source: sasmodels/sasmodels/models/pringle.py @ 99658f6

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 99658f6 was 99658f6, checked in by grethevj, 10 months ago

updated ER functions including cylinder excluded volume, to match 4.x

  • Property mode set to 100644
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Line 
1r"""
2Definition
3----------
4
5The form factor for this bent disc is essentially that of a hyperbolic
6paraboloid and calculated as
7
8.. math::
9
10    P(q) = (\Delta \rho )^2 V \int^{\pi/2}_0 d\psi \sin{\psi} sinc^2
11    \left( \frac{qd\cos{\psi}}{2} \right)
12    \left[ \left( S^2_0+C^2_0\right) + 2\sum_{n=1}^{\infty}
13     \left( S^2_n+C^2_n\right) \right]
14
15where
16
17.. math::
18
19    C_n = \frac{1}{r^2}\int^{R}_{0} r dr\cos(qr^2\alpha \cos{\psi})
20    J_n\left( qr^2\beta \cos{\psi}\right)
21    J_{2n}\left( qr \sin{\psi}\right)
22
23.. math::
24
25    S_n = \frac{1}{r^2}\int^{R}_{0} r dr\sin(qr^2\alpha \cos{\psi})
26    J_n\left( qr^2\beta \cos{\psi}\right)
27    J_{2n}\left( qr \sin{\psi}\right)
28
29and $\Delta \rho \text{ is } \rho_{pringle}-\rho_{solvent}$, $V$ is the volume of
30the disc, $\psi$ is the angle between the normal to the disc and the q vector,
31$d$ and $R$ are the "pringle" thickness and radius respectively, $\alpha$ and
32$\beta$ are the two curvature parameters, and $J_n$ is the n\ :sup:`th` order
33Bessel function of the first kind.
34
35.. figure:: img/pringles_fig1.png
36
37    Schematic of model shape (Graphic from Matt Henderson, matt@matthen.com)
38
39Reference
40---------
41
42Karen Edler, Universtiy of Bath, Private Communication. 2012.
43Derivation by Stefan Alexandru Rautu.
44L. Onsager, Ann. New York Acad. Sci. 51, 627-659 (1949).
45
46* **Author:** Andrew Jackson **Date:** 2008
47* **Last Modified by:** Wojciech Wpotrzebowski **Date:** March 20, 2016
48* **Last Reviewed by:** Andrew Jackson **Date:** September 26, 2016
49"""
50
51import numpy as np
52from numpy import inf, pi
53
54name = "pringle"
55title = "The Pringle model provides the form factor, $P(q)$, for a 'pringle' \
56or 'saddle-shaped' disc that is bent in two directions."
57description = """\
58
59"""
60category = "shape:cylinder"
61
62# pylint: disable=bad-whitespace, line-too-long
63#   ["name", "units", default, [lower, upper], "type","description"],
64parameters = [
65    ["radius",      "Ang",         60.0,   [0, inf],    "volume", "Pringle radius"],
66    ["thickness",   "Ang",         10.0,   [0, inf],    "volume", "Thickness of pringle"],
67    ["alpha",       "",            0.001,  [-inf, inf], "volume", "Curvature parameter alpha"],
68    ["beta",        "",            0.02,   [-inf, inf], "volume", "Curvature paramter beta"],
69    ["sld", "1e-6/Ang^2",  1.0,    [-inf, inf], "sld", "Pringle sld"],
70    ["sld_solvent", "1e-6/Ang^2",  6.3,    [-inf, inf], "sld", "Solvent sld"]
71    ]
72# pylint: enable=bad-whitespace, line-too-long
73
74
75source = ["lib/polevl.c", "lib/sas_J0.c", "lib/sas_J1.c",
76          "lib/sas_JN.c", "lib/gauss76.c", "pringle.c"]
77effective_radius_type = ["equivalent cylinder excluded volume", "equivalent volume sphere", "radius"]
78
79def random():
80    alpha, beta = 10**np.random.uniform(-1, 1, size=2)
81    radius = 10**np.random.uniform(1, 3)
82    thickness = 10**np.random.uniform(0.7, 2)
83    pars = dict(
84        radius=radius,
85        thickness=thickness,
86        alpha=alpha,
87        beta=beta,
88    )
89    return pars
90
91tests = [
92    [{'scale' : 1.0,
93      'radius': 60.0,
94      'thickness': 10.0,
95      'alpha': 0.001,
96      'beta': 0.02,
97      'sld': 1.0,
98      'sld_solvent': 6.3,
99      'background': 0.001,
100     }, 0.1, 9.87676],
101
102    [{'scale' : 1.0,
103      'radius': 60.0,
104      'thickness': 10.0,
105      'alpha': 0.001,
106      'beta': 0.02,
107      'sld': 1.0,
108      'sld_solvent': 6.3,
109      'background': 0.001,
110     }, 0.01, 290.56723],
111
112    [{'scale' : 1.0,
113      'radius': 60.0,
114      'thickness': 10.0,
115      'alpha': 0.001,
116      'beta': 0.02,
117      'sld': 1.0,
118      'sld_solvent': 6.3,
119      'background': 0.001,
120     }, 0.001, 317.40847],
121]
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