Simple model with facilitated dynamics for granular compaction

TL;DR

This paper introduces a simple lattice model to study granular media compaction, capturing key experimental behaviors such as inverse logarithmic relaxation and providing analytical expressions for relevant time scales and asymptotic density.

Contribution

It presents a new analytical approach to model granular compaction dynamics, aligning theoretical predictions with simulation results.

Findings

Relaxation of density follows inverse logarithmic law.

Analytical expression for relevant time scale derived.

Asymptotic density predictions match Monte Carlo simulations.

Abstract

A simple lattice model is used to study compaction in granular media. As in real experiments, we consider a series of taps separated by large enough waiting times. The relaxation of the density exhibits the characteristic inverse logarithmic law. Moreover, we have been able to identify analytically the relevant time scale, leading to a relaxation law independent of the specific values of the parameters. Also, an expression for the asymptotic density reached in the compaction process has been derived. The theoretical predictions agree fairly well with the results from the Monte Carlo simulation.