Re: Barnes-Hut treecode (was Re: Galaxy Interaction Simulations)

Wayne Hayes (
9 Mar 94 05:55:26 GMT (Steinn Sigurdsson) writes:
>Systems for which "N" approaches the actual number of particles
>do exist. Trivially, N=3-10 are instances, (actually 1-10 is a better
>range :-) - certainly the solar system people use the actual "N"
>by and large.

Yes, and they usually use specially-designed code with *very* high
order integrators (like 12th or 13th order), unlike large-N researches
who are often content with 4th or even 2nd order integrators. That's
because we're interested in fundamentally different things: solar
system researchers want to integrate paths of specific objects very
accurately over a very long time; useful galactic dynamics research
can be done by just following the essentually "fluid" motion of the
huge number of particles. (This isn't a flame; I just wanted to
make it clear for interested bystanders.)

>To model globular clusters with unsoftened particles (ie including
>2bod relaxation) is not possible,

You mean not possible with current machines/techniques, or fundamentally
impossible, even in principle? I was under the impression that it's
only a matter of not enough CPU cycles to accurately model large-N
systems without softening.

>the HARP project is probably the closest. For those interested in
>collisionless dynamics, which still allows modeling of some
>interesting aspects of globulars, I have a working code that
>has done a full realisation of globular clusters, anything from
>Pal 1 to Omega Cen for, say, 1000 dynamical times - but it doesn't
>include two body relaxation and has limited application.

You lost me here. I thought globulars were highly collisional? How
can a collisionless code model globulars. (For the uninitiated:
``collisional'' essentially means ``high density'', where the paths
of individual particles can be substantially altered by close passes
of neighbors; this opposed to ``collisionless'' systems, where the
particle trajectories are governed almost solely by some global
potential. The solar system is an extreme example of a collisionless

>We're in a race with the cosmology code people for the largest N,
>our (non-interacting) galaxy simulations have hit N=10^7 and we'll
>get to N=10^8 in a matter of months.

Wow! Surely this is *with* softening, though? When I said "ideal"
N-body, I meant that each particle in the simulation is representative
of one particle in the system -- thus you wouldn't use softening.

"The money spent on the Mars Observer was not sent to Mars. A few tons of metal
were.  The engineering lessons and experience from building the spacecraft and
instruments will remain on Earth to benefit future missions if we choose to
undertake them." -- Steve Collins    || Wayne Hayes