Steady state representation of the homogeneous cooling state of a granular gas

TL;DR

This paper introduces a stationary state representation for the homogeneous cooling state of a dilute granular gas, enabling easier analysis and simulation of its properties over time.

Contribution

It presents a novel mapping of the cooling state to a stationary state through a time scale change, facilitating analysis of granular gas dynamics.

Findings

Simulation results match theoretical predictions

Velocity autocorrelation functions are accurately computed

Self-diffusion coefficients are validated against theory

Abstract

The properties of a dilute granular gas in the homogeneous cooling state are mapped to those of a stationary state by means of a change in the time scale that does not involve any internal property of the system. The new representation is closely related with a general property of the granular temperature in the long time limit. The physical and practical implications of the mapping are discussed. In particular, simulation results obtained by the direct simulation Monte Carlo method applied to the scaled dynamics are reported. This includes ensemble averages and also the velocity autocorrelation function, as well as the self-diffusion coefficient obtained from the latter by means of the Green-Kubo representation. In all cases, the obtained results are compared with theoretical predictions.