  Granular fluids consist of collections of activated mesoscopic or macroscopic
particles (e.g., powders or grains) whose flows often appear similar to those
of normal fluids. To explore the qualitative and quantitative description of
these flows an idealized model for such fluids, a system of smooth inelastic
hard spheres, is considered. The single feature distinguishing granular and
normal fluids being explored in this way is the inelasticity of collisions. The
dominant differences observed in real granular fluids are indeed captured by
this feature. Following a brief introductory description of real granular
fluids and motivation for the idealized model, the elements of nonequilibrium
statistical mechanics are recalled (observables, states, and their dynamics).
Peculiarities of the hard sphere interactions are developed in detail. The
exact microscopic balance equations for the number, energy, and momentum
densities are derived and their averages described as the origin for a possible
macroscopic continuum mechanics description. This formally exact analysis leads
to closed, macroscopic hydrodynamic equations through the notion of a "normal"
state. This concept is introduced and the Navier-Stokes constitutive equations
are derived, with associated Green-Kubo expressions for the transport
coefficients. A parallel description of granular gases is described in the
context of kinetic theory, and the Boltzmann limit is identified critically.
The construction of the "normal" solution to the kinetic equation is outlined,
and Navier-Stokes order hydrodynamic equations are re-derived for a low density
granular gas.
