star_polymer model

[richardh]

numerically unstable at extreme small Q, likely also the same in mono_gauss_coil and poly_gauss_coil

suspect needs Taylor expansion

[richardh]

Also it is fitting <Rg^{2> not Rg, is this to be expected for this type of model?}

[pkienzle]

poly_gauss_coil has been fixed.

[pkienzle]

Maybe use sinc() in lamellar.py.

Glatter(1982) gives:

    I(q) = 2 pi/q^2  drho^2 T^2 [sin(q T/2) / (q T/2)]^2

This doesn't help with the divergence at q=0 though.

Note that we have

    I(q) = 2 pi/q^2 drho^2 4 [sin(q T/2)]^2 / (q^2 T)

which differs by a factor of T.

Are we really sure that we want to return 1.0 as the form volume? Or do we not want to volume normalize by lamellae thicknesses when computing the polydispersity average?

[smk78]

Did you really mean to add that last comment to this ticket, Paul? Those formulae don't look like a star polymer…

[richardh]

The star_polymer calculation is rather noisy at very small Q when Rg is small and the number of arms is 2 or larger. This requires further investigation.

( A star_polymer_v2 is now in model marketplace, which fits Rg not Rg², it also corrects isssue in the docs, for which see #962 )