Hard spheres dynamics: weak vs hard collisions

Abstract

We consider the motion of a finite though large number $N$ of hard spheres in the whole space ${\mathbb{R}}^n$. Particles move freely until they experience elastic collisions. We use our recent theory of Compensated Integrability in order to estimate how much the particles are deviated by collisions. Our result, which is expressed in terms of hodographs, tells us that only $O(N^2)$ collisions are significant.

References in corpus (2)

• Examples of exponentially many collisions in a hard ball system
• A lower bound for the number of elastic collisions

Cited by in corpus (2)

• A splash in a one-dimensional cold gas
• An improved upper bound on the number of billiard ball collisions