Thermalization of an anisotropic granular particle

TL;DR

This paper analyzes the energy distribution of an anisotropic needle in a thermalized particle bath, deriving analytical expressions for its translational and rotational temperatures and validating them with simulations.

Contribution

It provides the first analytical expressions for the translational and rotational temperatures of an anisotropic granular particle in a thermal bath.

Findings

Translational temperature exceeds rotational temperature.

Temperature difference decreases with increasing moment of inertia.

Analytical results agree well with numerical simulations.

Abstract

We investigate the dynamics of a needle in a two-dimensional bath composed of thermalized point particles. Collisions between the needle and points are inelastic and characterized by a normal restitution coefficient $\alpha<1$. By using the Enskog-Boltzmann equation, we obtain analytical expressions for the translational and rotational granular temperatures of the needle and show that these are, in general, different from the bath temperature. The translational temperature always exceeds the rotational one, though the difference decreases with increasing moment of inertia. The predictions of the theory are in very good agreement with numerical simulations of the model.