Changes in sasmodels/models/ellipsoid.py [3b571ae:925ad6e] in sasmodels

File:

• sasmodels/models/ellipsoid.py (modified) (4 diffs)

sasmodels/models/ellipsoid.py

@@ -18 +18 @@
 .. math::
 
-    F(q,\alpha) = \Delta \rho V \frac{3(\sin qr  - qr \cos qr)}{(qr)^3}
+    F(q,\alpha) = \frac{3 \Delta \rho V (\sin[qr(R_p,R_e,\alpha)]
+                - \cos[qr(R_p,R_e,\alpha)])}
+                {[qr(R_p,R_e,\alpha)]^3}
 
-for
+and
 
 .. math::
 
-    r = \left[ R_e^2 \sin^2 \alpha + R_p^2 \cos^2 \alpha \right]^{1/2}
+    r(R_p,R_e,\alpha) = \left[ R_e^2 \sin^2 \alpha
+        + R_p^2 \cos^2 \alpha \right]^{1/2}
 
 
 $\alpha$ is the angle between the axis of the ellipsoid and $\vec q$,
-$V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid, $R_p$ is the polar
-radius along the rotational axis of the ellipsoid, $R_e$ is the equatorial
-radius perpendicular to the rotational axis of the ellipsoid and
-$\Delta \rho$ (contrast) is the scattering length density difference between
-the scatterer and the solvent.
+$V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid , $R_p$ is the polar radius along the
+rotational axis of the ellipsoid, $R_e$ is the equatorial radius perpendicular
+to the rotational axis of the ellipsoid and $\Delta \rho$ (contrast) is the
+scattering length density difference between the scatterer and the solvent.
 
-For randomly oriented particles use the orientational average,
+For randomly oriented particles:
 
 .. math::
 
-   \langle F^2(q) \rangle = \int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)\,d\alpha}
+   F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha}
 
-
-computed via substitution of $u=\sin(\alpha)$, $du=\cos(\alpha)\,d\alpha$ as
-
-.. math::
-
-    \langle F^2(q) \rangle = \int_0^1{F^2(q, u)\,du}
-
-with
-
-.. math::
-
-    r = R_e \left[ 1 + u^2\left(R_p^2/R_e^2 - 1\right)\right]^{1/2}
 
 To provide easy access to the orientation of the ellipsoid, we define
@@ -58 +48 @@
 :ref:`cylinder orientation figure <cylinder-angle-definition>`.
 For the ellipsoid, $\theta$ is the angle between the rotational axis
-and the $z$ -axis in the $xz$ plane followed by a rotation by $\phi$
-in the $xy$ plane.
+and the $z$ -axis.
 
 NB: The 2nd virial coefficient of the solid ellipsoid is calculated based
@@ -101 +90 @@
 than 500.
 
-Model was also tested against the triaxial ellipsoid model with equal major
-and minor equatorial radii.  It is also consistent with the cyclinder model
-with polar radius equal to length and equatorial radius equal to radius.
-
 References
 ----------
@@ -111 +96 @@
 *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*,
 Plenum Press, New York, 1987.
-
-Authorship and Verification
-----------------------------
-
-* **Author:** NIST IGOR/DANSE **Date:** pre 2010
-* **Converted to sasmodels by:** Helen Park **Date:** July 9, 2014
-* **Last Modified by:** Paul Kienzle **Date:** March 22, 2017
 """