From chemistry-request@ccl.net Sun Mar 15 22:12:09 1992
Date: Sun, 15 Mar 92 18:12:01 -0800
From: rec@snll-arpagw.llnl.GOV (Ray Cline)
Subject: cutoffs and the speed of light
To: columbus@Think.COM
Status: R


Since I was the one who incorrectly introduced the term cut-off into
the speed-of-light/force discussion let me try to clarify. Point one:
Force travels at the speed of light (c). Point two: when you do a MD
simulation you have a discrete approximation to the differential
equation with a time step T. Now, when a particle moves only those
particles within a distance c/T should "know" its new position (i.e.
feel the force due to its current position) in this timestep. If a
particle is between a distance c/T and 2c/T it should use the
position/force from the last timestep, resulting in a wavefront of
delayed interactions throughout the sample. You should not ignore the
force between particles separated by greater than c/T (as my word
suggested but I did not intend), but you should take the transport
delay into account. Until now we have not had to worry about such
things, since we could not calculate samples large enough to be
affected by these concerns. These considerations are for purely
nonrelativistc classical forces and result from the discrete
approximation to the differential equation. Though you may think that
it would be alright to go ahead and just let all particles interact, I
believe that this would greatly bias the answers that you would obtain
for the simulation of crack propagation, phase transitions, and other
phenomena. You may be able to use the "everybody interacts" method to
simplify the calculation of bulk properties, but I would not rely on
it for the calculation of time-dependent properties or calculations
involving critical behavior.

Raymond E. Cline, Jr.
Organization 8300-A
Combustion Research Facility
Massively Parallel Computer Research Laboratory
Sandia National Laboratories
Box 969
Livermore, CA 94551
phone: (510) 294-1395
email: rec@sandia.llnl.gov
FAX  : (510) 294-2276