Changeset 4cdc4b1 in sasmodels for sasmodels/models

Timestamp:

Jul 9, 2018 6:01:08 PM (6 years ago)

Author:

GitHub <noreply@…>

Branches:

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

Children:

9a99993

Parents:

dc76240 (diff), c9fc873 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.

git-author:

Paul Butler <butlerpd@…> (07/09/18 18:01:08)

git-committer:

GitHub <noreply@…> (07/09/18 18:01:08)

Message:

Merge pull request #71 from SasView?/ticket-1112

Ticket 1112 - Guinier model does not allow negative Rg²

Andrew is on extended holiday leave so not likely to review in timely fashion. It has been reviewed fairly extensively in the ticket stage and is only a very minor change to code and docs. Since SasView? 0.97 has already been tagged and will be used for beta release it should be safe to merge this now. It should be good for the full 4.2.0 release.

Location:

sasmodels/models

Files:

• guinier.py (modified) (4 diffs)
• core_shell_sphere.py (modified) (1 diff)

sasmodels/models/guinier.py

@@ -7 +7 @@
 .. math::
 
-    I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2R_g^2}{3} \right]}
+    I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2 R_g^2 }{3} \right]}
             + \text{background}
 
@@ -19 +19 @@
 
 .. math:: q = \sqrt{q_x^2 + q_y^2}
+
+In scattering, the radius of gyration $R_g$ quantifies the objects's
+distribution of SLD (not mass density, as in mechanics) from the objects's
+SLD centre of mass. It is defined by
+
+.. math:: R_g^2 = \frac{\sum_i\rho_i\left(r_i-r_0\right)^2}{\sum_i\rho_i}
+
+where $r_0$ denotes the object's SLD centre of mass and $\rho_i$ is the SLD at
+a point $i$.
+
+Notice that $R_g^2$ may be negative (since SLD can be negative), which happens
+when a form factor $P(Q)$ is increasing with $Q$ rather than decreasing. This
+can occur for core/shell particles, hollow particles, or for composite
+particles with domains of different SLDs in a solvent with an SLD close to the
+average match point. (Alternatively, this might be regarded as there being an
+internal inter-domain "structure factor" within a single particle which gives
+rise to a peak in the scattering).
+
+To specify a negative value of $R_g^2$ in SasView, simply give $R_g$ a negative
+value ($R_g^2$ will be evaluated as $R_g |R_g|$). Note that the physical radius 
+of gyration, of the exterior of the particle, will still be large and positive. 
+It is only the apparent size from the small $Q$ data that will give a small or 
+negative value of $R_g^2$.
 
 References
@@ -42 +65 @@
 
 #             ["name", "units", default, [lower, upper], "type","description"],
-parameters = [["rg", "Ang", 60.0, [0, inf], "", "Radius of Gyration"]]
+parameters = [["rg", "Ang", 60.0, [-inf, inf], "", "Radius of Gyration"]]
 
 Iq = """
-    double exponent = rg*rg*q*q/3.0;
+    double exponent = fabs(rg)*rg*q*q/3.0;
     double value = exp(-exponent);
     return value;
@@ -66 +89 @@
 
 # parameters for demo
-demo = dict(scale=1.0, rg=60.0)
+demo = dict(scale=1.0,  background=0.001, rg=60.0 )
 
 # parameters for unit tests

sasmodels/models/core_shell_sphere.py

@@ -21 +21 @@
 .. math::
 
-    F^2(q) = \frac{3}{V_s}\left[
+    F(q) = \frac{3}{V_s}\left[
        V_c(\rho_c-\rho_s)\frac{\sin(qr_c)-qr_c\cos(qr_c)}{(qr_c)^3} +
        V_s(\rho_s-\rho_\text{solv})\frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3}