source: sasmodels/sasmodels/models/surface_fractal.py @ 33875e3

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Last change on this file since 33875e3 was 33875e3, checked in by Paul Kienzle <pkienzle@…>, 8 years ago

surface_fractal: set the default surface dimension limits to the valid range

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File size: 3.3 KB
Line 
1r"""
2This model calculates the scattering from fractal-like aggregates based
3on the Mildner reference.
4
5Definition
6----------
7
8The scattering intensity $I(q)$ is calculated as
9
10.. math::
11
12    I(q) = scale \times P(q)S(q) + background
13
14.. math::
15
16    P(q) = F(qR)^2
17
18.. math::
19
20    F(x) = \frac{3\left[sin(x)-xcos(x)\right]}{x^3}
21
22.. math::
23
24    S(q) = \frac{\Gamma(5-D_S)\zeta^{5-D_S}}{\left[1+(q\zeta)^2
25    \right]^{(5-D_S)/2}}
26    \frac{sin\left[(D_S - 5) tan^{-1}(q\zeta) \right]}{q}
27
28.. math::
29
30    scale = scale\_factor \times NV^2(\rho_{particle} - \rho_{solvent})^2
31
32.. math::
33
34    V = \frac{4}{3}\pi R^3
35
36where $R$ is the radius of the building block, $D_S$ is the **surface** fractal
37dimension,| \zeta\|  is the cut-off length, $\rho_{solvent}$ is the scattering
38length density of the solvent,
39and $\rho_{particle}$ is the scattering length density of particles.
40
41.. note::
42    The surface fractal dimension $D_s$ is only valid if $1<surface\_dim<3$.
43    It is also only valid over a limited $q$ range (see the reference for
44    details)
45
46
47References
48----------
49
50D Mildner and P Hall, *J. Phys. D: Appl. Phys.*, 19 (1986) 1535-1545
51
52"""
53
54from numpy import inf
55
56name = "surface_fractal"
57title = "Fractal-like aggregates based on the Mildner reference"
58description = """\
59    [The scattering intensity  I(x) = scale*P(x)*S(x) + background, where
60        scale = scale_factor  * V * delta^(2)
61        p(x) = F(x*radius)^(2)
62        F(x) = 3*[sin(x)-x cos(x)]/x**3
63        S(x) = [(gamma(5-Ds)*colength^(5-Ds)*[1+(x^2*colength^2)]^((Ds-5)/2)
64             * sin[(Ds-5)*arctan(x*colength)])/x]
65        where
66        delta        =  sldParticle -sldSolv.
67        radius       =  Particle radius
68        surface_dim  =  Surface fractal dimension (Ds)
69        co_length    =  Cut-off length
70        background   =  background
71
72        Ref.   :Mildner, Hall,J Phys D Appl Phys(1986), 19, 1535-1545
73        Note I : This model is valid for 1<surface_dim<3 with limited q range.
74        Note II: This model is not in absolute scale.
75"""
76category = "shape-independent"
77
78# pylint: disable=bad-whitespace, line-too-long
79#             ["name", "units", default, [lower, upper], "type","description"],
80parameters = [["radius",        "Ang", 10.0, [0, inf],   "",
81               "Particle radius"],
82              ["surface_dim",   "",    2.0,  [1, 3],   "",
83               "Surface fractal dimension"],
84              ["cutoff_length", "Ang", 500., [0.0, inf], "",
85               "Cut-off Length"],
86             ]
87# pylint: enable=bad-whitespace, line-too-long
88
89source = ["lib/sph_j1c.c", "lib/sas_gamma.c", "surface_fractal.c"]
90
91demo = dict(scale=1, background=0,
92            radius=10, surface_dim=2.0, cutoff_length=500)
93
94tests = [
95    # Accuracy tests based on content in test/utest_other_models.py
96    [{'radius': 10.0,
97      'surface_dim': 2.0,
98      'cutoff_length': 500.0,
99     }, 0.05, 301428.66016],
100
101    # Additional tests with larger range of parameters
102    [{'radius': 1.0,
103      'surface_dim': 1.0,
104      'cutoff_length': 10.0,
105     }, 0.332070182643, 1125.00421004],
106
107    [{'radius': 3.5,
108      'surface_dim': 0.1,
109      'cutoff_length': 30.0,
110      'background': 0.01,
111     }, 5.0, 0.00999998891322],
112
113    [{'radius': 3.0,
114      'surface_dim': 1.0,
115      'cutoff_length': 33.0,
116      'scale': 0.1,
117     }, 0.51, 2.50120147004],
118    ]
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