Granular discorectangle in a thermalized bath of hard disks

TL;DR

This paper analyzes the steady-state behavior of a granular discorectangle in a thermalized bath of hard disks using the Enskog-Boltzmann approach, revealing non-equipartition and effects of anisotropy and restitution coefficients.

Contribution

It provides analytical expressions for granular temperatures and explores the impact of anisotropy and restitution coefficients on energy distribution.

Findings

Absence of equipartition in the system

Analytical formulas for granular temperatures

Equipartition occurs under specific restitution ratios

Abstract

By using the Enskog-Boltzmann approach, we study the steady-state dynamics of a granular discorectangle placed in a two-dimensional bath of thermalized hard disks. Hard core collisions are assumed elastic between disks and inelastic between the discorectangle and the disks, with a normal restitution coefficient $\alpha<1$. Assuming a Gaussian ansatz for the probability distribution functions, we obtain analytical expressions for the granular temperatures. We show the absence of equipartition and investigate both the role of the anisotropy of the discorectangle and of the relative ratio of the bath particles to the linear sizes of the discorectangle. In addition, we investigate a model of a discorectangle with two normal restitution coefficients for collisions along the straight and curved surfaces of the discorectangle. In this case one observes equipartition for a non trivial ratio of normal restitution coefficients.