Power law in the angular velocity distribution of a granular needle

TL;DR

This paper demonstrates that inelastic collisions cause a power-law decay with exponent -3 in the angular velocity distribution of anisotropic granular particles with small moments of inertia, analyzed via Boltzmann kinetic theory.

Contribution

It reveals a specific power-law behavior in angular velocity distribution caused by inelastic collisions in granular particles, extending understanding of granular dynamics.

Findings

Power law with exponent -3 in angular velocity distribution.

Persistence of the power law for a wide range of velocities.

Relevance for small mass ratio between particle and bath.

Abstract

We show how inelastic collisions induce a power law with exponent -3 in the decay of the angular velocity distribution of anisotropic particles with sufficiently small moment of inertia. We investigate this question within the Boltzmann kinetic theory for an elongated granular particle immersed in a bath. The power law persists so long as the collisions are inelastic for a large range of angular velocities provided the mass ratio of the anisotropic particle and the bath particles remains small. Suggestions for observing this peculiar feature are made.