Random loose packing and an order parameter for the parking lot model

TL;DR

This paper determines the random loose packing fraction in the parking lot model and introduces an order parameter to connect statistical mechanics with granular hydrodynamics.

Contribution

It introduces an order parameter for the parking lot model and links Edwards' statistical mechanics to granular hydrodynamics.

Findings

Random loose packing fraction obtained at infinite compactivity.

Order parameter $ ho$ characterizes deviation from steady state.

Configurations with $ ho<1$ are aging.

Abstract

We have obtained the random loose packing fraction of the parking lot model (PLM) by taking the limit of infinite compactivity in the two-variable statistical description of Tarjus and Viot for the PLM. The PLM is a stochastic model of adsorption and desorption of particles on a substrate that have been used as a model for compaction of granular materials. An order parameter $\rho$ is introduced to characterize how far from a steady state situation the model is. Thus, configurations with $\rho<1$ age. We propose that $\rho$ can be a starting point in order to stablish a connection between Edwards' statistical mechanics and granular hydrodynamics.