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Re: [ESPResSo-users] Lubrication correction in Stokesian dynamics

From: Lei Liu
Subject: Re: [ESPResSo-users] Lubrication correction in Stokesian dynamics
Date: Thu, 12 Jan 2017 17:50:12 +0900

Dear all,

by reading related documents, now I understand that the terms containing log(s) come from R^{lub}.
The only left question is about the variables {r2bcorr_para_self, r2bcorr_para_mix, r2bcorr_perp_self, r2bcorr_perp_self} in function "sd_compute_resistance_matrix_sparse()".

The first two variables corresponds to \alpha_{s} and \alpha_{m} in equations (3.17), (3.21) in David's thesis.
But how about the latter two ?
Would anyone like to do me a favour, and to explain a little bit where they come from ?
I get confused because they are different from my expectation,
\beta_{s} or \beta_{m} in equations (3.19) and (3.23).

With my best wishes

On Wed, Jan 11, 2017 at 8:30 PM, Lei Liu <address@hidden> wrote:
Dear all,

I am trying to understand the lubrication correction
in Stokesian dynamics implemented in current developing version of ESPResSo.

According to David Schwoerer's thesis, the function "sd_compute_resistance_matrix_sparse()"
computes the lubrication correction described in equation (3.24) as R^{lc} = R^{lub} - R^{2b,ff}.
In addition, there is one comment in the code
referring R^{lub} to 'N.-Q. Nguyen and A. J. C. Ladd, PHYSICAL REVIEW E 66, 046708 (2002) equation (34)'.

But I still do not understand this function quite well, especially the terms containing the variable "ls = log(s) = log(|r|/a - 2)",
which I cannot find neither in section 3.1.2 in the thesis nor in Ladd's paper.
Would anyone like to give me more references about how ESPResSo calculates this correction?

Many thanks in advance

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