Jamming transition in granular media: A mean field approximation and numerical simulations

TL;DR

This paper explores the jamming transition in granular media through a mean field theory and numerical simulations, revealing glass-like features and confirming the connection between jamming and glass transitions.

Contribution

It introduces a cavity method mean field theory applied to a lattice model and demonstrates glassy dynamics in three-dimensional simulations of granular media.

Findings

Jamming transition exhibits glassy relaxation features.

Two-step decay in relaxation functions observed.

Dynamic heterogeneities similar to glassy systems.

Abstract

In order to study analytically the nature of the jamming transition in granular material, we have considered a cavity method mean field theory, in the framework of a statistical mechanics approach, based on Edwards' original idea. For simplicity we have applied the theory to a lattice model and a transition with exactly the same nature of the glass transition in mean field models for usual glass formers is found. The model is also simulated in three dimensions under tap dynamics and a jamming transition with glassy features is observed. In particular two step decays appear in the relaxation functions and dynamic heterogeneities resembling ones usually observed in glassy systems. These results confirm early speculations about the connection between the jamming transition in granular media and the glass transition in usual glass formers, giving moreover a precise interpretation of its nature.