96 lines
20 KiB
Plaintext
96 lines
20 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n",
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"# Random walk exercise\n",
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"\n",
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"Plot distance as a function of time for a random walk\n",
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"together with the theoretical result\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 400x300 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# 参数设定:1000 条随机行走轨迹,每条 200 步\n",
|
||
"n_stories = 1000\n",
|
||
"t_max = 200\n",
|
||
"\n",
|
||
"# 时间轴 [0, 1, 2, ..., 199]\n",
|
||
"t = np.arange(t_max)\n",
|
||
"\n",
|
||
"# 生成每一步:randint(0,2) 返回 0/1,映射到 -1/+1\n",
|
||
"rng = np.random.default_rng()\n",
|
||
"steps = 2 * rng.integers(0, 1 + 1, (n_stories, t_max)) - 1\n",
|
||
"\n",
|
||
"# 沿每条轨迹(axis=1)累加步长,得到各时刻的位置\n",
|
||
"positions = np.cumsum(steps, axis=1)\n",
|
||
"\n",
|
||
"# 计算均方位移:先平方再按轨迹求平均\n",
|
||
"sq_distance = positions**2\n",
|
||
"mean_sq_distance = np.mean(sq_distance, axis=0)\n",
|
||
"\n",
|
||
"# 作图:绿色点线=模拟结果 ⟨x²⟩^(1/2);黄色直线=理论 √(t)\n",
|
||
"plt.figure(figsize=(4, 3))\n",
|
||
"plt.plot(t, np.sqrt(mean_sq_distance), \"g.\", t, np.sqrt(t), \"y-\")\n",
|
||
"plt.xlabel(r\"$t$\")\n",
|
||
"plt.ylabel(r\"$\\sqrt{\\langle (\\delta x)^2 \\rangle}$\")\n",
|
||
"plt.tight_layout()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3 (ipykernel)",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.12.11"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
}
|