  Granular media such as sand and sugar are ubiquitous in nature and industry
but are less well understood than fluids or solids. We consider the behavior of
rapid granular flows where the transfer of momenta by collisions dominates. The
physics is quite different for the opposite limit of static or slowly moving
grains (e.g., sand piles). To gain understanding of granular flows we consider
two problems that have been investigated with experiments, particle simulations
and hydrodynamic theory: vertically oscillating granular layers and flow past
an obstacle. Oscillating granular layers spontaneously form spatial patterns
when the container acceleration amplitude exceeds a critical value, about 2.5
times the gravitational acceleration. Simulations with hard spheres that
conserve linear momentum and dissipate energy in collisions are in qualitative
accord with some but not all aspects of the observed patterns. It is necessary
to include friction and angular momentum conservation in the simulations to
achieve quantitative accord with observations. [Abridged]
