Kinetics of a one-dimensional granular medium in the quasielastic limit

Publisher Website
Google Scholar
Abstract
The dynamics of a one‐dimensional granular medium has a finite time singularity if the number of particles in the medium is greater than a certain critical value. The singularity (‘‘inelastic collapse’’) occurs when a group of particles collides infinitely often in a finite time so that the separations and relative velocities vanish. To avoid the finite time singularity, a double limit in which the coefficient of restitution r approaches 1 and the number of particles N becomes large, but is always below the critical number needed to trigger collapse, is considered. Specifically, r→1 with N∼(1−r)−1. This procedure is called the ‘‘quasielastic’’ limit. Using a combination of direct simulation and kinetic theory, it is shown that a bimodal velocity distribution develops from random initial conditions. The bimodal distribution is the basis for a ‘‘two‐stream’’ continuum model in which each stream represents one of the velocity modes. This two‐stream model qualitatively explains some of the unusual phenomena seen in the simulations, such as the growth of large‐scale instabilities in a medium that is excited with statistically homogeneous initial conditions. These instabilities can be either direct or oscillatory, depending on the domain size, and their finite‐amplitude development results in the formation of clusters of particles.

This publication has 9 references indexed in Scilit: