# Changeset 416f5c7 in sasmodels

Ignore:
Timestamp:
Oct 7, 2016 3:51:36 PM (5 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:
5df888c
Parents:
8749c1c4
Message:

fixes for numref warnings in docu, new equations core_shell_bicelle core_shell_ellipsoid

Location:
sasmodels/models
Files:
7 edited

Unmodified
Removed
• ## sasmodels/models/core_shell_bicelle.py

 radc753d I(Q,\alpha) = \frac{\text{scale}}{V} \cdot F(Q,\alpha)^2 + \text{background} where .. math:: \begin{align} F(Q,\alpha) = &\frac{1}{V_t} \bigg[ (\rho_c - \rho_f) V_c \frac{J_1(QRsin \alpha)}{QRsin\alpha}\frac{2 \cdot QLcos\alpha}{QLcos\alpha} \\ &+(\rho_f - \rho_r) V_{c+f} \frac{J_1(QRsin\alpha)}{QRsin\alpha}\frac{2 \cdot Q(L+t_f)cos\alpha}{Q(L+t_f)cos\alpha} \\ &+(\rho_r - \rho_s) V_t \frac{J_1(Q(R+t_r)sin\alpha)}{Q(R+t_r)sin\alpha}\frac{2 \cdot Q(L+t_f)cos\alpha}{Q(L+t_f)cos\alpha} \begin{align} F(Q,\alpha) = &\bigg[ (\rho_c - \rho_f) V_c \frac{J_1(QRsin \alpha)}{QRsin\alpha}\frac{2 \cdot sin(QLcos\alpha/2)}{QLcos\alpha} \\ &+(\rho_f - \rho_r) V_{c+f} \frac{J_1(QRsin\alpha)}{QRsin\alpha}\frac{2 \cdot sin(Q(L/2+t_f)cos\alpha)}{Q(L+2t_f)cos\alpha} \\ &+(\rho_r - \rho_s) V_t \frac{J_1(Q(R+t_r)sin\alpha)}{Q(R+t_r)sin\alpha}\frac{2 \cdot sin(Q(L/2+t_f)cos\alpha)}{Q(L+2t_f)cos\alpha} \bigg] \end{align} #             ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["radius",         "Ang",       20, [0, inf],    "volume",      "Cylinder core radius"], ["radius",         "Ang",       80, [0, inf],    "volume",      "Cylinder core radius"], ["thick_rim",  "Ang",       10, [0, inf],    "volume",      "Rim shell thickness"], ["thick_face", "Ang",       10, [0, inf],    "volume",      "Cylinder face thickness"], ["length",         "Ang",      400, [0, inf],    "volume",      "Cylinder length"], ["length",         "Ang",      50, [0, inf],    "volume",      "Cylinder length"], ["sld_core",       "1e-6/Ang^2", 1, [-inf, inf], "sld",         "Cylinder core scattering length density"], ["sld_face",       "1e-6/Ang^2", 4, [-inf, inf], "sld",         "Cylinder face scattering length density"],
• ## sasmodels/models/core_shell_ellipsoid.py

 r9272cbd The geometric parameters of this model are shown in the diagram above, which shows (a) a cross section of the circular equator and (b) a cross section through shows (a) a cut through at the circular equator and (b) a cross section through the poles, of a prolate ellipsoid. For a fixed shell thickness *XpolarShell = 1*, to scale the shell thickness pro-rata with the radius *XpolarShell = X_core*. pro-rata with the radius set or constrain *XpolarShell = X_core*. When including an $S(q)$, the radius in $S(q)$ is calculated to be that of this moves to the $S(q)$ volume fraction, and scale should then be 1.0, or contain some other units conversion factor (for example, if you have SAXS data). The calculation of intensity follows that for the solid ellipsoid, but with separate terms for the core-shell and shell-solvent boundaries. .. math:: P(q,\alpha) = \frac{\text{scale}}{V} F^2(q,\alpha) + \text{background} where .. math:: \begin{align} F(q,\alpha) = &f(q,radius\_equat\_core,radius\_equat\_core.x\_core,\alpha) \\ &+ f(q,radius\_equat\_core + thick\_shell,radius\_equat\_core.x\_core + thick\_shell.x\_polar\_shell,\alpha) \end{align} where .. math:: f(q,R_e,R_p,\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} and .. math:: r(R_e,R_p,\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, either $(sld\_core - sld\_shell)$ or $(sld\_shell - sld\_solvent)$. For randomly oriented particles: .. math:: F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha} References
• ## sasmodels/models/cylinder.py

 r551398c .. math:: P(q,\alpha) = \frac{\text{scale}}{V} F^2(q) + \text{background} P(q,\alpha) = \frac{\text{scale}}{V} F^2(q,\alpha) + \text{background} where .. math:: F(q) = 2 (\Delta \rho) V F(q,\alpha) = 2 (\Delta \rho) V \frac{\sin \left(\tfrac12 qL\cos\alpha \right)} {\tfrac12 qL \cos \alpha} first order Bessel function. For randomly oriented particles: .. math:: F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha} To provide easy access to the orientation of the cylinder, we define the axis of the cylinder using two angles $\theta$ and $\phi$. Those angles are defined in :numref:cylinder-angle-definition. are defined in :numref:cylinder-angle-definition . .. _cylinder-angle-definition:
• ## sasmodels/models/ellipsoid.py

 ra807206 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: .. math:: F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha} To provide easy access to the orientation of the ellipsoid, we define
• ## sasmodels/models/parallelepiped.py

 ra807206 | This model calculates the scattering from a rectangular parallelepiped | (:numref:parallelepiped-image). | (\:numref:parallelepiped-image\). | If you need to apply polydispersity, see also :ref:rectangular-prism.
• ## sasmodels/models/triaxial_ellipsoid.py

 ra807206 we define the axis of the cylinder using the angles $\theta$, $\phi$ and $\psi$. These angles are defined on :numref:triaxial-ellipsoid-angles. :numref:triaxial-ellipsoid-angles . The angle $\psi$ is the rotational angle around its own $c$ axis against the $q$ plane. For example, $\psi = 0$ when the
Note: See TracChangeset for help on using the changeset viewer.