Mean field theory of dense granular media

We briefly review some recent analytical results on the Statistical Mechanics of dense granular media. In particular, by mean field calculation we derive the phase diagram of monodisperse and bidisperse granular assemblies. We show that "jamming" corresponds to a phase transition from a "fluid" to a "glassy" phase, observed when crystallization is avoided. The natureofsuch a "glassy" phase turnsouttobe the same found in mean field models for glass formers. This gives quantitative evidence to the idea of a unified description of the "jamming" transition in granular media and thermal systems, such as glasses. We also discuss mixing/segregation transitions in binary mixtures and their connections to phase separation and "geometric" effects. © 2005 Taylor & Francis Group.