# source:sasmodels/sasmodels/models/lamellar.py@0507e09

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
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1r"""
2Polydispersity in the bilayer thickness can be applied from the GUI.
3
4Definition
5----------
6
7The scattering intensity $I(q)$ for dilute, randomly oriented,
8"infinitely large" sheets or lamellae is
9
10.. math::
11
12    I(q) = \text{scale}\frac{2\pi P(q)}{q^2\delta} + \text{background}
13
14
15The form factor is
16
17.. math::
18
19   P(q) = \frac{2\Delta\rho^2}{q^2}(1-\cos(q\delta))
20        = \frac{4\Delta\rho^2}{q^2}\sin^2\left(\frac{q\delta}{2}\right)
21
22where $\delta$ is the total layer thickness and $\Delta\rho$ is the
23scattering length density difference.
24
25This is the limiting form for a spherical shell of infinitely large radius.
26Note that the division by $\delta$ means that $scale$ in sasview is the
27volume fraction of sheet, $\phi = S\delta$ where $S$ is the area of sheet
28per unit volume. $S$ is half the Porod surface area per unit volume of a
29thicker layer (as that would include both faces of the sheet).
30
31The 2D scattering intensity is calculated in the same way as 1D, where
32the $q$ vector is defined as
33
34.. math::
35
36    q = \sqrt{q_x^2 + q_y^2}
37
38
39References
40----------
41
42.. [#] F Nallet, R Laversanne, and D Roux, *J. Phys. II France*, 3, (1993) 487-502
43.. [#] J Berghausen, J Zipfel, P Lindner, W Richtering, *J. Phys. Chem. B*, 105, (2001) 11081-11088
44
45Source
46------
47
48lamellar.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/lamellar.py>_
49
50Authorship and Verification
51----------------------------
52
53* **Author:**
55* **Last Reviewed by:**
56* **Source added by :** Steve King **Date:** March 25, 2019
57"""
58
59import numpy as np
60from numpy import inf
61
62name = "lamellar"
63title = "Lyotropic lamellar phase with uniform SLD and random distribution"
64description = """\
65    [Dilute Lamellar Form Factor](from a lyotropic lamellar phase)
66        I(q)= 2*pi*P(q)/(delta *q^(2)), where
67        P(q)=2*(contrast/q)^(2)*(1-cos(q*delta))^(2))
68        thickness = layer thickness
69        sld = layer scattering length density
70        sld_solvent = solvent scattering length density
71        background = incoherent background
72        scale = scale factor
73"""
74category = "shape:lamellae"
75
77#   ["name", "units", default, [lower, upper], "type","description"],
78parameters = [
79    ["thickness",          "Ang", 50, [0, inf],    "volume", "total layer thickness" ],
80    ["sld",         "1e-6/Ang^2",  1, [-inf, inf], "sld",    "Layer scattering length density" ],
81    ["sld_solvent", "1e-6/Ang^2",  6, [-inf, inf], "sld",    "Solvent scattering length density" ],
82    ]
84
85# No volume normalization despite having a volume parameter
86# This should perhaps be volume normalized? - it is!
87form_volume = """
88    return 1.0;
89    """
90
91Iq = """
92    const double sub = sld - sld_solvent;
93    const double qsq = q*q;
94    // Original expression
95    //return 4.0e-4*M_PI*sub*sub/qsq * (1.0-cos(q*thickness)) / (thickness*qsq);
96    // const double alpha = fmod(q*thickness+0.1, 2.0*M_PI)-0.1;
97    // Use small angle fix 1-cos(theta) = 2 sin^2(theta/2)
98    const double sinq2 = sin(0.5*q*thickness);
99    return 4.0e-4*M_PI*sub*sub/qsq * 2.0*sinq2*sinq2 / (thickness*qsq);
100    """
101
102def random():
103    """Return a random parameter set for the model."""
104    thickness = 10**np.random.uniform(1, 4)
105    pars = dict(
106        thickness=thickness,
107    )
108    return pars
109
110demo = dict(scale=1, background=0,
111            sld=6, sld_solvent=1,
112            thickness=40,
113            thickness_pd=0.2, thickness_pd_n=40)
114#  [(qx1, qy1), (qx2, qy2), ...], [I(qx1,qy1), I(qx2,qy2), ...]],
115tests = [
116    [{'scale': 1.0, 'background': 0.0, 'thickness': 50.0,
117      'sld': 1.0, 'sld_solvent': 6.3, 'thickness_pd': 0.0},
118     [0.001], [882289.54309]]
119]
120# ADDED by: converted by PAK? (or RKH?)
121# ON: 16Mar2016 - RKH adding unit tests from sasview to early 2015 conversion
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