Memory effects in a gas of viscoelastic particles

TL;DR

This paper investigates memory effects like the Mpemba and Kovacs phenomena in a viscoelastic granular gas, revealing unique behaviors during thermal relaxation through theoretical and simulation methods.

Contribution

It demonstrates the presence of significant memory effects in a viscoelastic granular gas, contrasting with simpler models, using analytical and computational approaches.

Findings

Observation of the Mpemba effect in granular gases.

Detection of the Kovacs effect during temperature relaxation.

Good agreement between kinetic theory and simulations.

Abstract

We study a granular gas of viscoelastic particles (kinetic energy loss upon collision is a function of the particles' relative velocities at impact) subject to a stochastic thermostat. We show that the system displays anomalous cooling and heating rates during thermal relaxation processes, this causing the emergence of thermal memory. In particular, a significant \textit{Mpemba effect} is present; i.e., an initially hotter/cooler granular gas can cool down/heat up faster than an in comparison cooler/hotter granular gas. Moreover, a \textit{Kovacs effect} is also observed; i.e., a non-monotonic relaxation of the granular temperature --if the gas undergoes certain sudden temperature changes before fixing its value. Our results show that both memory effects have distinct features, very different and eventually opposed to those reported in theory for granular fluids under simpler collisional models. We study our system via three independent methods: approximate solution of the kinetic equation time evolution and computer simulations (both molecular dynamics simulations and Direct Simulation Monte Carlo method), finding good agreement between them.