CONTINUUM LIMITS OF INTERACTING PARTICLE-SYSTEMS

We study the continuum limits of discrete particle systems with short range repulsive forces. We establish the existence of a class of short range interparticle force laws with the property that the asymptotic trajectories of two sufficiently energetic particles of equal mass ent ering and leaving the region of a binary interaction are the same as t he asymptotic trajectories of particles which undergo a simple point-m ass elastic collision. Using such force laws, we consider the evolutio n of an N particle gas, each particle having mass 1/N, for initial dat a which are guaranteed to generate only binary collisions. We show tha t such problems are exactly solvable and we characterize the continuum limit (N --> infinity) of such solutions, These limit flows are indep endent of the details of the repulsive forces and are the same as obta ined if one replaces the interparticle force law by the elastic collis ion rule which simply interchanges particle velocities during a collis ion.