Edwards-like statistical mechanical description of the parking lot model for vibrated granular materials

TL;DR

This paper extends Edwards' statistical mechanical framework to the parking lot model, capturing key features of vibrated granular materials and their memory effects, especially in slow compaction regimes.

Contribution

It introduces a generalized flat measure incorporating available volume, enabling a better description of vibrated granular media behavior.

Findings

Good agreement with model behavior in slow compaction regime

Captures memory effects observed in experiments

Extends Edwards' approach to finite tapping strengths

Abstract

We apply the statistical mechanical approach based on the ``flat'' measure proposed by Edwards and coworkers to the parking lot model, a model that reproduces the main features of the phenomenology of vibrated granular materials. We first build the flat measure for the case of vanishingly small tapping strength and then generalize the approach to finite tapping strengths by introducing a new ``thermodynamic'' parameter, the available volume for particle insertion, in addition to the particle density. This description is able to take into account the various memory effects observed in vibrated granular media. Although not exact, the approach gives a good description of the behavior of the parking-lot model in the regime of slow compaction.