Stationary states and energy cascades in inelastic gases

TL;DR

This paper identifies a broad class of stationary states in inelastic gases characterized by algebraic velocity distributions with tails that depend on system parameters, supported by analytical and numerical evidence.

Contribution

It introduces a general analytical framework for stationary states with algebraic tails in inelastic gases, applicable across dimensions and collision rules.

Findings

Stationary states with algebraic velocity tails are found in inelastic gases.

The tail exponent varies continuously with system parameters.

Numerical simulations confirm the existence of these states under energy injection.

Abstract

We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transfered 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) ~ v^{-sigma}. The exponent sigma 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.