Velocity distributions and correlations in
homogeneously heated granular media
Abstract:
We compare the steady state velocity distributions from our
three-dimensional inelastic hard sphere molecular dynamics simulation
for homogeneously heated granular media, with the predictions of a mean
field-type Enskog-Boltzmann equation for inelastic hard spheres [T. P.
C. van Noije and M. H. Ernst, Granular Matter 1, 57 (1998)].
Although we find qualitative agreement for all values of density and
inelasticity, the quantitative disagreement approaches ~40% at high
inelasticity or density. By contrast the predictions of the
pseudo-Maxwell molecule model [J. A. Carrillo, C. Cercignani, and I. M.
Gamba, Phys. Rev. E 62,
7700 (2000)] are both qualitatively and quantitatively different from
those of our simulation. We also measure short-range and long-range
velocity correlations exhibiting nonzero correlations at contact before
the collision, and being consistent with a slow algebraic decay over a
decade in the unit of the diameter of the particle, proportional to r-(1+a
), where 0.2< a <0.3. The existence of these
correlations implies the failure of the molecular chaos assumption and
the mean field approximation, which is responsible for the quantitative
disagreement of the inelastic hard sphere kinetic theory.
Phys. Rev. E 64,
031303 (2001).
Manuscript available in PDF and PS formats.