Mpemba-like effect protocol for granular gases of inelastic and rough hard disks

TL;DR

This paper investigates the emergence of a Mpemba-like effect in granular gases of inelastic, rough hard disks driven by thermostats that split noise into translational and rotational components, using theoretical analysis and simulations.

Contribution

It introduces a protocol for generating initial states to observe the Mpemba effect in granular gases with inelastic and rough particles, combining theoretical and simulation approaches.

Findings

Mpemba effect characterized by temperature curve crossings

Temperature overshoot observed in the evolution

Good agreement between theory and simulations

Abstract

We study the conditions under which a Mpemba-like effect emerges in granular gases of inelastic and rough hard disks driven by a class of thermostats characterized by the splitting of the noise intensity into translational and rotational counterparts. Thus, granular particles are affected by a stochastic force and a stochastic torque, which inject translational and rotational energy, respectively. We realize that a certain choice of a thermostat of this class can be characterized just by the total intensity and the fraction of noise transferred to the rotational degree of freedom with respect to the translational ones. Firstly, Mpemba effect is characterized by the appearance of a crossing between the temperature curves of the considered samples. Later, an overshoot of the temperature evolution with respect to the steady-state value is observed and the mechanism of Mpemba effect generation is changed. The election of parameters allows to design plausible protocols based on these thermostats for generating the initial states to observe the Mpemba-like effect in experiments. In order to obtain explicit results, we use a well-founded Maxwellian approximation for the evolution dynamics and the steady-state quantities. Finally, theoretical results are compared with direct simulation Monte Carlo and molecular dynamics results, and a very good agreement is found.