88 Pages


The static properties of an aggregate of granular mate­ rial are inexorably linked to the process by which it was formed. This, in itself, is not peculiar to granular mate­ rials; for example, rapidly solidified metallic alloys may well behave differently from their slowly cooled counter­ parts, and the behavior of a plastic depends on the ex­ truding process used in its formation. This sensitivity implies that the system, although static, is far from thermodyamic equilibrium. In the cases of the plastic and the metal, solidification takes place as the system cools down due to contact with the external environment. In contrast, for a granular material, the cessation of mo­ tion of the grains arises from the dissipation of kinetic energy. If this dissipation is very rapid, the system is un­ able to explore much phase space, and it jams, arriving at a state which may well be special in ways which will be discussed in the following. A system which expends its energy slowly, so that it has ample time to “find” a favorable state (whatever that may be), should not be said to have jammed, and its properties may be quite different from those of a jammed state. As physicists, it is incumbent upon us to ask whether there are any sta­ tistical properties which typify the jammed state, and if so, what their physical consequences are. For granular materials, at stake is an understanding of stress propa­ gation, fluctuations in the forces between grains, and the probability distribution of stress itself. Although much effort has been expended on these questions, hard results remain elusive. And this issue is not academic - the various possibilities are fundamentally different. There is one property, however, which derives directly from the jamming scenario: the critical importance of the specifics of the construction history on the physics of the mate­ rial. Since a jammed system does not have the ability to explore its phase space, we would expect, at least with re­ spect to some physical properties, that each system will be different (Of course, it may certainly be that other physical properties ” self-aver age” , that is, all similarly prepared systems will have the same values.). This pic­ ture is dramatically different from non-jamming systems, for example an ordinary fluid, for which the macroscopic constraints (e.g., size and shape of container, or tem­ perature) determine all the properties precisely, and no variation is found.