# Changeset 62dc889 in sasmodels

Ignore:
Timestamp:
Mar 28, 2019 2:08:22 PM (11 months ago)
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
Parents:
6607260
Message:

Reworked documentation

File:
1 edited

### Legend:

Unmodified
 r0507e09 solvent. We currently provide up to 9 shells with this model. NB: *radius* represents the core radius $r_0$ and *thickness[k]* represents the thickness of the shell, $r_{k+1} - r_k$. .. note:: *radius* represents the core radius $r_0$ and *thickness[k]* represents the thickness of the shell, $r_{k+1} - r_k$. Definition j_1(x) = \frac{\sin(x)}{x^2} - \frac{\cos(x)}{x} and the volume is $V(r) = \frac{4\pi}{3}r^3$. The volume of the particle is determined by the radius of the outer shell, so $V_\text{particle} = V(r_N)$. Now lets consider the SLD of a shell defined by and the volume is $V(r) = \frac{4\pi}{3}r^3$. The volume of the particle is determined by the radius of the outer shell, so $V_\text{particle} = V(r_N)$. Now consider the SLD of a shell defined by .. math:: thickness of the $k^\text{th}$ shell in the equation above, respectively. For $A > 0$, .. figure:: img/onion_geometry.png Example of an onion model profile. **Exponential SLD profiles** ($A > 0$ or $A < 0$): .. math:: - 3CV(r_{\text{shell}-1}) \frac{j_1(\beta_\text{in})}{\beta_\text{in}} for where .. math:: B&=\frac{\rho_\text{out} - \rho_\text{in}}{e^A-1} & C &= \frac{\rho_\text{in}e^A - \rho_\text{out}}{e^A-1} \\ \alpha_\text{in} &= A\frac{r_{\text{shell}-1}}{\Delta t_\text{shell}} & \alpha_\text{out} &= A\frac{r_\text{shell}}{\Delta t_\text{shell}} \\ \beta_\text{in} &= qr_{\text{shell}-1} & \beta_\text{out} &= qr_\text{shell} \\ \end{align*} where $h$ is and .. math:: h(x,y) = \frac{x \sin(y) - y\cos(y)}{(x^2+y^2)y} h(x,y) = \frac{x \sin(y) - y\cos(y)}{(x^2+y^2)y} - \frac{(x^2-y^2)\sin(y) - 2xy\cos(y)}{(x^2+y^2)^2y} For $A \sim 0$, e.g., $A = -0.0001$, this function converges to that of the linear SLD profile with $\rho_\text{shell}(r) \approx A(r-r_{\text{shell}-1})/\Delta t_\text{shell})+B$, so this case is equivalent to **Linear SLD profile** ($A \sim 0$): For small $A$, say, $A = -0.0001$, the function converges to that of of a linear SLD profile with $\rho_\text{shell}(r) \approx A(r-r_{\text{shell}-1})/\Delta t_\text{shell})+B$, which is equivalent to .. math:: \end{align*} For $A = 0$, the exponential function has no dependence on the radius (so that **Constant SLD** ($A = 0$): When $A = 0$ the exponential function has no dependence on the radius (meaning $\rho_\text{out}$ is ignored in this case) and becomes flat. We set the constant to $\rho_\text{in}$ for convenience, and thus the form factor contributed by \frac{j_1(qr_\text{in})}{qr_\text{in}} .. figure:: img/onion_geometry.png Example of an onion model profile. The 2D scattering intensity is the same as $P(q)$ above, regardless of the orientation of the $q$ vector which is defined as * **Author:** * **Last Modified by:** * **Last Reviewed by:** * **Last Reviewed by:** Steve King **Date:** March 28, 2019 * **Source added by :** Steve King **Date:** March 25, 2019 """ description = """\ Form factor of mutishells normalized by the volume. Here each shell is Form factor of multishells normalized by the volume. Here each shell is described by an exponential function; II) For the exact point of A_shell == 0, f(r) = sld_in ,i.e., it crosses over flat function Note that the 'sld_out' becaomes NULL in this case. Note that the 'sld_out' becomes NULL in this case. background:background, # TODO: n is a volume parameter that is not polydisperse # NOTE: Joachim Wuttke has suggested an alternative parameterisation #       in Ticket #1107 # pylint: disable=bad-whitespace, line-too-long #   ["name", "units", default, [lower, upper], "type","description"], ["radius_core", "Ang", 200., [0, inf], "volume", "Radius of the core"], ["sld_solvent", "1e-6/Ang^2", 6.4, [-inf, inf], "sld", "Solvent scattering length density"], ["n_shells", "", 1, [0, 10], "volume", "number of shells"], ["n_shells", "", 1, [0, 10], "volume", "number of shells (must be integer)"], ["sld_in[n_shells]", "1e-6/Ang^2", 1.7, [-inf, inf], "sld", "scattering length density at the inner radius of shell k"], ["sld_out[n_shells]", "1e-6/Ang^2", 2.0, [-inf, inf], "sld", "scattering length density at the outer radius of shell k"],