From: Mark Abraham (Mark.Abraham_at_anu.edu.au)
Date: Thu Oct 19 2006 - 20:20:09 CDT
Marc Baaden wrote:
> could you elaborate what you mean by "the external ones under PBC are
> irrelevant" ? I don't quite understand your statement.
Under PBC, any point is equivalent to any other for choosing an inertial
reference frame. Choosing a particle to keep at a particular location is
just as good a choice as picking a random point in space. You could
simulate a box of water, choose one water, fix it to its location to
make a new inertial reference frame, adjust the momenta of all the other
waters and keep simulating and the time evolution would be the same as
if you just kept simulating the original system, if the complete
algorithm conserves energy and momentum. Since this water is a rigid
body, the "fixing" algorithm need only be to do a normal non-fixed
integration to get velocities and then subtract off the velocity of the
fixed water from all waters. This won't work for two fixed particles,
but that wouldn't be physical anyway. Round-off error would prevent an
exact duplication, of course, since these systems are chaotic. The
ensembles sampled are the same, however.
Of course, the above exercise is pointless - since all you are doing is
moving the reference frame!
> I don't know which application is intended, but eg for forming protein
> assemblies, I could imagine that rigid individual proteins might be a
> useful first approximation..
> ..where do I get it wrong?
Right, rigid bodies might be a useful approximation here, but fixing
them in space is not the answer - you need a more sophisticated
implementation of distance constraints to treat this case. Probably
SHAKE with 3N-6 "bonds" per rigid body would work here.
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