{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "
\n", " 数値計算による常微分方程式解法(python版)\n", "
\n", "\n", "
\n", " ordinary differential equation(ODE)\n", "
\n", "\n", "
\n", " cc by Shigeto R. Nishitani, 2020-23\n", "
\n", "\n", "\n", "* /Users/bob/Desktop/maple_ode/python_ode.ipynb\n", "* origin\tgit@github.com:daddygongon/maple_ode.git (fetch)" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true, "slideshow": { "slide_type": "slide" }, "toc": "true" }, "source": [ "

Table of Contents

\n", "
" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Euler法による落下運動\n", "\n", "## 重力場中の運動\n", "重力場中のボールの落下を考えて,1軸で考えた運動方程式を立てます.\n", "\n", "$$\n", "\\begin{aligned}\n", "v &= \\frac{dx}{dt} \\\\\n", "a &= \\frac{d^2 x}{dt^2}\n", "\\end{aligned}\n", "$$\n", "質量を$m$, 重力加速度を$g$として,働く力が$F=-mg$であるとすると,ニュートンの運動方程式$F=ma$は,\n", "\n", "$$ \n", "-mg = m \\frac{d^2 x}{dt^2}\n", "$$\n", "となります.\n", "\n", "\n", "\n", "![image.png](attachment:image.png)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Euler法\n", "1次の微分方程式の一般形は\n", "\n", "$$\n", "\\frac{dx}{dt}=f(x,t)\n", "$$\n", "と書けます.この微分方程式を簡単な近似から求めるオイラー法を示します.\n", "$x(t+\\delta t)$をテイラー級数展開すると,\n", "\n", "$$\n", "x(t+\\delta t) \\simeq x(t) + \\frac{dx}{dt} \\delta t\n", "$$\n", "となります.これらを代入すると,計算アルゴリズムはつぎのようになります,\n", "\n", "$$\n", "x_{i+1} = x_i + f_i\\,\\delta t\n", "$$\n", "ここで,$f_i$は点($x_i, t_i$)における関数の値です.このアルゴリズムを適用して,$t+\\delta t$の座標$x_{i+1}$を一つ前の時間の座標$x_i$から導くことができます.これを重力場中の運動方程式に適用します.\n", "\n", "## 重力場中の運動をEuler法で解いたら\n", "Euler法は一階の微分方程式に対する定式化をしています.ところが,重力場中の運動は2階の微分方程式です.このようなときには媒介変数を導入して1次連立方程式に置き直します.\n", "\n", "媒介変数として速度$v$を使って,2階の運動方程式\n", "$$\n", "\\frac{d^2x}{dt^2} = -g \n", "$$\n", "が,1階の連立方程式\n", "$$\n", "\\begin{aligned}\n", "\\frac{dv}{dt} & = -g \\\\\n", "\\frac{dx}{dt} & = v \n", "\\end{aligned}\n", "$$\n", "で置き換えられると考えることに相当します.アルゴリズムにすると,\n", "\n", "$$\n", "\\begin{aligned}\n", "v_{i+1} &= v_i - g\\, dt \\\\\n", "x_{i+1} &= x_i + v_i\\, dt\n", "\\end{aligned}\n", "$$\n", "なる連立方程式を解くことに置き換わります.これをpythonで関数にして,さらに計算結果を表示させてみます." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "def euler(x0, v0):\n", " v1 = v0 - g * dt\n", " x1 = x0 + v0 * dt\n", " return x1, v1" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Eulerは$x_i$, $v_i$を受け取って,先ほど導いた簡単な計算によって,$v_{i+1}$, $x_{i+1}$を順次計算して返します.結果は," ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "\n", "def my_plot(xx, vv, tt):\n", " plt.plot(tt, xx, color = 'b', linestyle='--',label=\"height\")\n", " plt.plot(tt, vv, color = 'r', label=\"velocity\")\n", " plt.legend()\n", " plt.xlabel('time')\n", " plt.ylabel('height and velocity')\n", " plt.grid()\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#g, dt =9.8, 0.01\n", "g, dt =9.8, 0.1\n", "tt,xx,vv=[0.0],[10.0],[0.0] #for compare rain_drop\n", "#tt,xx,vv=[0.0],[0.0],[9.8]\n", "#tt,xx,vv=[10.0],[0.0],[0.0]\n", "\n", "\n", "t = 0.0\n", "\n", "for i in range(0,250): #250 for compare rain_drop\n", " t += dt\n", " x, v = euler(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "# print(xx)\n", "# print(vv)\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "位置(height:$x$)と速度($v$)の時間($t$)変化を表示させています.\n", "\n", "\n", "時間とともに位置は放物線状に変化し,速度は一定の傾きで増加していく,等加速度運動を再現しています.Euler法ではこのように非常に簡単なcodeによって微分方程式で表される現象をシミュレートできることがわかるでしょう." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## 空気抵抗がある水滴の落下\n", "ballの落下ではわかりにくいですが,より小さな質量の水滴では,速度に比例する空気抵抗が効いてきます.この様子を見ましょう.微分方程式には,\n", "\n", "$$\n", "F_x = - C v_x\n", "$$\n", "\n", "項が付与されます.そうすると運動方程式は\n", "\n", "$$\n", "m \\frac{dv_x}{dt} = - C v_x - mg\n", "$$\n", "となります.これにともなったv_xの時間変化に対して,今までは単純に重力加速していたのが,v_xに比例する空気抵抗を記述する項が付与されます.この変化をEuler2に入れ込むと少しの修正ですが,結果は劇的に変化します.\n", "\n", "\n", "![image.png](attachment:image.png)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "その前に,ここで示した修正がどれほど普通の微分方程式の解法としてややこしいかを少し示しておきます.\n", "$$\n", "m \\frac{dv_x}{dt} = - C v_x - mg\n", "$$\n", "を整理すると,\n", "$$\n", "\\frac{dv_x}{dt} = - \\frac{C}{m} v_x - g\n", "$$\n", "です.右辺を$v_x$の係数でくくって,変形していくと,\n", "$$\n", "\\begin{aligned}\n", "\\frac{dv_x}{dt} & = - \\frac{C}{m}\\left(v_x - \\frac{m}{C}g\\right) \\\\\n", "\\frac{1}{\\left(v_x - \\frac{m}{C}g\\right)}dv_x & = - \\frac{C}{m}dt\n", "\\end{aligned}\n", "$$\n", "これで変数分離されているので積分をとって,\n", "公式$\\int \\frac{1}{x+a} dx = \\log |x+a| + C_1$を使うと\n", "$$\n", "\\log \\left|v_x - \\frac{m}{C}g \\right| = - \\frac{C}{m} t + C_1\n", "$$\n", "なんですが,両辺の指数をとって「適当」に変形すると\n", "$$\n", "\\begin{aligned}\n", "\\left| v_x - \\frac{m}{C}g\\right| & = \\exp(- \\frac{C}{m}t + C_1 ) \\\\\n", "v_x &= \\frac{gm}{C} + \\exp(- \\frac{C}{m}t + C_1 )\n", "\\end{aligned}\n", "$$\n", "となります.最後の絶対値の変形は怪しいんであまり信頼しないでね.\n", "\n", "これをpythonが用意している数式処理libraryのsympyを使うと次の通りとなります." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle v{\\left(t \\right)} = \\frac{- g m + e^{cc \\left(C_{1} - \\frac{t}{m}\\right)}}{cc}$" ], "text/plain": [ "Eq(v(t), (-g*m + exp(cc*(C1 - t/m)))/cc)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import *\n", "v, f = symbols('v f', cls=Function)\n", "cc, t, m, x, g= symbols('cc t m x g')\n", "# dsolve(f(x).diff(x, x) + f(x), f(x))\n", "dsolve(v(t).diff(t)+cc/m*v(t)+g,v(t))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def euler2(x0, v0):\n", " v1 = v0 + (-cc * v0- g) * dt\n", " x1 = x0 + v0 * dt\n", " return [x1, v1]\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "g, dt, cc=9.8, 0.01, 1.0\n", "# tt,xx,vv=[0.0],[0.0],[-10]\n", "tt,xx,vv=[0.0],[10.0],[0.0]\n", "t = 0.0\n", "for i in range(0,500):\n", " t += dt\n", " x, v = euler2(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ちょっと気をつけたいのは,$-Cv$の向きです.vは例えば自由落下の時には下向きのベクトルなんで,抵抗は反対向き,すなわち上むき,数値的には正,になります." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# 高精度計算\n", "\n", "## バネの運動\n", "今度はバネの運動です.空気抵抗との違いはほんの少しで,\n", "$$\n", "F_x = -k x\n", "$$\n", "と今度は,位置xに力が比例することです.そうすると運動方程式は,\n", "\n", "$$\n", "m \\frac{dv_x}{dt} = - k x\n", "$$\n", "となります.\n", "\n", "連立方程式は\n", "$$\n", "\\begin{aligned}\n", "\\frac{dv}{dt} & = - \\frac{k}{m}x \\\\\n", "\\frac{dx}{dt} & = v\n", "\\end{aligned}\n", "$$\n", "となるんで,アルゴリズムに置き換えると,\n", "\n", "$$\n", "\\begin{aligned}\n", "v_{i+1} & = v_i - \\frac{k}{m} x_i\\, dt \\\\\n", "x_{i+1} & = x_i + v_i\\, dt\n", "\\end{aligned}\n", "$$\n", "なる連立方程式を解くことに置き換わります.これをpythonで関数にして,さらに計算結果を表示させてみます.\n", "\n", "\n", "![image.png](attachment:image.png)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def euler3(x0,v0):\n", " v1 = v0 +(- k * x0) * dt\n", " x1 = x0 + v0 * dt\n", " return [x1, v1]\n", "\n", "t, dt, k=0.0, 0.01, 0.01\n", "tt,xx,vv=[0.0],[0.0],[0.01]\n", "for i in range(0,100000):\n", " t += dt\n", " x, v = euler3(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "kはあらかじめ$m$で割られて正規化されているとします.これをEuler法で計算すると上のような結果が得られます.\n", "\n", "徐々に発散していく様子がわかると思います.本来,摩擦のないバネは定常的に振動します.この発散の原因は,Euler法の計算誤差が大きいせいです.そこで,より精度の高いRunge-Kutta法を導入します.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2次のRunge-Kuttaの導出\n", "一般にRunge-Kutta法と呼ばれる手法は,4次の古典的Runge-Kutta法を指します.導出は意外と面倒なので,2次の場合のさわりを紹介して,そこからの類推としましょう.$x,v,t$などのパラメータ名を変更しますのでご注意あれ.\n", "\n", "(「ANSI Cによる数値計算法」堀之内聰一,酒井幸吉,榎園茂,森北2002, p.133)\n", "テイラー展開により,$h^2$の精度まで展開する.\n", "$$\n", "y(x_0+h) = y(x_0) +y_0'h+\\frac{1}{2!}y_0''h^2 + O(h^3)\n", "$$\n", "\n", "この式において,$y_0' = f(x_0,y_0)$は既知とする.一方,$y_0''$は$f(x_0,y_0)$から直接的には求められない.したがって,この式の右辺と$h^2$の項まで一致する近似値を,$f(x_0,y_0)$だけを既知として算出する方法を考えよう.\n", "\n", "平均値の定理より,\n", "$$\n", "\\Delta y = y(x_0+h)-y(x_0) = hy'(x_0 + \\theta h), \\, 0<\\theta<1\n", "$$\n", "\n", "$y'(x_0 +\\theta h)$の近似値として,$\\theta=0, \\theta=1$の場合を考えると,\n", "$$\n", "\\begin{aligned}\n", "\\Delta y &\\simeq hy'(x_0) \\, &{\\textrm where}\\, &\\theta=0\\\\\n", "\\Delta y &\\simeq hy'(x_0+h) \\, &{\\textrm where}\\, &\\theta=1\n", "\\end{aligned}\n", "$$\n", "これらの値は単独では$\\Delta y$に対して$h^2$の精度をもつ近似値にならないが,これらの一次結合$\\alpha h y'(x_0)+\\beta hy'(x_0+h)$を$\\alpha, \\beta$をうまく定めることによって,$\\Delta y$の$h^2$の精度をもつ近似値にすることができる.実際,\n", "$$\n", "\\begin{aligned}\n", "\\alpha h y'(x_0)+\\beta hy'(x_0+h) & =\\alpha h y'(x_0)+\\beta h \\{y'(x+0)+y''(x_0)h+O(h^2)\\} \\\\\n", "& =(\\alpha+\\beta)hy'_0 + \\beta h^2 y_0'' + O(h^3)\n", "\\end{aligned}\n", "$$\n", "\n", "したがって,テイラー展開式と係数を比較して,\n", "$$\n", "\\begin{aligned}\n", "\\alpha + \\beta = 1, \\, \\beta = \\frac{1}{2}\\\\\n", "\\alpha = \\frac{1}{2}, \\, \\beta =\\frac{1}{2}\n", "\\end{aligned}$$\n", "となり,\n", "\n", "$$\n", "\\Delta y = \\frac{1}{2}hy'(x_0) + \\frac{1}{2}hy'(x_0+h)+O(h^3)\n", "$$\n", "\n", "いま,\n", "$$\n", "k_1 =hy'(x_0) =hf(x_0,y_0)\n", "$$\n", "\n", "とおこう.上式に代入して,\n", "$$\n", "\\begin{aligned}\n", "hy'(x_0+h) &= hf(x_0+h,y(x_0+h)) \\\\\n", "& =hf(x_0+h, y(x_0)+y'(x_o)h+O(h^2)) \\\\\n", "& =hf(x_0+h, y_0+k_1+O(h^2)) \\\\\n", "& =hf(x_0+h, y_0+k_1)+O(h^2)\n", "\\end{aligned}$$\n", "\n", "したがって,\n", "$$\n", "k_2 = hf(x_0+h, y_0+k_1)\n", "$$\n", "とおけば,\n", "$$\n", "\\Delta y = \\frac{1}{2}k_1 + \\frac{1}{2}k_2 + O(h^3)\n", "$$\n", "となる.これより,\n", "$$\n", "k = \\frac{1}{2}(k_1+k_2), y_1 = y_0 +k\n", "$$\n", "\n", "とおくと,$y(x_0+h) = y_1+O(h^3)$となり,$y_1$は$h^2$の精度の近似値となる." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Runge-Kutta2次公式\n", "こうして得られたRunge-Kuttaの2次の公式を定義すると次の通りです.\n", "\n", "微分方程式\n", "$$\n", "\\frac{dy}{dx} = f(x,y), \\, where \\, y(x_0)=y_0\n", "$$\n", "\n", "の数値解は,刻み幅を$h$,$x_n=x_0+nh$として,次の漸化式\n", "$$\n", "y_{n+1} = y_n +k (n=0,1,2,\\cdots)\n", "$$\n", "で与えられる.ここに,$k$は次で定める.\n", "$$\n", "\\begin{aligned}\n", "k_1 & = hf(x_n,y_n), \\\\\n", "k_2 & = hf(x_n+h, y_n+k_1), \\\\\n", "k & = \\frac{1}{2}(k_1+k_2)\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Runge-Kutta4次公式\n", "2次と同様の考え方で,$h^4$の精度を持つRunge-Kutta4次公式を作ることができる.\n", "\n", "微分方程式\n", "$$\n", "\\frac{dy}{dx} = f(x,y), \\, {\\textrm where}y(x_0)=y_0\n", "$$\n", "\n", "の数値解は,刻み幅を$h$,$x_n=x_0+nh$として,次の漸化式\n", "$$\n", "y_{n+1} = y_n +k (n=0,1,2,\\cdots)\n", "$$\n", "で与えられる.ここに,$k$は次で定める.\n", "$$\n", "\\begin{aligned}\n", "k_1 & = hf(x_n,y_n), \\\\\n", "k_2 & = hf(x_n+\\frac{h}{2}, y_n+\\frac{k_1}{2}), \\\\\n", "k_3 & = hf(x_n+\\frac{h}{2}, y_n+\\frac{k_2}{2}), \\\\\n", "k_4 & = hf(x_n+h, y_n+k_3), \\\\\n", "k & = \\frac{1}{6}(k_1+2k_2+2k_3+k_4)\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 連立方程式にRunge-Kutta4次公式を\n", "連立微分方程式\n", "$$\n", "\\begin{aligned}\n", "\\frac{dy}{dx} &= f(x,y,z), &\\, \\, where \\, y(x_0)=y_0 \\\\\n", "\\frac{dz}{dx} &= g(x,y,z), &\\, \\, where \\, z(x_0)=z_0 \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "の数値解は,刻み幅を$h$,$x_n=x_0+nh$として,次の漸化式\n", "$$\n", "\\begin{aligned}\n", "y_{n+1} & = y_n +k &\\, (n=0,1,2,\\cdots) \\\\\n", "z_{n+1} & = z_n +l &\\, (n=0,1,2,\\cdots) \\\\\n", "\\end{aligned}\n", "$$\n", "で与えられる.ここに,$k,l$は次で定める.\n", "$$\n", "\\begin{aligned}\n", "k_1 &= hf(x_n,y_n,z_n), \\,\n", "&l_1 &= hg(x_n,y_n,z_n), \\\\\n", "k_2 &= hf(x_n+\\frac{h}{2}, y_n+\\frac{k_1}{2}, z_n+\\frac{l_1}{2}), \\,\n", "&l_2 &= hg(x_n+\\frac{h}{2}, y_n+\\frac{k_1}{2}, z_n+\\frac{l_1}{2}), \\\\\n", "k_3 &= hf(x_n+\\frac{h}{2}, y_n+\\frac{k_2}{2}, z_n+\\frac{l_2}{2}), \\,\n", "&l_3 &= hg(x_n+\\frac{h}{2}, y_n+\\frac{k_2}{2}, z_n+\\frac{l_2}{2}), \\\\\n", "k_4 &= hf(x_n+h, y_n+k_3, z_n+l_3), \\,\n", "&l_4 &= hg(x_n+h, y_n+k_3, z_n+l_3), \\\\\n", "k &= \\frac{1}{6}(k_1+2k_2+2k_3+k_4), \\,\n", "&l &= \\frac{1}{6}(l_1+2l_2+2l_3+l_4)\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def runge_kutta4(x0,y0,z0,h):\n", " k1= h * ff(x0, y0, z0);\n", " l1= h * gg(x0, y0, z0);\n", " k2= h * ff(x0 + h/2, y0 + k1/2, z0 + l1/2)\n", " l2= h * gg(x0 + h/2, y0 + k1/2, z0 + l1/2)\n", " k3= h * ff(x0 + h/2, y0 + k2/2, z0 + l2/2)\n", " l3= h * gg(x0 + h/2, y0 + k2/2, z0 + l2/2)\n", " k4= h * ff(x0 + h, y0 + k3, z0 + l3)\n", " l4= h * gg(x0 + h, y0 + k3, z0 + l3)\n", " kk= 1.0/6*(k1 + 2*k2 + 2*k3 + k4)\n", " ll= 1.0/6*(l1 + 2*l2 + 2*l3 + l4)\n", " return [kk,ll]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Runge-Kuttaの4次公式をそのままcodingすると上のようになります.これを先ほどのバネ運動の問題に当てはめてみましょう.\n", "\n", "先ほど導出した運動方程式の漸化式\n", "$$\n", "\\begin{aligned}\n", "v_{i+1} & = v_i - \\frac{k}{m} x_i\\, dt \\\\\n", "x_{i+1} & = x_i + v_i\\, dt\n", "\\end{aligned}\n", "$$\n", "\n", "とRunge-Kutta4次公式を示した連立微分方程式\n", "$$\n", "\\begin{aligned}\n", "\\frac{dy}{dx} &= f(x,y,z), \\, where \\, y(x_0)=y_0 \\\\\n", "\\frac{dz}{dx} &= g(x,y,z), \\, where \\, z(x_0)=z_0 \\\\\n", "\\end{aligned}\n", "$$\n", "とを比べて,変数の表記の違いと関数$f,g$を具体的に書き下します.\n", "\n", "| 4次の公式 | 運動方程式 |\n", "|:-----:|:-----:|\n", "|x | t |\n", "|y | x |\n", "|z | v |\n", "|f(x,y,z) | f(t,x,v) = v |\n", "|g(x,y,z) | g(t,x,v) = -k x |\n", "\n", "この変数の書き換えを吸収する中間関数としてEuler3を書き換えます.RungeKutta4の仮引数を上の表に従って置き換えて,数値を渡しています.また,関数$f,g$も定義しておきます." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def ff(t,x,v):\n", " return v\n", "\n", "def gg(t,x,v):\n", " return -k*x\n", "\n", "def ode(x0, v0):\n", " kk,ll = runge_kutta4(0, x0, v0, dt)\n", " x1 = x0 + kk\n", " v1 = v0 + ll\n", " return [x1, v1]\n", "\n", "t, dt, k=0.0, 0.1, 0.1\n", "tt,xx,vv=[0.0],[0.0],[0.01]\n", "for i in range(0,10000):\n", " t += dt\n", " x, v = ode(xx[-1],vv[-1])\n", " tt.append(t)\n", " xx.append(x)\n", " vv.append(v)\n", "\n", "my_plot(xx, vv, tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "これを前と同様に走らせると\n", "発散も収束もすることなく,定常的に振動を繰り返していることが見て取れます." ] }, { "attachments": { "image-2.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# 太陽系\n", "\n", "## 分子動力学=Verlet(ベルレ)法\n", "\n", "惑星の軌道は摩擦のない宇宙空間での2体の重力だけで考えることができる単純な動きなので,比較的容易に再現することができます.\n", "この運動を記述する方程式がニュートンの運動方程式\n", "$$\n", "F = ma\n", "$$\n", "です.ここで$F$はForce(力),\n", "$m$はmass(質量),\n", "$a$はaccelleration(加速度)です.\n", "\n", "$a$ を微分で明示すると,\n", "$$\n", "F = m \\frac{d^2}{dt^2}r(t)\n", "$$\n", "となります.\n", "$r(t)$がある時間での惑星の位置をさしているとします.\n", "これを微小時間$h$で級数展開して\n", "$$\n", "r(t + h) = r(t) + \\frac{dr}{dt} h + \\frac{1}{2} \\frac{d^2r}{dt^2} h^2 + O(h^3)\n", "$$\n", "と\n", "$$\n", "r(t - h) = r(t) - \\frac{dr}{dt} h + \\frac{1}{2} \\frac{d^2r}{dt^2} h^2 + O(h^3)\n", "$$\n", "での和をとって高次項を無視して,$r(t+h)$について解いて,$d^2r/dt^2=F/m$を代入すると,\n", "$$\n", "r(t + h) = 2r(t) - r(t-h) + \\frac{F}{m} h^2\n", "$$\n", "となり,$r(t+h)$の位置を$r(t - h)$と$r(t)$での情報から予測することができます.\n", "\n", "このように微分方程式を差分方程式に変換し,数値的に解いていく方法がVerlet法で,そのほかの種々の分子動力学法の手法の基本となる考え方です.\n", "\n", "![image-2.png](attachment:image-2.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 太陽系=重力\n", "\n", "実際の粒子(剛体球)の運動を記述するには粒子にかかる$F$(力)を知る必要があります.\n", "惑星の軌道を考えるときには太陽を中心とする重力\n", "$$\n", "F = -G\\frac{mM}{d^2}\n", "$$\n", "ですので非常に単純になります.\n", "$G$は重力定数,\n", "$m, M$は2体それぞれの質量,\n", "$d$は2体間の距離(distance)です.\n", "\n", "適当に規格化して,太陽が原点(0,0)にあり,\n", "惑星の位置をr=(x,y)とすると,距離 $d=\\sqrt{x^2+y^2}$ として,\n", "力は\n", "```python\n", "F=1/d** 2\n", "```\n", "で与えられます.\n", "その力ベクトルを位置によって分解すると,[-x/d,-y/d]となるので,\n", "```python\n", "L=(x*x+y*y)**(3/2)\n", "force=[-x/L,-y/L]\n", "```\n", "で求めることができます(たぶん).\n", "将来,現場で宇宙空間のシミュレーションを実行する際は,この導出が正しいか確かめて,間違ってたら教えてください.\n", "初期値r(0 - h), r(0)\n", "を適当におけば,後はVerlet式に従って芋ずる式で惑星の未来の軌跡をシミュレートすることができます.\n", "\n", "こうしてKeplerの第1(楕円軌道),第2(面積速度一定)法則が理解できます.\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "def force(pos):\n", " x=pos[0]\n", " y=pos[1]\n", " L=(x*x+y*y)**(3/2)\n", " return [-x/L,-y/L]\n", "\n", "def Verlet(r0,rh):\n", " f=force(r0)\n", " x=2*r0[0]-rh[0]+h**2/m*f[0]\n", " y=2*r0[1]-rh[1]+h**2/m*f[1]\n", " return [x,y]\n", "\n", "h=0.04\n", "dx, dy=0.0, h\n", "m=0.2\n", "xx=[2.0, 2.0-dx]\n", "yy =[0,-dy]\n", "for i in range(1,90): \n", " x1, y1 = Verlet([xx[-1],yy[-1]],[xx[-2],yy[-2]])\n", " xx.append(x1)\n", " yy.append(y1)\n", "\n", "plt.plot(xx,yy,'o',color='r')\n", "plt.show\n", "\n" ] }, { "attachments": { "image.png": { "image/png": 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gnC/WvkDrf4xRR5kt7alTo0x1EP/BBx/41iZPnpxqOlN+zdCRvmjZSl1z9aFSdFg7hkCIgAkAIRp2X3cI/OhHPxLWlgkYqt11110V7YPu7aZRXOnWWtBdCmrRH0dfvsypI4IDdVMOIU21JZkYNvF4FySEBpWZ8sf1JYyL9kuf9RrmLfd9R/tQbrqs/uZGwASA5h7/hui987aW6gduZisZUFVr4AjfQgPMKI4hXXHFFXLiiSf6P2WKhdZNfuchzxfLdj5CR5hTHM1x9Gnd0BGWCe/DctiAUCYbvWH+8D5ap7atefSZazSv5omL150qmqejV61b6ehoPVbOECgVAmYEWCokrZ6qIbDgggum2n7hhRdS95W4oW1U6zBpvLux3S3THvs4euKYARbse+21l7d3YHsjtg4dDQMHDvRFMZyEqVJftgCTiqMpWiafPFomjvFlKs9SBVhGl1PyoStTnUpHeM2UNy4+3OkR1lHovdateBRa3vIbAqVGwDQApUbU6qs4AiFTU5V3pYjAyE2t62Gwzhd80U2zbQ+DQhjFBhts4L30dbTShRZayBelrihTjatTmZSmsf2PQ2ziTt4rByNTeqO0RulS+kIaMA6FVpZismlNMtWldUavcX2P5rFnQ6AeETABoB5HzWhOQ0DXlokMHfOkZSrjQ3gC4PHHH190S3gz1IB/+2KCWv5TB1vs4kLIRMN0hJBFF11UFllkEX+GQJjGfSGMNN+8Si87P/LR5oT1uoOGPK3QzLHB0aCCInXnGzCijAoj+ZaN5gtpjabZsyFQDQRMAKgG6tZmSRHA9a/ux9e9+CVtIEdlGCIut9xyPhf77q+88socJTIn43nvf//7n8+wyiqr+KNyw9yZmHWYJ7zniF53ep6Puuyyy2LXvuMYE+3gDlh3VaiWI6y7kPt819HV5z804dkxGrL1H38QBHYbcJaB5tXrxFZXzXiRzDeoC+W4/FpvXFpcXKH54+qwOEOglAiYAFBKNK2uqiGgW9zwE1DpALPiMCJlpLil5aS6QgN74A877DBfDJfI55xzTrsqtI12CRki8JPAYTmEp59+2h+ekyFrWjTq9DPOOMPHTXIugFXA6SgTy5duBJbFFlvMM2+8+kWZdaZ6Zs6cKddcc42n9yc/+YlfNtG8ep0wYYJPZ0bPjpFcYdasWakzBuLyar1xadni8hWGstVhaYZAKRAwAaAUKFodVUeAA2wIfLSrEThe9+CDD/ZNY8S39tpry4033pg3KWgONt10U++1j0IcIxueJJd3RTEZjzjiCH/8Lkl4S3z44YdjcqVHIYhwiBCB8ho6yvS0fD5XfPoT0OZssskmksuug3ycAMkRwWiDDjnkkNhmOCUQ+jHUPProo2PzaCR5cIVcKoESwUnPuVCtirZlV0OgWgjYLoBqIW/tegR0RlksYxk7dqywBRCLbRgG1uTUnaneW2+91Z9615FhwElNePSv1sGpeawv/+1vf/OCCEfa4n+fc+9RScfRwsyVA3ouvvhiz5ioCybNKYelCsOGDfMn5G299dbejfKaa64p2CpAV+gfALygB0GGHQ2E9dZbT/bYY4+cpOg45syYRwZcAO+zzz7e7oBTARGE0IbEGUSyTAG9r7zyisf3pJNOkilTpqRaCd8BDAwRsjCyZIxgyGDPuxKOzcsvv+zHgMOmKIN2KRSawjppKJ++U/+4ceM8XbynuGdWB1YpYu3GEKg0Au7ltWAIVA0Bd/hLwr3z/s995DtEh1OpJtxBMKl6/v3vf8fWs99++6XyaJuFXt2HPOEYdGz9RDrVecLN3hPu457WlnODm3C2Agmnjk+4mWXCzVgTzolQWh63Vz7hjrLNWHexCc42IeH22afadIcXeZq23377hDtFMeGYXcJtYUyluxlzws2AE+AbF5yBXCqv03bEZUm40/98HrcdMTY9UyRtMl7gzRi53RaJMWPGJJwQkHAnBCacEJNwWp+0dHDPFZynwYQ74yBFN3g4Xw6JLbfcMrHNNtsklllmmVSdTshLuOWChNNC+PzO30Rs9U74SNV35513xuYh0mk2UvmcoaJ/F7bYYouE07BkLGMJhkA5EUB6tWAIVA0BGIcy4Y4KABB/7733pupx6vjY/sQJADCYbH8wHtL1Cq2hAJCJOT755JOecbg1+BRd2s/oFcZPnW+//XYs3aWMdGvfntk5VXlGuhBWzj333IRTg2dtOpcAADbFCAA07rZVJlZcccUUU1aBIMSQ8c7GeKOd+OijjxLOe2RK2InW6XaVeIHS+U7wwk+pBADqW2KJJdrh7jQzURLt2RCoCAKdaMX9mCwYAg2JAK+3+8DH9i1bWmyBSGQ+5fENcP311/tz6vFz/+GHH/p16qFDh4qb0Qpn3q+++uopj32RJsr2yBa/22+/3e/vZ9kCdTRLBRjhLb300qn16mIJyAejfNrAcI/dEeAHpixdsOwDfhgpZhrjbHXTb/w2YGjI0hF2JDh2YjxCV8TROorpE8aVLEHgq4AlCG1v9OjRHepDlDZ7NgQKQcAEgELQsrxlQ6CYj2o+RJW7/nxoaJQ8pcKyVPV0BNdStl3KujrSFytjCHQUAdsF0FHkrFxJEejIDK4QAspdfyG0hHlhHhrCe42rpavSVyosS1WP0hXFSuP1Gk0v1XO2fpS77VL1weppTgRMAGjOca+ZXpf7A1nu+jsCZEiTMg/i9L4jdVaiDPSFtBfaZray2dIytaNlMuGm8XoN64nGaV1hnlLcR9spRZ1WhyFQKgRsCaBUSFo9DY0ADKJeP+b50J5PnmwDXGz5UtZdS7Rk65elGQLVRsAEgGqPgLVvCBgChoAhYAhUAQFbAqgC6NakIWAIGAKGgCFQbQRMAKj2CFj7hoAhYAgYAoZAFRAwAaAKoFuThoAhYAgYAoZAtREwAaDaI2DtGwKGgCFgCBgCVUDABIAqgG5NGgKGgCFgCBgC1UbABIBqj4C1bwgYAoaAIWAIVAEBEwCqALo1aQgYAoaAIWAIVBsBEwCqPQLWviFgCBgChoAhUAUETACoAujWpCFgCDQOAngejAvuOGThxEF3bHJRLpTj6rY4Q6AUCJgAUAoUrQ5DwBAwBCIIHH744bLUUksJ13p1Ix3pkj02GAImADTYgFp3DAFDoLIIZGLup512mowbN07WWGONyhJkrRkCeSJgZwHkCZRlMwQMAUOgEAS++uorGTx4sLzwwgsyZcqUQopaXkOgIgiYBqAiMFsjhoAh0EwIYBdw3333yfDhw/Ni/pnsCJoJM+tr5RHoWvkmrUVDwBAwBBoPgXnz5skVV1wh33zzjV/7v/vuu2X69Ompjr7zzjvy73//W4YOHSpbbrmlj//000/lwgsvlEMPPVS6deuWyms3hkAlEDANQCVQtjYMAUOgoRH4+uuvZfPNN5chQ4bI3nvvLW+99ZZcddVVMmPGDN/vb7/91j+TdsABB8jbb7/t45966in59a9/LU8++WRD42Odq00ETACozXExqgwBQ6COENhtt91kscUWk/XXX99v+Vt77bXlzTffTGkA/v73v8t2223n42bNmiV9+/b1vfvxj38s5B04cGAd9dZIbRQEbAmgUUbS+mEIGAJVQeB///ufXH311fLGG2/49tkV8Nhjj/n1/0UWWcTHoQkYMWKEnHjiiV4owDiQdX/yrrzyyrLAAgtUhXZrtLkRMA1Ac4+/9d4QMASKROCvf/2rwOgnTJiQqon1f7b/6RbBhRZayKddeeWVsvXWW6fycdOnTx/p0qVLWpw9GAKVQMAEgEqgbG0YAoZAwyLw6quvykorrZTWv7vuusvP9Jnlv/766z7to48+kmeffTZlF4BwQNnJkyenlbUHQ6BSCJgAUCmkrR1DwBBoSARQ7fOn4d1335XHH39cVl99dXnmmWdSAsCXX37pZ/qhuv/666+XTTfdVIva1RCoKAImAFQUbmvMEDAEGg2BPfbYQx599FHfLZj/ZZddJqNHj/bb/W699daUJ8AFF1xQJk6c6O0DyHzdddfJqquuKl27milWo70T9dIf8wRYLyNldBoChkDNIaCGfKj8Ue+zDXCbbbbx2/ruvPNOWW+99WSJJZZI0Y2AgB0AVv/Tpk2TRRddNJVmN4ZApREwAaDSiFt7hoAh0BQIqHDQFJ21TtYlArYEUJfDZkQbAoZALSEAs48G3QEQjW/25zismh2TavXfBIBqIW/tGgKGQMMgUCyzj2OKcXG1BlhHaCwWq1rDoJ7pMQGgnkfPaDcEDIGiEHjiiSfk4YcfTtXx4osvCpb57733XiruueeeS4vrCNNLVRa50bpginqvWXIxymh+LVfO6/z58+Xmm29OuTLm/IN77rlHbrrpJpk9e7Zveu7cuYIfhFtuuUV++OGHjOSAMeU4D8FCdRAwAaA6uFurhoAhUAEEsjFJGD/ues877zz585//LKeccopgpLfMMsvIuuuu6436fv/738sXX3zh43Dby9G+uRhzId0K6wrvc9VBv7Llz9bvXHVnSwcrdjKAxf333y9nnHGGDBgwwG9vZNsjBx6dddZZMnbsWC8Q4Awpjpazzz5bTjrpJFl88cXlb3/7m+ywww7yhz/8IVvTllYGBGz/SRlAtSoNAUOgNhDIxiSZuR522GFy2223yamnnioPPPCA4KKXgHOePffc08921U8/cbfffrv3+pet3kJ7nouZa32XXHKJP21Qn8Mr9ISMFs+CnDIII84U8m1XyzObp8zCCy8sn3/+uXC+wbnnnuuTp06d6rc3/ulPf5LjjjvOx40cOVJ++tOfygcffOC3RRJJeQQETkUEy86dO/vDk/CGuNVWW/ly9l/lEDABoHJYW0uGgCFQQwgsu+yynhoY/8EHH5xi/kSyFPCLX/wi7ZCel19+WXbaaae0mTczXk72U2aqV+oI73nOFDTf0ksv7d0CZ8q3yy67CH+lCKju8V3Q0tKStToEC3waMOtHVc+2RnBAADj22GNTZcGLvJx0qIF83bt391sjNQ61/9FHHy3XXnttCkc9QwENgoXKImACQGXxttYMAUOgiggos4UE1NiczMca/1prrZWiirjXXnvNp2skLntZLuBQnzDg5pfDgHQGzrWQAD38MRPGQyAzYUJIZ676suXNlMbxxfgpYE0/V1hqqaW8ADBmzBif9YILLhDihg4dmir60EMP+bhhw4al4tCs4OgIIUAD5ybQ1xkOR8UKe4Ell1wyTdjS/HYtLwImAJQXX6vdEDAEaggBZTpKEssAMLbQPe99990no0aNEj3ABybKaX8wM1z+YuzWo0cPXwVr3PyFIRPTDfPkuo/SSf477rhDHnnkkbyEA8pzRDEMOY6eQYMGyZFHHpmLjNh0BB4YeBjuvffe1NHHGg9mO++8s2f0LB/07NnT21Asv/zy0q1bN83mBagohqlEuykrAiYAlBXefCpHBdc5n4yWxxAwBEqMAMxs+vTpabXi1S9kcDDTyy+/XPbbbz+f77TTTsuLecYx3rSGWh80n141T/QZV8JxpwZG81GeWXb//v19VXHChLbRkSszdowBwwCOoRHfSy+95M9BYF3/lVde8Z4RucdTYkjPd999J//973/loosuCquz+wohYAJAhYCmmfQfqjJ+Zf76HBCEb5HCNIpBYbs1BAyBXAjAuPbZZ5+0bAgA4Vo2v1uY2AYbbCAwv1yzVWVwek2rPOZB8+mVLOnfiuQzxw2HRw7HVFW2KKUHHDjVMFyvZ63/ww8/TMNl5syZgo0FGpNLL71UDjroIE/b9ttvL5ydgO3B999/720vPvvss7T6ytYJq7gdAiYAtIOkfBH8wNt4ujL++Pb0BxefarGGgCFQCgRQkW+88cZpVbEksMkmm6Ti+N2efPLJfrvalClTZIsttkil5bqBEbI+/vHHH3uVPKp3Ddl+46EwQP7oc1g2vNe6S33V9tkSyZY9ZvIaiIOp6w4K4tdee235z3/+I2z323DDDVNLJqj/2QXA9krsHdhRwFkJYVmt167lR8DOAig/xplbaJMG5OtvvpM33v5Ellx0Qub8lmIIGAI1hUAu5ovx4F/+8hdh2QDLedbBCRjfYf2OWr9RQi4s4vq53XbbeTsFhAILlUcg+zS08vQ0ZoswegJafhf4ofDn1fvu8srr78i0jfeV/zvtwmSG1P+tBVLPdmMIGAK1hIDOjDPRBINntrzSSiulmD952dPPTDoM/psQRuS4D/PrvV5zFC1Lci4s2PoXLrewlMBxydGtjdXsQ1mAqeFKTQAo8+D4l1nX8VvR5oeiP5ab7nhIVtpwb1l1hSXk6vOPiVBjwxMBxB4NgZIjUG6Gg91AaFRIB9iCx3HAYdBvQhiX7T7Mr/d6zVaulGmZsIuLx+0vywXffPONdx+MTwXdUqg0Ua7SfdC2m/FqSwBlHnUm/5381L9zsP6f1AKcfM7f5YSzL5PTjz1A9tpufZexS5vNX4sr2ZnSJgSUeYisekOgndFdMZCETAxjt+HDh8tVV10la665Zqpa7AzwooenvHoKYd8KpZvtk2yxxB6C/i+33HIpvweF1mX5S4OAGQGWBseMtTD5TySY8Sc1/mT89rsfZKcDfycPPP6s3P6PM2SVFRdzsRF1f2dK8mfBEDAEyo0As85czC1M13u9Kn0wfPzjs8bfu3dvGTdunJ/xrrzyyt6REMZvX375pbeaZ0bM/vmjjjqqbpzg5DM7j2Ki2OA7AedL0ZApfzSfPZceAdMAlB7TthqT03//nEjgcauzvPb2+7LZrkdJr1495NqLTpAxI9usadsK2p0hYAjUGwIw/W222cYzub322suT/6Mf/Uj0xDztD/7y//jHPwonEVowBKqJQF3ql5EYaynA3GNpSpvAd5bb7n5MVtpgX1l+qUXknmvOktEjCmf+0Xaiz4XiUmz5Qtuz/IZAoyIAU8eFMIcIaeAgIfUboL+1OJsAzW9XQ6CSCNSlAJCPGipfEPVHmW/+aL45c+a4k8TOdFa+0/yWns0228zv+9V8SVGlRX533t9l092PluOP2E0uPv0wvy+2U6eI2l8LBVfO1F5//fW9q9LVVlvNn/AVHuBRLBbFlldSi8VR67GrIVCPCODq9phjjhG2telvit8EroYRALjXeHUmZL+ZehzpxqK5LgWAjgxBph+b/ig7UufcuXM9c77kkj87Rxi7eacXeOr60Yw1ve9w6vzerff/bN8T5Ow/XSO3/P1k2XdH52AkpRloD39IJ040cDqywgoryDnnnCNbb721nHDCCe22D3WE9lKXKQbHUtNi9RkClUYAZz94tEPlr+GZZ56Rr776ylv76+8DT3p4zcP9sMZpfrsaApVGoOGNAEPJOwSXeBg4knshf7ivxJqVMpwi9tZbb8kTjz0p/Qb09T9ovF5xrOeee+8lUxddRnb4+cn+4ItHbj5fxo0a7knIRBOJ+lHgmNEjjjhCMBQKPyqbbrqpP3Xr+uuvl5/85Cdhl2r2Plt/a5ZoI8wQKAABmH/Xrl1l8cUXT5Vipo/wjsc79ruvu+66XiPAyXfqEfCGG25I8zqYKmw3hkAFEKgLAeCDDz4QjpZUxgvz5R5mnIt5k48DJ7SsluPKiVR45sI6tVevXv6eZ/541niOs4ymk4eTuTggpP/Afn6Ln44X+1sP+7/jZOWN95YtN15Lzv/dIdKzR9vpV8rkdV9gHINE9c+HImT+1D927FivZsSpBqeVcegH9XHVv/A5vI/mDdOy3Wu/OnqlbguGQCMjsNhii3kBgN8ygW8OPvD5/RLHZAEB4Pnnnxd2BBAQ8tkSZ8EQqBYCdSEAPPvss/70rY022iiNYXPaFb68lWlnuiozj6YXwpjimDSnWA0YMCBpABhhcgP7dJW9nbr/uF8f4MaWtX5d7w/U/q18MY6Ob7/9NnWaV/TloN98SLbcckt/qAa0YRegf9mewzS916uW1yvxhGzCQb5CBfkOP/xw2XfffaPdsWdDoO4RmDp1qveHf+GFF3rf9g888IDX4F133XXe6x++8Qmo/hEMHnzwQXn44Yfl5z//ed333TpQvwjUxTZAZv+nn366V6PBlOIYZjWG4NBDD/WSPbP1MCCwcBLW66+/7vcBh2nJe4SBQBBwT9F+8XFg9kAdOBLRPrOliLp33333in08QgEhes/Wp2hcKEBwTzjppJO8849f/epX/tn+MwQaEQEEczSTHHpDeOGFF6Rfv35p3wFOz0NDsMwyyzQiBNanOkKgLjQAIZ7KCMO4St6HjPqQQw7xzBj/1scdd5wMHTrUr/HtuuuufqaLE5D4kM78yRPtF77DURmut956cvHFF/uPxdtvvy20ybIHbVQqQBvnkMedRZ4vDXo2eb75LZ8hUI8IsBQQhkUXXTR89PdoC0oaUNTZKltJIW2WytpzombpeQf7GTLq0aNHC2eHY+3LudfYDGAEiDMQNBbFhssvv9yvF7JmSN0TJ070Mwf8iPft27fY6q28IWAI1DgCyUW4JJHJ+5akvVEqwWnYUsxflxlrvFNGXs0gUHcagGojF2oAoGWRRRaR+++/X9577z1/3OcCCyzgDQZLQSe2CzgXOeWUU+TNN9/0QgbLARYMAUOgORDQc0TobZLPO6Pf1hl/8lvUNofD5bhbTGynTWwOpKyXHUHABIACUUMDoEKAXqmCwy34KyZQHyFsg2fWEJdYYgluLRgChkBTIdDG4LXb7jBx+LwPad8Mx/8RDsLvkpaxqyEQh4AJAHGo5IjTZQC9avZif3hhfeG91h9ei20rrMvuDQFDoD4QwHfJJffPlLc//c5tLHLLAS3uoDF3aig+CAh8F9ZfcoysOHmE3xZcH70yKquFgAkAJUQ+F9MuYVOm5islmFaXIVAHCKAg/Oabb+TO596Rlz79wZ842L1L1+T2Xzf7x0g3MW++TBzYVZYdP0TwX2LBEMiGgAkA2dCpQprN7KsAujVpCNQBAs7Th98BNH/uPJH5LdK1U2dJuGsX52PDSQPSMm+uYAbANkS251owBHIh0H6BKVcJSy8pAjD8MFRSixC2a/eGgCFQ2wh0xsi/xTn9cgYAONYiwPDnu2+It//r3MkvBajvDZ/B/jMEsiBgAkAWcCqRZAy/EihbG4ZA/SMAk2/dBOjX+rVHzi7ZB74lxvwVFbvmg4AJAPmgZHkMAUPAEKgBBEImr9pDmL5OJJL3XWqAUiOhHhAwAaAeRsloNAQMAUOgFQFl+DB9hACe+dPAvQoHGmdXQyAOATMCjEPF4gwBQ8AQqHEElMlj/a8aAK76V+PkG3k1gIBpAGpgEIwEQ8AQMATyRSBlAOhm/yGzRyBAGDANQL5IWj4TAOwdMAQMAUOgThDQWT9MPpz5ex8ATgDQ7X+qEaiTbhmZVULAlgCqBLw1awgYAoZAIQiEs30EAJ65EvSZezQECAr8mSAAIhYyIWAagEzIWLwhYAgYAjWGAIwexq5MPmTwbQJCUjgI02qsG0ZOjSBgAkCNDISRYQg0GwI6S222fqf3t816Xw/4SU9ve1LGj9efJLNPzvT9OQCdnRtg5wio1T+Q7QJog83usiBgAkAWcCzJEGgWBGAulQ5tM9ZKt1xj7Sn0rQ59slGHIyB8AaIJaGmZ7xk9911c2U7OS2CnTvgAcEcGu+UBH7TubJVaWtMiYAJA0w69ddwQaEMgxTDaouyuIgi4T3ABvNqxdu//119b6Zs3z50N4MK8eXNaY5IXz/vJrsJdIAyk4tJK2EOzIWBGgM024tZfQ6AGEYAhNbsQghwwd16Lt+TnvqUVE8WGmf737iAgN++XeW72T0AQ6OLU//6+c1fP7NkJ8MPsue6Y4PjPO3V37x6f5iuy/5oGAXsLmmaoraOGQP4IKNPJv0T2nJnq0/hmZ/6gB+N+dOb7ss8/HvEqfrb2YexHPPiAFUKABtIJ84lrSe4IIO8lT3wslz55hxcOOD8ADQHlvK2Ayz92QC+5Zv8fSbce3X0eX4n915QI2BJAUw67ddoQyI5AqRlypvoyxWenrnFSk1r5tq18Y/rMk9F9unrGTy9h+uEVvJJ/SY0JDJ/Q4tb/dWcAzJ57tARcYfyahsZg+sS+Mnv2bOkULAn4Suy/pkPABICmG3LrsCGQjsD7778vRx99dHqkPVUEAdTxKPL9/45ZY8S39NC2mX6oIUH1rwIA+RPzk4w+GZfc/088mgGEAOI1uKr9M9flR7mZPzfOmNBCcyOQfPOaGwPrvSHQlAh89tlnsttuu8nIkSPlqaeekiuvvLKsOHz99dfy+eeft2sDJkfa999/79N01tsuY4NHwJT79+/rZugDpVuXrqkZOrN8MOnaqbPMme9sAPysv7M/Ghgmj4qfssr0URpwT5jvbAY0kGfqQLcEMHSI9OjRwwsbmmbX5kTAbACac9zrotc6+yk3sXPmzJFXX31VPvjgAxk/frxMmjQptV5a7rY7Un8uXPj4X3PNNTJw4MC0WSDMQpkrTGPAgAHSq1cvOfXUU+WPf/yjTJ8+XTbYYAPp169fR8hKKxNH44UXXigPPvigXH311Wl5oWvXXXeVNdZYQ/bff/80mtMyNvgDOPTq3UPGjxomCw+YJc9/kTTwY6w6OeafSLRIj67dvADAGCMkzEstAbTN5skH/mgCVEBIzHfbB7u0yPRxvWXQkIE+rcHhtO7lgYAJAHmAZFnaI7DIIov4mUf7lPQYPkCETz/91H+MLr744rQMpCtTIkHzb7jhhnLmmWem5S3lA22+9tprcsghh8idd94pU6dO9R/F119/Xfr27SvHH3+87LDDDnk1+eWXX8rNN9/sGWcc4wsr4cO9yiqryJAhQ8Jofw9Gd9xxh2y11Vbt0sIIxSiMi95fcskl0rt37xSemq70QceKK64oJ598siy11FKy7bbbyr/+9a805p8vPVp3eI2jkVlnt27dwmype9ap1agtFelulN4wrpHuWYZvU9Q7Q70u3f27AaN+9rNv/fglGTn7/pPr/F2d1T/+AGD5zOoVN+4JYMb46rWzyz/XCQpDu86XFSYNl769+wRLAKYE9qA16X8mADTpwBfb7RtvvLHgj3O2jzlpYSjFLDSsL3o/c+ZMz4hXXXVVefvtt2Xw4ME+C+rVq666yqvG0QygIg9DXB8QAP785z/72XQc4wvL33777XL33XfHCgBvvfWWHH744V4Vf9FFF8mgQYPConnfwwhuuummvPPfcMMNMmrUKBk3blxamVLRk1ZplgdlZGGWXHiGeev/vrNjzJ28ELbMhGEy9KXv5LO5SZ/+Lc7KHyEJw7357j9nCuiEA5h3m/Ef4z53rtv+54Tq7t27e00BcWgEOnfrKiuP6S5Dhw6VHt26t0JlzL/+35niemACQHH4NW3pBRZYwPe9Xj/Qu+++u0ybNk2uu+661AyKDsGEfvazn/n16AMPPNDPjFGTa4jrL8sGMPYwxAkKpMNk4+ogbdlll5Wnn35aoI3Z+a233iqTJ08mKTb84x//EAQY2i8mLLbYYrHFoQfbgD322KND9Hz33Xdy+umne40Kfb733nvljTfekLPOOiutPbBCIONKGa7ffPONHHTQQWkaibRCDfLQNvtPdgic0JQMHz5UVhjxrtz01tzkbL0LBoKd3Ja/5JZAcs+dO8cLBbyzCKsIr0mGnxQKyOPfQycAONFB1ligf3JZyNXlQ7r6IRln/zcVAiYCNtVwF99ZPigEPkb8dTRoPR0tX0y5J598Uu677z75zW9+k8b8wzpRiS+55JJC3o6EbNhkS2Nd/p///KewBMJSwUsvveQ/4lEafvjhBzn00EO9NiGaVsxzdFywI4jSE1c/28qi9FAX2pFZs2b5JSCYO4yKpYXwD2NE0jAC1HjKRWmJPsfR0QhxMPRBAwbKGpOcjYabufO+dGvdKcC9GgWqxgRMCeF7BVaar5OzFVh4UCdZYMxwp6XqQ8YkTB3/+SbL2/91j4BpAOp+CCvbgfAjU0zLuerhA5YrT0fbRwWPDcPyyy+fsQpmYQgJYfj5z3/uZ1xnnHFGGF3QfT59Ig+zZGhkdh9XBlsKli222267tPYx5GNbn84Ew7LcxzFRGAVaAJYCwvxaMXEhPRofXlkCgZ7tt98+Fd2nTx857bTT/DPt/uEPf5AHHnjA21ekMrXePPvss7Llllum+hM3/nG0ResJn+PqKCQ9zFvue52Me/Ha4d2rT2+ZMHqoTBnwuTcGnOfU/j0SnWW2w1EZP/3TP8abwDNGgwTyzZ8/lztZY1xft6Q0zMWxeOCCNsi9haZFwASAph362u54oR/7Qnrz5ptvii5hRMtlYhrEDx8+PKMRW7QefY7Wx3O2oOn0f6+99orNihr9yCOPlL///e8pZqAZr7jiCh+nTELjqW+llVaSU045xVv7azxXBACMxjIF7QP0KH1h3pAeZURhOve0n21Mmf2zbp0pIPCwvk391BNHR7Qseahz5513jib552z0xBYoY6Tz4+eYMn3zpn3uPevi1+tXG/OOPD3ra+kuPWROYp7j2+79YTnAGQQqDklGP98Lp4yjxjOuXbp0k0E95svyCwyVfk6oSI2PlwKSbZWxW1Z1jSNgAkCND5CRV3oEvv32W8/M42qOMgVlfsT/3//9X1yRrHFx9WUrEM0fzYu6d+utt5addtpJ1l9//WiyjB49ul2cRnzyySey0EILecaicflcQ5rCe8pCD7sWdtxxx1h68qmfPKj+2X2hQdtR/B9//HHvQyDFwDRjlivMEK1EVADQOrMUrUKSm8F7ppycyeMQqF+/AbL0xCEy4hW3NDLHMX6Xzvy9s7tFjEwaASZPBgQv/lSQU5y6OEPBlUf2kGFDhnrXv9oxX751WUHj7Np8CJgA0HxjXtUeV/rjG9feiBEj5LnnnssLB2VEeWUOMsW1S3JH66MsggtqcrbSMZMvJLDTgVk2AkCpAvTA/Jll50MPdgu6Xh3SAFZoEeJoU7zOPffcsEhR91pnUZWUqbC+N9DIMtSIEcNk+eHvyy3vwLLbvP15aQCtDUKBy0vgyh8aAbb+ISag8l9tQj9v/Ke2f0gPrUV8OfuveREwI8DmHfuq9Fw/VpVqPK491tVhOLnCY4895n0F5MqXTzof9kIC+cMyrOvPmDHDCwG33HJLVnV5XDv4KcDmoWfPnnHJGeOUBr1qRqUHa33ogVnlClj1s3MhGthpgFCTaVkmmr+Rn8P3lVn8oAGDvWfA7m57oL4TvEpe1e84OnFaJukwSDUByTMCFuzXIguMHS49e7udLE6r4ENSXmhkGK1veSJgAkCeQFm2xkFg9dVX9xqAbFoAGNuaa67pt6d1pOf6UdayPOsHXOO4Rhmrxml5rOtx1oNBINvy1OFQWIfex9VFGrNunCrtsssumjXvq9Kh13zpiaOFfexx6/x4IkRNrxjlTVyDZ0QAwJnTxDEjZGr/5LtCXHL23iZQgjXYhYf7EIfNxKpje8mQwQO9fQAl2ko1OHjWvbwQsCWAvGCyTJVAQD9k5W5r0UUX9evVJ5xwgjek0/XSsF2YLkZ/a621VhidNuPShEceeUTQFjCLpS76oX2JMjX1d69llbHqM1fi3nnnHU8bLnqZXeOnf7311guztbuPq4uZIsZ7rK/jbjdbUJrDPBrHEgKz93zpiaNF69U6eUYwwT3w+eef75OzldPyzXTlncJr5CpjespzX/4g89jT79b19T3j6sz+nFGgWw5wWoLOrYJAIjFfBnftLCtNHiG9+wxIHftrAkAzvT25+2oCQG6Mmj5H+MFWMM4+++ykGjI5HdHodlfKErjGMVo++Fo/V73HNW+ckVu7BvKM0Ho1+0knnSRrr722n3med955KQM0Zk2sZ7N9Dcc1fIA1sNWN9dWdI1blX3zxhfcXQJoysOhVP9jMxnWbltarV+pHkGCrHPv/8Y0PLZtvvrlvV/Ple8XV8T777OM9HeLuGPqyBaVZ82B5/+ijj+ZFD/gSonVoXeGVPOz9Z1slGP/3v/91h+C4KW5riI6VxjfTNcQAr5jLTRoig1950xkDdpUWN9XHux848udETklgC+AAohwjgRHhtHHOodCwIU7r0vaZN+1/M71Fufva9mbkzms5mhSBuI86M0L96OeCBQtvXAcr46S+XGXjfOXnaidberQPOPlh5r7FFlt4N7g8w6Sff/55mTJlimd6qNzDgGe+uG1l66yzjvCXT4D5Z3JzzKyfvfPHHnuszHDr/Tjh6UigDc4xwLf/bs6V8bXXXpsScAqpjzFWelgOwUkRIRw77sE2im+mdtBI7Lfffl67gUEjng+j/cy3rkxtNEK8YsA72aNHN6+NWmHU+3Lzm2z36+y2biaF5ZZ5zvtf16TgifCaNAB0GgInDkyf3M8LVqHgreOVPArYVoAb4V0ppg+d3AtR81qh2267zbsU5QNsof4QePHFFz2jhbnWYmC2zWwZZsfyAKr/UoS2j20paiusDn4raFEmTpyYsWBH6OtImSgBzPoxxJwwYUI0yZ5jEEBowjPivY8+Icfc645T9hb+Sf8NCAoweG8U6O4ZH4SAqf1b5LgNF5dJk9zJlt3btFgx1VtUEyNgGoAmHvxiu14KZlAsDaUov/DCCwt/pQ46iytFvSHW3BOy1b/uuuvmbDZb+UyFKRPSkilftniMMC3kjwCYYww4efQw7xnwpS9x4JP09MdVx9GPi3s1eD1WH99HBg4elHPZh/IWmhcB0wE179gX3XP98BRdkVWQE4EQa+7D55yFS5yhmm2XuCt1UR14J40Bh8nqY3q5Gb/b5++WANSmQz05km++sw3o3y0hK08e5h0JdUpt/q+LrhqRFUbABIAKA27NGQKGgCFQKAKs6mMoudykYTKoq9vj7xg7an8NMH80AAgF00Z2k2HDnN//bvZ5V3zsGo+AvSHxuFisIWAIGAI1g4A7JsBvBx01crgsP6Kbt/p3yn8vBISGf92cmf+MBQckPf+57YIWDIFsCNgbkg0dSzMEDAFDoAYQYPsejJ4dEzPcMcHOw6+b8Sc1AGqTgbp/yqDO7tjfkdKjV8/Ybbc10BUjoYYQMAGghgbDSDEEDAFDIBMCqPl79erlPANiDJg0BGVpAKc/81t9/K02vp8/AKlr606BTHVZvCEAAiYA2HtgCBgChkCdIIAx4NChQ2W10c63vwvuLEAnACQ/4/27tXjjP3YMsDUQwcCCIZANARMAsqFjaYaAIWAI1BACMHbcOq+40HDp38XN+50ioLNzAdzJrQasNLJ7q+e/7p5ivAFaMASyIWACQDZ0LM0QMAQMgRpDAG+Uw4YMlRWdMWCX1hMBuzj3wDMmDfReJv3s32kGLBgCuRAwASAXQpZuCBgChkBVEUhn5l2dBeCAge6YYOfqtxNnAjgtwJQBnWWh8SO9jQC2AskTAqpKtDVeBwiYAFAHg2QkGgKGQDMj0PaZ9qZ/jsH37tVNJo0eJQs7q//5bh1g9Qn9klv/urU5d2XngAVDIBsCbW9WtlyWZggYAoaAIVB1BJSpYww4fMhgmTamtwzs0UmmLThE+vXp66y6NUfVSTUC6gCBNnGxDog1Eg0BQ8AQaFoEkjv/nP8fN29zhn+9+/aR6VNHSkvnz2Tk8BH+VMCmxcY63iEETADoEGxWyBAwBAyBCiPA5L5VCGCm37NnTxk7dqxs6dz+4iCoa1f7nFd4ROq+OXtj6n4IrQOGgCHQNAgEGn48Aw4YMMC7A4b5Y/xnwRAoBAETAApBy/IaAoaAIVAjCMDwEQL4415dAnvyUssFNUKskVGTCJgAUJPDYkQZAoaAIeAQgJFnmdinZv0uX+oe4ILlAh4tGAJxCNgugDhULM4QMARqCgFmt4WEUuQvtI5C6Ms7bxbmn1ZHXL64uLRC9ftQE2NTv/ClKDcBIAWF3RgChkCtIpA2u82DyFLkL7SOPMiyLCVCwMamNECaAFAaHK0WQ8AQKAMCNtMrA6hWpSHQioAJAPYqGAKGQM0iYDO90g2NCVOlw7JRajIBoFFG0vphCDQhAnFMLS4uCk0+eaJl7Ln8CDAuNjblx1lbsF0AioRdDQFDoO4QUA3B999/L3/5y1/k008/9cfl7rLLLtK/f/+M/dFyGTM0YEK99Lle6GyEV8Q0AI0witYHQ6CJEWDG+Nvf/la23XZbOfLII71XvJVXXlm+++67dqiEs8vwvl3GBomotz6GzL/eaK/HV8YEgHocNaPZEGgSBDIxgdmzZ8tbb70lzz77rLz99tty5plneo94wLLTTjvJ559/LnfddVc7lJTBUO/8+fPlvvvu85qDm2++WT755JO6Uz9nwueLL76Ql156Sd5///2Mffroo4/khhtukMsuu0yeeOIJmTdvXju8qhVBv/iLjk+16GnUdk0AaNSRrZF+ZfpA5UNeMWXzqd/y1D4CyrCjlF5yySWy2WabyQ477CDjx4+Xm266yc/8yTdnzhz5+uuvU8/RsjC6s846S1gmYOlg/fXXl2HOn/5uu+0mJ598ckqQqIf3Lw6fzz77TI477jhZdtll5aqrrkp3EOTAeP311z1uF154oUydOlXWXnttef7552XNNdf0gkAUr0o/I5j9/ve/lx133FG+/fZb2XDDDWXEiBGy5557ygknnOAFt0rT1LDtuZe85sOtt96aWGeddWqeTiOwPQItLS2JF154IbHoooumJRJvwRAoBoGdd945ceCBB7ar4ne/+11im222aRdPhLMRSKy++uoJx0gS0Xdw7ty5icUWWyzhtAmxZesp8ocffki4w4ISbmafRvZ1112XcEw/4Rh+WjwPt9xyS2LIkCGJjz/+uF1apSKc8JKYPn164je/+U278XGCQWLJJZdMnHLKKZUip+HbMQ1Aw4p2leuY+5VkbCxuhkLmTPEZK7IEQyCCwP/+9z9xzCIt9t///re88cYb8te//tXHh+8mNgFrrbWWnxljKxB9BzlQZ5999pGjjz7azzzTKq6zh4ceekh69eolSy+9dIpytCQsj6AVcAJ5Kl5v1l13XXECgJx00kkaVdEr2hi0EYsvvrgcc8wx7canc+fOsu+++3rtBhoeC8UjYAJA8Rg2fQ3RD2nTA2IAlB0B1v/5W2ONNVJrU+BCjQAAQABJREFU3DC4d955R/74xz96Bo59QPhu/vznP/fr/BgMhoJBSCwqcZiL01plzBPmr9X7u+++W5ymI9X/9957T7bbbjs55JBDZIkllmhHNnjwR/8feeSRdumViDj44IO9zYKb4WfEHvq++eYbee655ypBUsO3YdsAG36IrYOGQP0jAHO64oor/Da/kSNHegbv1PV+xkrvrr/+em8HwHq+U3PLk08+KZtsskmq40899ZRgN4CxYO/evVPx0RtO1iOgRVhhhRWiyTX7jAEjWo9+/frJiiuuKAgAG220kacX7NBqsLb+i1/8IrYPKijR/9deey02TzkjYegXXXSRwPz79OmTsalwfKZNm5YxnyXkh4AJAPnhZLmKRICPkAVDoCMIYNS3++67e8a2//77y4svvuiZ2wYbbOCrmzVrlpxzzjni1vC95bu2ccQRR+itYPCGCvlnP/tZKi7u5pVXXvHRgwcPjkuuyTi0Fc4eQv75z3/KxIkTvYEjSwCnnXaap5cZ89///nfZcsstvY+EbJ2g/ywDVDowPgRnu5HWNN8NFU5I0PGpBo1phDXIgwkADTKQtdwNPsxs2/rvf//rt2fxox4+fLgst9xyfsZSy7QbbdVHwBmEebU8zJ+wyCKLeEt/1P+EoUOH+nfLP2T4zxm4yVJLLeXfuwxZfPTtt98uzDKZRddDcMZ+svHGG8vpp5/umT80oxnp0aNHav2f7ZD8/n784x9n7RLLBAgT7IaodGB8sEsYNWpUWtMh8+e7UW/jk9aZGnwwAaAGB6VeSeIHes8994jbtSHsMX7zzTe9OpF1WWdx7Q18wr717dtX+LhnUkuGee2+ORHgHTrjjDO8il8R4H169913/fq/xnGNzhY1jXePMiowaHz0CpO87bbb/Fp5Ni+C0XLVfGZJAyEgXO5g9s/6v6rLsZUAGwSgTIH0G2+80SfvvffembKVJZ628eWAhiJbYCLBtwUtzqBBg7JltbQ8ETABIE+gLFtuBJDW77zzzpQV8cCBA2XBBRf0syn28TJzQ3XH7AQHJRdccIEceuihfuay+eab527AcjQcApmYtnb0mmuu8ap79qhrYEbLLJe9+2EIZ4thPKp/GPqAAQPC6Hb37D1HCGAPfSlCrr6Voo1//OMfXrCmjxrAB1sIDfwOCdn6zzILSwZbbbWV18yVgvZ862DcoI2/bGXOPfdc792xVOOj+BRyzUZfIfXkyputnWxpueqNppsAEEXEnotCADUtzllQ8WOQlOmjTCNbb721LLTQQnLqqaeKCQBFwV63hbO9H3SK2avb+y3du3dP9REDN53NYzzGtrFo0I+kXrF8/+CDD1IMBmc4M2fO9Grxbt26pXYHYIQ2YcKEaHV5P2t7FMjVN/KE+XmOC9nyoCFh66IGtAFoAJwvBN8nDP8UH4TuSZMmeW0cy3E4UFp44YV90bPPPtvbUPBbJORDu8+Y5b9C6mCMGR8tgxHmyy+/LD/60Y/82HPGw/HHH+8nF5MnT87SanmTlL5StJJtXLO1ky2tULraxMZCS1p+QyAGAWZlzPqZceV6UdEGbLHFFn7bEUsGFgwBRYCPI2HcuHFp6t6vvvpKcNuLipvteg888IAWSbvqu6dXNE2o9zGIe/zxx+Wxxx7z2+Fwg4t/AATQww8/XNgqWEzQ9vKtI5/82fKMHTs2DR/U+GgDlllmGcEnAto27vF/cO2113qymEkvsMAC3o0yghBau/PPP1/uuOMOj3e+tJcyH9sTEUq+/PJLv4MDIQahgAOe8A/A8gDbBPmrx6Dvc0g74xoXH+bJdN/RctH6TACIImLPBSEQ9yLGxWWqlK085OejbMEQUASU6eG4Bi0Avv1Z98faf/nllxfn5U5Qf//kJz/RIlmvbInbb7/9vHYKQQBV9+jRo+Xpp5/2RnTMon/1q19lraNciYX8XqI0INigEaEODOk+/PBDbxSJSp+tgbpW/qc//cnnAzM0HggAK620kuy6664eU2x3ENzDUAxdYT353LNkcdBBB/nxQcBjNwAGgWh4MHLEMPGoo47Kp6qy5+kILvo+43IZYUtDJiGAMxoQzDIFrS9Ter7xnVxnan5/Fj9YrFwxALFQvwjwqkVf3Hvvvdd7c2NWgpcvC42NAAZ5v/zlL/12LnzWY8HPLH+99dbzf3G9h/Hj5AetEjNBDrq58sorhRP/mN1G36m4OjSOmT8fVwQItAH4D3jwwQdTRwdfeumlfkud5q/kFRU3h/Ig8MCgmd1j+IaGYqLb3odxHktr0YAAgNMjtCJ4/qM/PCPk6Po/ZagLXwFspWOvPVo3lgwQDgi0jTdEZt7VCkwEGB+WfDgHgHsOBNJ+4MuBMxwqHXj/eOdYckHDgj0Tyywsc2pAw4IdCe/4lClTvPFqaEzqXCx7DdPf/vY3j7OWy3RF24Hgo0s4mfIVFY8AUOvBzgKo9REqnD73I/GFnnnmGQTQhPv4FV6JlahbBI499tiEm4lm9Duv70e5O+jWmBNu/3zCGf8lnLOchPuIF9RkSGd4TyXR57iKyRPmc85wEk6gSbgteanspLvZb8I5QEo4Jz2peL0Jy2tcPld+e84GJ+EEoYQTChJupp1wByXlUzSVp6NtpyrIckPdnAHjtBZ+fHhnGKtqBadR8d8qp3XJSMIee+yRcEJlbLo7rjrhllx8WhQ33j0nyKWVY1yce+YEZyCUK9gSQFHikxXuKAI6a2PGQcBYKQzuhQ8f7b7BEEDlzEwztOQPx1zfj3J3mxkaxqhsSWXmnO+SgtIV0sk9KnUNYZrGRa/kCfOBC+5uWZ7QQPoBBxzg1fvsnAkDmIXlw7Rc91jdow1gmYA2mW3q1sFcZTU9bBtHRCxDFBOi7wA0shzA+HD2AydAViugrUITkcleSTU34ZZMpfXhhx/2viswwiSEuLFcg4YbzULYf7Q0eKNk2UZDmK5xxVxtF0Ax6FnZohFAvUmIuv8MfyBFN2IV1BQCfPBgttEln0LHvCPML1rm17/+tVc1Y/mPSjfcTlcoaNSNJXsxAXV+uIVP68JJD/hEGXShmGl9XNkFwKE7MFYEl0KFn7Au7llSKYYe6qB8OEZ4c2TJh2UidmhE+0+ZSgYYOMsAcYGdFOFBSmE/ENxC4TAsz9KL0wj47dLR/nN+A8cgcy1HMAGgHKhanbEIhD8IzaAfzKgHME23a+MhwGwIwU+38nW0h4UwG333omWYYWFjVIoQrbvQOt9wW99wiBOHy3nnnScTnR1AsbsUojThiKvaQcdG6QhxxFsotl9hnOarxpUxePTRR9s1ffXVV3v31Oy60KA00z92ZODQKgy4tGZrJrYDbG28//77vUYsXPNnm+ZLL70k2MvgnlrrDOsp5t4EgGLQs7I5EeDlJ/Dixr28bh3Sp8cdT+oT7L+GQwA1NzM5jNYqFeLevUq1nW87zMQJoQCAuhkHPTAAcOMgpFoJUcatv3WlL5qu8dFrrrHJlR6tT58xcAS3bAEaVfWOs7JcGgY0ABiOosVS3xRsTWUWzymTGsK+c7gSSwdqyKh5MHJkiyNaH3ZD8cxyTLS/7HrhhEYMZUsdTAAoNaJWn0eAH8Wrr77q1WVIuWxJQkXojIz8OeVYOMMA2LfMS69HlIY/HIOyMRGA0WGtzvpuptAo70Eh/QCXMWPG+NkiuLBHn10JHJSjDnoy4VWN+CijyvVcaRrZPRCun8e1H44PLslzTUTQAKCuR1Oj2yYR0KL+CUIs+P7FCW4wdnZmYOPAEsFqq60WR6L3nsq3NBpC2qNp+T6bAJAvUpYvFgFeQvyss31HHaywd5eXnrRcgR8K3gPVGDD84eQqa+n1hwAzJ5z37LXXXrHE68yK94D3im2ilQj6MaVd7vnj8Jzoh1vzoZZl1hcNvPecvKdB86+99tppBo+aHl6ZCeKvgDVfDTjwwfCNQ3oQmsOAwIBtQDkC29vYfx8G7QtxbM9DoNdAGks7bK+EqYUBh1/Omj2MSrvn+GZmwtGg3wLq1hCOD+6hQ2NJzaNXsOOvlAEBgIBwhgBAn9myGRqz+gzBf0x+Mgm7fDN1/T8oknYLfvjBKEcwAaAcqDZRnTgewWGFCgA4VlHDvigMWPLihATtgFr98+PGwMdCcyDAPnxUnaGaO+w51tDqkIcPo74nYZ5C75VpaLmQkWWLo/1oUKZEGtosDdoGdYfxpJMWV5eW5cqMEivyKC4wGTweMpuNHmVcKnxCOhQbrtGgfSeePkb7yVhFcSFvrjHUMlq/0kBZxZV7DZoeR6PmKdeVJQAC9hr0H2HvrLPOytoc50toP7SPWgAhDvW/LidofHilTFx6tK6wTL73JgDki5Tli0UA472d3Vnk/BH4UbDmxYyFKx81XQJQxs9HDaaPygvPbqi/DjvsMF8+/E9/6GGc3dcvAownB9Ww5hq3/s9sSj+w9BLLfM6VKHUoxXuFqjhOXQxD2HHHHQsmmdk/dM2YMSOtLGu/hNDhjGYID0jSuEpd47bjMfNXZ03Z6Ajx575c54DgWviqq67KRorHXJkzngjjxjSsQDUA7ATAMBPnTLkYMcZ7uDiOy8e4h2OOs6CosyfKlss5kwkA4ejafdEIoMpnTzF/+QR2AbCGhkoteshH3A8mnzotT20iwHii0udYWnVRq5Qyy1V//RpX6qsynnK9V1o/dIf3+fSDmSAHY0V3w6jFObYBBBiPMqF86i0mT6F9yLetEP/wPt/y+eSDdiYYeOTLN2RbTtA60GLCoDHIZL8/HgFzBb5rcUs10MhyGFtRCZzFwBJKVABAyxp9L8hfivExAQAkLVQNAQxheJGfeuqplABQihe7ah2yhmMRwCIbIQ8BAFW2LhOhFWL7E/u9p0+f7g1EYysoQSTMhnfriiuu8OcKcMIce99RwYaBPIRCmVOYP7wP647eY/OAEIwDHQQjBKFwtt+7d29fBBUw2jVc+VbKJ36+fdA+FZpfy5XjCi0wU3wdlDqgmZo1a5YceOCBeVWNYMcsHn8G4U4A3jMmTAh31IftVFinfgexNVlxxRXbtVUKvGtWANDOt+u1RdQlApnGU9f/8feuoRQvttaV7ZqJpmxlSp1WCzSUuk9hfdo/9kDD9NVa+sQTT0xjsAgFxTg7+eMf/+hnx8yesOaOC9CC2haDNCyvUbdyIA6Hs4RGarx/5O1IKLQcfvjZqsb+flToWPtzMBHGh9BBX/htQDd7wsOjf+PoU7zDNJbhLr/8cu/BDpyjAk+Ytxr3cTRDB7ZF7JEnHWaOMRwGw+y1Z2cE3hGrEXhnWLaApnwC47jBBhv42T5XDSyFcb4Af4x3tD+Uw1MjWgyWEaIhE27RfNmea1YA0B8hVwv1j0CmcdTZDhJypUMmmipJRy3QUM7+av9UzVloW/l+5DbccENvhxJdK8UolY8ngia0cBALH27sUBAWNt10Uz+rDgWAQmkM87OXPF+aKccJhdkCa+p//vOfs2VJS1O8w0j6yY4GGD+2OiF9OKgBu7hyYR353OPNExV5oSHaNjssWFtnLDEI1eUPBCEESGbSum240LZKkR+7pUIDu14wcA0FAOrItVPh4osvTtsVErYbxS1My/e+5s4C4OXUUIoOal12LR8C4ZiFrWSK1zxheniv6bVwVbr0Wm6aCmknmjf6XG5aS1V/KehG1ctMl2WEMKBVCI9VZSYcWtOjfo9u9aN8vt+eKO3s28+3rNIZrUPjS3Xt1auXP/WPrWgsMyh92BdwuiLLEKUInKkQ58a4kLoZK3ZCwOg5WU+ZP3WwDZLjodEKRHdLFNJGNfKussoqfgcUNhwaco07u2VQ/7tDhLRIya81JwDoy1nynlqFZUMg05hlildCSNe9xOGxmZpeC1ftg17LTVOudnTtHDo0r35I9LncNJayfmjPRne2tJAOttHxcQ0FAFT87EYJdxxgkKXnTjz55JM+/fDDDw+rSt0rrqmImJsofdHnmCLtoqJl8mmXSvLNR16szcEhPOuAONaWQ/e15K1WYA38pz/9qRxyyCEZzyVYddVVvZaBo6DrLZx55pnCu6bbJ6PjHu0Pyz96SFA0rVTPNScAlKpjVk99IICzF4LaAtQD1YV8ePPtTz51sg6M0ST7isOgHxL2W7OWDOPTwAfEHTGrj2nXfNpMK1CGB6Vdq85GU1yazl6ZObKFixPbNGBwyHs1qXXvtsZzRVjADuH222/P6MQlSltYPtN9HI2Z8maKz7fdXPmgBbsCrjD7cLsZbbPzQONKQXcxdeALgOWJic7RTiYbDmjGVS9aBrQa1QjF9BFL/v/7v/8T7D5yBZwjbbHFFqLnAmi7es1VPt/0mrUByLcDlq+2EOAFzfVhCinGgRCh0mt6/BDxU5DLVWhIq95r/9gKxHqk+g/P1Hfisf7N5OqTerVObSN6/de//iVHHnmkV3/GOQUhP3RgDPfLX/4yVRzL+7gtRGTI1Waqkhq5UXrBE4dC9JVZLdb8rPWrWphjadlexbYq1N7MKBdbbDHZfffdfU9w4oIRmdoDsF+8VB7jlMZqQBa+fyeffLJ3uISXOpxv4WOB7bYIidhj4HmPQ5CwwQEfVOssDxQTiuk7DI9vAWOqXkEz0XLCCSek2TFkyleO+GL6CD3YNYR2KuGYhfRimxIGbVevYVox9zUhAGQCoZiOWdnqIMALijqWk67wXx06AmKLE+ovpHfWbGGI11xzjZf6C9mvW2jP4t4vZo7RmXSh9TLDhNFk+2DRNsZLGGJ19Kx0Zv6c2sapaHHbgUK6mUmFsyPaz0ZfWLYW7vP5wMHY2S4F/hj4scca1SrW1IStttrK/yFUwtyYWWpAIMKSnjw47eEdwM1qqQQAbafS1/Ad32OPPfwyh3qoQ9OBEMD5CwiJHHuMAMVM9JJLLslozR7WWe7+IIizPMG45Arl/FbkarvU6fm876VuM6yv6gIAszBUltGtKZV8+UJA7L4wBHBSwUwY6Z2PCkYrzIrjAmuvfIgQBPh4MwMjhGdox5UrNq5cPzJm5PkELHlzeSSLqwec2Br04IMPeg96zGKzBXXFGm5PQiAoV/+z0VKuNGauMDhmuLo1im8FQTUA3ON//fnnn0+LIx6LevbWY/2uIZclvuYr9JrvNyzffLSfKa+O8U033eSFarxvaqAMmhLVVBGPR0bW0fVdiatX69R6ynnlu4HzMB3TcrZldbchUHUBAMbx0EMPtRMAKvnytcFhd4UiwMwW1SHMR/+effbZ2GM4sWrVEI5vuGYd9yHSMrV2zZfWsK/59gHnOLiUxdMY7mAzHSYS1oezHWZR+lEnjTGpJw1A2B/uoxjDwBE6OTRHA8yMPfK8ixpY30bLFF3/ZzZcqZDvuOebD7oz5VWcjj76aH+IT/gOgE/0KNlw/T9bvZXCCmPgXG54oSXOlqFSNDZiOxUXAPRFbUQwm7FPMBx1/YtzFQ18pNHuYGzFVitmZHh9YwmAGRhbelgCQJWLdzMcoIQzFK2n2ldUxnw8Ud9XwlUxyyes0aLuR5PClqd8mD84sRbOmm7IJNAAhJbf1caz0PbDvlAWxsUyiFrya5was2n9UQan8Y16BSc0RsykQ40GSxxokNCYaOA3iAYO18u18j2G+fN9yBb4puAYJzrW2cpYWnYEyi4ARF8wXlQYA2vEBF5YPrL/+c9//DOONLB0tlDfCLC3mrFk205c0PeCI0eZtbAFKNyjHFemGnEY3DGLZOmi1EEx4IrW5Oyzz5arr75att9+e8EZCs5qQgao+TPRgSZFreA1LwJALQpWmfqQKx4th1pGa15sAmBwLA/cfPPN/vhcGJy6VUUwYpkqalil5Rvlil0L4x7iA/Pn3V1mmWX80gBOf9gaSV6WAHi/WH/Hr30oVFUaE45LZhKAcBJqrPQ95sqhYXpSZKXpa9T2yr4NMPyAKYgYh8Hw+UMAwCqXNTn+WEfWwKBbqB8EouMVN/baG01Ty2PWa2sxoKlgNh5uU4z2MxfdmfJjIAnj4kPMrIbZ+zPPPCN/+MMfvNtTxUjrjz5H6505c2ZKS6F5M2kA0DRgFV5vAVsh9R0B7TAvtpIuu+yyfkuf7iZhUrHccsv57mGDsc466/j7KGY+skH+w1UufucVH5g8hoAY/8FU+c6yNMAVexLuMYBEcKwm8wd+TgPlN8ZkIAy8x/i+YOlm1113jT0WN8xv94UhUHYNQBw5uN1U15ts2cEGAF/h0aAfsWi8PdcmAh0ZL92iFhot1WbvOk5VJlz48LI9C0t1NCF68EtcSzCuaD36rGnUxUwvDJk0ALgzZWmm3gJ+DnbbbTdvvc7MHoEAr3F4+GOphJksYc899/SGl2zxA1tlcIpZvfU7X3qxkcC6n6U3lt0QJlmaY3sdQhKBY4T53l522WVeAAiXDPJtp9T50LSxbMNYMoZ4KGTM0IQhqHBUb0fcDJeazkarryoCQDYQ9WOWLY+l1T8COs76ow493NV670rFRFjLZv9zsQF6cPhy/fXXy1/+8pe06uIEAE5eZPsXAkO9Bd4XtvuxXsw99g0sMzHr1XeJPqHdYE1cz5qot352lF6s/bGtAR+1HYGxog1Qw0As7Vki4TcXYtbRNktVDrp4fxlLlsR4d1kaYAz5XlgoPQJVFwA4gzm0/izVx7X0UFmNmRDQH2d07JTJx5XTvDAuQq0bqmXrS1z/Sh2neGWqF29/rP+HrnDJG10CYFbISWY4U8FJTL2GqOvoOEbWbMxf31HeFWX+jC+/LZi/pmtcHGa18D5AV3RbeK73vxborkcaqioA8EIirfJnoX4RyPTjjMaHHyDtrZ4COGjQoLQPlKbXyjXaF+hCjR463clEK1v6CNp/vYZxPkMH/2O3wHHHHSeXxhxEEwoAbLnFvSiuVjltrd5CiJvSHhenaVxzpYd56/0+7h0N+5QrXfMqZnrV+Epd820333yVorse2ym7AIDippP/rz08+b6Q7Uumx2SoPj2TPVUdgeh48wPGIIkw0fkAD9Mr8eNmj3zomyAECKMpDkn56KOPPHPFOIldDWFgfZI6CNCu9If3pGGkxiwsTCeeoHHJp/T/wUBDHB7EocbFup3jXtWuRstwhT523OAGFyNbDiQJt2uGeWv9Pg6ruLiwH7nSw7w1f1+hD51iptdK45Jvu/nmqzT99dRe2QWATqDh/2sPy1PPvSYJSX5A26e2xbz+zkfyzeyEPPncTB8Z9zFEyGhxtQ3s308mTxjt8rW0VlD2jQ5thNpdVgQYt9AxDT9gXOlyVYttraASP+4bbrgh4xoovtGZUTO7xhUvHvmiZ72fe+65Sm7WKwfV4IwlnxC+22yJCgWMaHkwwgUuwkqmA0YwrsLlLeeRs9MCS3ELdYpAhu+o9iZ8dzTOroZANgQ6uZembZqRLWfJ0mDMSaa81Fq7eRVdR6qGbGZVCVfdfMfsuzopI+F+IGtMW0bOOeGAjlRpZYpEAHUzs2IOZnn55ZfTzgKYNWuWN8pi3NiXzJYfln7YCjrJ7bPnbPJqBOiphLBRaN/Akn3RzNbxaJcpoMHgd5BpKQJDONLCvdWZ6rL4+kCgQoqA+gDDqCwKgfILAJV4WyvRRlEwN25hDmJhnzXHqnK+uu5Bjusx23qYkWKhrDNb8p1//vl+hhpXplRxhTD6QvJ2hL5o/dHnjtRpZRocAfvGNfgAV6d75RcAytivTB/OTPFlJKWpqwZv9h1jZMYfW3jwNsbaN2rsTAGBAO9tnAAWdyxvKcexlHVl6k+txxsGtT5CedCXjyDg87RpWvOo1bI0KQKVEwBaX9zwI5TPu9yk49IQ3WaLH0JAeBYAcTi8YQkAxyQ4/GB9HKcumdTYxYIRvnMdrUvr0GtH67FyhkD5EYD5E8z+KYmD/Z8JgbIbAUYbZr1VGX82mxb70EaRq79n1vo5QCd6iE7YExx9cIQpywerrLJKmFSy++gaf7Z3K5qmz1qHXjtKnNZXaPls5bKlFdqO5a8xBPhYuuC/me6DiW2Ifwfdd1S/n4w/gfjku2CM3wNi/+VEoHICgH9bk5Jpp4hkqh+w77+f7V/g1nc+jXjNE0bywnft0qm9f2hXQcL9K/ZjHbZl9/khEDdOcSU1nzqBwmhQBQBNiytXirhs70U0LfpcbPsdrS9bOU0rN27F9t3KdwCBVi6vzL7FmTzf+NQ78tFns70wIJ2cQCBd/LcOY9D5nebKGguOkUXGDEQiSAkJHWjZijQBAmUXALzkmgIyXjLVD9hyG+wlr73xfip3Pjf777qpnHbU3ilmrx9B/+qnN55PdZangwikcHcfnUKCnl7HfnsNvA9an8bZNTcC+jvKndNy1CMC/Ca+//YH+ef9r8pLn3zrBQB2d6AV4MRHxh/j2t6ucwsOTxrc1mM/jebKIVB2AaCNHcQbpSR5dDLt+bsuLVpiTfsItjVeOUSbtKU03PPAQPPruj/nlmsw5q9I2NUQSEcAx09z581JRfJbYeavxrY8kwehwIIhkAuB+Cl5rlIdSk82BcMPQ8ijuecFLioUWbyotq1wwQhwvjuB7YEaVDjQZ7saAoZA8tvIDF+/kcz6uddnmD4agTCP4WYIZEOgggJAkoyQ4ROT5PeOjJYk5y76459qwPkFNGEg29iXLE0/QMnxzA16mJ/zyAm6FOAf7D9DwBDIikD4G9KMUYFA4+1qCGRCoCICAC9rJrbAknEi4dwBd05x7pREm6lMtDPt8+lyQ/uUaFl7Lh6BUGgL76MfKX0O82D8R1hwwQWLJ8RqMASaAIGW+UkDZ3Wmpb8rus5SQPj7agI4rItFIFARAYAXso29O2ojfLlTpy5pXdAXOK1MWo70h7h8/Ci0nvTc9lQpBKL4R5+hg7PK2S4YPQugUjRaO4ZAPSHAd023AurviWcVAjROn+upb0Zr5REouxFgbJdCjo0wED77Aq0z+Ni02BojkZy8Fomyx4og8Mwzz/hzAIYPHy4TJ06UsWPHegvluMZnzpwp119/vay11loSPd89Lr/FGQLNjEBqUtN6vCrMXuMwBLRgCBSKQHUEgFYqF1x5G2lxjDpOWuVgH/+eF9AjfhA/XnVZ+dNphxVQyrKWEoFrrrnGH5+rdWLcN2nSJO8MCGGAtX7i3n//fSEvKkuO2iXox0zL2tUQMATaEOD7xl+S2Sc1Adzzx3IAV90WSD4LhkAuBCogAOh6fHtSbrv8FOe4wp3ol6auR5KlDCG8T8bwvwoM+pKH5fv0arMmbythd5VAgHHYdtttZbHFFhP29XM+wGuvvSavvPKKd/erFv/QwtgtueSScvLJJ8vKK6/syYsbz0rQbW0YAjWLQEQLym+MP7X45x7mzzIabraTQb+f7qm1PPn87ytSX8322wirCAIVEADaVFOpl7C1a5MXGOfukutX+vFP73W8AJCeJ/rU1l40xZ7LiwBjOHXqVP8XtvTiiy/KZpttJvfee6988cUXPglNwMCBzltZTIh/F2IyWpQh0IgIOCad8mQaTOTRihL4ffgZv1s7dV9PHze3Jbk9kJ0AXkOgRtWuTOq7q/W2X3P1ddh/zYdABQSANlDjPuzOjYV7odvy+Du2BBLp46Magkhee6wLBPgowfRtu19dDJcRWU0E/KcPxp7+YQyXRPk9KfP3woCb4Xfpwuc8KRDotmq6kfruerfByQlS+9rJaaHZEKj6dFlf8eRr26q6SjH/5HCkXuCco9NmDZszq2UoGQLMMHKFfPLkqsPSDYGGRiDtZ9T6aU6La+u94//euJbfFTY1rP1TIvu3Mvjc5/GbbWvN7hoVgeCNKE8XM334o/FJQaCVHJUKUrYASdqiZYhNxrWteWX/AZSnj81eaz6Yh3nixrHZMbT+NycCab+F1HcvDovkNw6fKZRJuPWAuXPn+XvsAQhoBJLq/9Zt1e2EB/tOxiHbzHFlFwDCD38IdPt4fcGTRi76kievyTjK6w9G45P1uGUCX3nZuxN2we7zQEDHKy6rjmFcmsUZAs2AQPvvYKTXXijg2+i+ce4enyn6m+rSheXTTqlzAFgK8MEtofo87QQKvo9t39lkZvu/mRGoqA1AdqA7y16Hny7vfPxJQdv/Nl1nNdl9u42SZdq98NlbtNTyI6AfOL3Sot7rtfxUWAuGQH0gkJzN60w9ybD5nbSIm+3PZ4kzqQFIMnu2BLrDgJ3hn/tVtf6uOGw9uRSaVAzMi3Q8WacTHShiockRqIAAkJRewRmpNP2jry86qZ1l8w2ny3ff/5CScIklsJ3syiuvlCOOOCIZEfy/4IQxySdn4JLcNpg0g7F3OwCpBm511lIDpBgJhkDNIMBSPCZPBJj/Y69+JKff/ry/Z52/c2eO+0269+U3NG/2PHn/m+R3lG8pKn8vGHRucTsD5qInkGufmyV3vX2fdO3czX9v57nTA533YPeMoNAig/r0kN9vO81vHUz/Hnsy7L8mQqACAgASZzK0f9na0sixzhortOZMvzz6aC+54tJZsun609MT0p7a6jLmnwaMPRgChkCNIqDMH/KY1Q/vPlc+/Pxr+fyHpGMfvpm6xk8ehAAVpjH8073/HKfC8gCM/pPv5skXc2e7pYFvkzYBrXVTnvrWn9pVZruJFuXbf5PJZaFZEGjjms3SY+unIWAIGAI1iADMuJPb67fU4KSLX0hUZq/35GHWz5U0riwBcPU7AVya3yLYahjoNQSoGVzQvKuM7OlUC8m2fIL917QImADQtENvHTcEDIFaQgBG3q9fP1l9Qn/p4jyk6r5/FQJIRxvAM1c0BjB1tAAho6dPqjUgLSkcdPN5xvacLwuNGSw9evTw8bXUf6Ol8giYAFB5zK1FQ8AQMATaIQCj7t27tyw8fphM6N02a1dmzhVGD+PX2T+VUI5AOvdcSSevCg1z587xcdMn9pLBgwdLN+80yBez/5oYARMAmnjwreuGgCFQXQR0dq9U4NRnyJBBstrY7jLPufclwMiVyfOsjn+IU0aPUACzJ3CvQoDWz3PPlrmyyuQRXsvQyW0hVKNpX8j+a0oETABoymG3ThsChkAtIOBW4tPIgKlzNPYqCw6XPq0m2sr8dUavTJ14mD5r/1xJh9Fzzx/5dAdBZ7cDYOmRXWXMCDf7dwcHWTAEQMAEAHsPDAFDwBCoIgLK0CEBpt6zZ08ZOWKYLDOkk8yZk1TdE68MXu91KQBmD+PnmTQCTJ77rl27J7UELu7HCw6RAQMGeeHAZ7L/mh4BEwCa/hUwAAwBQ6BqCDh+rUxbaWDvPydlrrnAgNRWPfIgKHBV9b7mDxm/LheQR4UCZv8T+3eWxcYP9cJFtD2tx67Nh4AJAM035tZjQ8AQqGEEYOJ9+vSRqWOHy6R+SQEBpo2qX4UAHPow8yfMnj3b/Z8UDBAGVGvQtgwwX1Yb01MGDRpi6n+PmP2nCJgAoEjY1RAwBAyBCiMQqv/DplHhc3T2KqN6etW+MnbyIAygJaAss3yMAufPn+cEgqTRAGXnzUseFIQQ0LdbF1l1yjBnW9DXLyOE7dh9cyNgAkBzj7/13hAwBKqIQCZ1PFoAbww4ebBj4Ek//zB81QDoFfU+2gAfnDBAPMwfxu82C/ro5UZ2kdHD3ey/h3MA1BrIZ8EQMAHA3gFDwBAwBGoEAWXMCAYYA44aOVyWG9YtZeCnhoCQm8zrGD683G3r69ItqQFAI+CXDJxrYJYNVh/fz9kUDG49C4CSSX8B3FlobgRMAGju8bfeGwKGQA0hEGoEYN447VltYlJ1P9+dBkjgRECYeHL273i/W//v7IQAZv5avqs7O9jJEDK2d4ssPmGE9OrVK5WW4FxhC4aAQ8AEAHsNDAFDwBCoMQSY3cPMe/XqIYuOGybjvWfApNq+S5du7gRAbAFUC5AkPtQezHEZWubNl2mju3shQg0Iycl5AxYMARAwAcDeA0PAEDAEagwBncl3794zaQw4pkfKgM+nucN8MABMbftr3U6o5ehOV2cFMH3ycOnbt38qX7Kb9tmvseGuGjn2JlQNemvYEDAEDIH0WXwUj07uUCCMAVebPER6dW07BEhn++SH6Xdq0Vl920mCK47u4WwIhrpdAu1PfQ/LR9u05+ZBwASA5hlr66khYAjUIALhrD1KXqdOLf7kPowBlxma/Fx3dZb/lEEDwLo/WwQ53IdrItG6I8BVNMM5EhowIOlMqH29bYJCNM2emwcBEwCaZ6ytp4aAIVB3CCRP9Bs4sL+sMXGAo77NIyCzeJYA+OPgIO8YqPUAofG9RRYfN9wLD5m6nE3wyFTG4hsLARMAGms8rTeGgCHQYAg4/u7X8RcbizGgm/U7Js9sX5k/jDzhdgh4DYBbMiCsOt55/hsyOKsA0GAwWXc6gIAJAB0AzYoYAoaAIVA5BDr7/fyDhw6RVVqNAZn94/HPHRTslwLY2YdAwLJAD2flv/qCw6Rfn75+qaBydFpL9YaACQD1NmJGryFgCDQPAtj2uT/U+xgDruqOCe7ZJXkOADN+5/uvde0/uW0QIWDZET1lzKgR3kVw8wBlPe0IAiYAdAQ1K2MIGAKGQAUQYGavfnt69OrpXPoOkqUGu3X/VlsAVP/s8UdAYPaPgeCMSX1kQL/+Pr4CJFoTdYyACQB1PHhGuiFgCDQ2Ao7/O1afDFj6Dx48VH7kjAFVKODa4v7UHmB0rxZZcuIo6d27t6n/G/vVKEnvTAAoCYxWiSFgCBgC5UUAY7/evfvK1PHDvYtfvyPAOQTCBwCaALQA0yf0lyFDBtmxv+Udioap3QSAhhlK64ghYAg0OgI49RnqGPy00T3dDN+JADB/ZxCILUDXlnmy6gKDpI/z/Gdb/Br9TShN/0wAKA2OVksWBEKvY+F9liKWZAgYAmkIJB38wNi9Z8AFBkv3TvN8Dmb+xC83socz/hsi3d3xweoXMK0KezAEIgiYABABxB5Lj0A4GwnvS9+S1WgINCYCzuWP7xi/H44JHjNiuCw9pIs3BhSnBXA+AJ2joL4ysP8gtxTgDgsyEaAxX4QS98oEgBIDatVlRuC7777LnBikmJYgAMNuDQGHgBoCAkbXrp1l0KBBjuH3c9Z/brbvEsf3FWf8Nyx17G9ntRI09AyBLAiYAJAFHEsqDQIDBw6UzTbbTFZZZRXZdNNN5cknn8xasWkJssJjiU2IgArFbrnfqfu7eCv/xceNlLG93Pq/O/Z3tbF9/A4BtgT6EEoMTYiXdTk/BEwAyA8ny1UEAqNGjZLjjz9eTj/9dJk1a5Yst9xyeQkCRTRpRQ2BhkIgJRS3Mvbu3bvLkGGDnWfA3sJhfzMWGurcBff12wEbquPWmbIiYAJAWeG1ykMEfvzjH8u9994rt912mwkCITB2bwjkiYBz/OtzIhD069dP1pg6TGZM6OttAhAKwmCGgCEadh+HgAkAcahYXFkQUDXmWmutFSsIPPXUU6l2NW8qwm4MgWZHwHN0Ptkt3uofY8DJE8bLPmsu4m0C2A0QBlsFCNGw+zgETACIQ8XiCkYgH4adUmO21q6CwK233ipPP/20LLvssrL55psLgkA0b8EEWQFDoNEQSHH05Gebw4CGDB4oo53f/z59+thvptHGuwL9abUYqUBL1kRdIwCDLyVTfuGFF+Suu+6Su+++22sDPvroIxk+fLhfw7zvvvtk6tSp3qK5rkEz4g2BMiOg5wDgCtiCIVAoAiYAFIpYk+bPxfyzpSM8wPBh9v/73//83yeffCLDhg2T6dOny1FHHSUzZsyQRRZZxIyYmvT9sm53DAF+d9l+ex2r1Uo1CwImADTLSFewnyHDV6YPw2eGv8Yaa8jRRx/tGf6iiy5qH68Kjos1ZQgYAoZAiIAJACEadt8hBGD4zz//vJ/hw/DvueceUYbPDP+YY44pmOGXesmhQx2zQoaAIWAINDACJgA08OCWu2vvvvuu/O53v5Mrr7zSM3zaYyvSzjvvLAcccIAsvvjieZEQx+xNrZkXdJbJEDAEDIEOI9DJfXxrfrvoo48+Kvvvv788/PDDHe6oFSwPArw+L7/8cmr2zxr/hx9+6I4kHSKrr766n/mzvo8wEN2mVB6KrFZDwBAwBAyBfBAwASAflCxPQQi8+OKLKWM/lgRUIGA5ABsABIIllljCDP4KQtUyGwKGgCFQWgRMACgtnk1dW5wqH0BeeuklryFAO4BAwJY/DjNBIEAYMIGgqV+bsnY+0ztZrkYr3V65+pGt3kx9/Pjjj2Xu3LkyZsyYbMXrKi1TX+uqE1mINQEgCziW1DEEsv1oWlpa5JVXXvGCAMIAQsEHH3zgDjIZXBMCQRztcXEdQ8ZKhQhUC9fvv/9e5s2b513p1gI9IQ31eH/11Vf7A76WWWYZwTnRTTfdJCuvvLLssssu9didpqK5c1P11jpbEQSyGfDhsAQnP7vttpscfPDBcuCBB8qUKVPks88+k3/9619y1lln+b8bb7yx7LTCgKIhjva4uAceeEDWX399XzyuHq33vffek/POO09WXHFFefzxxzU6df38889l8uTJgmAUF2gDG4u4kK3duPy1EMcs8cEHH6waKWij1l13Xb8VVYnggKqTTjrJb1PlfUQwrbdQjXdh9uzZstNOO3kB/sQTT5QttthCfvKTn8j5558vl1xyifznP/+pNxhT9FYDz1TjFbyxXQAVBLuZm2LGBQPUWT/e/r755huZOHGiXwL49a9/7a8TJkzwMFXiB6iMnbb0Pt8x6tWrl/zwww8+O2W5f/XVVwWGD8PGnfEjjzwiHIWMy+MLLrhAmCFFQ//+/eXLL7/09hBxdLCdMpPxZKE0R9uu5DN9O/PMM+Xkk0+WI4880s8QC6U/Dp9C+7DwwgvLiBEjvC2Klh06dKgXCk444QQ59dRT/U4WTauXa6FYlqJf++yzjxea2PETBmhBELjwwgtlww03DJPq5p4+lOJ9q/UOmwBQ6yNUp/TFMfyvv/5aJrYy/HPOOcd/hHmOC6X8oOkPGUY7evTotOZoh2NUx44dKxtttJHfvsgOhlxBXbBqvueee85/9LbaaitZaKGFZL311pNnn31WEHSyBZi7MnjoBCP16x5igIZAP0pz5syR+fPn+3zZ6q6VNGjdfvvt5YknnvA+ImDCHQkhHoWWB1sNnEiJQEbQdwPBdNq0aXXB/JVm7U81ro899pjf/stW4LjAduD3338/Lqlu4op53+qlkyYA1MtIVZnOXB8djH+Y4auh3/333++Z2aRJk/zMHoY/wxn8McOP1hV9LkdXaYPw3XffeabMsgOBHzmaCJj1scce69cvYRA9evTw6dH/mOXz0WOm/9VXX/mtqTBw1j6XXHJJP8ulDGnMdDOFmTNnyjvvvCOc6AZ2CAow/7322kt69+6d0khA3yabbJJWDQIA22IPOuigtPhaffjtb3/rj4B+8sknZfz48UWRCfZnnHGGxxshDOEC/FhSwrNkNDDu2Jj8+f/bO7dQOYqtj885HBAE8cUH87AhXkBMRAUjggnihQgKES+IRomoGBUDijdUkCQk+CIqKFERc6KJxoii4gUv0cTvUUREFLyAJlHRN0GEKPjSX/3qnDWnpnb1TM9M90z1zH/B3j3dXZdV/+qqWrVq1ap//9svtfz0009eA4DNCWSdPAIA3+e06MEHH/TfjOVvQiECK4LJqlWr7FWXZ9xrb9++vYsFOPA9bdmypRu27h/WVl9++WWPF8a89izMi8O9qvoBCeNN+jcGyQ8//LAX/PgWWNagvbFbyYi2/sgjj3hs+d4uvvjiqX4rxlctV1d52ZNTpRZuDTV7PueNQdcZF27ttHBrqoU7m5wRtnADYeFme8Xzzz9fHDp0KCtIfv/9d8+j6ziTfP3222+efzcYJN/z8M033yxuvPHG4sorryyctXNx8803F05wKJzKv3Dr9T3xjj322J778Oadd94pbr311sIN5IVbTig2bNhQOKdKYZCe304D0HPflhsncBVOw1K48x5qYxksnGq5AF/XOfdN19lYFKeffnrhllJ8ODc4Frfffns3Dmm5Tr1wSzWFE/y6z6fx49FHHy3cIFQ4I1mfvdOiFU4wLVavXl24QadwxouL2IJ3t8Tkv0Ur46JANT6w73Dt2rXFXXfd5VO2Z5bN4cOHC3fOR+E8gtqjrK/gfNZZZxVO81e4Lcs9vFrZ3njjjeLMM88snA2Jf2/PewK38EYagFrEqPlIxH3f3dkHJWa7D6pdrsxUmP0fOHCg4xqL9wzIzAtJesWKFX6WkgtKlCNFzArRWLBLIZwBhGGZHfD35ZdfeiNGDJ6YOTDjYdnDCRF+FsEsHa3AJ5984tf3sRHA0PH888/vsO7PLMLWR/GkuG3btm42+E3A6RUzXIwm4ZeZx/Lly/0sthuwBT+YWaNhufDCC2vjFryxsXAD46IlHcvEvlW0Bee6mT3r/BBLNVdffbX/bWHQTFBfbhDoee5vhvjHLPGee+4ZIkZvUL4hDGRPPPFE/wItALNovG1yVPbOnTu9hiiMxfeBJgDDRiujvbfy2X3qCj5uIE+9Sj4De4hlHNo6xLeJZmapW84jTzRptBEcgbWBwPm0007zbZrzSkKy8rJ85YT/zpIlS/xrex6GbeNvCQBtrLUp8Zz66Fk7X7dunf+DLdTadPoIA88++2zngQce8GvsZ599tu+IzzvvvM4ZZ5wxVYGg7OhUBuiDBw/2qKmxCic8BmwxgYdhwpV10SuuuMKrE1kDpTNEtcuyB0sKdJRsj0IAsHhxmtzDA50yVtVGH3zwQee+++7rCgBVOneLO82r07r4ssYdKzyNWgYENNSy51ZQ2SNIsaxCXhDnVLArg6UAW47gW+X7RGCD+tWND1Dy76OPPhpLAKDd2M6SMAvjnTLHxFISa+0pLFLlCDFH6AEPduNAqfBxfnbvtFd+WYK89+zZ44UnPLYijGBrYzYWFn7Ua8jvqGlUiYfwwvZQlgScZqknCt8QQpkN/j0vW34jAaDlFZgb+wsLC4sEgo8//rgrELAujpHbypUrfadFxzVpgcA6VOtcuDILdKphv12PWbq9w2K8X8dIJ8rgzGDCWm249YmZEAMf1tL9iLycSrHD1kespyE8JTLzM0I4QSNg1I8nC5PLlfKlhK5Ry8CADaUGPSuzpU3HjfDF/auvvuq/PYQzsL7enVkBffjhh6UaHx+g4j/Ls2LwnmAIfQglqTIxwKKduu6663ricFMFizBSzCP38bMwfNlvvmtwY9suAz52K7t27eq4ZQwvTLHd0ow9rS2VpdXv+Si89Uuv7B2aP4h6CAUA7CrAn3LOIv1zFgulMk0GARr2IEIgoOPCCAuVobML6Dz55JNedYuGgEGTzg2rebaIsUecRtckkSeW/qhMyRvDKYQQZ8fgB3MGWut42J6IFiMm1NqcgMjWPmZhEIN4SMwqMYaEyrBiYCctVLwYH0IsF8BTTMZT/LwN9yHvZVhULQeDHpon/CcMoq1bt/rlgt27d3dOOOEEv2+dDv2qq67ysz22/ZGOzYbH5W0QP2Xvmf1D4dITvKD237t3b+f999/vLg34gP/9Rzz4N21G+K7K73HKi2YLAzqWwdAIMHAygLKcZd89PIR1X4WnMIzxZ9fwXZ2/0QBA8B8S2qJBAnwYvm2//zelaBvn4ndqCNAYadSDGraFCxmlo0Ig4I+BDi9idNLMounoSJPBENW5zYbD+HX8fv311/1WPdIiP1R/OPbBqv6VV17p68GMmSOCCxoDVIKoUNlGyPptPMtFy7F+/Xov0Jh62fhn9vT00097lSkz1H379nmhhPfsIMB/QEgprFP4hnFy/Z0qyzC8MuilZsopPBDwwt0YfFtG+HK499577XaoayqvoRKIAiPUMKtGg4QgiVBJm7j//vv90lL8/Vh0sGD9P6a6+YvTD++tPlnewibosssu8+0oDDPqb0vbrqSDwHzNNdd4oS18nsoDHJhc0Lb7YRJqACwdhAEEQ+wyZpUkAMxqzTZUrn6NyLK0MDRO+807tthgFEenRYfHbJ9nbMljBsHsBxsB1O5NEgM3mgkjeGTvPhoKBuV+LkwxGGILHjzefffdfvAnHSurpcmVAQbDMjwcul0DXhDAQBJfAahM2brGmi8zp9D3AAZVVdYbB3V+IS+z8vuHH37wBmfhTNnKFuOBQSaeFsso/DbjMBi2Un8pYrsma8UxscWUbaLht8BvZsrh8k0cj3vaw+WXX9656aabuq/RUDHDxq4kJQCQV9X1f9T0OJUyouwMbs5i3xu98tzw47rUzYhtK6LFsSueE7HtiAn+qReELjR9EBiCZZ2EwP3WW29VTpKyQla+VESEL9qk8U2cJ554wmslU+Fn5ZkEgFmpyQmUo1+HGWZvDY0ZPt7wsAFg0MeYhmdI1Mzg3BY6fw3X3MJ0quYXxhnlt/GLxfWgtT6s9yF2AYRknQyzdzQZ7JPGspgOHQ0HAsCPP/7o00cAQDtQRvgkQBAqIzBklkiHNW/EdwTx/cTfB7swWId22zR9GHwroFmJyerK6t3ec2/vEPLMV4S9tyvq7dDWw54zeDz++OOLBAAMOhlQy4h4/MVCDY6pWH5CaKa8UFhm2hVk7/xNyT8EDLROIWGUitDLQBcSOKB5iJ1mWd4sVVneYbzUbzAEy2lSXM8hL1Ymwix1dWRLANiLXHrppaX+QMI02vxbAkCba2/CvPdrSLDCwERnRWdDR81vZvgYA9FJ2Sy/bMCPizMovzj8uPfMuFAvWqcQp1f2nHValgIoNz7/ERJQLdu2MhzhEIYZFfYHMYXlZGCno3b75uNg3XsGCwwWETTmjcCY9X/bKheWn6UdhC4jlpDiZaSyOrQ4qWscB5UyfzExI8fhVYriNMIwlIlvIB7I2bJoRHwo/FaIZ+v/qfTDZ7Z91dLjigYAYdR4DsOH4ey35Y2Kn79RaFAeVdKkT3nxxRf9rpoq4ZlwxMKVxbMycY8AgBtvtEZsM6XdllEd5ShLe5LPJQBMEu0W55X64G3ANyt/ZvjxgE+nFqr0Sccolaa9m8YVAYABGHWprcHv2LHDd7osC4SdRcgfM3tm9BgMYmgWE4M/e9ZRHWPMFVOICQZqdFj91KaoYMMlgzi9Wb5n0Et15mDrnE95T479yk8domHB7z9r1rYFblCcsvdVv+H42wnjUSZmygjG4XPsUiC+BeKzxBBqfRCyU+v/xmucpz23a/jd8WxQeIsXX1kOQfOBgHv00Ud7fxgIwS+99JLXfoXLF+QRljFOq8o9+dBW0WBUIbbdQoPyPc7tBGArJ4ahLO+FFMcdFaswzRx+SwDIoRZawEPqg2f9kMEIS3auCASsdTovYN0/Gl/YeMJ0wt9NQhDm3y8f7ADYoojqGPUrxCwb477YLoDOx/hnfz7rzVjug0VIhKPTZimE9VrbGmVh4M0Iw0I0BwwIKQJjBKz9+/d7p0CpMLk9M4yMr6p1YeHDK3vM2SoXCwDYkrDUggFaFWKph62AoSYKZ0xoVqjLYXiMy1clf8JYPHa8MOhccMEFPqo954YBn3trQyxPIWRCCDH4BWCnCRTG8w8m9O+FF17wyy7s7AmXTDggCNfg4eBvLI3LK31MrNmxtPtdB+W71GkA0IqcfPLJiwTsQXH75ZvzOwkAOddO5rwxC8VZjTms4ahXU4W/9tprXvqno0UVjiaAP2ZdDJSTbFCWF7OTcMCN4YUvlgCMCMtafkisf9IJM9DjLwCiI8ZQC4Mny8vi0MFzGiDqRPIPiTh4/UMowLkNszlmsQgiMTGjYtbKtiTUvnS4OVHZoBnjHeNTpQyoZPFvj5MpVO8IaN98843X1iAU8Z7ZG0fTQmW8WF7wgJCFgZ0Rywf2HY/Co6UzzJVvAqGDZSEGe2wF2P2CER3ELBQtAIapCAF4METbxGwbgz7U92DBjgGOM0ZQHVT2kD/KGddP+H7Qb7b2su8fB1ihZoI0EcYw1msTob2jrVYVJNtUtjJe/+Eq639TkLJQU36Oh3ZOA4AAAA8RSURBVCkMSVAxi9qDAAIBHS2qSq7M4NjyhkDALI4/Or8ya+umSsonP2onz4DOgA/P4dJGGa/98sJVMhoCjK3ovBEqrPMvS69tz1EDX3vttd46PrU80mR5QuwxEGSLJ88YTHHZy3ovAyx/+KDAKJUBwAS7YXlbs2aNdzA0bLxB4dEu8V0M882GZS9Ln28PIQJhPUX90kDtj6DKrhbTXoRp8G2zm8X5zw8fZ/0bPPhO6KPmhSQAzEtNZ1DOUCBAKGAWh4YArQDaAf5MQ9AUu/06tTDPquHCOPq9GAH847OswSzd7CoI1QS+YZrhbzp1tqht2rTJO3y67bbbvOBl7mr5DhkIUauPQ5SR0/HaQmDEdr4ynkMM4zKxc4DZPxqMYQSTOJ1c7/uVPVeeR+Hrn6NEUpz5QoDGUAex15btcKiv8aKH+huVNrMF3Oay9Y3OiBkYB29Mk0bp1OrCaZrlHifvVPkR9DCQDAd/8hgF30G8hWmGv1GhY5eCt0cI2xWETSN4DO/t+bDXsoF0UDop3AbFqeM9GPXjOcQwzo8dD3jBLAtDm24zlZWrzWVK8S4bgBQqetaDQJ2NgTV29lHT6bIswPohqjd3ZKvvhG1poF/H1MPckDfjlIWOmvh2jbMuS9vC2zWONyv3cflZunv33XcbUYsPg5k7ernrG4B4fHesmbPjg6UX7m39354Nk34uYcf5viyuXQeVieUchHijMB6aPpYVpr3/33jTtRwBaQDKsdGbCAEa+bDEbOu9997zDk1Y72ctE4M23JyyZ551WQy5sIDnxD2cb9jgP0p+ZfzVkZYNcHYtyyt+buHtGr+3+zp4tLSmfcVYDbU7/gzs2ONJ82R4MsjjOwDCMp1tZBiwYsQGsYuAo2uZ1eIAZhSyvEaJO+i7qJrmOOlYXLsOynPt2rVe/Y9nRoh4YEB7x68AuzLGwWRQ/npfDwLSANSD41ykUqVzYD82lsnMqmyGT0dw6qmn+hk+HsbOOeec7iDfD7gq+fWLH74bNi14tk4tvIZp8tvCxc9HuR+Wx1HyqDtOqvwIdfjff+ihh7rHRNedb5X0DM/Nmzd3OAwIoQRtE7NXDrDhQCAIIzYEUraxMnCNQpbXKHGnFSdVd1V5YTkPA0B2xCDIL3Vb6NjmCvEsdZhV1bQVbnIIyAhwcljPZE424LP9D4dAzLDoWPDIhjr/XLfWyuzKZvUzCYIK1YOA7fJg2yJGntMkG+S4QjZQt1nVPy08EZrwwId6P9wBg8dCZv0cYQ2+uNPFHfOyZcumxaryrYiANAAVgVKw/yBgHSp3bPPBoA9HJqjwmV3R4XPSH6p8Bn62XInmCwF8JeDDHqM7PB/282rYNDI24NvV8mNZQFSOQNjOLRR2EmhTmP0bcTIm2yg5AhgnWhCTAoRAfCvEjq8snq55IKBWkEc9ZM9FPIOCYdZVMabC2Is97JzQhY96jsbFUxfrrKgH2QbG4Sm42BXNPgIIgWwRw/0xOzvYHifKGwFr38ZlLDDxHMEOrZ69Y9bPSZfYUtjgT7ijjjrKOy3q50ufcDlSiEP423hNPbN3bbxqCaCNtdYCnhns6TCwA/g/Z/HP4Ro0HrYOMSjQkaxatWqRd7ywaIS3ziZ8rt/tQAC3xTiLQRi0A2fawfl8cplqb6jzacOs6bN7Bze5+FHAJTMqftp16mAmlgu2b9/ud/nMJ5rtKLWWANpRT63jEre3+NM3n/oIBKFxIBb/JhBgJ4BAwJJB6C5Xg3/rqr2HYTyq4e74ueee88cgo3ZXnfZAlNVNXDfsjuD8Afz9o9bHQJIzLWi3PMPOJzX4Uyh2Bxzn3DO3iT7//HO/rGmeABFgFxYW/KQlLEdKUArft+m3lgDaVFst5pWBne1g+F/HpTPuTXH2gzYAA0K2jLFksGLFis7GjRs7f/31V4tLK9YNAewAEP5wDBMPMBZG1/wQwEjy+uuv97YcZsiJap81feoRHwC01RQxQNK2p7X9M8VTlWecXUC5L7roIn92B+6+zXiZMhnN0ncsAcBqVdeJIoBxIB0EW8XWr1/vT2ZD8maL4IYNGyZ+PsBECz9DmYUdY6pY7LmHmE0NCpuKr2eTQSCuGw4YYtaPgy6I5Tw0dGY8iWEn52KkiAOtGDgxBm4TcZohS1Zgccstt3gbFrY3QrM06PsC/feflgBCNPS7cQRoXDQmOo+dO3d6SZuDRTiIhaNYwyNaG2dGGYyNQKpjtMEkfhffj525EqgNgbhuqENznkQmGPths8PhTizrccATf7TjPXv2+DbNcgCaO9o13hdNWKiNyYYToszYK0EsSc4DSQCYh1rOqIwczLJr1y5/tC0uQxn4cQ4U7is2dk1YsHtd24FAPJi0g2txGSKAsR8DPoZ8EM6T0Apg7c9SAJoBrPyZKWMgyBIe53lwmiLun2nnKcq5TfPdYvCIJmCaW1dTuDX1TAJAU8gq3R4EaPg7duzwKn8OAaLjGDTj10DSA6FuhMBEELBB+rHHHvMD+b/+9Z9hAj8ftqQDI+zuuOSSS/zx2HhRRBDAu+KBAwc6+/bt69xxxx1enR624/D3RAozIBMrK8H4jT0SPkzmhSQAzEtNT7mcHLlKh4AlMQP/kiVLpsyRshcCQiAcAA2NcJC2wZ934eAfhrWlAtbLsfzniqEvFKZlcca9cqAYBw0hkFQhNBlMOFIU8kcfxXLkvKj/wUMCQOqr0LPaELAO5o8//vDnAbCtSCQEhEAeCIQDYBlH1obL3tvzTZs2+WUDdvawoydFVdMK48ZxsNZHO4EAMIh/4hK+CrH+T3psS54XkgAwLzU9pXJaA7WrsRE36vh52XsLp6sQEAL1IRC2N9bvzX9Hqt2Sa/icuOEzsxvgGY6/8BZqFMazZ4OuqTicKlo3IQCcdNJJc6WdlABQ91ek9JIIWCdhL1ONmnf23K4WXlchIASaQyBsb6j9OcNhVAqFiVHT6BeP9LEzYM9+FUJYSGkkjE/rm+Zt/R/sJABU+YIUZmwEwg5m7MSUgBAQAlNF4KmnnuocOnTIHw505JFH9vBCW7fBtedFTTeHDx/2hw+Rhw3e/ZLGYdG6desWBbE+ievXX3/t1/9N/d8k/4sYmeIDCQBTBH+esp6XBjVPdaqyzi8COPHixD88exph3Lt169bSI6DjPiC+t3QGXVnTx5V4ncRR5pAZAJpwUGceOabVCk+A81IZOX4gdfJEgxfNFwJmgMW6suq//XVvdfjZZ591jeV49uuvv3onQeY2ONVnx8/i+2mg8/bbb/sTTNFoHHPMMZ0tW7b4cw6mwcs08myFBsA+umkAlEOelD+HxlI3FrNarrpxanN6p5xyimefM+MxsBK1FwG8/HGgF2vqOMxhtsw6PL9xFXz88cf7/f+4DDZBIPfSrlmzpsPfvFIrNACpyqlDKKgjjRRvdT+bxcEfjGa1XHXXf5vTO87tC2cfNicCtqW9tRnvJnin3r7//vvODTfc4A8DYg1+9+7d/iAv8sPvPxqB1atXe+Eg5S+gCb6U5vgItFYAqGPwqCON8atguimoU54u/vOQ+7Zt2/y58Zs3b56H4s5cGekj8Pt/5513+uNxly1b5mf4nAyIv3+OBf7uu+86a9eu9dv+JAC05xNorQDQHojz5rQuIUiCRN71PE3uGCD279/vXUFzxCxHQYvagwAe8n755Rdv9AfXqPvNWI57XHv/+eef/rwA7meB5qU/kwAwC19rBmWoIkjMS6PKoDqyY4GtWAwkuIDeuHFjdvyJoTQCtFkG+OXLl3cD7N271x/bzYl/f//9t/efbwIBJwNWddHbTTDDH/Rn89BftcIIkO/jq6++8uolVE78oWayK5Vl9/a+37VKWMKk0k3FJZzxYld7FvJRlqbFCcOGv1N5hu/D3/3C9ntnacRhcApCWUIs+D0KjRpvlLwUJz8E2BEQeoXLj0NxFCNAm125cqXv39grTz/8888/+9MADx486JcCMPjjhEAOADriiCOSZwbE6bbhfh76q384KSf7vVlYn+L5ibOnsTrlDykT1rnas9R11Pf90o/ThA/LO35nz+06TLoWJ7xWST8MH/8eNr7xa+lwD5mgQCMx4cGu9s7uCUM8Ttl65pln2tD2xaMQEAIBAhj+ffHFFx12dSDIffrpp37t35wAffvtt/6o4IWFhSCWfuaOQCsEgNxBnEf+EAgGCRNxGKyFOU9cJASEgBAQAtNHQALA9OtAHAgBISAEhIAQmDgCMgKcOOTK0BBoweqTsaqrEBACQmDmEJAAMHNVOrkClQ3gZc9jzubByCYus+6FgBAQArkgoCWAXGpCfAgBISAEhIAQmCAC0gBMEGxlJQSEgBAQAkIgFwQkAORSE5nzUVWtnyrGOHFT6emZEBACQkAIjI+ABIDxMZyLFEZdr2fwD+NyL4FgLj4ZFVIICIHMEZANQOYVJPaEgBAQAkJACDSBgDQATaCqNIWAEBACQkAIZI6ABIDMK0jsCQEhIASEgBBoAgEJAE2gqjSFgBAQAkJACGSOgASAzCtI7AkBISAEhIAQaAIBCQBNoKo0hYAQEAJCQAhkjoAEgMwrSOwJASEgBISAEGgCAQkATaCqNIWAEBACQkAIZI6ABIDMK0jsCQEhIASEgBBoAgEJAE2gqjSFgBAQAkJACGSOgASAzCtI7AkBISAEhIAQaAIBCQBNoKo0hYAQEAJCQAhkjoAEgMwrSOwJASEgBISAEGgCAQkATaCqNIWAEBACQkAIZI6ABIDMK0jsCQEhIASEgBBoAgEJAE2gqjSFgBAQAkJACGSOgASAzCtI7AkBISAEhIAQaAIBCQBNoKo0hYAQEAJCQAhkjoAEgMwrSOwJASEgBISAEGgCAQkATaCqNIWAEBACQkAIZI6ABIDMK0jsCQEhIASEgBBoAgEJAE2gqjSFgBAQAkJACGSOgASAzCtI7AkBISAEhIAQaAIBCQBNoKo0hYAQEAJCQAhkjoAEgMwrSOwJASEgBISAEGgCAQkATaCqNIWAEBACQkAIZI6ABIDMK0jsCQEhIASEgBBoAgEJAE2gqjSFgBAQAkJACGSOgASAzCtI7AkBISAEhIAQaAIBCQBNoKo0hYAQEAJCQAhkjoAEgMwrSOwJASEgBISAEGgCAQkATaCqNIWAEBACQkAIZI7A/wO/eoM7UYzYUgAAAABJRU5ErkJggg==" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# RLC回路の応答\n", "電気回路の応答を考えましょう.R(resistor,抵抗) L(inductor,コイル) C(capacitor,コンデンサー)をそれぞれふたつずつ組み合わせてみていくのが常套手段なんですが,一個ずつだと面倒なので,まずは全部入れた方程式を立てます.そこからパラメータを変えて回路の挙動を観察します.こんなとこから進めていけるのが,数値計算の利点です.どんなんでも解けるから.\n", "\n", "コンデンサに蓄えられた電荷を$Q(t)$, 回路に流れる電流を$I(t)$とします.\n", "\n", "* 自己インダクタンス$L$のコイルにかかる電圧は$L \\frac{dI}{dt}$\n", "* 容量$C$のコンデンサにかかる電圧は$\\frac{Q}{C}$\n", "* 抵抗値$R$の抵抗に掛かる電圧は$RI$\n", "\n", "となります.コイルにかかる電圧,コンデンサにかかる電圧,抵抗にかかる電圧の和が,この回路にかけた電圧$V(t)$であることを使うと,\n", "\n", "$$\n", "L \\frac{dI}{dt} + \\frac{Q}{C} + RI = V(t)\n", "$$\n", "\n", "となります.ここで電流$I$とコンデンサの電荷$Q$の関係$I=\\frac{dQ}{dt}$を使うと,\n", "\n", "$$\n", "L \\frac{d^2Q}{dt^2} + \\frac{Q}{C} + R\\frac{dQ}{dt} = V{t}\n", "$$\n", "が得られます.\n", "\n", "先ほどの重力系の問題と比べると\n", "\n", "$$\n", "v \\rightarrow i \\\\\n", "x \\rightarrow q\n", "$$\n", "と置き換えれば良さそうです.\n", "\n", "そうするとアルゴリズムは,\n", "$$\n", "\\begin{aligned}\n", "i_{i+1} & = i_i + (V - RR \\, i_i -qc \\, q_i) \\, dt \\\\\n", "q_{i+1} & = q_i + i_i \\, dt;\n", "\\end{aligned}\n", "$$\n", "となりそうです.RRやqcには適当に規格化した値をいれます.\n", "\n", "![rlc_circuit](./figs/ode.005.jpeg)\n", "\n", "![image.png](attachment:image.png)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "def euler_rlc(q0, i0):\n", " i1 = i0 + (v - r * i0 - qc * q0) * dt\n", " q1 = q0 + i0 * dt\n", " return [q1, i1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "コンデンサー($C$),コンダクター($L$)を1として,抵抗値を0.5として,入力電圧を1Vと設定してコンデンサーにたまる電荷と電流の変化を確かめたのが次の図です.\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dt, r, qc, v =0.01, 0.5, 0,1\n", "ii=[0.0]\n", "qq=[0.0]\n", "tt=[0.0]\n", "t = 0\n", "for i in range(0,2000):\n", " t += dt\n", " q, i2 = euler_rlc(qq[i],ii[i])\n", " tt.append(t)\n", " qq.append(q)\n", " ii.append(i2)\n", "\n", "my_plot(qq,ii,tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "入力電圧を0V,コンデンサーにあらかじめ1クーロン貯めたと設定して電荷と電流の時間変化を確かめたのが次の図です.\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dt, r, qc, v =0.01, 1.0, 1, 0\n", "ii=[0.0]\n", "qq=[1.0]\n", "tt=[0.0]\n", "t = 0\n", "for i in range(0,2000):\n", " t += dt\n", " q, i2 = euler_rlc(qq[i],ii[i])\n", " tt.append(t)\n", " qq.append(q)\n", " ii.append(i2)\n", "\n", "my_plot(qq,ii,tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 課題\n", "\n", "## 雨粒\n", "空気抵抗を受ける雨粒の速度の変化を自分の言葉で説明しなさい.\n", "\n", "## 大砲\n", "free fallの初期設定を変えて,x=0から鉛直方向にv=9.8で投げ上げたボールの時間変化を示しなさい.\n", "\n", "# 自由課題\n", "以下は 2021年度は不要です.\n", "\n", "## RLC回路\n", "抵抗が0の場合の電荷,電流の変化を確認しなさい.\n", "\n", "## RLC回路\n", "抵抗が0の場合にも,エネルギー保存が成り立つようにコードを改良しなさい.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Raw Cell Format", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": { "height": "192px", "width": "252px" }, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": "block", "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }