source: sasmodels/sasmodels/models/lamellar_hg.py @ 830cf6b

ticket-1257-vesicle-productticket_1156ticket_822_more_unit_tests
Last change on this file since 830cf6b was 0507e09, checked in by smk78, 5 years ago

Added link to source code to each model. Closes #883

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1# Note: model title and parameter table are inserted automatically
2r"""
3This model provides the scattering intensity, $I(q)$, for a lyotropic lamellar
4phase where a random distribution in solution are assumed. The SLD of the head
5region is taken to be different from the SLD of the tail region.
6
7Definition
8----------
9
10The scattering intensity $I(q)$ is
11
12.. math::
13
14   I(q) = 2\pi\frac{\text{scale}}{2(\delta_H + \delta_T)}  P(q) \frac{1}{q^2}
15
16The form factor $P(q)$ is
17
18.. math::
19
20    P(q) = \frac{4}{q^2}
21        \left\lbrace
22            \Delta \rho_H
23            \left[\sin[q(\delta_H + \delta_T)\ - \sin(q\delta_T)\right]
24            + \Delta\rho_T\sin(q\delta_T)
25        \right\rbrace^2
26
27where $\delta_T$ is *length_tail*, $\delta_H$ is *length_head*,
28$\Delta\rho_H$ is the head contrast (*sld_head* $-$ *sld_solvent*),
29and $\Delta\rho_T$ is tail contrast (*sld* $-$ *sld_solvent*).
30
31The total thickness of the lamellar sheet is $\delta_H + \delta_T + \delta_T + \delta_H$.
32Note that in a non aqueous solvent the chemical "head" group may be the
33"Tail region" and vice-versa.
34
35The 2D scattering intensity is calculated in the same way as 1D, where
36the $q$ vector is defined as
37
38.. math:: q = \sqrt{q_x^2 + q_y^2}
39
40
41References
42----------
43
44.. [#] F Nallet, R Laversanne, and D Roux, *J. Phys. II France*, 3, (1993) 487-502
45.. [#] J Berghausen, J Zipfel, P Lindner, W Richtering, *J. Phys. Chem. B*, 105, (2001) 11081-11088
46
47Source
48------
49
50`lamellar_hg.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/lamellar_hg.py>`_
51
52Authorship and Verification
53----------------------------
54
55* **Author:**
56* **Last Modified by:**
57* **Last Reviewed by:** S King and P Butler **Date** April 17, 2014
58* **Source added by :** Steve King **Date:** March 25, 2019
59"""
60
61import numpy as np
62from numpy import inf
63
64name = "lamellar_hg"
65title = "Random lamellar phase with Head and Tail Groups"
66description = """\
67    [Random lamellar phase with Head and Tail Groups]
68        I(q)= 2*pi*P(q)/(2(H+T)*q^(2)), where
69        P(q)= see manual
70        layer thickness =(H+T+T+H) = 2(Head+Tail)
71        sld = Tail scattering length density
72        sld_head = Head scattering length density
73        sld_solvent = solvent scattering length density
74        background = incoherent background
75        scale = scale factor
76"""
77category = "shape:lamellae"
78
79# pylint: disable=bad-whitespace, line-too-long
80#             ["name", "units", default, [lower, upper], "type","description"],
81parameters = [["length_tail", "Ang",       15,   [0, inf],  "volume",  "Tail thickness ( total = H+T+T+H)"],
82              ["length_head", "Ang",       10,   [0, inf],  "volume",  "Head thickness"],
83              ["sld",         "1e-6/Ang^2", 0.4, [-inf,inf], "sld",    "Tail scattering length density"],
84              ["sld_head",    "1e-6/Ang^2", 3.0, [-inf,inf], "sld",    "Head scattering length density"],
85              ["sld_solvent", "1e-6/Ang^2", 6,   [-inf,inf], "sld",    "Solvent scattering length density"]]
86# pylint: enable=bad-whitespace, line-too-long
87
88# No volume normalization despite having a volume parameter
89# This should perhaps be volume normalized?
90form_volume = """
91    return 1.0;
92    """
93
94Iq = """
95    const double qsq = q*q;
96    const double drh = sld_head - sld_solvent;
97    const double drt = sld - sld_solvent;    //correction 13FEB06 by L.Porcar
98    const double qT = q*length_tail;
99    double Pq, inten;
100    Pq = drh*(sin(q*(length_head+length_tail))-sin(qT)) + drt*sin(qT);
101    Pq *= Pq;
102    Pq *= 4.0/(qsq);
103
104    inten = 2.0e-4*M_PI*Pq/qsq;
105
106    // normalize by the bilayer thickness
107    inten /= 2.0*(length_head+length_tail);
108
109    return inten;
110    """
111
112def random():
113    """Return a random parameter set for the model."""
114    thickness = 10**np.random.uniform(1, 4)
115    length_head = thickness * np.random.uniform(0, 1)
116    length_tail = thickness - length_head
117    pars = dict(
118        length_head=length_head,
119        length_tail=length_tail,
120    )
121    return pars
122
123demo = dict(scale=1, background=0,
124            length_tail=15, length_head=10,
125            sld=0.4, sld_head=3.0, sld_solvent=6.0,
126            length_tail_pd=0.2, length_tail_pd_n=40,
127            length_head_pd=0.01, length_head_pd_n=40)
128
129#
130tests = [
131    [{'scale': 1.0, 'background': 0.0, 'length_tail': 15.0, 'length_head': 10.0,
132      'sld': 0.4, 'sld_head': 3.0, 'sld_solvent': 6.0},
133     [0.001], [653143.9209]],
134]
135# ADDED by: RKH  ON: 18Mar2016  converted from sasview previously, now renaming everything & sorting the docs
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