Dilute Limit Approximations

[martintb]

PRISM is often used in the limit of dilution for particulate systems in order to calculate the potential of mean force. For a two component system in this limit, the coupled set of PRISM equations reduce to where they can be solved sequentially and independently of one another. For example:

pyPRISM should support this use case, allowing users to designate certain components as "infinitely dilute". Users could even be automatically prompted to use this feature when setting site densities below a cutoff. The benefit of this method is that the PRISM equations become much easier to solve for systems with disparate particle diameters. The challenge will be generalizing this approximation to any number of dilute and non-dilute components.

[martintb]

After some thinking, it may be worth just implementing this for the two-component (one infinitely dilute) case. This could be achieved by creating a new PRISM object (PRISM_2CompDilute?) which assumes that the component with the lowest density is 'infinitely dilute'. Some sanity checks could be made to make sure users are actually using this correctly.

With the above said, we should still explore the full generalization of this approach to any number of dilute and non-dilute components, but it making a two-component specification to start may be a good intermediate checkpoint.