{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# The Non Random Two Liquids (NRTL) model for *excess Gibbs energy* ($g^E$) and a case study of the Gibbs energy of mixing of water+ethanol+ethyl acetate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Non Random Two Liquids (NRTL) model\n", "\n", "Calculates excess Gibbs energy and its derivatives: e.g. activity coefficients $\\underline{\\gamma}$ and excess molar enthalpy $h^E$ at given $T$, $P$ and composition $\\underline {x}$ for a liquid mixture.\n", "\n", "\n", "## Model overview\n", "\n", "\n", "$$ \\frac{g^E}{RT}=\\sum_{i=1}^n \\left[ x_i\\frac{\\sum_{j=1}^n \\left[ \\tau_{j,i} G_{j,i} x_{j} \\right] }{\\sum_{k=1}^n \\left[ G_{k,i} x_k \\right] } \\right] $$\n", "\n", "Where\n", "\n", "> $\\tau_{i,j}= \\frac{g_{i,j}-g_{j,j}}{RT}=\\frac{A_{i,j}}{T}$\n", ">\n", "> $G_{i,j}=\\mathrm{exp}(-\\alpha_{i,j} \\tau_{i,j})$\n", "\n", "And either each $(g_{i,j}-g_{j,j})$ difference, in units of energy, or each $A_{i,j}$ binary parameter, in units of temperature, are usually fitted to experimental data and published.\n", "\n", "The activities coefficients are calculated from the derivative of excess gibbs energy with respect to mole number of componente i ($n_i=N x_i$) with T, P and mole number of every other component held constant, ($RTln(\\gamma_i) = {\\partial g^E}/{ \\partial n_i}$)therefore:\n", "\n", "\n", "$$ln(\\gamma_i)= \\frac{\\sum_{j=1}^n\\left[\\tau_{j,i} G_{j,i} x_{j}\\right]}{\\sum_{k=1}^n\\left[G_{k,i}x_{k}\\right]} + \\sum_{j=1}^n\\left[ \\left(\\frac{\\ G_{i,j} x_{j}}{\\sum_{k=1}^n\\left[G_{k,j}x_{k}\\right]}\\right) \\left(\\tau_{i,j}-\\frac{\\sum_{k=1}^n\\left[\\tau_{k,i} G_{k,i} x_{k}\\right]}{\\sum_{k=1}^n\\left[G_{k,j}x_{k}\\right]} \\right) \\right] $$\n", "\n", "## References:\n", "\n", "### The NRTL model' original paper\n", "* Renon H., Prausnitz J. M., Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures, AIChE J., 14_1, S.135–144, 1968 [doi:10.1002/aic.690140124](https://doi.org/10.1002/aic.690140124)\n", "\n", "\n", "\n", "### The NRTL model in some books\n", "* Prausnitz, Lichtenthaler & Azevedo, Molecular Thermodynamic of Fluid Phase Equilibria, 1998 [ISBN-10: 0139777458](https://books.google.com.br/books?id=VSwc1XUmYpcC)\n", "\n", "### More papers on the NRTL model\n", "* Abreu, C. R. A., Matrix Algebra and Matrix Differentiation Rules Applied to Excess Gibbs Energy Models, Lecture notes available [here][Abreu, yyyy, LN, Matrix algebra...].\n", "\n", "[Abreu, yyyy, LN, Matrix algebra...]: https://github.com/iurisegtovich/PyTherm-applied-thermodynamics/blob/master/Get_involved/4_Texts_Library/AbreuC.R.A.%2C%20Matrix%20Algebra%20and%20Matrix%20Differentiation%20Rules%20Applied%20to%20Excess%20Gibbs%20Energy%20Models.pdf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Starting the computational implementation of the model:\n", "\n", "Gather the needed packages here" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from matplotlib import pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "R = 8.3144598\n" ] } ], "source": [ "#unit system constant\n", "from scipy.constants import R\n", "print('R = ',R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model inputs\n", "\n", "Experimental parameters from Renon et al., (1969)\n", "\n", "### References:\n", "\n", "Renon, Henri, and J. M. Prausnitz. \"Estimation of parameters for the NRTL equation for excess Gibbs energies of strongly nonideal liquid mixtures.\" Industrial & Engineering Chemistry Process Design and Development 8.3 (1969): 413-419.\n", "[DOI:10.1021/i260031a019]( https://doi.org/10.1021/i260031a019)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Thermodynamics *degrees of freedom*\n", "Excess gibbs energy, and activity coefficients are natural functions of temperature $(T)$, pressure $(P)$ and composition $(\\underline{x})$.\n", "Here, we will consider the system studied by Renon et al. (1969), they regressed parameters with which the model is valid for constant pressure of 1 atm.\n", "The remaining thermodynamics *degrees of freedom* required to calculate a set of activity coefficients are the temperature and composition.\n", "We set trial values below:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#trial temperature and composition:\n", "T = 293.15 #K\n", "x=np.array([.1,.3,.6]) #normalized" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitted parameters\n", "Renon et al. (1969) fitted 1 $\\alpha$ valid for all 3 binary interactions $\\{(1,2),(1,3),(2,3)\\}$ parameter and 6 $A_{i,j}$ parameters, two for each binary interaction filling a non symmetric $A$ matrix." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Ethyl acetate (1) + water (2) + ethanol (3)\n", "\n", "alpha12 = 0.4\n", "\n", "alpha23 = 0.3\n", "\n", "alpha13 = 0.3\n", "\n", "# 6 binary Aij parameters\n", "Dg12 = 1335 * 4.184 #J/K\n", "Dg21 = 2510 * 4.184 #J/K\n", "\n", "Dg23 = 976 * 4.184 #J/K\n", "Dg32 = 88 * 4.184 #J/K\n", "\n", "Dg13 = 301 * 4.184 #J/K\n", "Dg31 = 322 * 4.184 #J/K\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Feeding the fitted parameters to the model in matrix structure:\n", "we will assemble the parameters in a matrix structure so that we can access each parameter by its index, as in\n", "`A[0,0]` and `A[0,1]`rather than as `A11` and `A12`, so we can loop trough all of them using an iterator, see below:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#assemble matrix with regressed parameters Dg_i,j, according to the model all diagonal terms are zero\n", "Dg = np.array([[0, Dg12, Dg13],\n", " [Dg21, 0, Dg23],\n", " [Dg31, Dg32, 0]])\n", "\n", "\n", "#assemble symmetric matrix alpha\n", "alpha = np.array([[0, alpha12, alpha13],\n", " [alpha12, 0, alpha23],\n", " [alpha13, alpha23, 0]])" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loop through its elements\n", "i,j,alpha[i,j],Dg[i,j]\n", "0 0 0.0 0\n", "0 1 0.4 1335\n", "0 2 0.3 301\n", "1 0 0.4 2510\n", "1 1 0.0 0\n", "1 2 0.3 976\n", "2 0 0.3 322\n", "2 1 0.3 88\n", "2 2 0.0 0\n", "whole matrix\n", "alpha=\n", "[[ 0. 0.4 0.3]\n", " [ 0.4 0. 0.3]\n", " [ 0.3 0.3 0. ]]\n", "Dg=\n", "[[ 0 1335 301]\n", " [2510 0 976]\n", " [ 322 88 0]]\n", "typing each element\n", "alpha12,alpha13,alpha23\n", "0.4 0.3 0.3\n", "Dg12,Dg13,Dg21,Dg23,Dg31,Dg32\n", "1335 301 2510 976 322 88\n" ] } ], "source": [ "#verify the assembled matrices\n", "\n", "#we can now automatically loop through its elements\n", "print('loop through its elements')\n", "print(\"i,j,alpha[i,j],Dg[i,j]\")\n", "for i in range(3):\n", " for j in range(3):\n", " print(i,j,alpha[i,j],Dg[i,j])\n", " \n", "#or even use the whole matrix at once\n", "print('whole matrix')\n", "print(\"alpha=\")\n", "print(alpha)\n", "print(\"Dg=\")\n", "print(Dg)\n", "\n", "# rather than typing each element individually\n", "print('typing each element')\n", "print(\"alpha12,alpha13,alpha23\")\n", "print(alpha12,alpha13,alpha23)\n", "print(\"Dg12,Dg13,Dg21,Dg23,Dg31,Dg32\")\n", "print(Dg12,Dg13,Dg21,Dg23,Dg31,Dg32)\n" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#finally calculate parameter A in units of K-1 from Dg and the constant R\n", "A = Dg/R \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model equations\n", "We first implement the model equations in a script-wise manner, considering the models input - the regressed parameters and thermodynamic degrees of freedom previously defined." ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tau=\n", "[[ 0. 0.5477184 0.12349306]\n", " [ 1.02979264 0. 0.40042933]\n", " [ 0.13210886 0.03610428 0. ]]\n", "G=\n", "[[ 1. 0.80325154 0.96362996]\n", " [ 0.66237921 1. 0.88680621]\n", " [ 0.96114244 0.98922716 1. ]]\n" ] } ], "source": [ "tau=np.zeros([3,3])\n", "for j in range(3):\n", " for i in range(3):\n", " tau[j,i]=A[j,i]/T\n", "print(\"tau=\")\n", "print(tau)\n", " \n", "G=np.zeros([3,3])\n", "for j in range(3):\n", " for i in range(3):\n", " G[j,i]=np.exp((-alpha[j,i]*tau[j,i]))\n", "print(\"G=\")\n", "print(G)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.4967744 1.28850578 1.01628367]\n" ] } ], "source": [ "Gamma=np.zeros([3])\n", "for i in range(3):\n", "\n", " Sj1=0\n", " Sj2=0\n", " Sj3=0\n", " for j in range(3):\n", " Sj1 += tau[j,i]*G[j,i]*x[j]\n", " Sj2 += G[j,i]*x[j]\n", "\n", " Sk1=0\n", " Sk2=0\n", " Sk3=0\n", " for k in range(3):\n", " Sk1+=G[k,j]*x[k]\n", " Sk2+=x[k]*tau[k,j]*G[k,j]\n", " Sk3+=G[k,j]*x[k]\n", " \n", " Sj3 += ((x[j]*G[i,j])/(Sk1))*(tau[i,j]-(Sk2)/(Sk3))\n", " \n", " Gamma[i]=np.exp(Sj1/Sj2 + Sj3)\n", " \n", "print(Gamma)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## *Functionize* the model\n", "\n", "> \"taking a block of code and converting it into a function that can be inherited (or included once) and called by various other programs sometimes over and over again.\" -[functionize](http://www.urbandictionary.com/define.php?term=functionize)\n", "\n", "In order for us to be able to re-use this model in different works we would like to functionize it, so we could call this function with different parameters and thermodynamic conditions, and with that make recursive usage to:\n", "* create plots for a given system - varying x and T\n", "* find solutions in phase equilibrium algorithms - varying x and T\n", "* study different systems - varying component-dependent parameters\n", "* perform parameter regression - varying parameter values to correlate data for a given system\n", "\n", "$$\\underline{\\gamma} \\leftarrow {\\gamma} \\left(T,\\underline {x}, \\underline {\\underline{\\alpha}}, \\underline {\\underline{\\tau}}\\right)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## def model(arguments):\n", "Functionizing the model is straightforward: we just copy the expressions already presented in the script-wise approach\n", "and then wrap them in a `def` block with clear inputs:\n", "\n", " def Gamma(T,x,alpha,A):\n", "\n", "and clear outputs:\n", "\n", " return Gamma" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def Gamma(T,x,alpha,A):\n", " tau=np.zeros([3,3])\n", " for j in range(3):\n", " for i in range(3):\n", " tau[j,i]=A[j,i]/T \n", " \n", " G=np.zeros([3,3])\n", " for j in range(3):\n", " for i in range(3):\n", " G[j,i]=np.exp((-alpha[j,i]*tau[j,i]))\n", " \n", " Gamma=np.zeros([3])\n", " for i in range(3):\n", "\n", " Sj1=0\n", " Sj2=0\n", " Sj3=0\n", " for j in range(3):\n", " Sj1 += tau[j,i]*G[j,i]*x[j]\n", " Sj2 += G[j,i]*x[j]\n", " \n", " Sk1=0\n", " Sk2=0\n", " Sk3=0\n", " for k in range(3):\n", " Sk1 += G[k,j]*x[k]\n", " Sk2 += x[k]*tau[k,j]*G[k,j]\n", " Sk3 += G[k,j]*x[k]\n", " \n", " Sj3 += ((x[j]*G[i,j])/(Sk1))*(tau[i,j]-(Sk2)/(Sk3))\n", " \n", " Gamma[i]=np.exp(Sj1/Sj2 + Sj3)\n", " \n", " return Gamma" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.4967744 1.28850578 1.01628367]\n" ] } ], "source": [ "#test it to see if results match\n", "ans=Gamma(T,x,alpha,A)\n", "print(ans) #ttest using those trial input" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "in ~pure Ethyl acetate liquid, Ethyl acetate's itself activity coefficient is 1.0\n", "ethanol infinite dillution activity coefficient is 1.28462711286\n", "and water infinite dillution activity coefficient is 3.42065358364\n", "in ~pure ethanol liquid, ethanol's itself activity coefficient is 1.54673254292\n", "Ethyl acetate infinite dillution activity coefficient is 4.34814054323\n", "and water infinite dillution activity coefficient is 1.0\n", "in ~pure water liquid, water's itself activity coefficient is 1.47876532665\n", "ethanol infinite dillution activity coefficient is 1.0\n", "and Ethyl acetate infinite dillution activity coefficient is 1.28545208207\n" ] } ], "source": [ "# test predictions of activity coefficients at infinite dillution\n", "ans=Gamma(T,[1,0,0],alpha,A)\n", "print(\"in ~pure Ethyl acetate liquid, Ethyl acetate's itself activity coefficient is \",ans[0])\n", "print(\"ethanol infinite dillution activity coefficient is \", ans[2])\n", "print(\"and water infinite dillution activity coefficient is \", ans[1])\n", "\n", "ans=Gamma(T,[0,1,0],alpha,A)\n", "\n", "print(\"in ~pure ethanol liquid, ethanol's itself activity coefficient is \",ans[2])\n", "print(\"Ethyl acetate infinite dillution activity coefficient is \", ans[0])\n", "print(\"and water infinite dillution activity coefficient is \", ans[1])\n", "\n", "ans=Gamma(T,[0,0,1],alpha,A)\n", "\n", "print(\"in ~pure water liquid, water's itself activity coefficient is \",ans[1])\n", "print(\"ethanol infinite dillution activity coefficient is \", ans[2])\n", "print(\"and Ethyl acetate infinite dillution activity coefficient is \", ans[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## As a first graphical result we can plot the Excess Gibbs energy as a function of mole fraction of one component ina binary mixture" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Ethyl acetate (1) + water (2) + ethanol (3)\n", "\n", "#consider a mixture of (2) and (3)\n", "\n", "T=298\n", "\n", "xEA=np.zeros(100)\n", "xW=np.linspace(0,1,100)\n", "xE=1-xEA-xW\n", "\n", "GE = np.zeros(100)\n", "GM = np.zeros(100)\n", "GIM = np.zeros(100)\n", "\n", "\n", "GIM[0]=0\n", "GIM[99]=0\n", "for i in range(1,99): # from 1 to 98, inclusive\n", " GIM[i]=(R*T*(xW[i]*np.log(xW[i])+\n", " xE[i]*np.log(xE[i])))\n", "\n", "\n", "for i in range(100):\n", " \n", " gammas=Gamma(T,[xEA[i],xW[i],xE[i]],alpha,A)\n", " \n", " GE[i]=(R*T*(xW[i]*np.log(gammas[1])+\n", " xE[i]*np.log(gammas[2])))\n", " \n", " GM[i]=GIM[i]+GE[i]" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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sEq2Uevu+OvmUUj8ppcItszZ/qpTyuq9OWaXUFqXUHaXUaaXUW659J0D79qYZ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\nbmM5SGPfxvy9z9+ZfPdkYpJjeGfzO8TuiOXuJnc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.ylabel(r'Gibbs Energy variations')\n", "plt.xlabel(r'$x_W$')\n", "plt.plot(xW,GE,label=r'$G^E$')\n", "plt.plot(xW,GM,label=r'$G^{M}$')\n", "plt.plot(xW,GIM,label=r'$G^{IM}$')\n", "plt.legend(loc=4)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(0, 1), (0, 2), (1, 2)]\n" ] } ], "source": [ "#for a 3 component system we can conceive 3 binary\n", "\n", "import itertools as it\n", "binaries = list(it.combinations([0, 1, 2],2))\n", "\n", "print(binaries)\n", "\n", "# figs = np.ndarray(3,dtype=object)\n", "# axs = np.ndarray(4,dtype=object)\n", "\n", "GE = np.asarray([np.zeros(100),np.zeros(100),np.zeros(100)])\n", "GM = np.asarray([np.zeros(100),np.zeros(100),np.zeros(100)])\n", "GIM = np.asarray([np.zeros(100),np.zeros(100),np.zeros(100)])\n", "\n", "for ibin in range(3):\n", "\n", "# figs[ibin], axs[ibin] = plt.subplots(1,1)\n", "\n", " \n", " T=298\n", "\n", " x=np.zeros([100,3])\n", " \n", "# print(binaries[ibin][0])\n", " compA=binaries[ibin][0]\n", "# print(binaries[ibin][1])\n", " compB=binaries[ibin][1]\n", " \n", " x[:,compA]=np.linspace(0,1,100)\n", " x[:,compB]=1-x[:,compA]\n", " \n", "# print(x[0,:]) \n", "# print(x[1,:]) \n", "# print(x[50,:]) \n", "# print(x[98,:]) \n", "# print(x[99,:]) \n", "\n", "# GIM[0]=0\n", "# GIM[99]=0\n", "\n", " for i in range(1,99): # from 1 to 98, inclusive\n", " GIM[ibin][i]=(R*T*(x[i,compA]*np.log(x[i,compA])+\n", " x[i,compB]*np.log(x[i,compB])))\n", "\n", " \n", " for i in range(100):\n", " gammas=Gamma(T,x[i,:],alpha,A)\n", " GE[ibin][i]=(R*T*(x[i,compA]*np.log(gammas[compA])+\n", " x[i,compB]*np.log(gammas[compB])))\n", " GM[ibin][i]=GIM[ibin][i]+GE[ibin][i]\n", " \n", "# axs[ibin].set_ylabel(r'Gibbs Energy variations')\n", "# axs[ibin].set_xlabel(r'$x_W$')\n", "# axs[ibin].set_title(str(compA)+str(compB))\n", "# axs[ibin].plot(x[:,compA],GE[ibin],label=r'$G^E$')\n", "# axs[ibin].plot(x[:,compA],GM[ibin],label=r'$G^{M}$')\n", "# axs[ibin].plot(x[:,compA],GIM[ibin],label=r'$G^{IM}$')\n", "# axs[ibin].legend(loc=4)\n", "\n", " \n", "# plt.show()\n", " " ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SHZpbsUITHKWUUklbq1Z2VOfxx+0Iz8MP20EAd7qnJEdEAkTkWILLtzuSuTfc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\nv+3c6R8LCiA/3zcxbd0Ke/dWPI+ZnyG4LEHLyPCPHTv6Wqr0dD8iTTU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aBMzseOD4o1T7I93tJf9j6+EtKHqKc+43M3scuNI51yioTlXgD+AM59xSM/sQ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\nFixYgLe3N60dKHErKanJEUIIIZyEv78/8fHxjBkzhoiICAIDA6latSq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3Xl8SbEKwIxMRkQzuTPwZHp/3OLeVuI3Gxe6Ad9+F+++HggWDHdp5+TKE/Blr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\ntWtf62GqWrV8ji8SwklIkiOEKLt8fMx4leKuraU1XL16rXcmr7cmN/f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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#for a 3 component system we can conceive 3 binary\n", "\n", "#import itertools as it\n", "#binaries = list(it.combinations([0, 1, 2],2))\n", "\n", "#print(binaries)\n", "\n", "figs = np.ndarray(3,dtype=object)\n", "axs = np.ndarray(4,dtype=object)\n", "\n", "#GE = np.asarray([np.zeros(100),np.zeros(100),np.zeros(100)])\n", "#GM = np.asarray([np.zeros(100),np.zeros(100),np.zeros(100)])\n", "#GIM = np.asarray([np.zeros(100),np.zeros(100),np.zeros(100)])\n", "\n", "for ibin in range(3):\n", "\n", " figs[ibin], axs[ibin] = plt.subplots(1,1)\n", "\n", " \n", "# T=298\n", "\n", "# x=np.zeros([100,3])\n", " \n", "# print(binaries[ibin][0])\n", "# compA=binaries[ibin][0]\n", "# print(binaries[ibin][1])\n", "# compB=binaries[ibin][1]\n", " \n", "# x[:,compA]=np.linspace(0,1,100)\n", "# x[:,compB]=1-x[:,compA]\n", " \n", "# print(x[0,:]) \n", "# print(x[1,:]) \n", "# print(x[50,:]) \n", "# print(x[98,:]) \n", "# print(x[99,:]) \n", "\n", "# GIM[0]=0\n", "# GIM[99]=0\n", "\n", "# for i in range(1,99): # from 1 to 98, inclusive\n", "# GIM[ibin][i]=(R*T*(x[i,compA]*np.log(x[i,compA])+\n", "# x[i,compB]*np.log(x[i,compB])))\n", "\n", " \n", "# for i in range(100):\n", "# gammas=Gamma(T,x[i,:],alpha,A)\n", "# GE[ibin][i]=(R*T*(x[i,compA]*np.log(gammas[compA])+\n", "# x[i,compB]*np.log(gammas[compB])))\n", "# GM[ibin][i]=GIM[ibin][i]+GE[ibin][i]\n", " \n", " axs[ibin].set_ylabel(r'Gibbs Energy variations')\n", " axs[ibin].set_xlabel(r'$x_W$')\n", " axs[ibin].set_title(str(compA)+str(compB))\n", " axs[ibin].plot(x[:,compA],GE[ibin],label=r'$G^E$')\n", " axs[ibin].plot(x[:,compA],GM[ibin],label=r'$G^{M}$')\n", " axs[ibin].plot(x[:,compA],GIM[ibin],label=r'$G^{IM}$')\n", " axs[ibin].legend(loc=4)\n", "\n", " \n", "plt.show()\n", " " ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "44\n", "[ 0. 0. 1.]\n", "1.0\n", "[ 0. 0. 0.]\n", "[ 0.33333333 0.55555556 0.77777778]\n", "[ 1. 1. 1.]\n", "[ 0. 0. 1.]\n", "[ 0. 0.11111111 0.88888889]\n", "[ 0.11111111 0.33333333 0.55555556]\n", "[ 0.88888889 0.11111111 0. ]\n", "[ 1. 0. 0.]\n", "testdata\n", "[ 0. 0. 1.]\n", "0.0\n", "[ 0. 0. 1. 0.]\n" ] } ], "source": [ "#we can make 1 meshgrid\n", "\n", "xEA = np.linspace(0,1,10)\n", "xW = np.linspace(0,1,10)\n", "xE = np.linspace(0,1,10)\n", "\n", "rawxizes = np.ndarray((10,10,10), dtype=object)\n", "\n", "flags = np.zeros((10,10,10))\n", "\n", "for i in range(10):\n", " for j in range(10):\n", " for k in range(10):\n", " rawxizes[i,j,k]=np.array([xEA[i],xW[j],xE[k]])\n", " if ( rawxizes[i,j,k][0] + rawxizes[i,j,k][1] + rawxizes[i,j,k][2] == 1 ):\n", " flags[i,j,k] = 1\n", " \n", "xizes = rawxizes[np.where(flags==1)]\n", "\n", "npts = xizes.shape[0]\n", "print(npts)\n", "\n", "print(xizes[0])\n", "print(xizes[0][2])\n", "\n", "GE = np.zeros(npts)\n", "\n", "for l in range(npts):\n", " gammas=Gamma(T,np.array(xizes[l]),alpha,A)\n", " GE[l] = R*T*(xizes[l][0]*np.log(gammas[0])+\n", " xizes[l][1]*np.log(gammas[1])+\n", " xizes[l][2]*np.log(gammas[2]))\n", "\n", " def xlogx(x):\n", " if x==0:\n", " return 0\n", " else:\n", " return x*np.log(x)\n", " \n", " GIM[l] = R*T*(xlogx(xizes[l][0])+\n", " xlogx(xizes[l][1])+\n", " xlogx(xizes[l][2]))\n", "\n", " GM[l] = GE[l]+GIM[l]\n", " \n", "print(rawxizes[0,0,0])\n", "print(rawxizes[3,5,7])\n", "print(rawxizes[9,9,9])\n", "\n", "print(xizes[0])\n", "print(xizes[1])\n", "print(xizes[10])\n", "print(xizes[42])\n", "print(xizes[43])\n", " \n", "\n", "import matplotlib.tri as tri\n", "\n", "# first load some data: format x1,x2,x3,value\n", "print('testdata')\n", "print(xizes[0])\n", "print(GM[0])\n", "\n", "test_data = np.zeros([npts,4])\n", "\n", "for l in range(npts):\n", " test_data[l,0:3] = xizes[l][:]\n", " test_data[l,3] = GM[l]\n", "\n", "print(test_data[0])" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HByr1aktQ9Yq6+6/tPcnldXvzbeuS+juLJhzkyrn03G1Pzmuhe422vSKJrB6k\nu//E3mT2rtOyQO2O7S6wP8Af7r4FJs+FVz6U7o9CiLLLjNJJPyMuYpaUw2cJj65P8t8n2DnkXYfH\nVrkt1mGwcPJ/Kzk+y3FN/6Ep3xLWug5RA7uScvS80zErdG3G8m2D9A/44ytYOMXhNcjOhilD9Pe3\n6uowWFj75kVYqH+f5dvVo+rt7Wk+82GqDujIxpsmcH7JZo68vYQ6I/uSlZzq9HW2/3W8w2Dh4srd\n7H40fz+GnXaOe3tIwTd5i5d/jXEYLOxaeZH3H/1bd3+F8nDfrVqW4Y7u0PYeiI2NJT4+nvj4eAID\nA3XPFUII4Vixzix02jCFiA6NULOznabPFV8fh90M1awsvaw/AL/4/zv3+6r94mjx3iP4V9J/kwb4\nZc1d4KiDYlaW7qMGAPqGQnpOujymBzz3IVSulf8YX9/CjQHgp8WEfbt9w8q6j5Jy9DxA7hoT5Zys\nh+Gsy6Szv5+1sc+TtP0IAPXbheWsMRFSYAwfH/3XmZ2t6o7xr+3LgdyXCUDvx2DZOm2bZBmEEGVJ\nmWvKpPhpLYkVHx98/Hwdfjlre6z4Oj7fNySIpm8OyZvL0GI0Z75ci+JbcOxf1t7NL2vvdvwmDtob\nvZ+f/ld4JRg8QZvLcOwfeKgt/LIg/3mFHcPqHXTpqv6k+FSBu0bBjBVcOpDKn62f5th7P2tv1nq/\nWyftqJ39/fiFBlHjwe50Wj+Z9JRsnu2wnm9fP6Ldvp8Pvn4+DgMFAB8fJfdY26+fYnrxU0z+OQ3+\nflqGQeYyCCFE4RXrYMGbeiTOp87IvkTd1Um3YsKoaoUCOt7qsGLCFO26w9wdZPcZxt+j5vJzu7dZ\n+mlrc15fjoi4xjTfOodao+8wrGLCmr1JkG2aSMWEEEIUlgQLOXwD/fHJyWTYVkz83ulNlq6809wb\nsK2YeOIGyMwwd8zgUBg9E2asgPMn4PFOkHrd8FJOa75BATSd+gBxaydzKimM5zpuIOmica/TXuWE\nbcVE506xnDhxwrAxhRCitCvWExz1ZKdnsD/hC+o9ezsBFc1binpblddhzvNw6pBWteANlizD4V3g\n5++dMXOyDOzdBEHBBXZbAoa+3b4xbMiIuMZ02TqNS3/+zcKKbQxZsMra2fKV8PVTgPO52yxZhhV/\nQc3EWpCILEwlhBAuKJGZhaRdxzn23s/82WI0Zxc7Lm/0VO4n6ojK0DzOlDF0hUVA667eHTM4VAsa\nHDA60+APQgx6AAAgAElEQVQbFEClnm0A89aesM00+PtDr85WB8gaE0II4VSJDBbCo+tzw+4ZlI9p\nwJY7prD9gbdIv5hkyLVNm5dQipj5+zFrsSqH3SBlJUshhHCoRAYLAEE1Ion5YSyt5o/k3A+bCp1l\n8DhIUFXnpYt6utwB9Vp6dq6nY8b1hUbRhR7Tnd9VZM/WhMc1cvl464DB09LeFt0q0PyGCgW2O1xz\nIidgKI7lxEIIUZSKdZ8FSwdHZ1JPJrJr+GzOL9lM9fu70fy9R3I7KzpT6E/JyxdpzZeeeg8qVi3c\ntVy1/if4eiY89wFUqeX8eCPs+BM+GgfPz4EaDXI3GzmPwVbv7dOYPeJvHv+gObWbhxp+/du3F2zS\ndeAYPBAP787bTHS0h0GVEEIUoTLXZ8FVlixD6wVPkHL8Ar5Brk0MNCSdXi4EdqyGwS3gt888/8Tv\nDv9AOLzT6RoThvLxgbNHYWhrLVDJWcnSzEcSX2T3Jykxg6fareOrKYcLtZKlPZZHE9bZhoxMSE2D\nDh1iGDduHOnp6Q6uIIQQZUOpyCxYU1XVaYMmu29wUx+C7ndDXB+3xgPg8nmYMRJWfKGt5eCNLENS\nzhoTS+dBhz7eyTJcvwYfjIVv34E23WDM3Nwsg1kZhqzUdEInjOW7aUdoEFOeJ+e3NCXLAHmZhoyM\nvDUmmtWD+Z9JlkEIUXJIZsEFjgIFh/MSVnyudVH0RERlSPgcXv7Se1mGfH0ZvJRlsO7LcO54viyD\nWRkG36AAUqZOz1vJ0qQsA+RlGqz7Mvj6SJZBCCFKXbBgj9cqHLrfBQt2Q3QP+O+9MM2cmf352HZ/\nTLjH/DEtfRn6DoW3n9Q6Tqqqqb/jJnERvLm1I7ePrsPCl/YztttfpgQMkDcJ0rb7Y/tWgaSkpJgy\nphBCFGclsimTO/K9gWVmwLY/ILaneQNasgzd7/ZeUyVLlqH7XdrjCW+wZBluHACnDjpfw6KQZjGc\nR4Nm8+DUxnTsX4UDf13F18+8WNcSMNy+fVnuSpa/rody+4KlkZMQoswpdXMWLOx+yv3tM+0T/y2D\n4Mm3oLzVsst9QuGhiXD3aM9uWuQys0LC6E6PrrJXOSFBgxCiOJI5Cy5w+Mjh5ntg7AJY9yM82ALW\nLPbuzdnKzMytKvDqmFlZpg5h+/vPzsxCNWhMV5s2ZWWpZGUZ92Zutz+DNHISQpQRpS5YcEhRoM9/\ntHkFTWLgxTtg4gNw9WLR3M/AurDgv94d8+G28N4zpg9jHTBs7D6enQ+9Z9i1XQkYXr1jK1MHbDNs\nTNDpAindH4UQZUCpChZcnmBXqTpM/iF/liEl2dybs7XmBzh/0js9Eiy2rIDDu7025tJV/bm8cT+X\n1vyDmm3smI4ChmN7rrFpyQWyMs15nfaChqNLFRISEkhLSzNlTCGEKErFes5Chz9eIbJbcxJ/38nG\nHgkOz+lxfh6/7Rmsf8D0x2DxrMLd2PfnIaKS52O0uwlm/K59P+MJrV8BwDenIbKatrrlvQ30zweY\n/Rc0jdXf/+lUmP2C42s4U9gxourBZ4e07xe9DrOeB6Db/ncIaRiFmp3Nz753O7yFtl8+S9RdnXT3\nn/58DdsGvuHwGs48/2VrutxVTXf/6s/PMG3gDt39igLZW7XvP/0J7n9R+37Tpk2W54VCCOF1ZsxZ\nKNbVEFlJWplaSNMatPzwMYfH+oYGOb5Yr0Haowd7VBWmDcv7ufO/oMvtBY8r56QZkKMxACKj8r4f\nPTMvWDh/QgsWwivBcx86HqNaHcf7O/SB8pH6+19/JO/75h3h1qEFKxkKO0aw1bLh9z6XGyxc232c\nkIZRoChO/z7DYxxPbA1v38DhNXY98j4AzbtGcNOD1e0e0zCmvMMxGrUvz4gPmzs8ZnGbmgDcxzIm\nz4VdB+DPz2OJiSl+QbgQQniqWGcW3KmGKHSNf59QuONxOLoH1i2xXzFhtLtqQq8HYNhk88awNbgl\nNIkFxSen+2NvLUAxs/vjyK5EtYC2i542bwwbm257FTUrm9ifXspt1GV2JcUX/7eMwydh9TytOzYg\nFRNCCK8rNpkFRVFGAM8C1YDtwBOqquou+agoSgAwAbg/55xTwH9VVZ3vyfimeOItaNoe6reCXz6G\nmaNg83J4drb9LIMRhk2B2k3Nubae/4yHKjWhZWetL8O0YVoAMeIN+1kGIwx8jtPB5WnLJeOvraPO\niD7go+Tr6Gk7z8Ho4KHpMzHUuZaFj4/VxMrtigQMQogSz+3MgqIo9wALgGHARuAp4G6gsaqqF3TO\n+R6oDLwEHASiAB9VVdfpHO/9zIKtC6e0N9J1S7RP/2PnW31cLEXyrTHRG175BoJcW7HTE2b2YPCU\nWRmHAr0ZJGgQQnhBcemz8BQwW1XV/6mq+g/wKHAdGGrvYEVR+gA3ALeqqrpCVdVjqqpu0AsUXHXt\nnxO535vSZti6YqJ6/aILFI7+46U1Jn6C6g0gsJx5Y6H/d5W87xSql3tOJB84TXZmFrMY7nL/BnfY\nK7M8dOiQVEwIIUoct94BFUXxB2KA3yzbVC01sRzQm7r+L2ATMEZRlBOKouxVFOV1RVGczEjUd3nD\nPlY3H82u4bPIuHrd08s4Z+nLMCTBvDEcOXccHmoD4wbAxbPmjtWxLzz1rultm6FgwJCZnMq6Li+x\noft4kg+cNn18gOyMTDb2SGB95xdJ2n0MwJSgwbrMMjsbbu/VgNiWQWzevNnQcYQQwkzuflyuBPgC\ntu9cZ9HmIthTHy2z0AK4ExgF3AW86+bYucLbN6T5uw9zauFq/mz1FGxa7umlircqtSB+Iez8Ex5s\nDssXebcvg4msAwa/kCDaffE0qScS+bP10xx5e4npWQYffz/afv4MmUkprIl+joOTvyE7U+syaVaW\n4cd2vVj4Kvj5QlxcLOPGjZMsgxCiRHBrzoKiKFHASaCTqqobrLZPBbqpqlogu6Aoyi9AV6CqqqrX\ncrb1A74EQlRVLfB/S8uchQrdmuMfnv/5edS9Xal+7w0AXD98lj8GfAlbV8C/hsFjr0OI43K4Euny\neZgxElZ8ATf0g6ffh4pVi/quDGE9hyHzWgp7X/iEY+/+TIUbmtFq7git1NJEWanp7J/wOYenLSY8\npj6t5o0grEXt3P1mzGfou2kZr34EE+dA07ow/zPpyyCE8MyiRYtYtGhRvm1Xrlxh1apVYOCcBXeD\nBX+0+QkDVFVdbLV9PhCuqmo/O+fMBzqrqtrYaltTYDfapMiDds5xeYLj0pV3wuLZMOs5rfb/+Y/M\nXVXS1okDWrmlWRUT1lZ+BW8+DtlZMOod6DHQK48NAK0l9tofoPd/DB/TdtJj4spd7Bz6LmlnLtNk\nyiDqjOyLYvKckcsb9rFj8DtcP3SWRgn3UO+5O/Dx883db0bQUOeLZQweDzsPwNix8cTHxxMYGGj4\nOEKIsqXIJziqqpoBbAZ6WLYpWm1aD2CtzmlrgOqKolinCJoA2cAJ+6e4wccH7nwM5u2CGg0h/k64\nkljoy7rslwXO15hIyPkqrO53aetaxPSEiffD0b8NuKiLVn8LkwfD87dqcykMZFn8y/IV2b0lXXe8\nQa2HevD3qLlc+HW7oePZExHXmC5bp1F39G3si1/E2a/X59tvxqOJo//uxcZPYPwwmDJlIvMnejyN\nRwghTOVJ6eS/gfloVRCW0sm7gKaqqp5XFGUyUF1V1Qdzjg8B9gDr0d4yKwMfAitUVX1UZwyXMgsF\nZtZnZ8ORPVC/pVuvCdDWTajRAKrWdn6sNVXN68sQEATPfgBd/qXtS3By7uXV8HwNrdrCXQd3QoNW\n7p+3a53WaKp2E/fPXf+TVk56Pcm9vgx//6WVY9Zr4f6YB3fSZ/C+fP0SXHF122FQFMq3qev2kEm7\njhHaopbumHpZhqO7kshIU512hrSn4TfLaFwH/PyQEkshRKGYkVnwqIOjoiiPA88DVYFtaE2ZNuXs\nmwfUUVX1ZqvjGwMzgS5AIvA5MM7efIWc4z0LFgqjTyg8NBHuHu3Z+dZ9GW4ZBClvgb+T7o9ra0LU\nw1AvIf/2BHsHG2RwSy0z8cQMz87P15ehDzz3gfPujyO7almfsfM9G9MOZ/0aNt32KoqfDzHfFXKd\nDB32AoY3Bu0k8UQqk1a29/i6+XozSNAghPBAsengqKrqe4DdNYdVVR1iZ9s+oLcnY5UYlr4Mj30M\nK0aBz3JoMhsqeTCXIcHwu8tzDi3H4/GTmghImOu97o86bANFbzd7sjyWMHouw+I2vfICBun+KIQo\nJor1QlKOeJxVyMwAP39jbwZy3uAVqPYfqNAT9g6DxJ89CxaMkJ0BPia8TsiZg3GrNk/k3adh1Tda\nsFAUcv4+bf89VOZV04bMzsjEx1/7T8eMoMHSl+H27cu0gAHIaJ6Ov79Jf59CCOFEKexf7MD21XB/\nY2P7MiRQMBMQWB1a/QCNPEz1F9b1/bC+AZw1sS9DAnndHyd+69WsQq4rifBAU/jqbW2+ipXzF6tx\nLrF6vomTRsi8lsKfrZ7K15cBzOvNsLhNL9LSoX3LAOnLIIQoMmUrWKhSS5tM+MwtMG04JF8t3PUS\nHOxTFPAJKNz1PeVXAcI7w577YNcASDep+2NCzp/+RfQ6A4Ig7lZtcumo7loZqwO2VReeUPx8qXpn\nB/bFL8rX/RFgP404hf3lsAtjSdue9O+hVUxI90chRFEokcGCx58So+rC9F/hqfdg+UIY0qp0dn8M\nqAQtPoMWX8KVP2FDc3OzDEWlXAiMngkzVsD5EzC0td0sgx5PggbfoACaTHmATmsn2e3+CMa3jfbz\n96Hte72YtqmTdH8UQhSJEhksFIptXwZLliEl2bv3kXYKMnT6Mhilyl3QYTdU7GleliHByf5rVwzv\ny1BAu+4wdwfc+lBeluGk4yyDNU+CBtu+DFqWIf/rNPrRRL02YYzb2TO3L4NkGYQQ3uJR6aTZbEsn\nk/Yc5/Br3+XuP3m2TsGTRs2E4DD9i/68QGsLbS07G5Z9nH9bnwf1r2E9RoKd/acXwOUVdnbkCG4G\ndcZo3+8aAOe/gdB20D6nsiX9HBx8Xv98gLoToFw9/f0XlsD5LwtuP/8VZFkFRNX+A+jMM/B0jLY5\nf0ZU1lpvA7z7DHzxhvb9ymzt8Ux2Nkx1MiHyzhHQzEEJ4p4N8P37BbdvWwlnjub9vCIrb8XQ6Y9C\neqr+NfsOgbY36lZWJO08yuHpiwtsv7xhP8n/nMz9ufr93VD88sfhTdgHQI8h1Wl5o35J7ZGdSXw/\n/ajufoBH32/GqX3XmX/POun+KIQooNiUTnrL9YOnCY+uT3ZKOtcPnAHg0tVIwM6nxqysgtusXT5v\n/9Nmqy5w5gicz/mf/c8LoH4r+2tMOBsj4zykOPhE62t1zUYztWDh2lZIXAqRfUHNcHw+QLaT1HPm\nJfvXCG0L6echRXvT4sz/oFxDCLCzxoSnY1gWHQ+4nrfU2DPj8oKF72dpWR1w/sk/5Zrz/fauUbkm\nhEbAgZyuj6O6w5i5ULMhnDoEaQ5WKc2Zw7J0VX+7AUPW9bTcf4fWAiLD8I1pwNXNWufyUwtX4RcR\nQliLvP4TWylPNc5w/Wqmw5eVdj2L0wccr6SqZqu5WYYBAcuZOHEiH383g6/nr5Q1JoQQpigRmQVr\nhjZistYrWJsAeeGka2tMJBgw5poaEBgFMRtB8dIToY0tIfMyZKeDmgWN34EqJq8xsaUrpByGjvvh\nlWDnxxvhhdu01TrDKsLFMzBsCvQfmZdlcJE7/Ru2D3qLM1+vp1zdyrprTICxZZazR/7NT+8ep17b\nMI7uvMaLY1+SLIMQZVyRrw1RqjXvCENeLjiXwV7FRIJBYyoKRN7mvUDBorIX5jLYqngL+AbnlZpa\nvsxSuyn8a3jBuQxOKiZsuTufISKukZ25DMfyHWPkBMgqdcvR/YEopm2M457x9Zk8ZRJNYivJXAYh\nhKEkWLCY8bu2imOZqZioDC0+L/qKiQTMCRoenwaPToXg0EJVTFi4EzD4BgXQdKrjigkwZgJkv2fr\n8tT/WuHn78PA8Q2YvqkjPn4KHeLaS8WEEMIwEizYY1sxMeclt99cSgzriomDL0B2StHcR4LJ17eu\nmJg3Xns04Sb3swx5FRMHJ31NypFzBY4xusyyXpuw3CzDa9NfZdY/Nxl2bSFE2VUyg4WLZ+HxzrBz\njbnjWLIMU39y+1m3IbKuw9bucKHgDHxDWbIMsZu0RwXepmbDjtth2EcwwcTMhiXLsHC/tpaHhzzJ\nMtx4+D1CGkbpHmdk0GDJMsw52o16bcJYXMqXZRFCmK9kBgtp17V0+RM3wDtPQ6rj2eOF4uMD4ZHm\nXd+RrOvgGwo774A9D5jflyGgsrnX15OdCv6RsPdh2NEXXjC5L0NE4V+nu1mGwMrhLh1nZJYhvHJe\nZ83F9JagQQjhsZIZLETVg3f+hEdfg+/fg4famp9lKAoBlbQ1JprOh8QfYGML87MMRcE3GJrNg9ZL\n4NpOrWJj2EclouOkketOWBj9aMKaBAxCCE+UzGABwNcXBj4Lc7ZppY7eyDLYk50GmUmenVt/ilYN\n4YiiQNSD2ryCsJjCZxnqjocq/3b/PFWFDA/Xta71HFRz0OzKIvJW7XVW7q9lGfr3Nb/7oz1X3H+d\nS1f1p+bQm6n79L88GjI9seC/ITMDhsX0JjHR43XKhRBlTIkKFux+gqvTVMsyPPa61tHvobYe/c/e\nY0df1T4JX/SgYqLaICgf69qxgTW0LEOzBZD4o5ZluL7P/TGr/FtbZMpdZ+bDhiZw9jP3P/FXvgMq\nuDjRzj8iL8uQvAsGtoAdf7p9ux7b8jvcUwe+nun2pNaNfhPYEjHZ7SGvbDrAytrDOTjFfsWEGUHD\niX+SqVmnKuPGjSM9Pd3w6wshSpcSFSzo8vWFe56Bj7ZBj3uhvH47XcNVG6J1Qtx+C+x91PMsgysU\nRWvT3GE3VH0Aguo7P8cokbdBhR6w517YfZf5fRkib4X2u6D6cPiijbljWWvaAfoMgbefhNE3wcmD\nbl/C3ccSoS1rU3tkX/a9lNOXYU/BbIrRQUO1BuXo93xdJk+ZROPYSLZsMaRvixCilCodwYJF7SYw\n9GXPuhHe3xh+nOP+eeXqQttfofF7cPYTz7MM7gisDg1fAx8vduu27stwebWW2fAky+AO/who+Dr4\nhblfWvnqgzD1IffHtO7LcO641pfBgyyDO3MZCvRlaPes3SwDFHw08Un8fib0cr8BU76+DL4K7TvE\nSpZBCKGrdAULhZF4yvl6BHoUH6jxmPZJ2FtZhqJi6cvgzSyDRQKuBw1XE7UvT1n6MvQdWugsg6tB\nQ76VLF3MMiRfzuTKOc/f4K37MkiWQQihR4IFI9lmGfbcX9R3ZA7bLMO2Xt6tXEjw0ji2WYYRnSHN\ns6ZVnmYZ1nUcS8Yl+0Gs0X0ZLFmGuE6xnDp1ypBrCyFKh7IVLFxJhDnxhauYSHCy3zrL0GCK5+MU\nRnaa1o3R7L4MlixD0w/NXYjKngS0AOWjceZXTFiyDAlfQGA5jy/jSZYh5rsx+FcI1T1uFy24gDF9\nQCxZhnE/RrOp+hApsxRC5CpbwcLfG+Dz6d7py1CuLoQ0N3cMPcm74dRs7/RlCKgM5TuYO4aesSfg\n83kwuCUsMbkvQ3AotL3RkEu5k2WIvLmVS8camWVoe0te8CEBgxACylqw0PFWrWIivFLR9WWwdnk1\npBwy/rph0fp9Ga6sg+t7jR/Tkat/aQGM0YJqaRmcsAHw2sPwfBH1ZbA4tAv2ujbZsCQ1c5Luj0KI\nshUsgFYxMXN1/r4MRdH9UVW1CYJn/mfO9QOrF+zLcGEx7H0ETr5vzpj2qCrsHw3HXjfn+v4R0Gyu\n1pdh+y4Y6IUsg56Fk+G9Z9w6pdBBg52XaWbQAKCWgM6aQghjebH2znMZl65xdfsR2O6gf0KrLuDn\nr7//+D64YDVpq3EMPDEDpj8KI7tq29b/BA3b6l/j2y7g42CM6/sgzcHEML8ICMu5/tFJkHYSMq/m\n7c9Kgasb9M8HLVvgF6a/P/VY/mxFYG1o/C7sHaZlGUAbs9Kdxo1hyycIwjtq359dCFfXgl/5vP2q\nCpf/0D8fIKSF47Uq0s9B8h6rMYOh0Ttw4Gkty2CxdaX+Neq1cLxOxKVzcGSP/n7Q5jMAbPsDln8K\nlWvk379rHWQ4WCa6RgOoUoulq/rTt9s3BXZnXL3O1S32f9dXtxzi2Hs/A5C4cleB/ZPowu38QLUG\nwVSuFaR7C9evZnJwy1Xd/QBNOoYTEOTL+/u68uYDO1n03u/ExMQ4PEcIUXoU62Ah9cQFwqPrc3Xr\nYTb2SHB88PfnIaKS/v4v3oTFsxxfY9Ov2peeLue19Rr0HH8TTjkYI+ImaPe79n1ANe3PE29Ctfu1\nN+j007DNSafDmL8cd308uwgOveD4GmnHHY9T2DGC6kGnnDc4S5Bw8WdI/Bki+wCq89fZ4kttAqWe\nSytgz0DH1wCt5FHPy19CdwdjbF0BLzsYQ1FgZU7/Bd+c/5TOn4SfF0CfnPbWL9/j+NHIY69rbcvJ\nm8tgHTQk/32CjTdN0D8/h94xG4Emr/+H157VX5L7+N/XiL9pk8Przzl6A5VrlyM7S2X/xqvExsby\n6quvMnbsWKf3JoQo+ZTimFJUFCUa2Nzxz0lU6NKUrOtppJ66yKqNDp6bRtXTOjnquXQOkh18erq/\nkfbn7L8gNML+MR/WA8XBGOnn8mcKbPmW09o2W6zIqSDofBoCq0F2BqQe1T8fILAm+Op/SiTjkuM1\nHDbkvM42y7Q3dTPGUPy0CZ4W65tAyj5ovxNCW2qZhRQnPQsCqoGffhUAmUmO+zts7Zq3v1wDaPIh\nPFcr/zEVq2kTF/VcT9KWQ3ekZsO871+6E/78Hqb9Au17adtOH4GsTP3zwyMhrEKBzZaAISs1ndQT\n+r/rXQ+/z8U/dtN48v1Uu6uT3WMCIsPwrxDKo8y2uz89NYvEEw6yH0DlOkH4+WtPLReM2cc3rx3h\niY9a0HNoDW7nF4fnCiG8a8uWLZbMX4yqqoY0TinWmQWfctoSu77BgYQ0jIJTDZ2c4UCFKtqXnnIh\n8NBEaOrgE7Wz6sCAKtqXqwJrQNTDWqAA2iOO4EK8RgD/CtqXnpAWUKEnVLzFvDFsBVSG8E5aoADa\nJ/LCvk6/MMePSsJitaCl+rCcRzB3wn/fgKih2vgJLowRHKZ9uapcTsWEJVAAiKrr+vlWrLMMIQ2j\ndI8LbVmLjMvJNHjB+bwHyzwG26AhIMiXqIbBLt+br79ClTpB9ByqBb6L6S0BgxClXLHOLHTe/Drh\n0XnrHxg9ezyfPqFasHD3aPv7E0wYM+Ug+IY7frRh+JiHwTfEvaCmsFKPgeIPgfpvesaPeUILCgJr\nQMZlbS7DmXlQsbeWZQjKyTIkGDhm4mnIzICqtQ28qMbefAaAtLOXyUpJJ7iue3+felkGV1w5n871\nq5lENSgYYEjQIETRMyOzUPaqIYqTcg28GygAlKvn3UABIKi2dwMFgKCaeY98rCsmkndp63ekntD2\nJRg4ZmSUKYEC6AfKgVUj3A4UoHAVE+GVA+wGCiB9GYQorUpmsJCdDYs/gHTHz1kNpapwag5kebkv\nw+n5judBmOHMJ+Z3f7R19nPvrWTZcLoWTFgk4L0W0ut/ghMHPDrV0zLLC7/tIGn3Mbv7zCqxnLqm\nA5s3u7/AlRCieCqZwcLeTTBjBAyLdbkJTqFd/wf2j4S/2sJlL/VlSD2ujbmxlfkrWVpkJML+J73T\n/dEiKxkOPAUbmmuVFmavZFn9Yfv7EjA3aMjOhg9f0lay/Optt1eytHAnYFBVlYOvfMWa6Oc4OFl/\nJUujg4ZvXz9Ch7j2jBs3jrQ0Lwb1QghTlMxgoVkH+GCTVq72WJy2PoCZWYYEIKQZxG4D/0jYegPs\nf9r8LENQLa2CoFyDnJUsh5ufZfCPhA477Xd/NItvCLTfDhV7wp77YNcA761kaU8C5gQNPj5aQ7Bb\nh8LMUTCqu+lZBkVRiP05XlvJMj5nJUsvZBme/7IN94zTVrJsEltJsgxClHAlM1gAaNgGZm+E/4yD\nhVMKn2Vo2kErpXMkpClE/wkNXoNT73kny1CuHrRdnrOS5ULvZBkCa2jdH5vOh8QfvLfGhGUlyyt/\neifL4EwCxgcNwaEw+h1483c4f8IrWQbLSpYd12grWXojy+Dn78PACTkrWfopkmUQooQrucECaB0b\nB0/In2WYE+9ZlmHG79DDhSY/ii/UfjYny1DJO1mG3JUsvZhlUBSIetBmjYlB3lvJ0jrLkKbfUMhw\naWdg90DtEZBFAsYHDdE3aStZ3vqQ17IMFTpqK1nmZhk6jTU9y2BZyfKe8ZJlEKIkK9nBgkVulmE8\nrPgCMtPNHzOkKUSvhgavw4VvvDPx0TrLkLjEOxMfLVmGZgvg0u+QccH8Ma2zDFc3QLqDFtpGSzuu\nZTY2toRTNmtMJBg8VnAojJ4JM1ZoWYajfxfqcq4EDZYsQ6e1k8i8lqrbShoMzjKMz8syzF47qNDX\nFEJ4V+nrs5CeBgGBxt1MggvHZKeBjwdjHn1Na6tc4Wb3z/V0zBNvQ1ADqPR/3hvz1AfgFwlVBnhv\nzDMfAz5aK2135evL0AeafJDXl8Eiwc55K76E61fh/x5yf0xP/92u+QHOHoX+I/Nt1uvLYC0rLQOf\nAD8UxVm3sfx9Gbb9msjh7Un0e7au27ebmZGNj6+Cj482pvRlEMJ40mfBFUYGCq7y5M0M4OTbcHmV\nd8c89QFccrD+hRljnvmfNvfBm2Oe+xzOf+nZufn6MuzUzzIk2Jy35ntY9rFnY3r67/avX2DJnAKb\nXcoyBPq7FChA/izDrj8u8tM79h9fOOPn75MbKID0ZRCipCh9wYIQRrH0Zag8APY+DDv6aiuDWkvA\nez0aPGB019NZDGcL0YZeczG9JWgQopgrW8GCqsLRf1w/PsGgcZML9yxaxnQyptl9GSxZhnKNtMXA\n7OqWbh0AACAASURBVEkAdph3Gxz9p1AVE54EDcn7TtmtmABIwo01M1y0mN4cPHhQKiaEKIbKVrCw\n4gsY0tL8vgzWEn/RSg+90ZfB4sp62NjcmIqJFRsKftmTvEdL13ujL4NF6jH4q413+jJE3gqNZzo/\n7ogJY1+/Bk90LVTFBLiXZchOz2Bjz5ed9mUwsjdDdrZK93+1kYoJIYqhshUsdOuvVUwY0ZfBVRV7\nahUTp973XvfH8h0K35fBUWBgb3twM2g2DxJ/9F73x6Da0PzT4tOXwSIBYx9NBIfCy18Z1pfBlaDB\nJ8Cfdl8+47QvAxhXZunjo/DsotbSl0GIYqhsBQt+/jB4vP3uj/c3hh8LThQrNMUXaj8D7YuiL8Mu\nKNfQ/b4MekGC7THWxykKVPuPTV8GL2QZ7PVlKMruj9YSMC5oaNfdsL4M4FqWISLOpi+DF7IM0pdB\niOKpxAQLhk7Usu7LYMkynNgPKdeMG8NWcJO8vgyWLEPaSfPGAyhXF9r+mj/LkLzb8TmuBAq2x1uf\nE1g9ry+DJctwxeRsir3uj4lLAC9mGdIvaL9je5mNBIwJGmz7MgxtDd++a2qWIV9fhtwsw7emZhls\n+zJIlkGIoles+yx02jCFiA6NuLT2H7bfN4OUNPvL4gLw4RYoX9HB/pdg+cKC288czfu+XCgsvqCV\nsR3aBY/d5vhG267U3pD1HJ2qBQa2Uo/m/9m/MvjqvDZPx7AIbgFtlkDKEfjnIbj8u7bdrwL4lbe5\nL8v/jF8HGulfk68BnRLBoEAIrKUFRmmnYO+wnDduoGsi+FcENRvW17d/vkXj97R5Anou/AD7nyi4\nPf08ZFtlbXyCIKCqsWPkUqDTYe3bUx9qrxWg07G8vgybOxdsKhVh9f39L8Ltw/SH2LcVxvUruD3l\nGlxJzL+tWh3713BhjHITHVcjdFwzCf/IMPZP+JzDr32Xu71cncp2j689si+vPavfefP0weuM77HJ\n4Zjjl0YT1TCYryYfZtGEgygK/PXXJkv9uBBChxl9FvyMuIhZUo9fgA6NCKgaQfVB3Th4rKn+wf5O\n6tSbx2mpcnsyM2DRa9r/gIfFwtj5EBkFVZ10mvNzMiM8rJ3+NdQsODZF+z7jPIR0h/Auxo4BEBCl\n/WnJMqz01X7OvATBjaFCT+3no9ZZjnDHY1If6GN/VyqQGqZlG26K07IMK3MSWBe+h6gh2vfOfreB\ntR3vD6rr+BpHJ2l/ZqcCvlB1IGDz91/YMayvV/0RODhG+72engP1Xta2V+4HmVcKntot58+6zR3f\nQ0QluMXBPXw8Ke/7qxeh30htwSprLoyR0k0LJhrUtl8t5BsSlJtluLrlEInLtdKPlOOJ1H/udhQ/\n33zHl29Tl1ncka+Zk7Xg8n7cOCjK4W2FVvDPzTKc3n+dlZ+cpkNce14c+xLx8fEEBhZBTxUhyqhi\nnVnwqIOjp/qEwo13w4FtcHgn3D8WjsZ73hTIFWtrQvgNWqbh6nqoORrqT9TPMhhhY0ttHkNmkpZl\nqD4MTt0DhJg3Zvgz4FteKz90sQlQoe24DTIuQVBNOPcFVOoHTd7XzzIYYc8gSN4FMRtc/3eTUMgx\nZ4yEjT9Dh77w7TvQ+gYYMxdqNvT4ks66P+6L/5Tjc36jxoPdOTxtMeEx9Wk1bwRhLfSDL72gwVXf\nTjvCogkH6D+mHl+8coiaTUP4ev5KyTIIYYd0cDTTv5/R2vRaz2XYFAtJJk+usjeXweyKiaC6eXMZ\nTn0M3A9sNG+8K0lwUfFeoGBRFCtZ+kW4F2AmUPiAoZyduQwmV0z4BvnbmctgXsVE4w7l6f98PZnL\nIEQRkWDBYujL0Lpr/ooJxQ82x8GheO05u1n0KiayM0wcM6digoVATeBJYApg4v94HZVjmslexYS3\nekG4KoHCBw32KibOHHV2li6PKiY6jSV5n/2FvwoTMLToVpGBExoA9ismduwwsyOWEKJEBQv50qNX\nTf6ffcM2ELMR6ozXJuopXvhVWWcZ0k5owYqZVmwAqgNvA88B5wB/c8e0jGsbNJj95m2dZcg4p018\nLAoZlxxnNhIoXNBgXTGRngoBhXud7lZMoCgoAfr/bs1YyTIwxJdVvo8V+ppCCH0lKljItX8b/Ls2\nfDIZMjPNG8fHH+qNh6YfmTeGLUuWocXn5qbt871Z+wADgOl49Z+EJWjISoZN0d7ry9ButbnzQvSo\n2bC9j7bGROpxx8cmFHKsdt1h1gaoaMwcDVezDJ02TCG4bhWnxxrVyKlemzBeW9eB2i1CZY0JIUzk\n0TuDoigjFEU5rChKiqIo6xVFae/ieV0URclQFKVwEy5qN4U7R8BH8TCiMxx20jugsLz9rN3sMU/o\nlbQVwesEWLUTUv+jrUzpje6PRfH3CVp2qt4EuKazkqWtBAoXNBj8Ol3JMri6iiUYl2WwHVMCBiGM\n53awoCjKPWgfQScA7YDtwC+KolRycl44sADwoPewjcAgeHQqvLMGrifBI9HmZxlKi+QU58d4nQL8\nH2R+DOkNvNf9sShE3qrNn6jcP28lS7OzDAZzWMLsASPXl7CQLIMQxnK7dFJRlPXABlVVR+X8rADH\ngbdVVX3NwXmLgH1ANnCHqqq669zqlU6CnXRoWirMmwCfT4PGMfDCPKjXwq3XpCvBhWPSzmhNd8I8\nWLY35SD4hkOAwziroIzLcH0PhHd277wVG4BTQBDgoIGVXanAbsCTUrUzaC09XHmdKrAUeBMCQqDJ\nbKh0u/tDpp7QPlkH1nDvPDUbLi6Dir3d/2SedhrUDG3NClck/qQ1cspMgoZvQNRQ52Mm2Px88Syk\npUBUXffuFWDDz9C+V8G+DM5cPg/JV6FGA6dllrbOL9tG5M2t8LHpy2BR2BJLe0J++3/2zjs8irLr\nw/emBwIJJfQOUgNIDSggqCjgJ76IBbAhCBZQQEVFA66CAoKAgAqKFBWxYHkp9hdQFKT3SA2EHkKA\nQEL6zvfHs5OtM1syM0lg7+vai83MPHNmQ3bmPOc553deomvXroSFhWl+7gABSiLFXjppMplCEU+L\n/8nbJOFt/A50Vhn3OFAfeMO/y7ThcnOSowzvbxBRhqfjXZXt9OTEu7CtIySNB0uub2MjG/ruKACc\neh+2d4HDL3jfY6IwR6EGvjsKAKuAEcBUINPHsdXwzlEAEWXoA3xhizKk/eKjPYS+gq+OAkDaT2K2\nv+8+33tMhFf33lEAEWXosBdi+4sow+mPPI8xO/1csap/jsKRPfBSbxjdA04d8W1sTCzUFJUJvmif\nXD12jm13vS16TCS6j6ZoHWVIT82lz9130Lh9JbZv1+SeGSDAdYmvyxCVgWDA+S6agngiuGAymW4A\n3gYekiQd6w+bx8OCHTDxO4iu5Pv4U0fgyiXfxzV4W1RMHJd1GQy4IdV9RVRMnPrAO10GTcoV70VU\nTPyM7roMAMQC04F3YXd540ouK98lKiYurRf5Eylf6qvLEBoDzRZC619FIy5vMFP0pYmGLUXFxLkT\nQpfh2zm6d7IsU68Knf6aJHQZ2rzIkSnudRnc5TJkXMzjbJLvzdeiY8N4Z2M8QcEmOnRsz/jx48nN\n9dGpDxAggG/LECaTqTpwCugsSdImu+1TgW6SJHV2Oj4I+AdYIEnSR9ZtZqCvN8sQFbo1JzTaMWu9\n+sAu7Ko50+tr9ppeUTB0Etw/2rbN7MP4jF3w72DI3AN1xkG98RCkc9jz6gH493Gh/lh7DNSf6Jrl\nr/lD9jTC99sK9ANGoqv6ozt6xOtvIzcVDo0U6o+x9woBKz3VH/3FXMTxVzPgo3FC/bF1N6H+aI0a\n+IM3yxIF2bmix4Ss/rh4JOWa13Z7rLws8f30Y3wzKYkvLt3q13Xl51lYPvmoUH9sVpbvFv9B27Z+\nLB0GCFDCWLZsGcuWLXPYlp6ezp9//gkaLkP46iyEAleB/pIkrbDbvhiIliSpn9Px0cBFIB9bqn2Q\n9X0+cIckSevc2FHMWQCdZJ+L6iyAEFFKngzJE6FMM2i22L9cBl+QCuDELDiaIBo4NV0EMdYeE7rN\nxi3A98BcRB+JV4GOOtlSwQin4dxyOPgMYIEb5kKVB4uvmkINcxHH71gHU4fAxRQYPgX6jfA9l8GK\nt3kMlzYdZPfguVxNSuGGNx6k/ov3KOYyVJ0+rkjOgszRXVd4b/Bekvdk8Oq41xg/fnwglyHANUex\n5yxIkpQHbANuk7dZExxvAza4GXIZiANuBFpbX/OA/db3fj3NfE2qckDPkLKsy9B+q9BLOK6Y76kd\nzuqPyRP1t1moyyCrP87H0HbQMms3wdp/9LUhqz9WuA2SXrE2pioGPP3dmot4fln9sfcQWDhBOA1+\n4u2yhL3645G3viX7eKrisRvp5Pf12GOv/jhtxtvM299dk/MGCHCt48/UYQYwzGQyPWoymZoiHv5l\ngMUAJpNpsslkWgIi+VGSpET7F0ImMFuSpH8lSTK2ji9pLzzb1XtdBrOfdqKs6o9NtM/sVkRWf2xu\nDUcZssYvqz/OoHg0GrKBp2HtNH0/r6z+2G4rBEfqZ0cJqUA0xvJGl6EoyOqPSw+JrqtFxBuHQVZ/\n7H70Q8o0cJv2VEgOYZqqPy5I7ka9VuUCJZYBAniBz86CJElfAy8CbwI7gFbAnZIkydOCaoD7Bcji\nJj9PVEoYocsQFAohnlo9a4wpGEIrGNx/IQjPLa31IhuRL/ESYIa1v+rbf8KfyhUtsOSIfAlvdBnM\nFN1piNHuc3obZQirXN7rc2pVMVG+sm35IaDLECCAOn4tSkqS9IEkSfUkSYqUJKmzJElb7fY9LkmS\n4sKiJElvqCU36krjNqJi4r7Rxqk/qpH8DlxcY7DRrwCdu1q68AOgx+eMQVRMTEB8pkHAn2LXWjOs\nLXKlrm+c+0bM/rUmuIyomGi1WrTAtld/PL8STs51HWPW/jIK2fIbfDndpyFa5xnpIeQEwK4SmI8S\nIEAJoHT2hqAIeQvOugxylKHAYPXH/HQ4MQ0u/Wmg0SyEs6B32aM9ucA3wF86nd9Ol4GmFEYZ+A5Y\nY1ynS0mCM59Aymf62XDWZdjdG84sEC93mNHHafhjuaie8BFvowzuyE297LJNK7loe1a0vkM4DLtM\npKYq51AECHC9oXNbQ224ejSFU0vWue5ItmtLO/AliFBpDrRhFRzY6rityz3wxVT4+FXx89wxkOGk\ntXDU7n2dl9QbEJ1fBVe2Ku+PqA/VHxPvD46EvPNwZZttf95FOPme8niAGsMhvIby/kt/YU0fcYM8\n6/0KiFIx8h+EzoESO4EtKvvLAw9a3y8CjiByXWUkQOEBV8jtCB0vJY7gGq1oivgP+9lu28fin7XW\nf+vVsu2q8gCUba5sImMvpC5XuQaT6PUAcGYhXLCKR0mSrWLixEzhGCpR8Q51Jc7sk67OQEQdKNfB\nZg/g6Oso5o2MuQNmqtg4dxJWe/j/uH8MREXD1t9hpVU8ymKxVUz8uAhSVNphN+sInfoAwmlwdvbz\nM7I4Ot19T5D0zYdI/WkHAAcTvsDkVDHxAjG0Zys3dIymfR/lv9usjHx+mH5M5UPCbY/XZEXrO2j0\n3a906FSF519MICEhgfDwcNVxAQJc65RoZ+HqkTNEt21AzumLnFjgpqVErl04vf9z6s7C3r/hVzez\nvtiakHrK9vPiN4QqXrD1V2P/jKv1nLqzkP63+syy/E02Z6HOi5DyOaStggu/QcWeUHBZeZZYeL39\n1J2FzN2AN42YPkHZIeiusg/gsAcb1bA5C3cjHIZUhArk/yGcBU/X2Bx1Z+GUyjlM2KoznD7nMeu/\n4WHigavmLGQnefj/sHMWKveFA7KNN6C+WbxPWSbkwJUIq6buLOSlKl9DcFnRsRPg2JviX3eqlWHV\nwHyTcpThUqpnZ+H/hglnobldVcLUITBusXi/cRX8qxLBKcgvdBbAtiwhOw0FWbnuv+OAJTuv8P2R\nt74FILymowrpCaBWfhva97mieAm5WRZ+W3BKcT9A216VqVI3kv13307jur8zadIk1v80ibVbLD41\nyQoQ4FrD594QRiDrLHTe+g4x7ZQFYjRdB701BIKCxU3NvseEWTsTLvxVFSiAm05BkIYzF9Ww+4OI\nB+2viCIWIxgG7AF+wbhkyOcR1bwrAJWWyVpqNSQ+DClLIf4QlGmk3XnVODhSyH+H1/S+x4S5iDYX\nJMBnb8EHG6FF0UsavVlSTJr+Xw6M/ZSyTWsKXQbzg9Qf616XQav+Er8uOMn7wxL5cS707gK0Lnn3\nygAB3FHsOgtG48mTL5LegjNhEfCkm1wGi465DOE1oc4r2joKHqkIPIpxjgKIRMQHMLZqojxwF6qO\nAmib0xASA5X7GecoyES1ds1l8FQxURQio6BJe00cBfA+lyEkukyhLsPBhGWix8S+4y7HaZXLEBYZ\nTIVqYeSNuENssOYyBAhwPVKinYViQe4xIVdMbL8JMnWqmOiwXSxHaI3qbPlDYLj2NlWZhpjpG4kZ\nGO/94Vo4DI3nQksNHVhfkHtMuKuYcIcZ/52Gh16Bj9RyVvzDF12GzhveEj0m2o7lyGTlHhNFoftD\n1Vl8pjsgEh9XtLZzGgIEuM4IOAvusK+YqHAF9g0QrYsDXNsYVTmhJ84VE2oJt6DvMpsf+KP+eDBh\nGSk/uK/w0aVaAgJRhgDXHaXSWci/ksXOQTPJPHxGX0NylCHuezAVw6/Kki+aU9lXTOiOBEwGdhls\ncwbGlnQCvE+hLoM9ejoNxyaKpEcjOll22APlO3g+3qzDNaz4CJbPLlInS0/IUYYuu9+lWn/lJRGt\nSyztowyr5pgYP348OTk5mp0/QICSSKl0FrKOp3Lpn4P81er5It2QvCI8wvg1aJm8VNHNcls8JI0X\nSn66cxlRlvgUMAuhkqg32VabzwFTgEwDbOYDSdh0GdyUN2rtNEgWyEyExEGwtz/k+t9/wSui4rw/\n1oy2TsOpwzBnFIzqDicP+3UKb6MM5VrU8apSQY8oQ9JJmDJlEu3jIti2zUinPkAAYymVzkK5FnXo\nsnsGtYbcWuQbUokmvLroMVF3PByfAlvbGxBliEY0hhqJEDZ6BP2jDJHAHGAsomLiIfSPMoQg1B/H\nIwSj7NQfndHKaTAFQYtl0OIbSP8LNjXXP8rgK2aNzvP0OzBzDaSehCGtdI8yeIvWUYZ6U+9g61II\nCYb4+PaBKEOAa5ZS6SwAhERF0mLuMDquMWtyQ+KBF0SGtzvMKuMki74VE0Ghopa//VYwhRgUZQhG\nPLA/RTgPRkQZ7DtZ1sSYKIMJUTHhrP6oIKKkVZRB7mRZ8faiRxkq9BSlkv5gyXW/3Yw2TkPbHqKT\nZZ8hRXbqD4QPpd6Yu/0aa8nNc9mmpcOQ/MAdjN9zO+OHBaIMAa5dSq2zIFOpR0vrDWmo7YZ0+YLv\nJxryBrTq4vu4k3OsFROJvo/1BbmTZd0JtihD1lHP44pEPWxRhu8RUQa9bdbANcqwX2ebVXDtMbHT\n/aFaOQxyJ0v7KEPaL57HORN7jxAL85Xs4/BPI88VE0WlTBSMnguz1tqc+p8/9f08rbtxuMeXPkcZ\n8i5fZX3cGI5Mca2Y0DLKEBIaRJsPHaMMU6ZM0eTcAQKUBEq9swDYWuvOWgvV60NUjHG2y3eCgiuw\npQ0kTzEgyjBBRBnKNBPKfEpoJjZkH2VohLqyo1bYRxmaG2TTvsfEjajqM2iZyyBHGSr1hggDm7UG\nl4cKt1t1Gfoo6zKY0cZpaNPd5tTHulGZ9AFfHIagsBCq3RvPwdesugyJrp9TjyjDhOFQPW9coGIi\nwDVDiVZwvGnbNKLbNvBqjNZd7Vwwq+wryIZjr8Px6VCuHTRbrC4jLLOnH1S+2/8wsifcPtDMQDNs\ncsxGMBXx8H3cQJtzEI7OM/qasXfKjr4pklIbz9HXppak/QgHhnun/mi2/rviI9j6K7yp1jfDGLwV\nZru06SC7B88V6o9vPEj9F13VH52VHzevPMd3U48x5a+Ofl1b312/2n4IqD8GMJDrTsGxRGFW2Rcc\nAQ2nQtsNvkUZrmwR4WBDOQio9CrQhSMI9X4jOYatEYSO2EcZsg5C5h79bWqJSydLD1EGgHPHXZuy\nFRPeThIcdBkUogzOyxKXUnL59+9LzqfyGhchp0CUIUApJuAsaEl0PLTfAbVHQ9JrkDiweK9Hy74H\nAdQpzWJODuqPe4T6Y46CQ2lGsWikuPC2xNJF/bHNi6RvT3I5TjchJwg4DAFKLdeMs+BVODL7Kqxa\noK8ug32UodZo/eyoIVng1HxRMWGYwyABP2CMLoM9KzFGl8GeH3FbMZFyXj+TKcv012WQowyNZqh3\nNgXwf8KtzoZVRdJl8AY5ytBs1uOUv7Ge22Pm8SR/cItf1+EOZ4dh/SJToGIiQKnimnEWvGLzzzBt\nmP8lXGYfjo2Oh5ibfbehBZe3wKGRNl0GQxyGY8BMjNFlkDlrtWmELoNMOqKMVEGX4dJl7aMM+Rlw\n+AVjdBlCY6DGUO+ONWts22KBT8YXqQzaW4chOCKMuk/3whRk3C3Qflli+qcBXYYApYvry1nodq9j\nCZf9DenUEbii13TJYKLjXXUZbrlRZ6P1ERUTMRin/lgN+ByohXHqj9GIKg0PugxaOgwhUdBhl3td\nhtzUYsh7scOMdk5DUBDMWe9YBi079VcuwmnXJQN3eLss4S16LEssnwYThgd0GQKUHq4pZ8GrpQj7\nEi77G9LQ1vDzYp2v0EDc6TK0D9HZaF1gHo66DHpHGWoAszFW/TEWV10GhR4TWuFOlyFlGRwzw56+\n2tnxF7NG57Evg7Z36ld+LNrG+0BJVn78qf0dTHiSgPpjgFJDiS6dbLtyHOXi6rg9JrJurFs9+MIb\nxKVUyFKZZUaUgWOJMHUIXDgLOVnwzLvwoLWVcm4OpCk0qppl/Te8ptA+UCLvIuQrqAGe+QSSJ0Hd\n16DBJLHNkgc5p5TPB0ICOihceX9+urBrT8Yu2D8Y8uXIST/gZev7AsDTWnhFIEJlfyaus+vjwCRA\nXsdvbv1ZSxv2BAEW4G1AztRvh2gWJXMGkVuhRDRQVmV/NuAs+HUeEdGQZ71lENEOJzq1Ef+GVoKQ\ncsomCrI85yYER8Kh5+Dc13bnVxHLCq0AIdHK+y05kOOhKVt4LQgKEcdtqKFsU07TiYqGchWUz5ef\nB6ke/tbLloeFr8P3c23b/rD7/7uQIr63SkSWhZhYxUmEJElkJae63VeQmc1fcWMAuOXohw77HuKL\nwvcRZYOJjg1TvARJkjiXrBxh65m4ngrl4b0vYOLH0LQeLP5yq1z2FiCAX+hROlminQW1Y+7M+9ql\nThrsnIU3BsKaL5VP0LUfTPoOrmbAR+NsN6Slh6BWIzi4HYZ5+MLGH1JvMnVknJjVe6LjXijbArKS\n4J+G6se22wLlFWSpAZKnQtIrnm2yGBFKTwfu9HDsbECt1vx7hJZCUSiqjfLArwiH4Xtgmpvz3gpc\nVTnHOOAelf3/YHsa+kmTj6HGE8r7036B3b3Uz9E1HULKw7nlsO9+zzYbToM6LyrvT98E25W7NgLQ\nORki6sDlzWJpyxOPvAZPqDiHxw/AI03Vz7FwFzRsBTvWwegeYtuz78G9I8WSxbi+sGGl8vieD0GC\nzXFzdhoKcvL4NWKAhw+izi0PVef5z1sq7s/LsXBfxO+q5/jvLOjbHXYdgC6PQ8ZVGDt2LBMnTiQ8\nXGViECCAAteds9B48kNEt3f/8Kx0a0vF5KSf/rwXjuyBiyoztJhYaNTa9vMt1ihFeCQMnwK9HoP9\nW9yPldVqo2+C4DLKNq4ehuxjyvt39RT/msKgvhlqjoTLHkLX5TuKB4USWccgSyV5s9BmMEiPAo8C\nnrQBmiBm3UqcQ13TwF6OuCHwJK5RhKLaCEZEEmQGYZvt/wd4FiEbXYAy9VBVbiQdOKCy3/5zVgLG\nIJwYO266V0SklMhLgys7VGwAMd3FLB9g34O2CENwOWj8IYRVdTy+zA0QUVf5fPnpIilWjeguotIH\n4OBIOPU+xPSAuq+6Pz6iHryj4khnZcK+jeo2m8dDGWsUZpEZFr8h3rfqCi8vhKwMSFepQKlYDRo4\ndt60dxgki4W0Ncp/+8lzf+Lcf22/l2azHieqhaPK5iPVfqNunHKkyGKR2L1GXX6+futyRMeG0XfX\nryz7CQaNE9vjGgWiDAH847pzFnxRcLTHr7XKXlEw6BUR2vx+ru2GVEvhhmf23YQLG2pB1YcByU79\ncZGIMujF5jiIuQVCq0LyRJDqIjovepjlFYnhiNyCG4CPEA/kBKC12qAi8gJCwrkzMBfhiLyKevSi\nqLyOcGruRlRphCGWe7o5HqZldcrBkSKHoW4CHHwGpAJoPBeqDFBWYiwqSQmQ8rlYhvBkw6yRzS+n\nw2eTYNIPtqXD4VNsUQYf8Fb18cSC39k77EM6/zPZpv5ofpD6Yx3VH52VH4tC7vRfuX8srFsAo6fB\nnsMwblwCCQkJgShDAK8JKDjqyaQfoOfD7pOr9NRlCHJWf2wLyZP17TFhsusxEVUOGIpoGKXQhVAT\ngrD1mDCqYsK+x4SRFRNyjwmFigkte0vUfAYaf6BtJ0tv8cYZMaONw3BLf3jzW+UEZR/wtVrCQf0x\nwar+uM9WgaJl4mPmw7fw8wdwU2vY/HmgYiJAyeGadBa8nTk40P52qF5PvHe+IY3tpa/DAE7qjwmw\no6tIeNQTuWKCIYiH+OPoX+7ormJCLXFRC9xVTJzT2aa7igmnEkctHIayzcVyGLivmMgwSvPCA2aK\n5jRUrw/tbhPv3VVMbPlVfbwbfHEYXNQf247l7Le2ZRStqiUqVAsn5+k7CA2F0FBcKiYWL15cZBsB\nAvhDqXQWJEki9ded6LqEYn9D6n6/a6jTrINNe/XHqgPVKy20IigUenyESHjshXpFglbYd7LshXqu\nglbYRxl6YXwnyz6Am1wFPWSi5ShD9aFQRs/lJRUyE933mDCj3XdHdurvGwVNVJJ+VfB1yVKO8dhI\nZAAAIABJREFUMjR46T/EdG7isl+rKIO9gFPrJiLKYH4KulR6PCAZHaBYKJXOQvrmQ2y9cyJbe08i\n64T7BCe/ogvuaNMd7h6mzbm8JToeaj3n+ThNuQExyzeSuoglECOpgVgCMfKGGwuMQDhJbtByWUIm\nLBYavaNeZqsnh18Q+TGnP3GvOGlGG6ehTBQMnwzlK/p9Cl+XJYIjwmg8cSARNdzb1HJZQnYYQkMh\nYRg0kivJAw5DAIMplc5CTHxj2q1+lSt7jvNX3BhOfPK72yiDZg6DEmZ9Tx/gOqM0N6NypvkyiL3X\n2smyt3onS7OB16VCSRVxcugrYU+gk2UAAymVzgJAlT7t6LpvFlXvjWfvEx+qRhlKLKFVIDjKYJuV\nIdhN6aWu/SOiAYM/J+WsL6NtqpS1ekNpcBiCoyDUwzJOaIyo7Gm1GjL2qEcZoMQ4DfYOQ1BkGOHV\nYop0Pt0dBgg4DAEM4ZoonTz34zb2Dp9HwZVsms54jFpDbnNQd9RyxuDCC9sg/W+hkWAyyPfK3A/n\nf4DaL9rq7bVA9UF1FlgFPAYYkEsBwEXgK2AwxuRSgKiUWGy1qabmqCU5wMeIZSC7/A09HThLPhxN\ngNpjXHUZtCbvEhx+Hs4ugop3CmGqiNqex5k1sC1JsORNUelU04PgmR1FjUoemfIdVfp2oFxz8Tm1\nKq/su0s5kXPW59Bt4DbatvVNFjvAtUegdFKBKn3a0XXvLKr278SBlz8n70KGccY7rIVDo2BHD8g6\nYozN9D8h6TXYfpNIJNMK1YfTHmAR4iG6XzubqiQCyzC2k+UBYDnGdrJMAv6LqJhYb9usZ5Qh6xCc\nWQibW0DKl/p3smy2UEQZMvcKu95g1sB2+nn45VNRMfHtHK+rmorSjCr/ShanPv2Dv9u8yJEp32HJ\nL9BsWcI+8dGenFz4/Efo2LEd48ePJzdXzzLoANcj14SzABAaU5ZWC0fQNfE9wio5hp+9miX8tBiS\n9vpueMCLcONayDkBm1vByTkg6VxmWWO4nS5DG0ieoq8uAwA9ETPuYGy6DDqXdnIzjroM76F/aWdb\nHHUZpqK/LkMzbLoMY3HQZfDkMKRvgFQ/ZsFlm4mKiQq3QeJA2Hef/roMlfpAh71Qd5z3Y8zWf4/s\nhp8/VTvSPTGx8Mku6D0EZj8nZKNPee/U++MwhJSL5Obt04Quw2tWXYZEkbPhyWFIOXqVXxecJC9H\n/R7i7DCEh8HGJfa6DOFs367JhDJAAOAachZkwqv4WYb33kjYpq7hrkiF7tBhN1QfIhr8GBFlcNBl\n0CHK4JYbgIXYdBkGo3+UwV6X4TuM72T5M8XXydIaZVBzGFK+gGNv+mfSXpfh0nrjogxByo2X3GJG\n6CjM8bNCyL4M+twJv6IMvuKiy+AUZVDi8LbLvD8skZwsNVlygbPDYK/LEBwUiDIE0JZrzllQQtfK\nCDMQEgWN5zhGGU59oJ9NcNRlKIwyvFO0c3pcJw9BRBYW4xhl0DP3xV6XwV79Uc9oijv1x6mI/AK9\nsNdlsI8yZOpTXikj6zLYRxny1PsZGM6vFD2oJOsy2EcZUo57HAb+L0s4qD9aowyZh07rmvgo6zLY\nRxn27PHU/yVAAHVKtLNwH99qer7e3b6D9DRNz+mCfZQh1337W82xjzLknjXGpkOUIQ1jdAvsowxp\nKOoWaIp9lOEcxiR32kcZ0gA7rQS9HAb7KENuKgRF6mPHE3kX1CMb5iKe3z7KkJsNYb4lzhY1yoDJ\nRFCYSErWQ8BJxj7KUDYSQg630sRWgOuXEu0saE3Kyi0wsAGsVinh0gI5ylBvgn42nJGjDI3eNc5m\nYZTBhzXoIiNHGd7EOGElOcowHeO+MnKUYTbi92yHnomPVe6DNn9AcDE4C5IFdt2prssA2iQ+tukO\nH/4DFdS6jLrH38THmPjGdP5nMpF1bTb11mNo3QQ2LIFmDQjoMgQoEiXeWdCyo1vFrs2p+UB7eOcJ\neKm3WL/UCrObbXp1/VNDC5s+l+wVxw3oOrep57JEcfzdgig9rv+GqJjwRpehyPb8/5z+LkuYFGzq\n6TC4mAw4DAH8oMQ7C1oiV0wwdTUc3QuD4/SPMqixp5/3ZWRakfgInHjPWJtMRZRdGskcQOecERc+\nQUQfDOSUzhUM7jj9Eey9T59zyxUTsf29U3/Uk79XwsguqodorfqoBaoCTjKBKEMAHykVzoKW0QWA\n3i9lw6K90K2/LcqQpXd5nBOysFK2dwlWmpB1FFI+h+yjno/VTBDoPPAjoGEUxyOXgZXAMQNtZgE/\nAAZpbQCidHUTZFw1zqRUAKfmw+Ut+tlw1mXYHAdnVHpM6MVPi2DP354P09Bh+OJnbRqceeUwAOwy\n8dtvv5GTo2fiboBrgRKt4Pju1ngatYvmyPbLTHr+iuqYtv99mdBoZcW9ozNWcG7F1sKfL6RXFm92\n/uF4YOtuyuHJt/4LUSqlmV/NgC9WKO+PagM3zBTv9/YX9fEhFaDLeRGCzTkNiYOUxwM0mQ9lXLvd\nFZLyhZj5ueOS3WeNvhlMCuqPsg3FMPcviAejEpWBidb37yGElQD+BMIAC6KxkhrDEJoHSmxFzOTd\nscPufXMcEgQ1swFiiUCOXnwNzLC+/x829cfXALXKgnsRGhZKHAWUKlzsP2dDoDzEuJGbrvE0VH1Q\n2URmIhx8RuUaEMmPYVXh/ErY01dsu/msTf3x4HOQuVt5fOV+UHuU8v68C7DXzUM3/5Jjm+2IBu7V\nH+sBXfuJDpRKXL4A4z082J99Dxq1FroOQ1qLbUsPQa1G4v1nb8NWZRXFBr0q0mTyw6omNt/xJlKu\nayXP1aMpZB8XkvWmkGBa3OxeOrxJ5xgenXyDqo3X79hGfq4oDa2UcdFl/7ihcOdNkJIGte6EGrHw\n7YottG/vX/fOACULPRQcNdQK1p6UpCwatYsmNDyIlrUucAjlL4jJuYW0E6EVooioVanw5xq1JE6f\nqw09H4KMS7Bxtdix60/hMFRxc0PyYINyFSC8lspF2M0ami4RzkL+RbjwC1TqLR7eauMBTB6y8YPL\nKZ8jtj+kWitM0jeKNtj+2KAMoJYYVsHu/QhszsJKRKIgHsaD8gNeJkLlHD2B36zvE4E7dbABjvkE\n92FzFhYhKjYAKqH+NSvj4RpCVK7hDkRNIYiIRhm41BWqVnY8zFP/EVOY5787ufKk8t3Ckbx6QGiK\ntPhKbA+LhXyVc4R46LFgCnZ/DeG1oGwcpCwVP2cniVfVQTj8/s8Av8WI/wYlgoIh1sPnDLX+TTRs\nJe4Nvy2FSQ+JZEiTSXS3VDlHUvqNqLjyAETUrIiU56qjEFGrEqeX/gmAlF9AWo0WNA5yjVSVq+S5\nIqdizXAK8uSJYHVqXTzjsL+MtQikaiWY8hy8OAM6dOhATk4OYWE+6mAEuC4o0ZGFGds60bCto3et\nZftXsAsh9oqCFjdBciJcvQIjZkCfIb4nQZl9OHZDLSjXEeK+NS6pbHMchFaFG3/zrpeFJkl0wxGa\nCB9hnH/6AnAKWIJnp0ArXkcIRi3FuL4S0xGRjOYIMadewBjo4WUY2h+SEuDETOh0CMJr6GfHnuPT\n4chYqPa45x4TZo1srloA04bBF4d96isB/uu6nFm+kZ33T6fzpinEdBSTI737Svz+D/R8Cn6cC73l\nFI3WJe+5EMB7Ar0h9KZTH9dcBl8rJsw+HFv5HjFDMjL7vGJvqP6YcU2vAOgA3IXxgaw6GOcoALQE\n7sY4R0GmMi7qj2un6WeubEuhI2KUoyATEu2ay+CuYsKskb0aDeDWAT47CuB/tURk7UpUH3AzUS1s\nTpDeiY9VK8GAXtC+ud3GQPJjACdKXWQBdIou9IqCoZPg/tFi4z8/wvThkHlZRBnuGur9Q92s6eUV\nP6WhbbILLyBC50VUtCzxTEdEMz6z/pwKTEE4DXcCz+sbZTCK49MheRJ0vSR+9qaTpdnwq3SLVuqx\nWiZ6q3WvdCEQZSh1BCILdljydG6cJEcZbrkP/lju21izhtdh0btZUwmxqat08/Vk0179cTtwuXic\nPUuegZ0sE91XFZn1M19IQYHHHhNaVUvIAk6SJFGQX7RmdV5XSwDsMiFJEnl5xXFfCFBSKJXOwj1H\nZvJHoxGcXrYeLSIjip5/uRh4ZSG8vaJ4hGryLsDmZnBytv6dLGUKMmFLa0iebEAnS5k8hGz0fMCo\npjcFiOTLWejfyVJGAl5EzPz1LNWV1R+/A6yzbT1FnNxx6FlR8WNEJ8tOhyHmZvf7zfqa58tpMKo7\nnDyselhRWl4789r8+rx802aO78so0nl8cRi+eieIts3D2LZtW5FsBii9lEpnoUz5EGI6NWbXoFns\n6D+NnJRL+hoMLabsYFMYVOwFh0bBju5wVf2GpA3BIuM9KcHayXKfhpoLSpiAbohGUY+jfydLmW4Y\n18lSpiui9NSITpZusuaNchoq3A7pf8Gm5pCyTN8og6culmb9TNO8E6SeFJ0sl882JMpQvk19Tl8p\nx5i2G1k+OalIUQZvHYZm9SEkGOLj2zN+/PiALsN1SKl0FqJjw5j/VRQ3fvMiF//6l/XNRxU5yhAc\n5LklrE+YNThHSBQ0ngs3roGck7Cllf5RhsJOln9bO1m2FVEGXcPnIcATuHay1DPKYN/JMhpbJ0s9\nowwmbJ0sayI6WeodZVBAdhr07mRZ8XahHWJElEENM/o4DXInyz5DYM4or6MMRUHuZFl79D0sTThc\n5CiDNw6D3Mly/DC5k2VEIMpwnVEqExzteS91AIkjF3D26w1U7RdPiw+HE17VQ023G87/vosyjarz\nx/GnfBuYeRky093rMoB2N6j8DEh6BU69D9FdoelCKNNIo5MrUJANx14XyWXl2sGVMUADfW2Sj3Aa\nFiGUdsYj2jX7yn7Ew9lT1TuIJYkvEQ5KVSABaO2HTV+wAN8DcxHOyqtARz/OcxS4AvjTVfAoUN/2\no14RpHPLheiTVCCc3yoDfF/WyzoKWUlQ8Tbf7WcmQplmNptm30/hFdvXwjtD4cJZGD4F7h2pqs2i\nReLjxX8OcvLxSZxNuspAc0P6ja1HcIj/c0BvEh93HYDBE2DPYRg3LoGEhATCw42sOgrgiUCCoxvC\nY6Np89ULtihDi9HkpqmrPbqj8u2tKVPP9w50fDrJmB4ThVGGtbYoQ+a/+tkDuyjDBhFlMA0G9ulr\n022UwR9p4aZ45yiAY5QhBhFlWOeHTV+QO1naRxlW+XGe+vjnKBwGBiGenOlik1FRhmMTPY9xJrK+\nf45Cbips7QC7+6h3stSCtj2sUYahIsrwzhOqh2uRx1ChU2Oa71hQGGV45wEVFU0v8CXKMGG4iDL0\n7hqhSe5YgJKNX5EFk8k0ApGpVQ2x2PusJElu7+gmk6kf8DRwI6LofR9gliRJ0YX1JbIAtlLKnNR0\nzq3cSu0hftxU7PDpC3zlErz/vNCR79gLxn7kPspgdjPWki/0DnzVPMjPgJRPhYyvrzM0S74YYwr2\nbVxBNpxZADWfFmN9erDkI2b5PtokHyErfQ9u1991ocBqsw/ga5tmeSnL189pQahbdkdEGYxAAn4C\nZiIkuF8BunoXXZAKhGMc5IduxrnlUK4NRPquXeA3aT/CgeGQfwUazYD5XoqtWSziFeLH59yxDsIj\nobl30Ro5yiBZLEgWCVNwkGKHSiUubTrIXVnf0rJ7RZ/GWSwSkkUiKNhUaNPb0spdB+DMeeh1M4ES\nyxJEiYgsmEymB4F3EXJ1bRDOwi8mk6mywpBuCE3a3ggh/rXASpPJpHmcNzw2usiOgs/IFRNTV8PR\nPcpRBrObsf/Ug2Nv+m4zJApqPuNfhcbWG+HwC76PC46AWiNtTkaPeMeXKs8Ab/lukxCEfq9RjgKI\nB31/fHcUAN7EJvPsC0EIh8goRwFsFRNfIKIwYwGzqMDxxNHXYZOfS2BV7jPWUQDXTpb39vFObO3H\nhXCbn397bbp77SiAbYJy9rtN/BL6APnpvjcHi4lvzN/dx/k8bveaC9wb+jvnkm35Ot4mPrZuYnUU\nINDJ8hrHn2WIMcB8SZI+lSRpPyJmexVR++aCJEljJEmaLknSNkmSjkiS9BpwCCF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Gb5RhKf+QipwELzuU9QfUAXTNZlA6+TH/NyxQw3xEeJjcsXYMNKuPNR9QoDs2+ndcvFdbB/COSe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\nG/MOG4e8SOM7+xHXt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# barycentric coords: (a,b,c)\n", "a=test_data[:,0]\n", "b=test_data[:,1]\n", "c=test_data[:,2]\n", "\n", "# values is stored in the last column\n", "v = test_data[:,-1]\n", "\n", "# create a triangulation out of these points\n", "#Tri = tri.Triangulation(cartx,carty)\n", "Tri = tri.Triangulation(a,b)\n", "\n", "# plot the contour\n", "#plt.tricontourf(cartx,carty,Tri.triangles,v)\n", "plt.tricontourf(a,b,Tri.triangles,v)\n", "\n", "\n", "# create the grid\n", "#corners = np.array([[0, 0], [1, 0], [0.5, np.sqrt(3)*0.5]])\n", "corners = np.array([[0, 0], [1, 0], [0,1]])\n", "triangle = tri.Triangulation(corners[:, 0], corners[:, 1])\n", "\n", "# creating the grid\n", "refiner = tri.UniformTriRefiner(triangle)\n", "trimesh = refiner.refine_triangulation(subdiv=4)\n", "\n", "#plotting the mesh\n", "plt.triplot(trimesh,'k--')\n", "\n", "plt.title('GM')\n", "#plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# prepare a pretty figure for the graphical abstract " ] }, { "cell_type": "code", "execution_count": 96, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(0, 1), (0, 2), (1, 2)]\n" ] }, { "data": { "image/png": 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gfOnnrFi8gy80Ka/p0Q/fvsWHu+H8F2+aKzsv486tuo3AG8B4EZmHEa0fVPWC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\n0M7GE3YwtSXQ0srxBVRqBCWrw+yhSkX8r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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#for a 3 component system we can conceive 3 binary\n", "\n", "from matplotlib import pyplot as plt\n", "%matplotlib inline\n", "\n", "import itertools as it\n", "binaries = list(it.combinations([0, 1, 2],2))\n", "\n", "print(binaries)\n", "\n", "figs = np.ndarray(3,dtype=object)\n", "axs = np.ndarray(4,dtype=object)\n", "\n", "fig, ((axs[0],axs[1]),(axs[2],axs[3])) = plt.subplots(2,2)\n", "\n", "for ibin in range(3):\n", " \n", "# figs[ibin], axs[ibin] = plt.subplots(1,1)\n", " \n", " T=298\n", "\n", " x=np.zeros([100,3])\n", " \n", "# print(binaries[ibin][0])\n", " compA=binaries[ibin][0]\n", "# print(binaries[ibin][1])\n", " compB=binaries[ibin][1]\n", " \n", " x[:,compA]=np.linspace(0,1,100)\n", " x[:,compB]=1-x[:,compA]\n", " \n", "# print(x[0,:]) \n", "# print(x[1,:]) \n", "# print(x[50,:]) \n", "# print(x[98,:]) \n", "# print(x[99,:]) \n", " \n", " GE = np.zeros(100)\n", " GM = np.zeros(100)\n", " GIM = np.zeros(100)\n", "\n", " GIM[0]=0\n", " GIM[99]=0\n", " for i in range(1,99): # from 1 to 98, inclusive\n", " GIM[i]=(R*T*(x[i,compA]*np.log(x[i,compA])+\n", " x[i,compB]*np.log(x[i,compB])))\n", "\n", " \n", " for i in range(100):\n", " gammas=Gamma(T,x[i,:],alpha,A)\n", " GE[i]=(R*T*(x[i,compA]*np.log(gammas[compA])+\n", " x[i,compB]*np.log(gammas[compB])))\n", " GM[i]=GIM[i]+GE[i]\n", " \n", " axs[ibin].set_ylabel(r'Gibbs Energy variations')\n", "\n", " axs[ibin].set_title(str(compA)+str(compB))\n", " axs[ibin].plot(x[:,compA],GE,label=r'$G^E$')\n", " axs[ibin].plot(x[:,compA],GM,label=r'$G^{M}$')\n", " axs[ibin].plot(x[:,compA],GIM,label=r'$G^{IM}$')\n", " axs[ibin].legend(loc=4)\n", "\n", "axs[0].set_xlabel(r'$x_{EA}$')\n", "axs[1].set_xlabel(r'$x_W$')\n", "axs[2].set_xlabel(r'$x_E$')\n", "\n", "axs[3].set_xlabel(r'$x_{EA}$')\n", "axs[3].set_ylabel(r'$x_{W}$')\n", "\n", "# barycentric coords: (a,b,c)\n", "a=test_data[:,0]\n", "b=test_data[:,1]\n", "c=test_data[:,2]\n", "\n", "# values is stored in the last column\n", "v = test_data[:,-1]\n", "\n", "# translate the data to cartesian corrds\n", "#cartx = 0.5 * ( 2.*b+c ) / ( a+b+c )\n", "#carty = 0.5*np.sqrt(3) * c / (a+b+c)\n", "\n", "\n", "# create a triangulation out of these points\n", "#Tri = tri.Triangulation(cartx,carty)\n", "Tri = tri.Triangulation(a,b)\n", "\n", "# plot the contour\n", "#axs[3].tricontourf(cartx,carty,Tri.triangles,v)\n", "axs[3].tricontourf(a,b,Tri.triangles,v)\n", "\n", "\n", "# create the grid\n", "#corners = np.array([[0, 0], [1, 0], [0.5, np.sqrt(3)*0.5]])\n", "corners = np.array([[0, 0], [1, 0], [0,1]])\n", "triangle = tri.Triangulation(corners[:, 0], corners[:, 1])\n", "\n", "# creating the grid\n", "refiner = tri.UniformTriRefiner(triangle)\n", "trimesh = refiner.refine_triangulation(subdiv=4)\n", "\n", "#plotting the mesh\n", "axs[3].triplot(trimesh,'k--')\n", "\n", "axs[3].set_title('GM')\n", "#axs[3].axis('off')\n", "\n", "plt.tight_layout()\n", "\n", "axs[3].spines['right'].set_visible(False)\n", "axs[3].spines['top'].set_visible(False)\n", "axs[3].yaxis.set_ticks_position('left')\n", "axs[3].xaxis.set_ticks_position('bottom')\n", "\n", "plt.show()\n", " \n" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [Root]", "language": "python", "name": "Python [Root]" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }