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@mikemhenry
Last active April 24, 2017 22:37
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{
"cells": [
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f98be5c9fd0>]"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Gw/r1YNbgPmaXY3cdadHHAiXAcqXUHqXUMqWUPxCmtS5ofU4hENbRIh3Z0qmx+Hu5S6te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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f98bf288e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"\n",
"\n",
"# In Eric's paper\n",
"\n",
"\n",
"def vde(phi):\n",
" k = 10\n",
" phi0 = 3.14\n",
" return k*(phi-phi0)**2\n",
"\n",
"# HOOMD\n",
"\n",
"def vdh(phi):\n",
" k = 20\n",
" d = 1\n",
" n = 1\n",
" return 0.5*k*(1+d*np.cos(n*phi))\n",
"\n",
"\n",
"def vdo(phi):\n",
" k1 = 30\n",
" k2 = 0\n",
" k3 = 0\n",
" k4 = 0\n",
" tot = (0.5*k1*(1+np.cos(phi))\n",
" +0.5*k2*(1-np.cos(2*phi))\n",
" +0.5*k3*(1+np.cos(3*phi))\n",
" +0.5*k4*(1-np.cos(4*phi)))\n",
" return tot\n",
"\n",
"phi = np.linspace(0,2*np.pi,100)\n",
"\n",
"plt.plot(phi, vde(phi))\n",
"plt.plot(phi, vdh(phi))\n",
"plt.plot(phi, vdo(phi))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"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": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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