# Changeset 34a9e4e in sasmodels

Ignore:
Timestamp:
Apr 11, 2017 6:11:36 AM (16 months ago)
Branches:
master, ESS_GUI, beta_approx, costrafo411, cuda-test, doc_update, ticket-1084, ticket-1102-pinhole, ticket-1105_mass_surface_fractal, ticket-1112, ticket-608-user-defined-weights
Children:
9ed43f4
Parents:
e645373
Message:

more docs fixes

Location:
sasmodels/models
Files:
2 edited

### Legend:

Unmodified
 r9802ab3 .. note:: The edge of the solid used to have to satisfy the condition that $A < B < C$. After some improvements to the effective radius calculation, used with an S(Q), it is beleived that this is no longer the case. The three dimensions of the parallelepiped (strictly here a cuboid) may be given in $any$ size order. To avoid multiple fit solutions, especially with Monte-Carlo fit methods, it may be advisable to restrict their ranges. There may be a number of closely similar "best fits", so some trial and error, or fixing of some dimensions at expected values, may help. The 1D scattering intensity $I(q)$ is calculated as:
 re645373 r^2 &= b^2(p_a \sin^2(\phi)(1 - u^2) + 1 + p_c u^2) Though for convenience we describe the three radii of the ellipsoid as equatorial and polar, they may be given in $any$ size order. To avoid multiple solutions, especially with Monte-Carlo fit methods, it may be advisable to restrict their ranges. For typical small angle diffraction situations there may be a number of closely similar "best fits", so some trial and error, or fixing of some radii at expected values, may help. To provide easy access to the orientation of the triaxial ellipsoid, we define the axis of the cylinder using the angles $\theta$, $\phi$ and $\psi$. These angles are defined analogously to the elliptical_cylinder below and $\psi$. These angles are defined analogously to the elliptical_cylinder below, note that angle $\phi$ is now NOT the same as in the equations above. .. figure:: img/elliptical_cylinder_angle_definition.png Definition of angles for oriented triaxial ellipsoid, where radii shown here are $a < b << c$ and angle $\Psi$ is a rotation around the axis of the particle. Definition of angles for oriented triaxial ellipsoid, where radii are for illustration here $a < b << c$ and angle $\Psi$ is a rotation around the axis of the particle. For oriented ellipsoids the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data, .. figure:: img/triaxial_ellipsoid_angle_projection.png Some example angles for oriented ellipsoid. Some examples for an oriented triaxial ellipsoid. The radius-of-gyration for this system is  $R_g^2 = (R_a R_b R_c)^2/5$. NB: The 2nd virial coefficient of the triaxial solid ellipsoid is calculated based on the polar radius $R_p = R_c$ and equatorial radius $R_e = \sqrt{R_a R_b}$, and used as the effective radius for calculated after sorting the three radii to give the most appropriate prolate or oblate form, from the new polar radius $R_p = R_c$ and effective equatorial radius,  $R_e = \sqrt{R_a R_b}$, to then be used as the effective radius for $S(q)$ when $P(q) \cdot S(q)$ is applied. description = """ Note - fitting ensure that the inequality ra