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One goal of this paper is to discuss the classical definition of granular temperature as an extension of its thermodynamic equivalent and a useful concept which provides an important characterization of fluidized granular matter. Following a review of some basic concepts and techniques (with emphasis on fundamental issues) we present new results for a system that can exhibit strong violations of equipartition, yet is amenable to description by classical granular hydrodynamics, namely a binary granular gas mixture. A second goal of this article is to present a result that pertains to dense granular and molecular solids alike, namely the existence of a correction to the elastic energy which is related to the heat flux in the equations of continuum mechanics. The latter is of the same (second) order in the strain as the elastic energy. Although recent definitions of temperatures for granular matter, glasses and other disordered many-body systems are not within the scope of this article we do make several general comments on this subject in the closing section., Comment: 30 pages, 5 figures, submitted to Powder Technology

The expansion of the velocity distribution function for the homogeneous cooling state (HCS) in a Sonine polynomial series around a Maxwellian is shown to be divergent, though Borel resummable. A convergent expansion for the HCS has been devised and employed to obtain the HCS velocity distribution function and (using it) the linear transport coefficients for a three dimensional monodisperse granular gas of smooth inelastic spheres, for all physical values of the coefficient of normal restitution. The results are in very good agreement with findings of DSMC simulations.

We measured the vertical pressure response function of a layer of sand submitted to a localized normal force at its surface. We found that this response profile depends on the way the layer has been prepared: all profiles show a single centered peak whose width scales with the thickness of the layer, but a dense packing gives a wider peak than a loose one. We calculate the prediction of isotropic elastic theory in presence of a bottom boundary and compare it to the data. We found that the theory gives the right scaling and the correct qualitative shape, but fails to really fit the data., Comment: 22 pages, 9 figures, submitted to Euro. Phys. J. E