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@dudung
Last active October 15, 2025 05:42
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{
"cells": [
{
"cell_type": "markdown",
"id": "60a6de72-3164-408f-95cc-fda6726eb116",
"metadata": {},
"source": [
"# random walk 1-d"
]
},
{
"cell_type": "markdown",
"id": "18db7f35-4bea-4c46-b896-ef62289c68a3",
"metadata": {},
"source": [
"## mean distance"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "5bb64fb5-5c2c-4fdb-a941-5c1e4f451696",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import random as rnd\n",
"\n",
"Nrep = 100\n",
"Nstep = 21\n",
"sx = [0] * Nstep\n",
"\n",
"# generate steps for random walk\n",
"for j in range(Nrep):\n",
" x = [0] * Nstep\n",
" for i in range(0, Nstep):\n",
" d = 2*rnd.randint(0, 1) - 1\n",
" x[i] = d\n",
" for i in range(0, Nstep):\n",
" sx[i] = sx[i] + x[i]\n",
"\n",
"# mean distance for Nrep\n",
"for i in range(0, Nstep):\n",
" sx[i] = sx[i] / Nrep\n",
"\n",
"import matplotlib.pyplot as plt\n",
"plt.plot(sx)\n",
"plt.xlabel('steps')\n",
"plt.ylabel('average distance')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "2ac1e6d8-0237-4afc-8f79-dfa0ce2524f4",
"metadata": {},
"source": [
"## assignment 1\n",
"1. Use above code to complete following plot.\n",
"2. Explain the influence of `Nrep` on the value of `mean distance`.\n",
"3. Cite a reference about it."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "e76ffeea-2329-4c84-a871-9d8d2242ef1b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# avarage distance for Nrep = 1E2\n",
"sx_1E2 = []\n",
"\n",
"# avarage distance for Nrep = 1E3\n",
"sx_1E3 = []\n",
"\n",
"# avarage distance for Nrep = 1E4\n",
"sx_1E4 = []\n",
"\n",
"# avarage distance for Nrep = 1E5\n",
"sx_1E5 = []\n",
"\n",
"# avarage distance for Nrep = 1E6\n",
"sx_1E6 = []\n",
"\n",
"import matplotlib.pyplot as plt\n",
"plt.xlabel('steps')\n",
"plt.ylabel('mean distance')\n",
"plt.grid()\n",
"plt.plot(sx_1E2, label='Nrep=1E2')\n",
"plt.plot(sx_1E3, label='Nrep=1E2')\n",
"plt.plot(sx_1E4, label='Nrep=1E3')\n",
"plt.plot(sx_1E5, label='Nrep=1E5')\n",
"plt.plot(sx_1E6, label='Nrep=1E6')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "1fec09d8-3e1a-4f08-a322-bcdf66359578",
"metadata": {},
"source": [
"## mean squared distance"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "3e9ede4f-a126-46d7-a247-5331ee308f80",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import random as rnd\n",
"\n",
"Nrep = 10\n",
"Nstep = 121\n",
"sx2 = [0] * Nstep\n",
"\n",
"# generate steps for random walk\n",
"for j in range(Nrep):\n",
" pos = 0\n",
" for i in range(0, Nstep):\n",
" d = 2*rnd.randint(0, 1) - 1\n",
" pos = pos + d\n",
" sx2[i] = sx2[i] + pos * pos\n",
"\n",
"# mean squared distance for Nrep\n",
"for i in range(0, Nstep):\n",
" sx2[i] = sx2[i] / Nrep\n",
"\n",
"import matplotlib.pyplot as plt\n",
"plt.plot(sx2)\n",
"plt.xlabel('steps')\n",
"plt.ylabel('mean squared distance')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "e8e3d39d-a4a1-40fb-bbf9-c1394b99200e",
"metadata": {},
"source": [
"## assignment 2\n",
"1. Use above code to complete following plot.\n",
"2. Explain the influence of `Nrep` on the value of `average squared distance`.\n",
"3. Cite a reference about it."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "2e2c72c4-7be5-4c68-8df8-eac6a9006d2c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# avarage distance for Nrep = 25\n",
"sx_025 = []\n",
"\n",
"# avarage distance for Nrep = 50\n",
"sx_050 = []\n",
"\n",
"# avarage distance for Nrep = 100\n",
"sx_100 = []\n",
"\n",
"# avarage distance for Nrep = 200\n",
"sx_200 = []\n",
"\n",
"# avarage distance for Nrep = 400\n",
"sx_400 = []\n",
"\n",
"import matplotlib.pyplot as plt\n",
"plt.xlabel('steps')\n",
"plt.ylabel('mean distance')\n",
"plt.grid()\n",
"plt.plot(sx_025, label='Nrep=25')\n",
"plt.plot(sx_050, label='Nrep=50')\n",
"plt.plot(sx_100, label='Nrep=100')\n",
"plt.plot(sx_200, label='Nrep=200')\n",
"plt.plot(sx_400, label='Nrep=400')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "02be7bca-bb25-485e-8d65-f15232f28ef3",
"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": "3.12.9"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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