From pinned billiard balls to partial differential equations

Abstract

We discuss the propagation of kinetic energy through billiard balls fixed in place along a one-dimensional segment. The number of billiard balls is assumed to be large but finite and we assume kinetic energy propagates following the usual collision laws of physics. Assuming an underlying stochastic mean-field for the expectation and the variance of the kinetic energy, we derive a coupled system of nonlinear partial difference equations. Our results are illustrated by numerical simulations.