Changeset 34a9e4e in sasmodels
- Timestamp:
- Apr 11, 2017 6:11:36 AM (8 years ago)
- Branches:
- master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
- Children:
- 9ed43f4
- Parents:
- e645373
- Location:
- sasmodels/models
- Files:
-
- 2 edited
-
parallelepiped.py (modified) (1 diff)
-
triaxial_ellipsoid.py (modified) (4 diffs)
Legend:
- Unmodified
- Added
- Removed
-
sasmodels/models/parallelepiped.py
r9802ab3 r34a9e4e 22 22 .. note:: 23 23 24 The edge of the solid used to have to satisfy the condition that $A < B < C$. 25 After some improvements to the effective radius calculation, used with 26 an S(Q), it is beleived that this is no longer the case. 24 The three dimensions of the parallelepiped (strictly here a cuboid) may be given in 25 $any$ size order. To avoid multiple fit solutions, especially 26 with Monte-Carlo fit methods, it may be advisable to restrict their ranges. There may 27 be a number of closely similar "best fits", so some trial and error, or fixing of some 28 dimensions at expected values, may help. 27 29 28 30 The 1D scattering intensity $I(q)$ is calculated as: -
sasmodels/models/triaxial_ellipsoid.py
re645373 r34a9e4e 66 66 r^2 &= b^2(p_a \sin^2(\phi)(1 - u^2) + 1 + p_c u^2) 67 67 68 Though for convenience we describe the three radii of the ellipsoid as equatorial 69 and polar, they may be given in $any$ size order. To avoid multiple solutions, especially 70 with Monte-Carlo fit methods, it may be advisable to restrict their ranges. For typical 71 small angle diffraction situations there may be a number of closely similar "best fits", 72 so some trial and error, or fixing of some radii at expected values, may help. 73 68 74 To provide easy access to the orientation of the triaxial ellipsoid, 69 75 we define the axis of the cylinder using the angles $\theta$, $\phi$ 70 and $\psi$. These angles are defined analogously to the elliptical_cylinder below 76 and $\psi$. These angles are defined analogously to the elliptical_cylinder below, note that 77 angle $\phi$ is now NOT the same as in the equations above. 71 78 72 79 .. figure:: img/elliptical_cylinder_angle_definition.png 73 80 74 Definition of angles for oriented triaxial ellipsoid, where radii shown 75 here are $a < b << c$ and angle $\Psi$ is a rotation around the axis 76 of the particle. 81 Definition of angles for oriented triaxial ellipsoid, where radii are for illustration here 82 $a < b << c$ and angle $\Psi$ is a rotation around the axis of the particle. 77 83 78 84 For oriented ellipsoids the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data, … … 83 89 .. figure:: img/triaxial_ellipsoid_angle_projection.png 84 90 85 Some example angles for orientedellipsoid.91 Some examples for an oriented triaxial ellipsoid. 86 92 87 93 The radius-of-gyration for this system is $R_g^2 = (R_a R_b R_c)^2/5$. … … 92 98 93 99 NB: The 2nd virial coefficient of the triaxial solid ellipsoid is 94 calculated based on the polar radius $R_p = R_c$ and equatorial 95 radius $R_e = \sqrt{R_a R_b}$, and used as the effective radius for 100 calculated after sorting the three radii to give the most appropriate 101 prolate or oblate form, from the new polar radius $R_p = R_c$ and effective equatorial 102 radius, $R_e = \sqrt{R_a R_b}$, to then be used as the effective radius for 96 103 $S(q)$ when $P(q) \cdot S(q)$ is applied. 97 104 … … 125 132 126 133 description = """ 127 Note - fitting ensure that the inequality ra<rb<rc is not 128 violated. Otherwise the calculation may not be correct. 134 Triaxial ellipsoid - see main documentation. 129 135 """ 130 136 category = "shape:ellipsoid"
Note: See TracChangeset
for help on using the changeset viewer.
