Velocity Distribution of a Uniformly Heated Hard Sphere Granular Gas

TL;DR

This study uses molecular dynamics simulations to analyze the velocity distribution in a uniformly heated inelastic hard sphere granular gas, revealing deviations from the Maxwell-Boltzmann distribution in steady state.

Contribution

It introduces an event-driven simulation method with a thermostat to study non-equilibrium steady states in inelastic granular gases, highlighting velocity distribution deviations.

Findings

Velocity distribution deviates from Maxwell-Boltzmann in steady state

Energy input balances energy dissipation in the system

Sonine polynomial coefficients quantify distribution deviations

Abstract

This paper presents a molecular dynamics simulation of an inelastic gas, where collisions between molecules are characterized by a coefficient of restitution less than unity. The simulation employs an event-driven algorithm to efficiently propagate the system in time, tracking molecular positions and velocities. A thermostat mechanism is incorporated to maintain the system's temperature by applying Gaussian white noise to the molecular velocities. The system's kinetic energy evolves towards a non-equilibrium steady state, with the initial dynamics governed by the interplay between energy input from the thermostat and energy dissipation through inelastic collisions. This steady state emerges when the energy gain from the thermostat balances the energy loss due to inelastic collisions. We calculate the coefficients of the Sonine polynomial expansion of the velocity distribution function to show that the velocity distribution exhibits a departure from the Maxwell-Boltzmann distribution in the steady state.