Power-law decay of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state

TL;DR

This paper investigates the decay behavior of the velocity autocorrelation function in a granular fluid's homogeneous cooling state, combining mode-coupling theory with simulations to reveal power-law decay and instability effects.

Contribution

It provides a theoretical prediction of power-law decay in the velocity autocorrelation function and validates it with molecular dynamics simulations, considering finite size and instability effects.

Findings

Power-law decay observed in the autocorrelation function.

Good agreement between theory and simulations after finite size corrections.

Approaching shearing instability influences decay behavior.

Abstract

The hydrodynamic part of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state has been calculated by using mode-coupling theory for a finite system with periodic boundary conditions. The existence of the shearing instability, leading to a divergent behavior of the velocity flow fluctuations, is taken into account. A time region in which the velocity autocorrelation function exhibits a power law decay, when time is measured by the number of collisions per particle, has been been identified. Also the explicit form of the exponential asymptotic long time decay has been obtained. The theoretical prediction for the power law decay is compared with molecular dynamics simulation results, and a good agreement is found, after taking into account finite size corrections. The effects of approaching the shearing instability are also explored.