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

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.

arXiv comment10 pages, 10 figures, submitted to Phys. Rev.E

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• Jamming transition in granular media: A mean field approximation and numerical simulations
• Glassy dynamics in thermally-activated list sorting
• Fluctuation-dissipation relation and the Edwards entropy for a glassy granular compaction model
• Exact correlation functions in particle-reaction models with immobile particles
• Optimal random deposition of interacting particles
• A Bose-Einstein Approach to the Random Partitioning of an Integer
• Emerging quasi-0D states at vanishing total entropy of the 1D hard sphere system: a coarse-grained similarity to the car parking problem