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

 From: David Schwörer Subject: Re: [ESPResSo-users] Lubrication correction in Stokesian dynamics Date: Thu, 12 Jan 2017 10:24:23 +0000 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:45.0) Gecko/20100101 Thunderbird/45.6.0

Hi Lei,

It's been a while since I looked at this, but I think:
r2bcorr_para_self is alpha_s+beta_s
r2bcorr_para_mix is alpha_m+beta_m
r2bcorr_perp_self is beta_s
r2bcorr_perp_mis is beta_m

the confusion is that in the one basis set is in rr and one, the other
in rr and one-rr, that is why in 3.17 b_s is substracted from alpha_s,
so that after adding the one beta_s, only the first part 1/(1-alpha_s^2)
remains.

I hope that helps.

Cheers,
David

On 01/12/2017 08:50 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 <address@hidden
>
>     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
>     Would anyone like to give me more references about how ESPResSo
>     calculates this correction?
>