Source Code for Module lib.order.order_parameters

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 2  #                                                                             # 
 3  # Copyright (C) 2010 Edward d'Auvergne                                        # 
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21   
22  # Module docstring. 
23  """Module for the conversion of order parameters to specific model parameters and vice versa.""" 
24   
25  # Python module imports. 
26  from math import acos, cos, pi, sqrt 
27   
28   
29 -def iso_cone_theta_to_S(theta): 
30      """Convert the isotropic cone angle to the order parameter S. 
31   
32      This uses Woessner's diffusion in a cone order parameter defined as:: 
33   
34          S = 1/2 (1 + cos(theta)) * cos(theta) 
35   
36   
37      @param theta:   The isotropic cone angle. 
38      @type theta:    float 
39      @return:        The order parameter value. 
40      @rtype:         float 
41      """ 
42   
43      # Convert. 
44      S = 0.5 * (1.0 + cos(theta)) * cos(theta) 
45   
46      # Return the order parameter. 
47      return S 
48   
49   
50 -def iso_cone_S_to_theta(S): 
51      """Convert the isotropic cone order parameter S into the cone angle. 
52   
53      This uses Woessner's diffusion in a cone order parameter defined as:: 
54   
55          S = 1/2 (1 + cos(theta)) * cos(theta) 
56   
57      The conversion equation is:: 
58   
59          theta = acos((sqrt(8.0*S + 1) - 1)/2) 
60   
61      Hence the cone angle is only between 0 and 2pi/3, as the order parameter for higher cone angles is ambiguous. 
62   
63   
64      @param S:   The order parameter value (not squared). 
65      @type S:    float 
66      @return:    The value of cos(theta). 
67      @rtype:     float 
68      """ 
69   
70      # Catch bad order parameters. 
71      if S > 1.0: 
72          return 0.0 
73      if S < -0.125: 
74          return 2*pi 
75   
76      # Convert. 
77      theta = acos(0.5*(sqrt(8.0*S + 1) - 1)) 
78   
79      # Return theta. 
80      return theta 
81