Continuous vs Discrete Chains¶
In Model Melt Chi AB, we discussed how to derive:
where
Discuss operator splitting and how this leads to a form that is similar to the discrete chains
Note that Nref means different things for continuous vs discrete chains. For continuous chains, it is the contour length (with Nref + 1 contour steps). For discrete chains, N is the number of beads. This means that the reference lengths
The different meanings of Nref for different chain types is necessary so that when a user specifies Nref = 100 and nbeads = 100, the lengths in the simulation don’t need to be correted by a factor of N/(N-1) (TODO: is this correct?).
Discrete chains¶
References: GHF, Koski2013, Matsen2012 (Macromol 45:8502)
where
The convolution can be solved using FFTs which requires the fourier transform of
For Rg units
Density operator:
the sum over s includes beads of species K.