Kinetic theory of cluster dynamics

Abstract

In a Newtonian system with localized interactions the whole set of particles is naturally decomposed into dynamical clusters, dened as nite groups of particles having an in uence on each other's trajectory during a given interval of time. For an ideal gas with short{range intermolecular force, we provide a description of the cluster size distribution in terms of the reduced Boltzmann density. In the simplied context of Maxwell molecules, we show that a macroscopic fraction of the gas forms a giant component in nite kinetic time. The critical index of this phase transition is in agreement with previous numerical results on the elastic billiard.