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Jupyter notebook version added
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‎ch10/Program_10.1_walk2d.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#\n",
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"# Program 10.1: Random walk in 2D (walk2d.ipynb)\n",
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"# J Wang, Computational modeling and visualization with Python\n",
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"#\n",
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"\n",
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"import numpy as np, random as rnd\n",
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"import matplotlib.pyplot as plt\n",
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"%matplotlib notebook\n",
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"\n",
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"def walknsteps(n): # walk n steps\n",
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" x, y = np.zeros(n+1), np.zeros(n+1)\n",
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" for i in range(n):\n",
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" phi = rnd.random()*2*np.pi # random in $[0,2\\pi]$\n",
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" x[i+1] = x[i] + np.cos(phi)\n",
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" y[i+1] = y[i] + np.sin(phi)\n",
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" return x, y\n",
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" \n",
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"nstep, N = 20, 4 # steps, num of walkers\n",
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"col = ['k', 'r', 'g', 'b', 'c', 'm'] # color codes\n",
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"plt.subplot(111, aspect='equal')\n",
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"for i in range(N):\n",
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" x, y = walknsteps(nstep)\n",
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" plt.quiver(x[:-1], y[:-1], x[1:]-x[:-1], y[1:]-y[:-1], scale=1,\n",
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" scale_units='xy', angles='xy', color=col[i%len(col)])\n",
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"plt.plot([0],[0],'y*', markersize=16)\n",
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"plt.xlabel('$x$'), plt.ylabel('$y$')\n",
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"plt.show()"
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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": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎ch10/Program_10.2_brownian.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#\n",
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"# Program 10.2: Brownian motion (brownian.ipynb)\n",
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"# J Wang, Computational modeling and visualization with Python\n",
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"#\n",
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"\n",
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"import numpy as np, random as rnd\n",
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"import matplotlib.pyplot as plt\n",
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"import matplotlib.animation as am\n",
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"%matplotlib notebook\n",
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"\n",
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"class BrownianMotion: # Brownian motion class\n",
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" def __init__(self, N=400, F=0.005, b=0.1, tau=2., h = 0.5):\n",
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" self.N, self.F, self.b, self.tau, self.h = N, F, b, tau, h\n",
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" self.r, self.v = np.zeros((N, 2)), np.zeros((N, 2))\n",
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" self.t = -np.log(np.random.rand(N))*tau # initial kick times\n",
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"\n",
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" def move(self, r, v, dt): # move between kicks\n",
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" edt = np.exp(-self.b*dt)\n",
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" return r + v*(1-edt)/self.b, v*edt\n",
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"\n",
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" def iterate(self): # advance one step\n",
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" r, v, t, h, F = self.r, self.v, self.t, self.h, self.F # alias\n",
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" for i in range(self.N):\n",
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" if t[i] > h: # no kick within current step\n",
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" dt = h # dt= time to end of step\n",
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" else: # suffers kicks before end of step\n",
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" tot, dt = 0., t[i] # tot=time to last kick\n",
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" while t[i] <= h:\n",
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" r[i], v[i] = self.move(r[i], v[i], dt)\n",
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" phi = rnd.random()*2*np.pi # apply kick\n",
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" v[i] += [F*np.cos(phi), F*np.sin(phi)] \n",
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" tot += dt\n",
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" dt = -np.log(rnd.random())*self.tau # sample dt\n",
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" t[i] += dt # next kick\n",
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" dt = h - tot # dt= to end of current step\n",
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" r[i], v[i] = self.move(r[i], v[i], dt) # no kick, just move\n",
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" t[i] -= h\n",
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" \n",
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"def updatefig(*args): # update figure data\n",
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" bm.iterate()\n",
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" plot.set_data(bm.r[:,0], bm.r[:,1]) # update data\n",
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" return [plot] # return plot object\n",
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" \n",
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"bm = BrownianMotion() # create Brownian model\n",
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"fig = plt.figure()\n",
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"plt.subplot(111, aspect='equal')\n",
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"plot = plt.plot(bm.r[:,0], bm.r[:,1], 'o')[0] # create plot object\n",
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"ani = am.FuncAnimation(fig, updatefig, interval=10, blit=True) # animate \n",
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"plt.xlim(-1., 1.), plt.ylim(-1., 1.), plt.show()"
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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": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎ch10/Program_10.3_mcint.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#\n",
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"# Program 10.3: Electrostatic energy (mcint.ipynb)\n",
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"# J Wang, Computational modeling and visualization with Python\n",
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"#\n",
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"\n",
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"import numpy as np, random as rnd\n",
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"\n",
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"def sample(r): # return a random point inside a sphere\n",
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" while True:\n",
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" x, y, z = rnd.random(), rnd.random(), rnd.random()\n",
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" x, y, z = r*(x+x-1), r*(y+y-1), r*(z+z-1) # map to [-r, r]\n",
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" if (x*x + y*y + z*z <= r*r): break\n",
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" return x, y, z\n",
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"\n",
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"r1, r2, d = 1.0, 2.0, 4.0 # radii and separation, d>r1+r2\n",
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"\n",
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"f, V, N = 0., (4*np.pi/3.)**2*(r1*r2)**3, 100\n",
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"for i in range(N):\n",
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" x1, y1, z1 = sample(r1)\n",
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" x2, y2, z2 = sample(r2)\n",
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" f += 1./np.sqrt((x1-x2-d)**2+(y1-y2)*(y1-y2)+(z1-z2)*(z1-z2))\n",
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" \n",
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"print ('MC=', V*f/N, 'exact=', V/d)"
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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": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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