Competition and cooperation: aspects of dynamics in sandpiles

In this paper, we review some of our approaches to granular dynamics, now well known (Mehta 1994 Granular Matter: an Interdisciplinary Approach ed A Mehta (New York: Springer)) to consist of both fast and slow relaxational processes. In the first case, grains typically compete with each other, while in the second, they cooperate. A typical result of cooperation is the formation of stable bridges, signatures of spatiotemporal inhomogeneities; we review their geometrical characteristics and compare theoretical results with those of independent simulations. Cooperative excitations due to local density fluctuations are also responsible for relaxation at the angle of repose; the Competition between these fluctuations and external driving forces can, on the other hand, result in a (rare) collapse of the sandpile to the horizontal. Both these features are present in a theory reviewed here. An arena where the effects of cooperation versus competition are felt most keenly is granular compaction; we review here a random graph model, where three-spin interactions are used to model compaction under tapping. The compaction curve shows distinct regions where 'fast' and 'slow' dynamics apply, separated by what we have called the single-particle relaxation threshold. In the final section of this paper, we explore the effect of shape-jagged versus regular-on the compaction of packings near their jamming limit. One of our major results is an entropic landscape that, while microscopically rough, manifests Edwards' flatness at a macroscopic level. Another major result is that of surface intermittency under low-intensity shaking.