Changeset 110f69c in sasmodels for sasmodels/models

Timestamp:

Nov 28, 2017 11:17:57 AM (6 years ago)

Author:

Paul Kienzle <pkienzle@…>

Branches:

master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

e65c3ba

Parents:

167d0f1

Message:

lint

Location:

sasmodels/models

Files:

• core_shell_bicelle_elliptical_belt_rough.py (modified) (6 diffs)
• ellipsoid.py (modified) (2 diffs)
• stacked_disks.py (modified) (1 diff)

sasmodels/models/core_shell_bicelle_elliptical_belt_rough.py

@@ -6 +6 @@
 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.
-In this version the "rim" or "belt" does NOT extend the full length of the particle,
-but has the same length as the core.
-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.
+In this version the "rim" or "belt" does NOT extend the full length of
+the particle, but has the same length as the core. 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.
 This version includes an approximate "interfacial roughness".
 
@@ -15 +15 @@
 .. figure:: img/core_shell_bicelle_belt_geometry.png
 
-    Schematic cross-section of bicelle with belt. Note however that the model here
-    calculates for rectangular, not curved, rims as shown below.
+    Schematic cross-section of bicelle with belt. Note however that the model
+    here calculates for rectangular, not curved, rims as shown below.
 
 .. figure:: img/core_shell_bicelle_belt_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.
 
@@ -30 +30 @@
 .. math::
 
-    \rho(r) = 
-      \begin{cases} 
+    \rho(r) =
+      \begin{cases}
       &\rho_c \text{ for } 0 \lt r \lt R;   -L/2 \lt z\lt L/2 \\[1.5ex]
-      &\rho_f \text{ for } 0 \lt r \lt R;   -(L/2 +t_{face}) \lt z\lt -L/2;  
-      L/2 \lt z\lt (L/2+t_{face}) \\[1.5ex]
-      &\rho_r\text{ for } R \lt r \lt R+t_{rim}; -L/2 \lt z\lt L/2
+      &\rho_f \text{ for } 0 \lt r \lt R;   -(L/2 +t_\text{face}) \lt z\lt -L/2;
+      L/2 \lt z\lt (L/2+t_\text{face}) \\[1.5ex]
+      &\rho_r\text{ for } R \lt r \lt R+t_\text{rim}; -L/2 \lt z\lt L/2
       \end{cases}
 
 The form factor for the bicelle is calculated in cylindrical coordinates, where
-$\alpha$ is the angle between the $Q$ vector and the cylinder axis, and $\psi$ is the angle
-for the ellipsoidal cross section core, to give:
+$\alpha$ is the angle between the $Q$ vector and the cylinder axis, and $\psi$
+is the angle for the ellipsoidal cross section core, to give:
 
 .. math::
 
-    I(Q,\alpha,\psi) = \frac{\text{scale}}{V_t} \cdot
-        F(Q,\alpha, \psi)^2.sin(\alpha).exp\left \{ -\frac{1}{2}Q^2\sigma^2 \right \} + \text{background}
+    I(Q,\alpha,\psi) = \frac{\text{scale}}{V_t}
+        \cdot F(Q,\alpha, \psi)^2 \cdot \sin(\alpha)
+        \cdot\exp\left\{ -\frac{1}{2}Q^2\sigma^2 \right\} + \text{background}
 
-where a numerical integration of $F(Q,\alpha, \psi)^2.sin(\alpha)$ is carried out over \alpha and \psi for:
+where a numerical integration of $F(Q,\alpha, \psi)^2\sin(\alpha)$ is
+carried out over $\alpha$ and $\psi$ for:
 
 .. math::
 
-        \begin{align}    
-    F(Q,\alpha,\psi) = &\bigg[ 
-    (\rho_c -\rho_r - \rho_f + \rho_s) V_c \frac{2J_1(QR'sin \alpha)}{QR'sin\alpha}\frac{sin(QLcos\alpha/2)}{Q(L/2)cos\alpha} \\
-    &+(\rho_f - \rho_s) 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_{c+r} \frac{2J_1(Q(R'+t_r)sin\alpha)}{Q(R'+t_r)sin\alpha}\frac{sin(Q(L/2)cos\alpha)}{Q(L/2)cos\alpha}
+    F(Q,\alpha,\psi) = &\bigg[
+      (\rho_c -\rho_r - \rho_f + \rho_s) V_c
+      \frac{2J_1(QR'\sin \alpha)}{QR'\sin\alpha}
+      \frac{\sin(QL\cos\alpha/2)}{Q(L/2)\cos\alpha} \\
+    &+(\rho_f - \rho_s) 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_{c+r}
+      \frac{2J_1(Q(R'+t_r)\sin\alpha)}{Q(R'+t_r)\sin\alpha}
+      \frac{\sin(Q(L/2)\cos\alpha)}{Q(L/2)\cos\alpha}
     \bigg]
-    \end{align} 
 
 where
@@ -63 +69 @@
 .. math::
 
-    R'=\frac{R}{\sqrt{2}}\sqrt{(1+X_{core}^{2}) + (1-X_{core}^{2})cos(\psi)}
-    
-    
-and $V_t = \pi.(R+t_r)(Xcore.R+t_r).L + 2.\pi.Xcore.R^2.t_f$ 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, $V_{c+r} = \pi.(R+t_r)(Xcore.R+t_r),.L$ 
-the volume of the core plus the rim, $R$ 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 
-setting radius to $R/Xcore$ and axial ratio to $1/Xcore$ gives an equivalent solution!
+    R' = \frac{R}{\sqrt{2}}
+        \sqrt{(1+X_\text{core}^{2}) + (1-X_\text{core}^{2})\cos(\psi)}
 
-An approximation for the effects of "Gaussian interfacial roughness" $\sigma$ is included, 
-by multiplying $I(Q)$ by $exp\left \{ -\frac{1}{2}Q^2\sigma^2 \right \}$ . This 
-applies, in some way, to all interfaces in the model not just the external ones.
-(Note that for a one dimensional system convolution of the scattering length density profile
-with a Gaussian of standard deviation $\sigma$ does exactly this multiplication.) Leave 
-$\sigma$ set to zero for the usual sharp interfaces.
+
+and $V_t = \pi (R+t_r)(X_\text{core} R+t_r) L + 2 \pi X_\text{core} R^2 t_f$ is
+the total volume of the bicelle, $V_c = \pi X_\text{core} R^2 L$ the volume of
+the core, $V_{c+f} = \pi X_\text{core} R^2 (L+2 t_f)$ the volume of the core
+plus the volume of the faces, $V_{c+r} = \pi (R+t_r)(X_\text{core} R+t_r) L$
+the volume of the core plus the rim, $R$ is the radius of the core,
+$X_\text{core}$ 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 $X_\text{core} R$
+so is circular, as for the core_shell_bicelle model, for $X_\text{core}=1$.
+Note that you may need to limit the range of $X_\text{core}$, especially if
+using the Monte-Carlo algorithm, as setting radius to $R/X_\text{core}$ and
+axial ratio to $1/X_\text{core}$ gives an equivalent solution!
+
+An approximation for the effects of "Gaussian interfacial roughness" $\sigma$
+is included, by multiplying $I(Q)$ by
+$\exp\left \{ -\frac{1}{2}Q^2\sigma^2 \right \}$. This applies, in some way, to
+all interfaces in the model not just the external ones. (Note that for a one
+dimensional system convolution of the scattering length density profile with
+a Gaussian of standard deviation $\sigma$ does exactly this multiplication.)
+Leave $\sigma$ set to zero for the usual sharp interfaces.
 
 The output of the 1D scattering intensity function for randomly oriented
 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 further details of the calculation and angular dispersions  see :ref:`orientation` .
+For oriented bicelles the *theta*, *phi* and *psi* orientation parameters
+will appear when fitting 2D data, for further details of the calculation
+and angular dispersions  see :ref:`orientation` .
 
 .. 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.
 
 
@@ -115 +127 @@
 description = """
     core_shell_bicelle_elliptical_belt_rough
-    Elliptical cylinder core, optional shell on the two flat faces, and "belt" shell of 
+    Elliptical cylinder core, optional shell on the two flat faces, and "belt" shell of
     uniform thickness on its rim (in this case NOT extending around the end faces).
     with approximate interfacial roughness.
@@ -173 +185 @@
 
     [{'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, 'background':0.0},
-    0.015, 189.328],
-#    [{'theta':80., 'phi':10.}, (qx, qy), 7.88866563001 ],
-        ]
+      'sld_core':4.0, 'sld_face':7.0, 'sld_rim':1.0, 'sld_solvent':6.0, 'background':0.0},
+     0.015, 189.328],
+    #[{'theta':80., 'phi':10.}, (qx, qy), 7.88866563001 ],
+]
 
 del qx, qy  # not necessary to delete, but cleaner

sasmodels/models/ellipsoid.py

@@ -53 +53 @@
     r = R_e \left[ 1 + u^2\left(R_p^2/R_e^2 - 1\right)\right]^{1/2}
 
-For 2d data from oriented ellipsoids the direction of the rotation axis of 
-the ellipsoid is defined using two angles $\theta$ and $\phi$ as for the 
+For 2d data from oriented ellipsoids the direction of the rotation axis of
+the ellipsoid is defined using two angles $\theta$ and $\phi$ as for the
 :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, for further details of the calculation and angular 
+in the $xy$ plane, for further details of the calculation and angular
 dispersions see :ref:`orientation` .
 
@@ -209 +209 @@
 qy = q*sin(pi/6.0)
 tests = [[{}, 0.05, 54.8525847025],
-        [{'theta':80., 'phi':10.}, (qx, qy), 1.74134670026 ],
+        [{'theta':80., 'phi':10.}, (qx, qy), 1.74134670026],
         ]
 del qx, qy  # not necessary to delete, but cleaner

sasmodels/models/stacked_disks.py

@@ -74 +74 @@
     the layers.
 
-2d scattering from oriented stacks is calculated in the same way as for cylinders,
-for further details of the calculation and angular dispersions see :ref:`orientation` . 
+2d scattering from oriented stacks is calculated in the same way as for
+cylinders, for further details of the calculation and angular dispersions
+see :ref:`orientation`.
 
 .. figure:: img/cylinder_angle_definition.png
 
     Angles $\theta$ and $\phi$ orient the stack of discs relative
-    to the beam line coordinates, where the beam is along the $z$ axis. Rotation $\theta$, initially 
-    in the $xz$ plane, is carried out first, then rotation $\phi$ about the $z$ axis. Orientation distributions
-    are described as rotations about two perpendicular axes $\delta_1$ and $\delta_2$
-    in the frame of the cylinder itself, which when $\theta = \phi = 0$ are parallel to the $Y$ and $X$ axes.
+    to the beam line coordinates, where the beam is along the $z$ axis.
+    Rotation $\theta$, initially in the $xz$ plane, is carried out first,
+    then rotation $\phi$ about the $z$ axis. Orientation distributions are
+    described as rotations about two perpendicular axes $\delta_1$ and
+    $\delta_2$ in the frame of the cylinder itself, which when
+    $\theta = \phi = 0$ are parallel to the $Y$ and $X$ axes.