dimer.py

   1 #!/usr/bin/python
   2 # -*- coding: iso-8859-1 -*-
   3
   4 import matplotlib as mpl
   5 mpl.rc('text', usetex = True)
   6 import pylab
   7 import numpy as np
   8 import matplotlib.cm as cm
   9 import matplotlib.mlab as mlab
  10 import matplotlib.pyplot as plt
  11 import matplotlib.patches as patch
  12 import matplotlib.colors as col
  13
  14 FOUT = "../latex/images/dimer_intro.png"
  15
  16 L = 2*np.pi
  17 w = 0.1
  18 tau = L/w
  19 angle1 = 30
  20 angle2 = 60
  21 transport_angle = 100
  22 phi = 0
  23 alpha = 135
  24 dimer_length = 0.4
  25 cofx = cofy = L/2
  26 pad = 0.01 # small padding so the ticks get drawn correctly...
  27 msize = 20
  28 hw = 0.15 # arrow head width
  29 res = (800/80,600/80) # default dpi is 80
  30 cmap = cm.gray_r # colormap
  31 shader = False # applies ultra cool shadows to the map!
  32 show_plot = False
  33 xticks = [-2*L,-L,0,L,2*L]
  34 yticks = [-2*L,-L,0,L,2*L]
  35 tlabel = ["-2L","-L","0","L","2L"]
  36 xlabel = r'$x$'
  37 ylabel = r'$y$'
  38 cblabel = r'$\cos{x}\cos{y}+\cos{x}+\cos{y}$'
  39 fs_ticks = 18
  40 fs_labels = 28
  41
  42 ################################################################################
  43
  44 PI = np.pi
  45 rad1 = angle1*PI/180
  46 rad2 = angle2*PI/180
  47 rad_transport = transport_angle*PI/180
  48 rad_phi = phi*PI/180
  49 rad_alpha = alpha*PI/180
  50
  51 limx_min = -L/2
  52 limx_max = 1.5*L
  53 # quadratic
  54 limy_min = limx_min
  55 limy_max = limx_max
  56
  57 print "generating basemap..."
  58 delta = 0.01
  59 x = np.arange(limx_min,limx_max, delta)
  60 y = np.arange(limy_min,limy_max, delta)
  61 X,Y = np.meshgrid(x, y)
  62 Z = np.cos(X)*np.cos(Y)+np.cos(X)+np.cos(Y)
  63 print "done."
  64
  65 fig = plt.figure(figsize=res)
  66
  67 ax = fig.add_subplot(111)
  68
  69 if (shader is True):
  70     print "applying lightsource..."
  71     ls = col.LightSource(azdeg=0,altdeg=90)
  72     rgb = ls.shade(Z,cmap)
  73     print "done."
  74     print "plotting basemap..."
  75     pot = plt.imshow(rgb, extent=[limx_min,limx_max,limy_min,limy_max])
  76     print "done."
  77 else:
  78     print "plotting basemap..."
  79     pot = plt.pcolormesh(X,Y,Z, cmap=cmap)
  80     print "done."
  81
  82 cb = plt.colorbar(pot)
  83 cb.set_label(cblabel, size=fs_labels)
  84
  85 print "plotting dimer onto the basemap..."
  86
  87 def make_circle(start,stop,r):
  88         t = np.arange(start,stop,0.01)
  89         #t = t.reshape((len(t), 1))
  90         ret_x = cofx + r * np.cos(t)
  91         ret_y = cofy + r * np.sin(t)
  92         return ret_x, ret_y
  93
  94
  95 varphi_plot_x, varphi_plot_y = make_circle(rad1, rad2, 2.0)
  96 psi_plot_x, psi_plot_y = make_circle(rad_phi, rad_transport, 0.8)
  97
  98 ax.scatter(cofx, cofy, c='yellow', marker='o', lw=0, s=msize*4,
  99 label='cof')
 100 ax.arrow(cofx, cofy, np.cos(rad1)*dimer_length*L,
 101                 np.sin(rad1)*dimer_length*L, color='r', lw=0.1, alpha=0.5)
 102 ax.arrow(cofx, cofy, np.cos(rad2)*dimer_length*L,
 103                 np.sin(rad2)*dimer_length*L, color='r', lw=0.1, alpha=0.5)
 104 ax.arrow(cofx, cofy, -np.cos(rad1)*dimer_length*L,
 105                 -np.sin(rad1)*dimer_length*L, color='r', lw=0.1, alpha=0.5)
 106 ax.arrow(cofx, cofy, -np.cos(rad2)*dimer_length*L,
 107                 -np.sin(rad2)*dimer_length*L, color='r', lw=0.1, alpha=0.5)
 108 ax.scatter(cofx+np.cos(rad1)*dimer_length*L,
 109                 cofy+np.sin(rad1)*dimer_length*L, c='blue', marker='o',
 110                 lw=0, s=msize, label='x1')
 111 ax.scatter(cofx-np.cos(rad1)*dimer_length*L,
 112                 cofy-np.sin(rad1)*dimer_length*L, c='purple', marker='o',
 113                 lw=0, s=msize, label='x1')
 114 ax.scatter(cofx+np.cos(rad2)*dimer_length*L,
 115                 cofy+np.sin(rad2)*dimer_length*L, c='blue',
 116                 marker='o', lw=0, s=msize, label='x2')
 117 ax.scatter(cofx-np.cos(rad2)*dimer_length*L,
 118                 cofy-np.sin(rad2)*dimer_length*L, c='purple',
 119                 marker='o', lw=0, s=msize, label='x2')
 120 ax.plot(varphi_plot_x, varphi_plot_y, color='black')
 121 ax.arrow(cofx, cofy, np.cos(rad_phi)*0.4*L, np.sin(rad_phi)*0.4*L,
 122                 head_width=hw, shape='full', color='red')
 123 ax.arrow(cofx, cofy, np.cos(rad_transport)*0.4*L,
 124                 np.sin(rad_transport)*0.4*L, head_width=hw,
 125                 shape='full')
 126 ax.plot(psi_plot_x, psi_plot_y, color='black')
 127 ax.arrow(cofx, cofy, np.cos(rad_alpha)*0.4*L, np.sin(rad_alpha)*0.4*L,
 128                 head_width=hw, shape='full', color='blue')
 129 ax.arrow(cofx, cofy, -np.cos(rad_alpha)*0.4*L, -np.sin(rad_alpha)*0.4*L,
 130                 head_width=hw, shape='full', color='blue')
 131
 132 plt.text(cofx+np.cos(rad_phi+0.025)*0.4*L,
 133                 cofy+np.sin(rad_phi+0.025)*0.4*L,
 134                 r'$F\vec{e}_{\phi}$',{'color' : 'k', 'fontsize' :
 135                         fs_labels})
 136 plt.text(cofx+np.cos(rad_transport-0.05)*0.4*L,
 137                 cofy+np.sin(rad_transport-0.05)*0.4*L, r'$\vec{v}$',
 138                 {'color': 'k', 'fontsize' : fs_labels})
 139 plt.text(0.5*L,0.65*L, r'$\psi$', {'color' : 'k', 'fontsize' : fs_labels})
 140 plt.text(0.65*L,0.65*L, r'$\varphi$', {'color' : 'k', 'fontsize' :
 141         fs_labels})
 142 plt.text(cofx+np.cos(rad_alpha-0.025)*0.4*L, cofy+np.sin(rad_alpha-0.025)*0.4*L,
 143                 r'$A\vec{e}_{\alpha}$', {'color' : 'k', 'fontsize' :
 144                         fs_labels})
 145
 146 ax.set_xlabel(xlabel, size=fs_labels)
 147 ax.set_ylabel(ylabel, size=fs_labels)
 148 ax.set_xticks(xticks)
 149 ax.set_yticks(yticks)
 150 ax.set_xlim(limx_min,limx_max)
 151 ax.set_ylim(limy_min,limy_max)
 152 ax.set_xticklabels(tlabel, size=fs_ticks)
 153 ax.set_yticklabels(tlabel, size=fs_ticks)
 154
 155
 156 print "saving to file.."
 157 plt.savefig(FOUT)
 158 print "done."
 159
 160 if (show_plot is True):
 161         print "showing plot..."
 162         plt.show()
 163         print "done."
 164