Relaxation and steady-state behavior of an analytically tractable one-dimensional model

Abstract

We study the dynamics of a particle of mass m making a series of collisions with a wall and a movable piston of mass M > m. Using collision matrix methods, we obtain exact analytical results for the evolution of the speeds and kinetic energies of the particle and pistons, as well as the steady-state kinetic energies in relation to mass ratio and restitution coefficients.