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Re: [ESPResSo-devel] Pressure calculation / P3M stress tensor

From: Markus Deserno
Subject: Re: [ESPResSo-devel] Pressure calculation / P3M stress tensor
Date: Fri, 03 Apr 2009 13:46:12 -0400
User-agent: Thunderbird (X11/20070801)

Hi all,

> as far as I can see it is not obsolete. In line 175 1/3 of the total  
> pressure is put on the diagonal of pressure tensor. This helps to make  
> the trace of the pressure tensor, which is the pressure itself,  
> correct. But all off-diagonal coulomb terms are 0. So e.g.  
> calculations of viscosity out of the pressure tensor will be wrong.

I suspected that this has not yet been done.  Someone needs to sit down
and concentrate real hard and code it...

Moreover:  The current solution seems wrong to me too, even in the isotropic
case.  Here's why:

The pressure is (1/3) times the trace of the stress tensor.

What the current code seems to assume (just like previous version
of the non-coulomb-stresses) is that the pressure is the trace of the
stress tensor, and hence the individual components are 1/3 of the
isotropic ones.  This is wrong.

So, for a system with isotropic pressure P and no off-diagonal
stresses the stress tensor is

    ( P   0   0 )
    ( 0   P   0 )
    ( 0   0   P )

(up to possibly a sign that I can't remember now.)

Please be aware of that.  One of my papers had a stupid factor
of 3 mistake because of that, and later in a different research project
it took me and Vagelis weeks to figure out that our research was
right but the stress tensor was a factor of 3 too small...

And: I fear all of that happened because the respective equation
is wrong in my PhD thesis, which might be the source of all that pain...



Dr. Markus Deserno
Associate Professor of Physics    ++1-412-268-4401 (office)
Carnegie Mellon University        ++1-412-681-0648 (fax)
5000 Forbes Avenue                ++1-412-268-8367 (Donna Thomas)
Pittsburgh, PA 15213              address@hidden

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