Granular Rough Sphere in a Low-Density Thermal Bath

TL;DR

This paper investigates the stationary states of a rough granular sphere in a thermal bath, revealing Gaussian velocity distributions and conditions for energy flow consistent with Fourier law.

Contribution

It introduces a model for a rough granular sphere in a thermal bath, deriving conditions for Gaussian velocity distributions and energy flow, which are novel insights.

Findings

Angular velocity distribution is Gaussian with lower effective temperature.

Joint translational and rotational velocities can be Gaussian with the same temperature.

Energy flow follows Fourier law under specific conditions.

Abstract

We study the stationary state of a rough granular sphere immersed in a thermal bath composed of point particles. When the center of mass of the sphere is fixed the stationary angular velocity distribution is shown to be Gaussian with an effective temperature lower than that of the bath. For a freely moving rough sphere coupled to the thermostat via inelastic collisions we find a condition under which the joint distribution of the translational and rotational velocities is a product of Gaussian distributions with the same effective temperature. In this rather unexpected case we derive a formula for the stationary energy flow from the thermostat to the sphere in accordance with Fourier law.