source: sasmodels/sasmodels/models/hollow_cylinder.py @ d86f0fc

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since d86f0fc was 2d81cfe, checked in by Paul Kienzle <pkienzle@…>, 6 years ago

lint

  • Property mode set to 100644
File size: 5.4 KB
Line 
1r"""
2This model provides the form factor, $P(q)$, for a monodisperse hollow right
3angle circular cylinder (rigid tube) where the form factor is normalized by the
4volume of the tube (i.e. not by the external volume).
5
6.. math::
7
8    P(q) = \text{scale} \left<F^2\right>/V_\text{shell} + \text{background}
9
10where the averaging $\left<\ldots\right>$ is applied only for the 1D calculation.
11
12The inside and outside of the hollow cylinder are assumed have the same SLD.
13
14Definition
15----------
16
17The 1D scattering intensity is calculated in the following way (Guinier, 1955)
18
19.. math::
20
21    P(q)           &= (\text{scale})V_\text{shell}\Delta\rho^2
22            \int_0^{1}\Psi^2
23            \left[q_z, R_\text{outer}(1-x^2)^{1/2},
24                       R_\text{core}(1-x^2)^{1/2}\right]
25            \left[\frac{\sin(qHx)}{qHx}\right]^2 dx \\
26    \Psi[q,y,z]    &= \frac{1}{1-\gamma^2}
27            \left[ \Lambda(qy) - \gamma^2\Lambda(qz) \right] \\
28    \Lambda(a)     &= 2 J_1(a) / a \\
29    \gamma         &= R_\text{core} / R_\text{outer} \\
30    V_\text{shell} &= \pi \left(R_\text{outer}^2 - R_\text{core}^2 \right)L \\
31    J_1(x)         &= (\sin(x)-x\cdot \cos(x)) / x^2
32
33where *scale* is a scale factor, $H = L/2$ and $J_1$ is the 1st order
34Bessel function.
35
36**NB**: The 2nd virial coefficient of the cylinder is calculated
37based on the outer radius and full length, which give an the effective radius
38for structure factor $S(q)$ when $P(q) \cdot S(q)$ is applied.
39
40In the parameters,the *radius* is $R_\text{core}$ while *thickness*
41is $R_\text{outer} - R_\text{core}$.
42
43To provide easy access to the orientation of the core-shell cylinder, we define
44the axis of the cylinder using two angles $\theta$ and $\phi$
45(see :ref:`cylinder model <cylinder-angle-definition>`).
46
47References
48----------
49
50L A Feigin and D I Svergun, *Structure Analysis by Small-Angle X-Ray and
51Neutron Scattering*, Plenum Press, New York, (1987)
52
53Authorship and Verification
54----------------------------
55
56* **Author:** NIST IGOR/DANSE **Date:** pre 2010
57* **Last Modified by:** Richard Heenan **Date:** October 06, 2016
58   (reparametrised to use thickness, not outer radius)
59* **Last Reviewed by:** Richard Heenan **Date:** October 06, 2016
60"""
61
62import numpy as np
63from numpy import pi, inf, sin, cos
64
65name = "hollow_cylinder"
66title = ""
67description = """
68P(q) = scale*<f*f>/Vol + background, where f is the scattering amplitude.
69radius = the radius of core
70thickness = the thickness of shell
71length = the total length of the cylinder
72sld = SLD of the shell
73sld_solvent = SLD of the solvent
74background = incoherent background
75"""
76category = "shape:cylinder"
77# pylint: disable=bad-whitespace, line-too-long
78#   ["name", "units", default, [lower, upper], "type","description"],
79parameters = [
80    ["radius",      "Ang",     20.0, [0, inf],    "volume",      "Cylinder core radius"],
81    ["thickness",   "Ang",     10.0, [0, inf],    "volume",      "Cylinder wall thickness"],
82    ["length",      "Ang",    400.0, [0, inf],    "volume",      "Cylinder total length"],
83    ["sld",         "1e-6/Ang^2",  6.3, [-inf, inf], "sld",         "Cylinder sld"],
84    ["sld_solvent", "1e-6/Ang^2",  1,   [-inf, inf], "sld",         "Solvent sld"],
85    ["theta",       "degrees", 90,   [-360, 360], "orientation", "Cylinder axis to beam angle"],
86    ["phi",         "degrees",  0,   [-360, 360], "orientation", "Rotation about beam"],
87    ]
88# pylint: enable=bad-whitespace, line-too-long
89
90source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "hollow_cylinder.c"]
91
92# pylint: disable=W0613
93def ER(radius, thickness, length):
94    """
95    :param radius:      Cylinder core radius
96    :param thickness:   Cylinder wall thickness
97    :param length:      Cylinder length
98    :return:            Effective radius
99    """
100    router = radius + thickness
101    if router == 0 or length == 0:
102        return 0.0
103    len1 = router
104    len2 = length/2.0
105    term1 = len1*len1*2.0*len2/2.0
106    term2 = 1.0 + (len2/len1)*(1.0 + 1/len2/2.0)*(1.0 + pi*len1/len2/2.0)
107    ddd = 3.0*term1*term2
108    diam = pow(ddd, (1.0/3.0))
109    return diam
110
111def VR(radius, thickness, length):
112    """
113    :param radius:      Cylinder radius
114    :param thickness:   Cylinder wall thickness
115    :param length:      Cylinder length
116    :return:            Volf ratio for P(q)*S(q)
117    """
118    router = radius + thickness
119    vol_core = pi*radius*radius*length
120    vol_total = pi*router*router*length
121    vol_shell = vol_total - vol_core
122    return vol_shell, vol_total
123
124def random():
125    length = 10**np.random.uniform(1, 4.7)
126    outer_radius = 10**np.random.uniform(1, 4.7)
127    # Use a distribution with a preference for thin shell or thin core
128    # Avoid core,shell radii < 1
129    thickness = np.random.beta(0.5, 0.5)*(outer_radius-2) + 1
130    radius = outer_radius - thickness
131    pars = dict(
132        length=length,
133        radius=radius,
134        thickness=thickness,
135    )
136    return pars
137
138# parameters for demo
139demo = dict(scale=1.0, background=0.0, length=400.0, radius=20.0,
140            thickness=10, sld=6.3, sld_solvent=1, theta=90, phi=0,
141            thickness_pd=0.2, thickness_pd_n=9,
142            length_pd=.2, length_pd_n=10,
143            radius_pd=.2, radius_pd_n=9,
144            theta_pd=10, theta_pd_n=5,
145           )
146q = 0.1
147# april 6 2017, rkh added a 2d unit test, assume correct!
148qx = q*cos(pi/6.0)
149qy = q*sin(pi/6.0)
150# Parameters for unit tests
151tests = [
152    [{}, 0.00005, 1764.926],
153    [{}, 'VR', 1.8],
154    [{}, 0.001, 1756.76],
155    [{}, (qx, qy), 2.36885476192],
156]
157del qx, qy  # not necessary to delete, but cleaner
Note: See TracBrowser for help on using the repository browser.