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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 2.0.0.6 (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...

Best,

Markus

--
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)