Density variations in a one-dimensional granular system

Abstract

In this work we examine a system of inelastic particles confined to move on a line between an elastic wall and a heat source. Solving a Boltzmann equation for this system leads to an analytic expression for steady state behavior. Numerical simulations show that the system is in fact capable of simultaneously displaying both the uniform density of the analytic solution, and a state in which the particles are collected into a cluster adjacent to the elastic wall. The boundary conditions for the Boltzmann treatment are then reworked to provide a theoretical description of how smooth particle distributions and clumping phenomena can coexist. From this, we gain a prediction for the time scale of clump formation in this system.