Effective potentials in a bidimensional vibrated granular gas

TL;DR

This study numerically investigates spatial correlations in a vibrated granular gas, deriving effective interaction potentials from pair distribution functions and validating them through Monte Carlo simulations.

Contribution

It introduces a method to extract effective potentials from granular gas correlations and explores how these potentials vary with dissipation and density.

Findings

Effective potentials increase at contact as restitution decreases.

Deeper potential wells are associated with more dissipative dynamics.

Resonant bouncing can enhance correlations contrary to general trends.

Abstract

We present a numerical study of the spatial correlations of a quasi-two-dimensional granular fluid kept in a non-static steady state via vertical shaking. The simulations explore a wide range of packing fractions, vertical accelerations and restitution coefficients, always staying below the crystallization limit. From the simulations we obtain the relevant Pair Distribution Functions (PDFs), and effective potentials for the interparticle interaction are extracted from these PDFs via the Ornstein-Zernike equation with the Percus-Yevick closure. The correlations in the granular structures originating from these effective potentials are checked against the originating PDF using standard Monte Carlo simulations, and we find in general an excellent agreement. The resulting effective potentials show an increase of the spatial correlation at contact with the decreasing values of the restitution coefficient, and a general tendency of the potentials to display deeper wells for more dissipative dynamics. An exception to this general trend appears for certain combinations of density and forcing, where resonant bouncing increases correlations.