Introduction

Many granular and particulate systems have been studied in the literature and there is a wide range of parameters and physical states that they support. Here we confine ourselves to jammed ensembles of perfectly hard particles. There are extensive studies in the literature of suspensions of particles in liquids or gases using various methods, including Stokes or Einstein fluid mechanics and Boltzmann or Enskog gas mechanics. These, however, are not jammed and we therefore discuss them no further. This chapter is not intended as a comprehensive review but rather as an interim report on the work that has been done by us to date.

The simplest material for a general jammed system is that of hard and rough particles, ideally perfectly hard and infinitely rough. To a lesser extent it is also useful to study perfectly hard but smooth particles. The former is easily available in nature, for example sand, salt, etc., and we prefer to focus on this case. Nevertheless, the discussion can be readily extended to systems of particles of finite rigidity, as has been shown recently. In jammed systems particles touch their neighbours at points, which have to be either predicted or observed. At these contact points the particles exert on one another forces that must obey Newton's laws. In general, determination of the structure and the forces requires prior knowledge about the history of formation of the jammed system.