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

 From: Georg Rempfer Subject: Re: [ESPResSo-users] Lubrication correction in Stokesian dynamics Date: Thu, 12 Jan 2017 11:35:17 +0100

Hello Lei,

I don't know anyone capable of answering your question other than David himself. Since he does not seem to answer here, try contacting him via address@hidden .

Greetings,
Georg

On Thu, Jan 12, 2017 at 9:50 AM, Lei Liu wrote:
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
Lei

On Wed, Jan 11, 2017 at 8:30 PM, Lei Liu 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?