source: sasmodels/sasmodels/models/hollow_rectangular_prism_thin_walls.py @ a807206

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Last change on this file since a807206 was a807206, checked in by butler, 7 years ago

updating more parameter names addressing #649

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1# rectangular_prism model
2# Note: model title and parameter table are inserted automatically
3r"""
4
5This model provides the form factor, *P(q)*, for a hollow rectangular
6prism with infinitely thin walls. It computes only the 1D scattering, not the 2D.
7
8
9Definition
10----------
11
12The 1D scattering intensity for this model is calculated according to the
13equations given by Nayuk and Huber (Nayuk, 2012).
14
15Assuming a hollow parallelepiped with infinitely thin walls, edge lengths
16:math:`A \le B \le C` and presenting an orientation with respect to the
17scattering vector given by |theta| and |phi|, where |theta| is the angle
18between the *z* axis and the longest axis of the parallelepiped *C*, and
19|phi| is the angle between the scattering vector (lying in the *xy* plane)
20and the *y* axis, the form factor is given by
21
22.. math::
23  P(q) =  \frac{1}{V^2} \frac{2}{\pi} \int_0^{\frac{\pi}{2}}
24  \int_0^{\frac{\pi}{2}} [A_L(q)+A_T(q)]^2 \sin\theta d\theta d\phi
25
26where
27
28.. math::
29  V = 2AB + 2AC + 2BC
30
31.. math::
32  A_L(q) =  8 \times \frac{ \sin \bigl( q \frac{A}{2} \sin\phi \sin\theta \bigr)
33                              \sin \bigl( q \frac{B}{2} \cos\phi \sin\theta \bigr)
34                              \cos \bigl( q \frac{C}{2} \cos\theta \bigr) }
35                            {q^2 \, \sin^2\theta \, \sin\phi \cos\phi}
36
37.. math::
38  A_T(q) =  A_F(q) \times \frac{2 \, \sin \bigl( q \frac{C}{2} \cos\theta \bigr)}{q \, \cos\theta}
39
40and
41
42.. math::
43  A_F(q) =  4 \frac{ \cos \bigl( q \frac{A}{2} \sin\phi \sin\theta \bigr)
44                       \sin \bigl( q \frac{B}{2} \cos\phi \sin\theta \bigr) }
45                     {q \, \cos\phi \, \sin\theta} +
46              4 \frac{ \sin \bigl( q \frac{A}{2} \sin\phi \sin\theta \bigr)
47                       \cos \bigl( q \frac{B}{2} \cos\phi \sin\theta \bigr) }
48                     {q \, \sin\phi \, \sin\theta}
49
50The 1D scattering intensity is then calculated as
51
52.. math::
53  I(q) = \mbox{scale} \times V \times (\rho_{\mbox{p}} - \rho_{\mbox{solvent}})^2 \times P(q)
54
55where *V* is the volume of the rectangular prism, :math:`\rho_{\mbox{p}}`
56is the scattering length of the parallelepiped, :math:`\rho_{\mbox{solvent}}`
57is the scattering length of the solvent, and (if the data are in absolute
58units) *scale* represents the volume fraction (which is unitless).
59
60**The 2D scattering intensity is not computed by this model.**
61
62
63Validation
64----------
65
66Validation of the code was conducted  by qualitatively comparing the output
67of the 1D model to the curves shown in (Nayuk, 2012).
68
69
70References
71----------
72
73R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854
74
75"""
76
77from numpy import pi, inf, sqrt
78
79name = "hollow_rectangular_prism_thin_walls"
80title = "Hollow rectangular parallelepiped with thin walls."
81description = """
82    I(q)= scale*V*(sld - sld_solvent)^2*P(q)+background
83        with P(q) being the form factor corresponding to a hollow rectangular
84        parallelepiped with infinitely thin walls.
85"""
86category = "shape:parallelepiped"
87
88#             ["name", "units", default, [lower, upper], "type","description"],
89parameters = [["sld", "1e-6/Ang^2", 6.3, [-inf, inf], "sld",
90               "Parallelepiped scattering length density"],
91              ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld",
92               "Solvent scattering length density"],
93              ["length_a", "Ang", 35, [0, inf], "volume",
94               "Shorter side of the parallelepiped"],
95              ["b2a_ratio", "Ang", 1, [0, inf], "volume",
96               "Ratio sides b/a"],
97              ["c2a_ratio", "Ang", 1, [0, inf], "volume",
98               "Ratio sides c/a"],
99             ]
100
101source = ["lib/gauss76.c", "hollow_rectangular_prism_thin_walls.c"]
102
103def ER(length_a, b2a_ratio, c2a_ratio):
104    """
105        Return equivalent radius (ER)
106    """
107    b_side = length_a * b2a_ratio
108    c_side = length_a * c2a_ratio
109
110    # surface average radius (rough approximation)
111    surf_rad = sqrt(length_a * b_side / pi)
112
113    ddd = 0.75 * surf_rad * (2 * surf_rad * c_side + (c_side + surf_rad) * (c_side + pi * surf_rad))
114    return 0.5 * (ddd) ** (1. / 3.)
115
116def VR(length_a, b2a_ratio, c2a_ratio):
117    """
118        Return shell volume and total volume
119    """
120    b_side = length_a * b2a_ratio
121    c_side = length_a * c2a_ratio
122    vol_total = length_a * b_side * c_side
123    vol_shell = 2.0 * (length_a*b_side + length_a*c_side + b_side*c_side)
124    return vol_shell, vol_total
125
126
127# parameters for demo
128demo = dict(scale=1, background=0,
129            sld=6.3e-6, sld_solvent=1.0e-6,
130            length_a=35, b2a_ratio=1, c2a_ratio=1,
131            length_a_pd=0.1, length_a_pd_n=10,
132            b2a_ratio_pd=0.1, b2a_ratio_pd_n=1,
133            c2a_ratio_pd=0.1, c2a_ratio_pd_n=1)
134
135tests = [[{}, 0.2, 0.837719188592],
136         [{}, [0.2], [0.837719188592]],
137        ]
138
139
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