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 entering and leaving the region of a binary interaction are the same as the asymptotic trajectories of particles which undergo a simple point-mass elastic collision. Using such force laws, we consider the evolution of an N particle gas, each particle having mass 1/N, for initial data which are guaranteed to generate only binary collisions. We show that such problems are exactly solvable and we characterize the continuum limit (N --> infinity) of such solutions, These limit flows are independent of the details of the repulsive forces and are the same as obtained if one replaces the interparticle force law by the elastic collision rule which simply interchanges particle velocities during a collision.