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

[Lei Liu]

Hello David,

thanks a lot for reading and answering my tedious questions.

Because I am a novice in this field, I try to understand more details.

As you said, r2bcorr_para_self is \alpha_s+\beta_s,

which equals to the first part on the right hand side of equ. (3.17),
and has corresponding implementation in Line 1410 in the source file "integrate_sd_cuda_kernel.cu".

How about r2bcorr_perp_self ?

If this term is \beta_s, based on equ. (3.19),
I would expect that a line of code like
"r2bcorr_perp_self = 1/( 1 - 9/16/dr2 - 3/4/dr4 - 1/4/dr6 )".

But in Line 1412 it equals to
"r2bcorr_perp_self = 1/( 1 - 25/16/dr2 )"

This is the point I get confused.

Would you please explain a little bit more ?

Best regards

Lei

On Thu, Jan 12, 2017 at 7:24 PM, David Schwörer <address@hidden> wrote:

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

> <mailto: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
>     Lei
>
>
>
>