Statistical mechanics of granular gases in compartmentalized systems

TL;DR

This paper models the behavior of granular particles in two compartments, revealing a transition from symmetric to asymmetric states driven by inelastic collisions and stochastic effects, using kinetic theory and simulations.

Contribution

It introduces a kinetic model combining inelastic collisions, stochastic driving, and compartment exchange, analyzing phase transitions in granular gases.

Findings

Identifies a phase transition from symmetric to asymmetric states.

Demonstrates the impact of stochastic driving on system behavior.

Validates the kinetic model with Direct Simulation Monte Carlo results.

Abstract

We study the behavior of an assembly of $N$ granular particles contained in two compartments within a simple kinetic approach. The particles belonging to each compartment collide inelastically with each other and are driven by a stochastic heat bath. In addition, the fastest particles can change compartment at a rate which depends on their kinetic energy. Via a Boltzmann velocity distribution approach we first study the dynamics of the model in terms of a coupled set of equations for the populations in the containers and their granular temperatures and find a crossover from a symmetric high-temperature phase to an asymmetric low temperature phase. Finally, in order to include statistical fluctuations, we solve the model within the Direct Simulation Monte Carlo approach. Comparison with previous studies are presented.