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Boltzmann Distribution
{
"metadata": {
"name": "",
"signature": "sha256:c48160c3a518320917eccf0efa6f8976a6ffae76badcc9d86baf8be90c6f5bca"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k = 1.3806e-23 # J/K\n",
"N = 6.022e23 # Avogadros Number\n",
"T = [30, 100, 273] # Temperatures considered\n",
"eps = np.arange(0, 2400, 50)/N # Energy values\n",
"len(eps)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"text": [
"48"
]
}
],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sums = [np.exp(-eps/(k*temp)).sum() for temp in T]\n",
"sums"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"[5.5047136094497242, 16.177631593242015, 29.95377831492873]"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"probabilities = [np.exp(-eps/(k*temp)) / sums[i] for i, temp in enumerate(T)]\n",
"plot(eps, probabilities[0], 'o:', label=\"{} K\".format(T[0]))\n",
"plot(eps, probabilities[1], 'o:', label=\"{} K\".format(T[1]))\n",
"plot(eps, probabilities[2], 'o:', label=\"{} K\".format(T[2]))\n",
"legend()\n",
"xlabel(\"Energy\")\n",
"ylabel(\"Probability\")\n",
"plt.savefig(\"boltzmann.png\", figsize=(9,5), dpi=300)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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20js2tkRrK05Tg3i9tVRVzefzz7Pp27eRm28eacnCmAxnCSM2ljBasbmkjOkeLGHExuaS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\nAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f9f5004a750>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"csums = [p.cumsum() for p in probabilities]\n",
"plot(eps, csums[0], 'o:', label=\"{} K\".format(T[0]))\n",
"plot(eps, csums[1], 'o:', label=\"{} K\".format(T[1]))\n",
"plot(eps, csums[2], 'o:', label=\"{} K\".format(T[2]))\n",
"legend(loc='lower right')\n",
"xlabel(\"Energy\")\n",
"ylabel(\"Cumulative Probability\")\n",
"plt.savefig(\"cum_boltzmann.png\", figsize=(9,5), dpi=300)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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sdoyq/re9FzM6h1NI6kcV/ppGqaAczMFsGIlBqJQYPYHXA69l+OsyND9OKnw+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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f9f5004a450>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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