Exact predictions from Edwards ensemble vs realistic simulations of tapped narrow two dimensional granular columns

Abstract

We simulate, via a discrete element method, the tapping of a narrow column of disks under gravity. For frictionless disks, this system has a simple analytical expression for the density of states in the Edwards volume ensemble. We compare the predictions of the ensemble at constant compactivity against the results for the steady states obtained in the simulations. We show that the steady states cannot be properly described since the microstates sampled are not in correspondence with the predicted distributions, suggesting that the postulates of flat measure and ergodicity are, either or both, invalid for this simple realization of a static granular system. However, we show that certain qualitative features of the volume fluctuations which are difficult to predict from simple arguments are captured by the theory.