We have performed a systematic, large-scale simulation study of granular media in two-and threedimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow vx(z) scales with height of the pile H, according to vx(z) ∝ H α , with α = 1.52 ± 0.05. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations.

We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard-spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from z = 6 as the friction coefficient µ between two particles is increased.

We discuss the onset of irreversibility and entanglement of vortex lines in high Tc superconductors due to point disorder and thermal fluctuations using a simplified cage model. A combination of Flory arguments, known results from directed polymers in random media, and a Lindemann criterion are used to estimate the field and temperature dependence of irreversibility, mechanical entanglement and thermal melting. The qualitative features of this dependence, including its nonmonotonicity when disorder is sufficiently strong, are in good agreement with recent experiments.

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in a mean field version of a model for a segmented fault system in a three-dimensional elastic solid [1,2]. The studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or "overshoot") effects ǫ and the normal distance L of the driving forces from the fault. In general, small ǫ and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large ǫ and large L lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters.The implications for realistic earthquake statistics are discussed.

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