Fermi Statistics of Weakly Exicted Granular Systems in a Vibrating Bed I: Molecular Dynamics Simulations

TL;DR

This study uses molecular dynamics simulations to test a thermodynamic theory of weakly excited granular systems, modeling them as spinless Fermions, and finds good agreement between theory and simulation results.

Contribution

It validates the thermodynamic theory of granular systems as Fermions through detailed molecular dynamics simulations and measurements.

Findings

Good agreement between theory and simulations in temperature estimation

Scaling behavior of <z(T)> and <( abla z(T))^2> matches theoretical predictions

Method effectively determines temperature from density profiles

Abstract

Molecular dynamics simulations were carried out to test the thermodynamic theory of weakly excited, two-dimensional granular systems [Hayakawa and Hong, Phys. Rev. Lett. 78, 2764 (1997)], where granular materials are viewed as a collection of spinless Fermions. We first determine the global temperature T by fitting the steady state density profile to the Fermi distribution function, and then measure the center of mass, <z(T)>, and its fluctuations, <(\Delta z(T))^2> as a function of T. We find a fairly good agreement between theory and simulations, in particular, in the estimation of the temperature and the scaling behavior of <z(T)> and <(\Delta z(T))^2>.