Changeset d529d93 in sasmodels for sasmodels/models/hardsphere.py

Timestamp:

Mar 17, 2016 8:16:55 AM (8 years ago)

Author:

richardh

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

3a45c2c, 0784c18

Parents:

c5dadbb

Message:

updated docs for several S(Q)

File:

• sasmodels/models/hardsphere.py (modified) (6 diffs)

sasmodels/models/hardsphere.py

@@ -3 +3 @@
 spherical particles interacting through hard sphere (excluded volume)
 interactions.
+May be a reasonable approximation for other shapes of particles that 
+freely rotate, and for moderately polydisperse systems. Though strictly 
+the maths needs to be modified (no \Beta(Q) correction yet in sasview).
 
-The calculation uses the Percus-Yevick closure where the interparticle
+radius_effective is the effective hard sphere radius.
+volfraction is the volume fraction occupied by the spheres.
+
+In sasview the effective radius may be calculated from the parameters
+used in the form factor $P(q)$ that this $S(q)$ is combined with.
+
+For numerical stability the computation uses a Taylor series expansion 
+at very small $qR$, there may be a very minor glitch at the transition point
+in some circumstances.
+
+The S(Q) uses the Percus-Yevick closure where the interparticle
 potential is
 
@@ -44 +57 @@
         systems. Though strictly the maths needs to be modified -
     which sasview does not do yet.
-    effect_radius is the hard sphere radius
+    radius_effective is the hard sphere radius
     volfraction is the volume fraction occupied by the spheres.
 """
@@ -51 +64 @@
 
 #             ["name", "units", default, [lower, upper], "type","description"],
-parameters = [["effect_radius", "Ang", 50.0, [0, inf], "volume",
+parameters = [["radius_effective", "Ang", 50.0, [0, inf], "volume",
                "effective radius of hard sphere"],
               ["volfraction", "", 0.2, [0, 0.74], "",
@@ -66 +79 @@
       double D,A,B,G,X,X2,X4,S,C,FF,HARDSPH;
 
-      if(fabs(effect_radius) < 1.E-12) {
+      if(fabs(radius_effective) < 1.E-12) {
                HARDSPH=1.0;
                return(HARDSPH);
@@ -75 +88 @@
       A= (1.+2.*volfraction)*D;
       A *=A;
-      X=fabs(q*effect_radius*2.0);
+      X=fabs(q*radius_effective*2.0);
 
       if(X < 5.E-06) {
@@ -138 +151 @@
 # VR defaults to 1.0
 
-demo = dict(effect_radius=200, volfraction=0.2, effect_radius_pd=0.1, effect_radius_pd_n=40)
+demo = dict(radius_effective=200, volfraction=0.2, radius_effective_pd=0.1, radius_effective_pd_n=40)
 oldname = 'HardsphereStructure'
-oldpars = dict()
+oldpars = dict(radius_effective="effect_radius",radius_effective_pd="effect_radius_pd",radius_effective_pd_n="effect_radius_pd_n")
 # Q=0.001 is in the Taylor series, low Q part, so add Q=0.1, assuming double precision sasview is correct
 tests = [
-        [ {'scale': 1.0, 'background' : 0.0, 'effect_radius' : 50.0, 'volfraction' : 0.2,
-           'effect_radius_pd' : 0}, [0.001,0.1], [0.209128,0.930587]]
+        [ {'scale': 1.0, 'background' : 0.0, 'radius_effective' : 50.0, 'volfraction' : 0.2,
+           'radius_effective_pd' : 0}, [0.001,0.1], [0.209128,0.930587]]
         ]
-
+# ADDED by: RKH  ON: 16Mar2016  using equations from FISH as better than orig sasview, see notes above. Added Taylor expansions at small Q,