Scaling and aging in the homogeneous cooling state of a granular fluid of hard particles

TL;DR

This paper investigates aging phenomena in the homogeneous cooling state of granular fluids, demonstrating that correlation decay slows over time, supported by simulations and analytical results, confirming the HCS as a solution of the Liouville equation.

Contribution

It provides a theoretical and simulation-based analysis of aging and correlation decay in granular fluids' HCS, including explicit analytical forms in low density.

Findings

Correlation decay slows with elapsed time in HCS

Molecular dynamics simulations confirm theoretical predictions

Explicit analytical form derived for low density limit

Abstract

The presence of the aging phenomenon in the homogeneous cooling state (HCS) of a granular fluid composed of inelastic hard spheres or disks is investigated. As a consequence of the scaling property of the $N$-particle distribution function, it is obtained that the decay of the normalized two-time correlation functions slows down as the time elapsed since the beginning of the measurement increases. This result is confirmed by molecular dynamics simulations for the particular case of the total energy of the system. The agreement is also quantitative in the low density limit, for which an explicit analytical form of the time correlation function has been derived. The reported results also provide support for the existence of the HCS as a solution of the N-particle Liouville equation.