Power-law velocity distributions in granular gases

TL;DR

This paper demonstrates that granular gases can exhibit steady and transient states with power-law velocity distributions, with the exponent depending on system parameters, and explores energy injection and dissipation mechanisms.

Contribution

It analytically derives the power-law velocity distribution solutions for inelastic granular gases, linking the exponent to system properties and describing driven and cooling states.

Findings

Power-law velocity distributions are analytically derived for granular gases.

The exponent of the power-law depends on dimension, inelasticity, and collision rate.

Steady and cooling states exhibit self-similar and cascade behaviors.

Abstract

We report a general class of steady and transient states of granular gases. We find that the kinetic theory of inelastic gases admits stationary solutions with a power-law velocity distribution, f(v) ~ v^(-sigma). The exponent sigma is found analytically and depends on the spatial dimension, the degree of inelasticity, and the homogeneity degree of the collision rate. Driven steady-states, with the same power-law tail and a cut-off can be maintained by injecting energy at a large velocity scale, which then cascades to smaller velocities where it is dissipated. Associated with these steady-states are freely cooling time-dependent states for which the cut-off decreases and the velocity distribution is self-similar.