Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2001-05-16
Phys. Rev. E 64, 031303 (2001)
Physics
Condensed Matter
Soft Condensed Matter
23 pages, 15 figures, Phys. Rev. E, in press
Scientific paper
10.1103/PhysRevE.64.031303
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 [van Noije & Ernst, Gran. Matt. {\bf 1}, 57 (1998)]. Although we find qualitative agreement for all values of density and inelasticity, the quantitative disagreement approaches $\sim 40%$ at high inelasticity or density. By contrast the predictions of the pseudo-Maxwell molecule model [Carrillo, Cercignani & Gamba, Phys. Rev. E, {\bf 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 non-zero 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 $r^{-(1+\alpha)}$, where $0.2 < \alpha < 0.3$. The existence of these correlations imply 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.
Moon Sung Joon
Shattuck Mark D.
Swift Brandon J.
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