Built upon sand: Theoretical ideas inspired by granular flows

Granulated materials, like sand and sugar and salt, are composed of many pi eces that can move independently. The study of collisions and flow in these materials requires new theoretical ideas beyond those in the standard stat istical mechanics or hydrodynamics or traditional solid mechanics. Granular materials differ from standard molecular materials in that frictional forc es among grains can dissipate energy and drive the system toward frozen or glassy configurations. In experimental studies of these materials, one sees complex flow patterns similar to those of ordinary liquids, but also freez ing, plasticity, and hysteresis. To explain these results, theorists have l ooked at models based upon inelastic collisions among particles. With the a id of computer simulations of these models they have tried to build a "stat istical-dynamics" of inelastic collisions. One effect seen, called inelasti c collapse, is a freezing of some of the degrees of freedom induced by an i nfinity of inelastic collisions. More often some degrees of freedom are par tially frozen, so that there can be a rather cold clump of material in corr elated motion. Conversely, thin layers of material may be mobile, while all the material around them is frozen. In these and other ways, granular moti on looks different from movement in other kinds of materials. Simulations i n simple geometries may also be used to ask questions like When does the us ual Boltzmann-Gibbs-Maxwell statistical mechanics arise?, What are the natu re of the probability distributions for forces between the grains?, and Mig ht the system possibly be described by uniform partial differential equatio ns? One might even say that the study of granular materials gives one a cha nce to reinvent statistical mechanics in a new context. [S0034-6861(99)0070 1-1].