| Granular materials range in size from micron-sized pharmaceuticals to mountain-sized asteroids. Despite this great range of scales, certain aspects of their underlying physics are universal. In the case of dense, dry granular materials the physics is dominated by interparticle contacts. Because the mobilization of friction introduces an element of history dependence, the actual state of a granular system is not necessarily apparent without a careful study of how that state came to be. Additionally, the distribution of forces carried by interparticle contacts has been shown to be highly irregular, even for regularly packed grains. In dense granular matter there are large force fluctuations, many times greater than the mean, that are carried long distances over filament-like chains of contacts, forming complicated force networks. Features such as this are due to the non-equilibrium nature of granular matter. Because the influence of temperature is negligible even for micron-sized particles, the smallest push can potentially cause a system-wide avalanche. Since non-equilibrium physics of any type is in its infancy, the study of dense granular matter is an attempt to explore potential approaches to understand any non-equilibrium system. I have adapted experimental and analytic techniques to the exploration of this physics. I have evaluated the applicability of soil mechanics-based continuum approaches to describe the non-linear phenomena of dense granular flows. I have also investigated continuum descriptions of static granular matter under gravity. In both cases, I have examined the influence of large fluctuations on their behavior and in the case of static systems I have proposed describing those fluctuations in the language of percolation theory. I have found that certain regimes exist in which the discrete nature of granular matter can be smoothed over by a continuum description, but more importantly I have found many places where granular phenomena cannot be ignored. |
