source: sasmodels/sasmodels/models/linear_pearls.py @ 925ad6e

core_shell_microgelscostrafo411magnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 925ad6e was 925ad6e, checked in by wojciech, 6 years ago

sph_j1c translated to sas_3j1x_x

  • Property mode set to 100644
File size: 2.9 KB
Line 
1r"""
2This model provides the form factor for $N$ spherical pearls of radius $R$
3linearly joined by short strings (or segment length or edge separation)
4$l$ $(= A - 2R)$. $A$ is the center-to-center pearl separation distance.
5The thickness of each string is assumed to be negligible.
6
7.. figure:: img/linear_pearls_geometry.jpg
8
9
10Definition
11----------
12
13The output of the scattering intensity function for the linear_pearls model
14is given by (Dobrynin, 1996)
15
16.. math::
17
18    P(Q) = \frac{scale}{V}\left[ m_{p}^2
19    \left(N+2\sum_{n-1}^{N-1}(N-n)\frac{sin(qnl)}{qnl}\right)
20    \left( 3\frac{sin(qR)-qRcos(qR)}{(qr)^3}\right)^2\right]
21
22where the mass $m_p$ is $(SLD_{pearl}-SLD_{solvent})*(volume\ of\ N\ pearls)$.
23V is the total volume.
24
25The 2D scattering intensity is the same as P(q) above,
26regardless of the orientation of the q vector.
27
28References
29----------
30
31A V Dobrynin, M Rubinstein and S P Obukhov, *Macromol.*,
3229 (1996) 2974-2979
33
34"""
35
36from numpy import inf
37
38name = "linear_pearls"
39title = "Linear pearls model of scattering from spherical pearls."
40description = """
41    Calculate form factor for Pearl Necklace Model
42    [Macromol. 1996, 29, 2974-2979]
43    Parameters:
44
45    sld_pearl: the SLD of the pearl spheres
46    sld_solv: the SLD of the solvent
47    num_pearls: number of the pearls
48    radius: the radius of a pearl
49    edge_separation: the length of string segment; surface to surface
50    """
51category = "shape:sphere"
52
53# pylint: disable=bad-whitespace, line-too-long
54#            ["name", "units", default, [lower, upper], "type", "description"],
55parameters = [
56    ["radius",      "Ang",       80.0, [0, inf],     "", "Radius of the pearls"],
57    ["edge_sep",    "Ang",      350.0, [0, inf],     "", "Length of the string segment - surface to surface"],
58    ["num_pearls",  "",           3.0, [0, inf],     "", "Number of the pearls"],
59    ["sld",   "1e-6/Ang^2", 1.0, [-inf, inf],  "sld", "SLD of the pearl spheres"],
60    ["sld_solvent", "1e-6/Ang^2", 6.3, [-inf, inf],  "sld", "SLD of the solvent"],
61    ]
62# pylint: enable=bad-whitespace, line-too-long
63single = False
64
65source = ["lib/sas_3j1x_x.c", "linear_pearls.c"]
66
67demo = dict(scale=1.0, background=0.0,
68            radius=80.0,
69            edge_sep=350.0,
70            num_pearls=3,
71            sld=1.0,
72            sld_solvent=6.3)
73
74"""
75Tests temporarily disabled, until single-double precision accuracy issue solved.
76
77tests = [
78    # Accuracy tests based on content in test/utest_model_pearlnecklace.py
79    [{'radius':      20.0,
80      'num_pearls':   2.0,
81      'sld':    1.0,
82      'sld_solvent':  6.3,
83      'edge_sep':   400.0,
84     }, 0.001, 185.135],
85
86    # Additional tests with larger range of parameters
87    [{'radius':     120.0,
88      'num_pearls':   5.0,
89      'sld':    2.0,
90      'sld_solvent':  2.3,
91      'edge_sep':   100.0,
92     }, 0.01, 45.4984],
93
94    [{'radius':       7.0,
95      'num_pearls':   2.0,
96      'sld':   10.0,
97      'sld_solvent': 99.3,
98      'edge_sep':    20.0,
99     }, 1.0, 0.632811],
100    ]
101"""
Note: See TracBrowser for help on using the repository browser.