The jamming transition of granular media

A statistical mechanical approach to granular material is proposed. Using lattice models from standard statistical mechanics and results from a mean-field replica approach we find a jamming transition in granular media closely related to the glass transition in supercooled liquids. These models reproduce the logarithmic relaxation in granular compaction and reversible-irreversible lines, in agreement with experimental data. The models also exhibit aging effects and breakdown of the usual fluctuation-dissipation relation. It is shown that the glass transition may be responsible for the logarithmic relaxation and may be related to the cooperative effects underlying many phenomena exhibited by granular materials such as the Reynolds transition.