Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases

Details Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases

2004-10-27

arxiv.org/abs/cond-mat/0410708v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1088/0953-8984/17/24/008

It is shown that the hydrodynamic modes of a dilute granular gas of inelastic hard spheres can be identified, and calculated in the long wavelength limit. Assuming they dominate at long times, formal expressions for the Navier-Stokes transport coefficients are derived. They can be expressed in a form that generalizes the Green-Kubo relations for molecular systems, and it is shown that they can also be evaluated by means of $N$-particle simulation methods. The form of the hydrodynamic modes to zeroth order in the gradients is used to detect the presence of inherent velocity correlations in the homogeneous cooling state, even in the low density limit. They manifest themselves in the fluctuations of the total energy of the system. The theoretical predictions are shown to be in agreement with molecular dynamics simulations. Relevant related questions deserving further attention are pointed out.

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