The inelastic Takahashi hard-rod gas

TL;DR

This paper investigates a one-dimensional inelastic hard-rod gas with additional square-well interactions, revealing how these interactions alter energy dissipation and enabling analytical and exact solutions in elastic and inelastic regimes.

Contribution

It introduces a simple yet rich model combining inelastic collisions and square-well potentials, providing analytical solutions and a theoretical framework for understanding its thermodynamics and dissipation behavior.

Findings

Square-well interactions significantly modify energy dissipation rates.

The elastic limit yields an exact thermodynamic solution.

Theoretical predictions align well with simulation results.

Abstract

We study a one-dimensional fluid of hard-rods interacting each other via binary inelastic collisions and a short ranged square-well potential. Upon tuning the depth and the sign of the well, we investigate the interplay between dissipation and cohesive or repulsive forces. Molecular dynamics simulations of the cooling regime indicate that the presence of this simple interparticle interaction is sufficient to significantly modify the energy dissipation rates expected by the Haff's law for the free cooling. The simplicity of the model makes it amenable to an analytical approach based on the Boltzmann-Enskog transport equation which allows deriving the behaviour of the granular temperature. Furthermore, in the elastic limit, the model can be solved exactly to provide a full thermodynamic description. A meaningful theoretical approximation explaining the properties of the inelastic system in interaction with a thermal bath can be directly extrapolated from the properties of the corresponding elastic system, upon a proper re-definition of the relevant observables. Simulation results both in the cooling and driven regime can be fairly interpreted according to our theoretical approach and compare rather well to our predictions.