Changeset 475ff58 in sasmodels

Timestamp:

Sep 7, 2018 11:49:04 AM (6 years ago)

Author:

smk78

Branches:

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

Children:

c11d09f, 1a3c0c6

Parents:

992299c

Message:

Clarified documentation for spinodal model. Closes #1167

File:

• sasmodels/models/spinodal.py (modified) (3 diffs)

sasmodels/models/spinodal.py

@@ -3 +3 @@
 ----------
 
-This model calculates the SAS signal of a phase separating solution
-under spinodal decomposition. The scattering intensity $I(q)$ is calculated as
+This model calculates the SAS signal of a phase separating system 
+undergoing spinodal decomposition. The scattering intensity $I(q)$ is calculated 
+as 
 
 .. math::
     I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B
 
-where $x=q/q_0$ and $B$ is a flat background. The characteristic structure
-length scales with the correlation peak at $q_0$. The exponent $\gamma$ is
-equal to $d+1$ with d the dimensionality of the off-critical concentration
-mixtures. A transition to $\gamma=2d$ is seen near the percolation threshold
-into the critical concentration regime.
+where $x=q/q_0$, $q_0$ is the peak position, $I_{max}$ is the intensity 
+at $q_0$ (parameterised as the $scale$ parameter), and $B$ is a flat 
+background. The spinodal wavelength is given by $2\pi/q_0$. 
+
+The exponent $\gamma$ is equal to $d+1$ for off-critical concentration 
+mixtures (smooth interfaces) and $2d$ for critical concentration mixtures 
+(entangled interfaces), where $d$ is the dimensionality (ie, 1, 2, 3) of the 
+system. Thus 2 <= $\gamma$ <= 6. A transition from $\gamma=d+1$ to $\gamma=2d$ 
+is expected near the percolation threshold. 
+
+As this function tends to zero as $q$ tends to zero, in practice it may be 
+necessary to combine it with another function describing the low-angle 
+scattering, or to simply omit the low-angle scattering from the fit.
 
 References
@@ -22 +31 @@
 Physica A 123,497 (1984).
 
-Authorship and Verification
-----------------------------
+Revision History
+----------------
 
-* **Author:** Dirk Honecker **Date:** Oct 7, 2016
+* **Author:**  Dirk Honecker **Date:** Oct 7, 2016
+* **Revised:** Steve King    **Date:** Sep 7, 2018
 """
 
@@ -34 +44 @@
 title = "Spinodal decomposition model"
 description = """\
-      I(q) = scale ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma))+background
+      I(q) = Imax ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma)) + background
 
       List of default parameters:
-      scale = scaling
-      gamma = exponent
-      x = q/q_0
+      
+      Imax = correlation peak intensity at q_0
+      background = incoherent background
+      gamma = exponent (see model documentation)
       q_0 = correlation peak position [1/A]
-      background = Incoherent background"""
+      x = q/q_0"""
+      
 category = "shape-independent"