\\Sigma_{a,fast}}{D_{fast}}\\Phi(r)_{1,fast}=h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}\\Phi(r)_{1,fast}\n",
    "\\end{gather*}\n",
    "\n",
    "Now we can develope a matrix based of the ith number of $\\Phi$. We may also recall the boundary condition for substitution of i=0\n",
    "\\begin{gather*}\n",
    "\\Phi_{0,fast}=S_{0}  \\\\\n",
    "\\Phi(r)_{2,fast}-2\\Phi(r)_{1,fast}+\\Phi(r)_{0,fast}+h\\frac{\\Phi(r)_{2,fast}-\\Phi(r)_{0,fast}}{r_{i}}-h^2\\frac{\\Sigma_{a,fast}}{D_{fast}}\\Phi(r)_{1,fast}=h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}\\Phi(r)_{1,fast}\n",
    "\\end{gather*}\n",
    "\n",
    "Then we repeat for the last matrix cell i=N. \n",
    "\\begin{gather*}\n",
    "\\Phi(r)_{N+1,fast}-2\\Phi(r)_{N,fast}+\\Phi(r)_{N-1,fast}+h\\frac{\\Phi(r)_{N+1,fast}-\\Phi(r)_{N-1,fast}}{r_{N}}-h^2\\frac{\\Sigma_{a,fast}}{D_{fast}}\\Phi(r)_{N,fast}=h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}\\Phi(r)_{N,fast}\n",
    "\\end{gather*}\n",
    "\n",
    "Note that our uknown now is N+1,  this is typically refered to as a \"ghost unknown\" because it does not exist within our doman. However, we can eliminate this term but solving for it in the boundary conditions and substituting it in the equation.\n",
    "\n",
    "\\begin{gather*}\n",
    "\\frac{\\Phi(r)_{N+1,fast}-\\Phi(r)_{N-1}}{2h}=\\frac{\\Phi_{N,fast}}{2} \\\\\n",
    "\\Phi(r)_{N+1,fast}=h\\Phi_{N,fast}+\\Phi(r)_{N-1}\n",
    "\\end{gather*}\n",
    "\n",
    "Lastly we consider all the inner nodes for i=2:N-1. The inner nodal terms are left as the ith term because a for loop is implemented. Therefore, it can be read as the (ith-1) group in the first column, (ith) group in the second column, and (ith+1) in the last column \n",
    "\n",
    "\\begin{gather*}\n",
    " \\Phi(r)_{i+1,fast}-2\\Phi(r)_{i,fast}+\\Phi(r)_{i,fast}+h\\frac{\\Phi(r)_{i+1,fast}-\\Phi(r)_{i-1,fast}}{r_{i}}-h^2\\frac{\\Sigma_{a,fast}}{D_{fast}}\\Phi(r)_{i,fast}=h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}\\Phi(r)_{i,fast}\n",
    "\\end{gather*}\n",
    "\n",
    "Thus we build the matrix.\n",
    "\\begin{gather*}\n",
    "\\begin{bmatrix} -2-h^2(\\frac{\\Sigma_{a,fast}}{D_{fast}}+\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}) & 1+\\frac{h}{r_{1}} & 0 & \\cdots & \\cdots \\\\ 1-\\frac{h}{r_{2}} & -2-h^2(\\frac{\\Sigma_{a,fast}}{D_{fast}}+\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}) & 1+\\frac{h}{r_{2}} & 0 &\\cdots \\\\ 0 & 1-\\frac{h}{r_{i}} & -2-h^2(\\frac{\\Sigma_{a,fast}}{D_{fast}}+\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}) & 1+\\frac{h}{r_{i}} &0 \\\\ 0 &0 & \\ddots & \\ddots &\\ddots \\\\ 0 & 0 & 0& 2 &-h -2 -\\frac{h^2}{r_{N}}-h^2(\\frac{\\Sigma_{a,fast}}{D_{fast}}+\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{fast}}) \\end{bmatrix} \n",
    "\\\\\n",
    "\\begin{bmatrix} \\Phi_{i=1} \\\\ \\Phi_{i=2} \\\\ \\Phi_{i=3:N-1 ; i++}  \\\\ \\Phi_{i=N}  \\end{bmatrix} \\\\ = \\begin{bmatrix} -\\Phi_{0}(1-\\frac{h}{r_{0}}) \\\\0 \\\\ 0  \\\\ 0  \\end{bmatrix}\n",
    "\\end{gather*}\n",
    "\n",
    "\n",
    "This process is then repeated for the second group.\n",
    "\n",
    " \\begin{align*}\n",
    " \\Phi(r)_{i+1,thermal}-2\\Phi(r)_{i,thermal}+\\Phi(r)_{i,thermal}+h\\frac{\\Phi(r)_{i+1,thermal}-\\Phi(r)_{i-1,thermal}}{r_{i}}-h^2\\frac{\\Sigma_{a,thermal}}{D_{thermal}}\\Phi(r)_{i,thermal}=-h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{thermal}} \\Phi(r)_{i,fast}\n",
    " \\end{align*}\n",
    " \n",
    "The descritized boundary conditions of Neumann and VacuumRobin are as followed:\n",
    " \\begin{align*}\n",
    " r \\rightarrow 0 ; \\frac {\\Phi(r)_{i+1,thermal}-\\Phi(r)_{i-1,thermal}}{2h}=0 \\\\\n",
    " r \\rightarrow b ; \\frac {\\Phi(r)_{N+1,thermal}-\\Phi(r)_{N-1,thermal}}{2h}= \\frac{\\Phi(r)_{N,thermal}}{2}\n",
    " \\end{align*}\n",
    "Where to couple the first and second group, the solution of the first group is substituted in the term. This becomes the B(i) term of the matrix\n",
    " \\begin{align*}\n",
    "-h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{thermal}} \\Phi(r)_{i,fast}\n",
    "  \\end{align*}\n",
    " \n",
    " For a final matrix of \n",
    "\\begin{gather*}\n",
    "\\begin{bmatrix} -2-h^2\\frac{\\Sigma_{a,thermal}}{D_{thermal}} & 2 & 0 & \\cdots & \\cdots \\\\ 1-\\frac{h}{r_{2}} & -2-h^2\\frac{\\Sigma_{a,thermal}}{D_{thermal}} & 1+\\frac{h}{r_{2}} & 0 &\\cdots \\\\ 0 & 1-\\frac{h}{r_{i}} & -2-h^2\\frac{\\Sigma_{a,thermal}}{D_{thermal}} & 1+\\frac{h}{r_{i}} &0 \\\\ 0 &0 & \\ddots & \\ddots &\\ddots \\\\ 0 & 0 & 0& 2 &-h -2 -\\frac{h^2}{r_{N}}-h^2\\frac{\\Sigma_{a,thermal}}{D_{thermal}} \\end{bmatrix} \n",
    "\\begin{bmatrix} \\Phi_{i=1} \\\\ \\Phi_{i=2} \\\\ \\Phi_{i=3:N-1 ; i++}  \\\\ \\Phi_{i=N}  \\end{bmatrix} = \\begin{bmatrix} -h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{thermal}}\\Phi(r)_{1,fast}\\\\\\ -h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{thermal}}\\Phi(r)_{2,fast}\\\\ -h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{thermal}}\\Phi(r)_{i; i>2 ,fast} \\\\ -h^2\\frac{\\Sigma_{s,fast \\rightarrow thermal}}{D_{thermal}}\\Phi(r)_{N,fast}  \\end{bmatrix}\n",
    "\\end{gather*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "So = 1e6\n",
    "N = 2000\n",
    "rn = 10\n",
    "r0 = 0.1\n",
    "phi0 = So\n",
    "alpha = 1\n",
    "\n",
    "#need correct parameters\n",
    "sigma_a_fast = 0.022\n",
    "sigma_fast_thermal = 0.022\n",
    "D_fast=0.87\n",
    "##############################\n",
    "\n",
    "h = (rn-r0)/(N+1)\n",
    "r = np.arange(r0+h, rn, h)\n",
    "R=rn\n",
    "A = np.zeros((N,N))\n",
    "B = np.zeros(N)\n",
    "solution=np.zeros(4)\n",
    "\n",
    "A[0,0] = -(sigma_a_fast/D_fast+sigma_fast_thermal/D_fast) * h**2 - 2\n",
    "A[0,1] = 1 + (h/(r0))\n",
    "B[0] = -phi0 * (1-h/r0)\n",
    "\n",
    "for i in range(1,N-1):\n",
    "    A[i,i-1] = (1-(h/r[i]))\n",
    "    A[i,i] = -(sigma_a_fast/D_fast+sigma_fast_thermal/D_fast) * h**2 - 2\n",
    "    A[i,i+1] = 1 + (h/r[i])\n",
    "    B[i] = 0\n",
    "\n",
    "A[-1,-1] = (-h - 2 - h**2 * 1/rn - (sigma_a_fast/D_fast+sigma_fast_thermal/D_fast) * h**2)\n",
    "A[-1,-2] = 1 + 1+h/rn-h/rn\n",
    "B[-1] = 0\n",
    "\n",
    "L = np.sqrt(D_fast/sigma_a_fast)\n",
    "\n",
    "group1 = np.linalg.solve(A , B)\n",
    "group1 = np.concatenate((np.array([phi0]),group1,np.array([group1[-1]])))\n",
    "\n",
    "r = np.concatenate((np.array([r0]),r,np.array([rn])))\n",
    "\n",
    "## Analytical Solution \n",
    "it=0 \n",
    "itmax = 30 \n",
    "emax=1\n",
    "tol = 1e-4\n",
    "for i in range (1,4):\n",
    "    phi=0;\n",
    "    emax=1\n",
    "    while emax>tol:\n",
    "   \n",
    " \n",
    "        phi_new=(So/(4*np.pi)+((So/(4*np.pi)*np.exp(-R/L)*(1-R/L)+phi*R/(2*D_fast))/(np.exp(R/L)*(1+R/L)-np.exp(-R/L)*(1-R/L))))*1/R*np.exp(-R/L)-((So/(4*np.pi)*np.exp(-R/L)*(1-R/L)+phi*R/(2*D_fast))/(np.exp(R/L)*(1+R/L)-np.exp(-R/L)*(1-R/L)))*1/R*np.exp(R/L)\n",
    "        emax=np.max(np.abs(( phi_new-phi)/phi_new))\n",
    "        phi=phi_new\n",
    " \n",
    "\n",
    "    solution[i]=phi\n",
    "\n",
    "\n",
    "r_a=np.linspace(.1,R,1000)\n",
    " \n",
    "phi_analytical=(So/(4*np.pi)+((So/(4*np.pi)*np.exp(-R/L)*(1-R/L)+solution[1]*R/(2*D_fast))/(np.exp(R/L)*(1+R/L)-np.exp(-R/L)*(1-R/L))))*1/r_a*np.exp(-r_a/L)-((So/(4*np.pi)*np.exp(-R/L)*(1-R/L)+solution[1]*R/(2*D_fast))/(np.exp(R/L)*(1+R/L)-np.exp(-R/L)*(1-R/L)))*1/r_a*np.exp(r_a/L)\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "plt.plot(r,group1,label=\"FD Solution\")\n",
    "plt.plot(r_a,phi_analytical,label=\"Analytical Solution\")\n",
    "plt.xlabel(\"Radius [cm]\")\n",
    "plt.ylabel(\"Neutron flux [N/cm^2]\")\n",
    "font = {'family' : 'DejaVu Sans',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 15}\n",
    "plt.rc('font', **font)\n",
    "plt.yscale(\"log\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.savefig(\"AnalyticalFDSolution.png\",dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Two group Finite Difference Method\n",
    "So = 1e6\n",
    "N = 2000\n",
    "rn = 10\n",
    "r0 = 0.1\n",
    "phi0 = So\n",
    "alpha = 1\n",
    "\n",
    "#need correct parameters\n",
    "sigma_a_fast = 0.022\n",
    "sigma_fast_thermal = 0.022\n",
    "sigma_a_thermal=0.022\n",
    "D_fast=0.87\n",
    "D_thermal=0.87\n",
    "##############################\n",
    "\n",
    "\n",
    "L1 = np.sqrt(D_fast/sigma_a_fast)\n",
    "h = (rn-r0)/(N+1)\n",
    "r = np.arange(r0+h, rn, h)\n",
    "\n",
    "A = np.zeros((N,N))\n",
    "B = np.zeros(N)\n",
    "\n",
    "A[0,0] = -sigma_a_thermal/D_thermal * h**2 - 2\n",
    "A[0,1] = 2\n",
    "B[0] = -sigma_fast_thermal*h**2*group1[0]/D_thermal\n",
    "\n",
    "\n",
    "for i in range(1,N-1):\n",
    "    A[i,i-1] = (1-(h/r[i]))\n",
    "    A[i,i] = -sigma_a_thermal/D_thermal * h**2 - 2\n",
    "    A[i,i+1] = 1 + (h/r[i])\n",
    "    B[i] = -sigma_fast_thermal*h**2*group1[i]/D_thermal\n",
    "\n",
    "\n",
    "A[-1,-1] = (-h - 2 - h**2 * 1/rn - (sigma_a_thermal/D_thermal) * h**2 )\n",
    "A[-1,-2] = 1 + 1+h/rn-h/rn\n",
    "B[-1] = -sigma_fast_thermal*h**2*group1[-1]/D_thermal\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "group2 = np.linalg.solve(A , B)\n",
    "\n",
    "\n",
    "x = np.linspace(0.1-h,10,N)\n",
    "y = So/(4*np.pi * x * D_fast)*np.exp(-x/L1)\n",
    "\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "plt.plot(r,group2,label=\"FD Solution\")\n",
    "\n",
    "plt.xlabel(\"Radius [cm]\")\n",
    "plt.ylabel(\"Neutron flux [N/cm^2]\")\n",
    "font = {'family' : 'DejaVu Sans',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 15}\n",
    "plt.rc('font', **font)\n",
    "plt.yscale(\"log\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.savefig(\"AnalyticalFDSolution.png\",dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,12))\n",
    "#plt.plot(df[\"x\"],df[\"u1\"],\"r-\",label=\"FEM Solution 1-Group\")\n",
    "#plt.plot(df[\"x\"],df[\"u2\"],\"b-\",label=\"FEM Solution 2-Group\")\n",
    "\n",
    "plt.plot(r,group1[1:-1],label=\"FD Solution 1-Group\")\n",
    "\n",
    "#newely added\n",
    "plt.plot(r,group2,label=\"FD Solution 2-Group\")\n",
    "\n",
    "plt.plot(r_a,phi_analytical,label=\"Analytical Solution for 1-Group\")\n",
    "plt.yscale(\"log\")\n",
    "#plt.xlim(0,100)\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.xlabel(\"Radius [cm]\")\n",
    "plt.ylabel(\"Neutron flux [N/cm^2]\")\n",
    "font = {'family' : 'DejaVu Sans',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 15}\n",
    "plt.rc('font', **font)\n",
    "plt.savefig(\"Analytical_FD_FEM_Sols.png\",dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Results and Analysis](#toc)<a id=\"ranalysis\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
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