Stationary States and Energy Cascades in Inelastic Gases

E. Ben-Naim and J. Machta

Phys. Rev. Lett. 94, 138001 – Published 6 April 2005

Abstract

We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transferred from large velocity scales to small velocity scales. These steady states exist for arbitrary collision rules and arbitrary dimension. Their signature is a stationary velocity distribution $f (v)$ with an algebraic high-energy tail, $f (v) \sim v^{- σ}$ . The exponent $σ$ is obtained analytically and it varies continuously with the spatial dimension, the homogeneity index characterizing the collision rate, and the restitution coefficient. We observe these stationary states in numerical simulations in which energy is injected into the system by infrequently boosting particles to high velocities. We propose that these states may be realized experimentally in driven granular systems.

Received 19 October 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.138001

Authors & Affiliations

E. Ben-Naim^1,* and J. Machta^2,†

¹Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
²Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA

^*Electronic address: ebn@lanl.gov
^†Electronic address: machta@physics.umass.edu

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Vol. 94, Iss. 13 — 8 April 2005

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