Re: Galaxy Interaction Simulations

Ben Weiner (
11 Mar 94 05:46:59 GMT (Jon Leech) writes:

[stuff deleted]

: I don't think this is *good*, in an abstract sense. Given fast enough
: machines (say, in 10 or 15 years :-), presumably the MD guys would run
: full-up quantum density functional theory and try to dispose of the
: mechanics models. But what it does seem to do is provide a bunch of differnt
: knobs to tune the models for particular *types* of MD - small inorganic
: complexes, amino acid residues, protein backbone segments in solution, and
: so on. And the tuning is getting good enough that the models seem to be
: developing predictive value - even though they *know* the models are not
: physically correct, they're close enough to be useful. Is there a potential
: analogy to the astrophysics models? Some terms that might be added to tune
: them to specific types of simulation?

Well of course in an astrophysical simulation you tend to have point
particles and the force law is rather simple, although it's generally
not really 1/r^2 - there is much art that goes into choosing things like
the softening parameter, essentially an approximation to the microphysics
that you can't resolve in the simulation. For ex. if you are simulating
a galaxy with 10^5 particles each of which is really 10^5 stars, there
is a lot of internal relaxation which goes on in the "particles" that
tends to damp out close particle-particle encounters.

However in the spirit of your question, one might ask, if you have
some prior knowledge about your system, how can you make the
simulation more efficient? One interesting idea that I'm trying to
assimilate is given in an article by Leeuwin, Combes and Binney,
"N-body simulations with perturbation particles" (MNRAS 262, 1013).

A big limitation of N-body codes is that they are effectively Monte
Carlo integrating the distribution function (the Monte Carlo part
comes from sampling the DF, ie picking where to start your particles -
the starting point for the characteristic curves which are solutions
of your PDEs). This is intrinsically awfully inefficient. The
perturbation particle idea is that if you have a DF which is an exact
solution of the collisionless Boltzmann equation, you can then add a
perturbation to the DF and use all the particles to integrate the
perturbation part of the DF (the diff. between the DF and the
underlying "equilibrium" DF).

Clearly this isn't a cure-all: you need an equilibrium solution of the
CBE, it becomes inefficient in the strongly non-linear regime, and it
sounds like choosing the sampling distribution is a pain. On the
other hand it is cool and has the potential to sometimes save a lot of
cycles with some extra thought which is nice (as opposed to "the
researcher with the best computer wins").

ALso, this paper has a neat discussion of the interpretation of N-body
simulation as Monte-Carlo sampling of the DF rather than each "body"
being a real object, which is worth reading in its own right.