source: sasmodels/sasmodels/models/core_multi_shell.py @ 0507e09

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 0507e09 was 0507e09, checked in by smk78, 7 months ago

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

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1r"""
2Definition
3----------
4
5This model is a trivial extension of the CoreShell function to a larger number
6of shells. The scattering length density profile for the default sld values
7(w/ 4 shells).
8
9.. figure:: img/core_multi_shell_sld_default_profile.jpg
10
11    SLD profile of the core_multi_shell object from the center of sphere out
12    for the default SLDs.*
13
14The 2D scattering intensity is the same as $P(q)$ above, regardless of the
15orientation of the $\vec q$ vector which is defined as
16
17.. math::
18
19    q = \sqrt{q_x^2 + q_y^2}
20
21.. note:: **Be careful!** The SLDs and scale can be highly correlated. Hold as
22         many of these parameters fixed as possible.
23
24.. note:: The outer most radius (= *radius* + *thickness*) is used as the
25          effective radius for $S(Q)$ when $P(Q)*S(Q)$ is applied.
26
27For information about polarised and magnetic scattering, see
28the :ref:`magnetism` documentation.
29
30Our model uses the form factor calculations implemented in a c-library provided
31by the NIST Center for Neutron Research (Kline, 2006) [#kline]_.
32
33References
34----------
35
36.. [#] See the :ref:`core-shell-sphere` model documentation.
37.. [#kline] S R Kline, *J Appl. Cryst.*, 39 (2006) 895
38.. [#] L A Feigin and D I Svergun, *Structure Analysis by Small-Angle X-Ray and
39   Neutron Scattering*, Plenum Press, New York, 1987.
40
41Source
42------
43
44`core_multi_shell.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/core_multi_shell.py>`_
45
46`core_multi_shell.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/core_multi_shell.c>`_
47
48Authorship and Verification
49----------------------------
50
51* **Author:** NIST IGOR/DANSE **Date:** pre 2010
52* **Last Modified by:** Paul Kienzle **Date:** September 12, 2016
53* **Last Reviewed by:** Paul Kienzle **Date:** September 12, 2016
54* **Source added by :** Steve King **Date:** March 25, 2019
55"""
56from __future__ import division
57
58import numpy as np
59from numpy import inf
60
61name = "core_multi_shell"
62title = "This model provides the scattering from a spherical core with 1 to 4 \
63 concentric shell structures. The SLDs of the core and each shell are \
64 individually specified."
65
66description = """\
67Form factor for a core muti-shell (up to 4) sphere normalized by the volume.
68Each shell can have a unique thickness and sld.
69
70        background:background,
71        rad_core0: radius of sphere(core)
72        thick_shell#:the thickness of the shell#
73        sld_core0: the SLD of the sphere
74        sld_solv: the SLD of the solvent
75        sld_shell: the SLD of the shell#
76        A_shell#: the coefficient in the exponential function
77
78
79    scale: 1.0 if data is on absolute scale
80    volfraction: volume fraction of spheres
81    radius: the radius of the core
82    sld: the SLD of the core
83    thick_shelli: the thickness of the i'th shell from the core
84    sld_shelli: the SLD of the i'th shell from the core
85    sld_solvent: the SLD of the solvent
86    background: incoherent background
87
88"""
89
90category = "shape:sphere"
91
92
93#             ["name", "units", default, [lower, upper], "type","description"],
94parameters = [["sld_core", "1e-6/Ang^2", 1.0, [-inf, inf], "sld",
95               "Core scattering length density"],
96              ["radius", "Ang", 200., [0, inf], "volume",
97               "Radius of the core"],
98              ["sld_solvent", "1e-6/Ang^2", 6.4, [-inf, inf], "sld",
99               "Solvent scattering length density"],
100              ["n", "", 1, [0, 10], "volume",
101               "number of shells"],
102              ["sld[n]", "1e-6/Ang^2", 1.7, [-inf, inf], "sld",
103               "scattering length density of shell k"],
104              ["thickness[n]", "Ang", 40., [0, inf], "volume",
105               "Thickness of shell k"],
106             ]
107
108source = ["lib/sas_3j1x_x.c", "core_multi_shell.c"]
109have_Fq = True
110effective_radius_type = ["outer radius", "core radius"]
111
112def random():
113    """Return a random parameter set for the model."""
114    num_shells = np.minimum(np.random.poisson(3)+1, 10)
115    total_radius = 10**np.random.uniform(1.7, 4)
116    thickness = np.random.exponential(size=num_shells+1)
117    thickness *= total_radius/np.sum(thickness)
118    pars = dict(
119        #background=0,
120        n=num_shells,
121        radius=thickness[0],
122    )
123    for k, v in enumerate(thickness[1:]):
124        pars['thickness%d'%(k+1)] = v
125    return pars
126
127def profile(sld_core, radius, sld_solvent, n, sld, thickness):
128    """
129    Returns the SLD profile *r* (Ang), and *rho* (1e-6/Ang^2).
130    """
131    n = int(n+0.5)
132    z = []
133    rho = []
134
135    # add in the core
136    z.append(0)
137    rho.append(sld_core)
138    z.append(radius)
139    rho.append(sld_core)
140
141    # add in the shells
142    for k in range(int(n)):
143        # Left side of each shells
144        z.append(z[-1])
145        rho.append(sld[k])
146        z.append(z[-1] + thickness[k])
147        rho.append(sld[k])
148    # add in the solvent
149    z.append(z[-1])
150    rho.append(sld_solvent)
151    z.append(z[-1]*1.25)
152    rho.append(sld_solvent)
153
154    return np.asarray(z), np.asarray(rho)
155
156demo = dict(sld_core=6.4,
157            radius=60,
158            sld_solvent=6.4,
159            n=2,
160            sld=[2.0, 3.0],
161            thickness=20,
162            thickness1_pd=0.3,
163            thickness2_pd=0.3,
164            thickness1_pd_n=10,
165            thickness2_pd_n=10,
166           )
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