Statistical Mechanics of jamming and segregation in granular media

This chapter discusses Edward's Statistical Mechanics approach to granular media in the framework of schematic hard spheres lattice models. As this approach appears to hold to a very good approximation, by analytical calculations of Edward's partition function at a mean field level, the chapter describes the derivation of the system phase diagram and shows that "jamming" corresponds to a phase transition from a "fluid" to a "glassy" phase, observed when crystallization is avoided. The nature of such a "glassy" phase turns out to be the same found in mean field models for glass formers. The chapter also focuses on mixing/segregation phenomena of binary mixtures--the presence of fluid-crystal phase transitions drives segregation as a form of phase separation and, within a given phase, gravity can also induce a kind of "vertical" segregation, usually not associated to phase transitions.