KatsuhiroMorishita/マクスウェル分布のシミュレーション.ipynb

## マクスウェル分布のシミュレーション.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 概要\n",
    "分子の運動速度の分布はマクスウェル分布に従うことが知られている。ここでは、分子が衝突を繰り返すうちにその速度分布がマクスウェル分布になることを確認する。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## マクスウェル分布\n",
    "まずは、マクスウェル分布の理論に従うグラフを作図する。  \n",
    "\n",
    "[リンク：理論の導出](https://www1.doshisha.ac.jp/~bukka/lecture/statistic/pdftext/std-02.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# マクスウェル分布\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# マクスウェル分布の計算\n",
    "m_H2 = 3.35 * 10**-27   # 水素の質量\n",
    "m_Hg = 3.35 * 10**-25   # 水銀の質量\n",
    "m = m_H2    # 計算に使う質量を選択\n",
    "T = 300   # 温度[K]\n",
    "k = 1.380649 * 10**-23    # ボルツマン定数（2019年に改訂された）\n",
    "N = ((2 * m**3) / (np.pi * k**3 * T**3)) ** 0.5\n",
    "dv = 10\n",
    "v = np.arange(0, 10000, dv)    # 速度の配列（dvステップで作成）\n",
    "P = N * v**2 * np.exp(-m * v**2 / (2 * k * T))   # 速度に対する確率を計算\n",
    "\n",
    "# グラフの描画\n",
    "plt.plot(v, P)\n",
    "plt.ylabel('P')\n",
    "plt.xlabel('v [m/s]')\n",
    "plt.grid(True)\n",
    "plt.xlim([0, 5000])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999998"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 面積が1であることを確認\n",
    "np.sum(P * dv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1774.3934364716943"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 平均速度を求める\n",
    "mean = np.sum(P * v) / np.sum(P)\n",
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1774.3934364233296"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#マクスウェル分布の平均値の理論値\n",
    "# http://www.kagaku1.kjmt.jp/chap6/mean-velocity.pdf\n",
    "((8 * k * T) / (np.pi * m)) ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1925.9299750138155"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 速さの二乗平均平方根（速さの二乗の平均値の平方根）の理論値\n",
    "# http://www2.meijo-u.ac.jp/~tnagata/education/react/2019/react_06_slides.pdf\n",
    "# 式の形はちょっと違うが、教科書と同じ式だ\n",
    "# この資料によると、根平均二乗速さに該当するらしい\n",
    "((3 * k * T) / m) ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1925.929975013815"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 速さの二乗平均平方根の計算値\n",
    "mean2 = np.sum(P * v**2) / np.sum(P)  # 速度の2乗の平均\n",
    "mean2 ** 0.5  # 根平均二乗速さ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2物体の衝突\n",
    "物体の衝突によって速度分布を求めてみる。  \n",
    "[リンク：参考文献](https://slash-mochi.net/?p=2617)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.0, 1.0)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_velocity(va, vb, ma=1, mb=1, e=1):\n",
    "    \"\"\" 衝突後の速度（衝突面に垂直な成分）を求める\n",
    "    va: float, aの速さ\n",
    "    vb: float, bの速さ\n",
    "    ma: float, aの質量\n",
    "    mb: float, bの質量\n",
    "    e: 反発係数\n",
    "    \"\"\"\n",
    "    va2 = (ma*va + mb*vb - e*mb*(va - vb)) / (ma + mb)\n",
    "    vb2 = (ma*va + mb*vb + e*ma*(va - vb)) / (ma + mb)\n",
    "    return va2, vb2\n",
    "\n",
    "get_velocity(1,2)   # 試し"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x軸方向の速さの総和（衝突前）： -58036.42182536679\n",
      "y軸方向の速さの総和（衝突前）： 1105703.9587506007\n",
      "x軸方向の速さの総和（衝突後）： -58036.4218253667\n",
      "y軸方向の速さの総和（衝突後）： 1105703.958750601\n",
      "↑変わっていなければ、運動量が保存されている。\n"
     ]
    },
    {
     "data": {
      "image/png": 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e+TEMZmYZcdI3M8uIk76ZWUac9M3MMpLlhVw7/lW7WL933cebHIlZubinb2aWESd9M7OMOOmbmWXESd/MLCNO+mZmGXHSNzPLiJO+mVlGnPTNzDLipG9mlhEnfTOzjPgxDJaVY/2Wgh/RYDlwT9/MLCNO+mZmGXHSNzPLiJO+mVlGnPTNzDIy4t07kjYAnwAORMQHUtl04C5gDrAXuDQiDkkScCtwEfAmsDwiHkvrdAN/lZq9ISI2NnZXzMbGP7xiOailp/8NYMmQstXA9oiYB2xP8wAXAvPSayVwO7x1klgLnA0sBNZKmjbW4M3MbHRGTPoR8SPg4JDipcBgT30jcHFF+Z1ReBBolzQDuADYFhEHI+IQsI23n0jMzGycKSJGriTNAbZWDO+8HhHtaVrAoYhol7QVWBcRD6Rl24FrgC7g5Ii4IZVfCxyJiJuG2dZKik8JdHR0nNXT01PXjg0MDNDW1jbssl39h+tqczx0nAL7j0x0FMeWe4zzZ05tSDvH+pssi1aIEVojzomMcdGiRTsjonO4ZWP+Rm5EhKSRzxy1t7ceWA/Q2dkZXV1ddbXT29tLtXWXH+Nbmc22av5Rbt5V7i9G5x7j3mVdDWnnWH+TZdEKMUJrxFnWGOu9e2d/GrYhvR9I5f3A7Ip6s1JZtXIzM2uiepP+FqA7TXcD91SUX6HCOcDhiHgFuA9YLGlauoC7OJWZmVkT1XLL5ncoxuRPlbSP4i6cdcAmSSuAl4BLU/V7KW7X7KO4ZfNKgIg4KOl64JFU77qIGHpx2KyUfCunHU9GTPoRcXmVRecPUzeAq6q0swHYMKrozMysofyNXDOzjDjpm5llxEnfzCwjTvpmZhlx0jczy4iTvplZRsr93foxOtaPYJuNle/ft1bknr6ZWUac9M3MMuKkb2aWESd9M7OMHNcXcs0mQrULvN9YMqXJkZi9nXv6ZmYZcdI3M8uIh3fMmmRX/+Fhf6rT9/VbM7mnb2aWESd9M7OMeHjHbIL5cQ7WTO7pm5llxD19s5LyJwAbD+7pm5llxEnfzCwjHt4xazEe9rGxaHrSl7QEuBWYBHw9ItY1Owaz45FPBlaLpiZ9SZOAfwI+BuwDHpG0JSKebWYcZjkZzS/IrZp/lOWrv+8TxXGs2T39hUBfRLwAIKkHWAo46ZuVyHj/1KhPKhNHEdG8jUmXAEsi4jNp/tPA2RHx2Yo6K4GVafZ04Lk6N3cq8LMxhNssrRCnY2wMx9g4rRDnRMb47og4bbgFpbuQGxHrgfVjbUfSoxHR2YCQxlUrxOkYG8MxNk4rxFnWGJt9y2Y/MLtiflYqMzOzJmh20n8EmCdprqQTgcuALU2OwcwsW00d3omIo5I+C9xHccvmhoh4Zpw2N+YhoiZphTgdY2M4xsZphThLGWNTL+SamdnE8mMYzMwy4qRvZpaR4zLpS1oi6TlJfZJWN3nbGyQdkPR0Rdl0Sdsk7Unv01K5JN2W4nxK0oKKdbpT/T2Suhsc42xJOyQ9K+kZSVeXLU5JJ0t6WNKTKcYvpfK5kh5KsdyVbghA0klpvi8tn1PR1ppU/pykCxoVY0X7kyQ9LmlriWPcK2mXpCckPZrKSnO8U9vtkjZL+omk3ZLOLVOMkk5P/36Dr59L+nyZYqxJRBxXL4oLxM8D7wFOBJ4Ezmji9j8KLACerij7e2B1ml4NfDlNXwT8ABBwDvBQKp8OvJDep6XpaQ2McQawIE2/E/gpcEaZ4kzbakvTJwAPpW1vAi5L5V8F/jRN/xnw1TR9GXBXmj4j/Q2cBMxNfxuTGnzMvwB8G9ia5ssY417g1CFlpTneqf2NwGfS9IlAe9lirIh1EvAq8O6yxlg19mZtqGk7BOcC91XMrwHWNDmGOfxu0n8OmJGmZwDPpemvAZcPrQdcDnytovx36o1DvPdQPA+plHECvwc8BpxN8Q3HyUOPNcUdYeem6cmpnoYe/8p6DYptFrAdOA/YmrZZqhhTm3t5e9IvzfEGpgIvkm4uKWOMQ+JaDPxXmWOs9joeh3dmAi9XzO9LZROpIyJeSdOvAh1pulqsTduHNMTwIYqedKniTMMmTwAHgG0UPeDXI+LoMNt7K5a0/DDwrvGOEfgH4C+A/0vz7yphjAAB/IeknSoedQLlOt5zgf8B/iUNlX1d0pSSxVjpMuA7abqsMQ7reEz6pRbFqb0U98lKagO+C3w+In5euawMcUbEbyLiTIre9ELgfRMZz1CSPgEciIidEx1LDT4SEQuAC4GrJH20cmEJjvdkimHR2yPiQ8AbFEMlbylBjACkazSfBP5t6LKyxHgsx2PSL+OjHvZLmgGQ3g+k8mqxjvs+SDqBIuF/KyK+V9Y4ASLidWAHxVBJu6TBLxVWbu+tWNLyqcBr4xzjh4FPStoL9FAM8dxashgBiIj+9H4AuJviJFqm470P2BcRD6X5zRQngTLFOOhC4LGI2J/myxhjVcdj0i/jox62AINX6LspxtAHy69IV/nPAQ6nj4n3AYslTUt3AixOZQ0hScAdwO6I+EoZ45R0mqT2NH0KxTWH3RTJ/5IqMQ7Gfglwf+p1bQEuS3fOzAXmAQ83IsaIWBMRsyJiDsXf2f0RsaxMMQJImiLpnYPTFMfpaUp0vCPiVeBlSaenovMpHrlemhgrXM5vh3YGYylbjNU16+JBM18UV81/SjEG/MUmb/s7wCvAryl6Lysoxm23A3uA/wSmp7qi+FGZ54FdQGdFO38C9KXXlQ2O8SMUH0GfAp5Ir4vKFCfwR8DjKcangb9O5e+hSIh9FB+vT0rlJ6f5vrT8PRVtfTHF/hxw4Tgd9y5+e/dOqWJM8TyZXs8M/p8o0/FObZ8JPJqO+b9T3NlSthinUHw6m1pRVqoYR3r5MQxmZhk5Hod3zMysCid9M7OMOOmbmWXESd/MLCNO+mZmGXHSNzPLiJO+mVlG/h/jBeAtAfu76QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "生データの平均と中央値： 1708.2254636998287 1609.1709668258766\n",
      "生データの最頻値： [3.00600393]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ヒストグラムから求めた最頻値： 1357.5767260721877\n",
      "速さの二乗平均平方根： 1926.0\n",
      "↑が1926と変わっていなければ、運動エネルギー量が保存されている。\n"
     ]
    }
   ],
   "source": [
    "# 衝突の向きを考慮していない部分があるので注意\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# 同じ速度の様々な向きの速度を生成\n",
    "v = []\n",
    "v0 = 1926                         # 速さの初期値\n",
    "for _ in range(100000):\n",
    "    theta = 2 * np.pi * np.random.rand()   # 向き\n",
    "    v.append(v0 * np.array([np.cos(theta), np.sin(theta)]))\n",
    "v = np.array(v)    # ndarray型に型を変換\n",
    "\n",
    "# 運動量の確認\n",
    "print(\"x軸方向の速さの総和（衝突前）：\", np.sum([speed[0] for speed in v]))\n",
    "print(\"y軸方向の速さの総和（衝突前）：\",np.sum([speed[1] for speed in v]))\n",
    "    \n",
    "for _ in range(1000000):\n",
    "    # 衝突角度（面）の作成\n",
    "    theta = 2 * np.pi * np.random.rand()\n",
    "    plane = np.array([np.cos(theta), np.sin(theta)])\n",
    "    \n",
    "    # 運動量を交換するペアを抽出\n",
    "    i = np.random.randint(len(v))\n",
    "    j = np.random.randint(len(v))\n",
    "    va1 = v[i]\n",
    "    vb1 = v[j]\n",
    "\n",
    "    # 衝突面に平行な成分と垂直な成分を求める\n",
    "    amp = np.dot(va1, plane)         # planeに並行な成分の大きさ\n",
    "    va11 = amp * plane               # planeに並行な成分\n",
    "    va12 = va1 - va11                # planeに直角な成分\n",
    "    va12_amp = np.linalg.norm(va12)  # planeに直角な成分の大きさ\n",
    "    \n",
    "    amp = np.dot(vb1, plane)         # planeに並行な成分の大きさ\n",
    "    vb11 = amp * plane               # planeに並行な成分\n",
    "    vb12 = vb1 - vb11                # planeに直角な成分\n",
    "    vb12_amp = np.linalg.norm(vb12)  # planeに直角な成分の大きさ\n",
    "    \n",
    "    # 衝突後の速さを求める（e==1なので、交換にすぎないのだが）\n",
    "    va22_amp, vb22_amp = get_velocity(va12_amp, vb12_amp)\n",
    "    \n",
    "    # 新しい速度を求めて、更新\n",
    "    #va22 = -va12 / va12_amp * va22_amp\n",
    "    #vb22 = -vb12 / vb12_amp * vb22_amp\n",
    "    va22 = vb12\n",
    "    vb22 = va12\n",
    "    va2 = va11 + va22\n",
    "    vb2 = vb11 + vb22\n",
    "    v[i] = va2\n",
    "    v[j] = vb2\n",
    "    #print(np.abs(va1 - va2))\n",
    "    #print(np.abs(vb1 - vb2))\n",
    "    \n",
    "# 運動量の確認\n",
    "print(\"x軸方向の速さの総和（衝突後）：\", np.sum([speed[0] for speed in v]))\n",
    "print(\"y軸方向の速さの総和（衝突後）：\",np.sum([speed[1] for speed in v]))\n",
    "print(\"↑変わっていなければ、運動量が保存されている。\")\n",
    "    \n",
    "# 速度の大きさを求めて、その分布を確認\n",
    "v_amp = np.array([np.linalg.norm(vector) for vector in v])\n",
    "plt.hist(v_amp, bins=50)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "def show_graph(v):\n",
    "    print(\"生データの平均と中央値：\", np.mean(v), np.median(v))\n",
    "    mode_val, mode_num = stats.mode(v)\n",
    "    print(\"生データの最頻値：\", mode_val)\n",
    "\n",
    "    hist, bins = np.histogram(v, bins=30)\n",
    "    X = []\n",
    "    for i in range(1, len(bins)):\n",
    "        X.append((bins[i-1] + bins[i]) / 2)\n",
    "    plt.plot(X, hist)\n",
    "    plt.show()\n",
    "    i = np.argmax(hist)\n",
    "    print(\"ヒストグラムから求めた最頻値：\", (bins[i] +  bins[i+1]) / 2)\n",
    "    print(\"速さの二乗平均平方根：\", (np.sum(v**2) / len(v)) ** 0.5)\n",
    "    print(\"↑が{}と変わっていなければ、運動エネルギー量が保存されている。\".format(v0))\n",
    "    \n",
    "show_graph(v_amp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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