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SasView / sasmodels

Package for calculation of small angle scattering models using OpenCL.
BSD 3-Clause "New" or "Revised" License
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Extend the fuzzy sphere model #459

Open butlerpd opened 3 years ago

butlerpd commented 3 years ago

In many real cases the fuzzy sphere actually is composed of polymer chains (for example dendrimers). The original fuzzy sphere does not account for the high q contributions from the fluctuations. Rathgeber et. al [JCP 117, 4047- 4062 (2002)] provide an extension that allows for this which would be nice to have in SasView. Moreover since it is an additive term setting the prefactor to that term to 0 will recover the original fuzzy sphere model. The Dendrimer paper by Wei-Ren Chen et al. [Macromolecules 40, 5887-5898 (2007)]uses this model (along with an appropriate structure factor) very successfully and delineates the additive nature of the terms. However, @yunliu01 says the math for that second term is given by equations 26, 29, and 30 of the Rathgeber paper.

Also we may want to consider the alternate way of estimating Rg given in the Macromolecules paper.

I would recommend creating a new model for now as changing the parameters of an existing model could cause backward compatibility problems, particularly with old project files.

SillyMichael commented 3 years ago

Comments on @butlerpd 's ticket. The existing Fuzzy Sphere model use a Gaussian function to treat the edge of a solid (uniform SLD) sphere directly. However this model can not describe the systems with internal SLD fluctuation. (nothing is uniform when you see it in enough high q). Rathgeber's paper extends this part by adding a second term to the model which can count for any SLD fluctuation inside the sphere within a length scale less than correlation length of blob. In their paper, they also extended the first shape term to an ellipsoid ( Sphere is a special ellipsoid). This task does NOT need to extend the shape part from sphere to ellipsoid, but ONLY needs to add the second part in equation <23>.

SillyMichael commented 3 years ago

From Rathgeber et. al [JCP 117, 4047- 4062 (2002)] , I have expanded equation (23) based on equation (24) (25) (26). image

Of course, it is ONLY form factor in above equation. I will paste Sasview code here later

butlerpd commented 3 years ago

Thanks @SillyMichael - looking good. However this is not the right place to put the code. Please post it on the marketplace and put the link to that code here. Eventually this should be put in a branch and pushed to the repo for proper review but that would be a next step as I think you may want to some help for that last process?