-                      r9802ab3
+                      r8f04da4
 core-shell scattering length density profile. Thus this is a variation
 of the core-shell bicelle model, but with an elliptical cylinder for the core.
 Outer shells on the rims and flat ends may be of different thicknesses and
+Outer shells on the rims and flat ends may be of different thicknesses and
 scattering length densities. The form factor is normalized by the total particle volume.
 …
 .. figure:: img/core_shell_bicelle_parameters.png
    Cross section of model used here. Users will have
    to decide how to distribute "heads" and "tails" between the rim, face
+   Cross section of model used here. Users will have
+   to decide how to distribute "heads" and "tails" between the rim, face
    and core regions in order to estimate appropriate starting parameters.
 …
 .. math::
     \rho(r) =
       \begin{cases}
+    \rho(r) =
+      \begin{cases}
       &\rho_c \text{ for } 0 \lt r \lt R; -L \lt z\lt L \\[1.5ex]
       &\rho_f \text{ for } 0 \lt r \lt R; -(L+2t) \lt z\lt -L;
 …
 .. math::
         \begin{align}
     F(Q,\alpha,\psi) = &\bigg[
+        \begin{align}
+    F(Q,\alpha,\psi) = &\bigg[
     (\rho_c - \rho_f) V_c \frac{2J_1(QR'sin \alpha)}{QR'sin\alpha}\frac{sin(QLcos\alpha/2)}{Q(L/2)cos\alpha} \\
     &+(\rho_f - \rho_r) V_{c+f} \frac{2J_1(QR'sin\alpha)}{QR'sin\alpha}\frac{sin(Q(L/2+t_f)cos\alpha)}{Q(L/2+t_f)cos\alpha} \\
     &+(\rho_r - \rho_s) V_t \frac{2J_1(Q(R'+t_r)sin\alpha)}{Q(R'+t_r)sin\alpha}\frac{sin(Q(L/2+t_f)cos\alpha)}{Q(L/2+t_f)cos\alpha}
     \bigg]
     \end{align}
+    \end{align}
 where
 …
     R'=\frac{R}{\sqrt{2}}\sqrt{(1+X_{core}^{2}) + (1-X_{core}^{2})cos(\psi)}
 and $V_t = \pi.(R+t_r)(Xcore.R+t_r)^2.(L+2.t_f)$ is the total volume of the bicelle,
 $V_c = \pi.Xcore.R^2.L$ the volume of the core, $V_{c+f} = \pi.Xcore.R^2.(L+2.t_f)$
+and $V_t = \pi.(R+t_r)(Xcore.R+t_r)^2.(L+2.t_f)$ is the total volume of the bicelle,
+$V_c = \pi.Xcore.R^2.L$ the volume of the core, $V_{c+f} = \pi.Xcore.R^2.(L+2.t_f)$
 the volume of the core plus the volume of the faces, $R$ is the radius
 of the core, $Xcore$ is the axial ratio of the core, $L$ the length of the core,
 $t_f$ the thickness of the face, $t_r$ the thickness of the rim and $J_1$ the usual
 first order bessel function. The core has radii $R$ and $Xcore.R$ so is circular,
 as for the core_shell_bicelle model, for $Xcore$ =1. Note that you may need to
 limit the range of $Xcore$, especially if using the Monte-Carlo algorithm, as
+of the core, $Xcore$ is the axial ratio of the core, $L$ the length of the core,
+$t_f$ the thickness of the face, $t_r$ the thickness of the rim and $J_1$ the usual
+first order bessel function. The core has radii $R$ and $Xcore.R$ so is circular,
+as for the core_shell_bicelle model, for $Xcore$ =1. Note that you may need to
+limit the range of $Xcore$, especially if using the Monte-Carlo algorithm, as
 setting radius to $R/Xcore$ and axial ratio to $1/Xcore$ gives an equivalent solution!
 …
 bicelles is then given by integrating over all possible $\alpha$ and $\psi$.
 For oriented bicelles the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data,
+For oriented bicelles the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data,
 see the :ref:`elliptical-cylinder` model for further information.
 …
 .. figure:: img/elliptical_cylinder_angle_definition.png
     Definition of the angles for the oriented core_shell_bicelle_elliptical particles.
+    Definition of the angles for the oriented core_shell_bicelle_elliptical particles.
 …
 description = """
     core_shell_bicelle_elliptical
     Elliptical cylinder core, optional shell on the two flat faces, and shell of
     uniform thickness on its rim (extending around the end faces).
+    Elliptical cylinder core, optional shell on the two flat faces, and shell of
+    uniform thickness on its rim (extending around the end faces).
     Please see full documentation for equations and further details.
     Involves a double numerical integral around the ellipsoid diameter
 …
           "core_shell_bicelle_elliptical.c"]
+demo = dict(scale=1, background=0,
+            radius=30.0,
+            x_core=3.0,
+            thick_rim=8.0,
+            thick_face=14.0,
+            length=50.0,
+            sld_core=4.0,
+            sld_face=7.0,
+            sld_rim=1.0,
+            sld_solvent=6.0,
+            theta=90,
+            phi=0,
+            psi=0)
+def random():
+    import numpy as np
+    outer_major = 10**np.random.uniform(1, 4.7)
+    outer_minor = 10**np.random.uniform(1, 4.7)
+    # Use a distribution with a preference for thin shell or thin core,
+    # limited by the minimum radius. Avoid core,shell radii < 1
+    min_radius = min(outer_major, outer_minor)
+    thick_rim = np.random.beta(0.5, 0.5)*(min_radius-2) + 1
+    radius_major = outer_major - thick_rim
+    radius_minor = outer_minor - thick_rim
+    radius = radius_major
+    x_core = radius_minor/radius_major
+    outer_length = 10**np.random.uniform(1, 4.7)
+    # Caps should be a small percentage of the total length, but at least one
+    # angstrom long.  Since outer length >= 10, the following will suffice
+    thick_face = 10**np.random.uniform(-np.log10(outer_length), -1)*outer_length
+    length = outer_length - thick_face
+    pars = dict(
+        radius=radius,
+        x_core=x_core,
+        thick_rim=thick_rim,
+        thick_face=thick_face,
+        length=length
+    )
+    return pars
 q = 0.1

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Changeset 8f04da4 in sasmodels for sasmodels/models/core_shell_bicelle_elliptical.py

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sasmodels/models/core_shell_bicelle_elliptical.py

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