Long-time tails in freely cooling granular gases

Abstract

The long-time behavior of the current auto-correlation functions for the velocity, the shear stress and the heat flux is investigated in freely cooling granular gases. It is found that the correlation functions for the velocity and the shear stress have the long-time tails obeying ${\tau }^{-d/2}$, while the correlation function of heat flux decays as ${\tau }^{-(d+2)/2}\exp (-{\zeta }^{\ast }\tau )$ with the dimensionless cooling rate ${\zeta }^{\ast }$, the spatial dimension $d$ and the scaled time $\tau$ in terms of the collision frequency. The result of our numerical simulation of the freely cooling granular gases is consistent with the theoretical prediction.

arXiv comment26 pages, 5 figures

References in corpus (19)

• A model for collisions in granular gases
• Patterns and Collective Behavior in Granular Media: Theoretical Concepts
• Extension of Haff's cooling law in granular flows
• Mesoscopic Theory of Granular Fluids
• Cahn-Hilliard Theory for Unstable Granular Flows
• Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow
• Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
• Velocity correlations in the dense granular shear flows: Effects on energy dissipation and normal stress
• Hydrodynamics and transport coefficients for Granular Gases
• Simple and efficent algorithm for large scale molecular dynamics simulation in hard disk systems
• A model for the atomic-scale structure of a dense, nonequilibrium fluid: the homogeneous cooling state of granular fluids
• Breakdown of the Sonine expansion for the velocity distribution of Granular Gases
• Diffusion in a Granular Fluid - Simulation
• The rheology of dense, polydisperse granular fluids under shear
• Diffusion in a Granular Fluid - Theory
• Green-Kubo Expressions for a Granular Gas
• Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
• Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog
• Simulation for the oblique impact of a lattice system

Cited by in corpus (6)

• Long-time tails and cage effect in driven granular fluids
• Spatial correlations in sheared isothermal liquids : From elastic particles to granular particles
• Fluctuating Navier-Stokes equations for inelastic hard spheres or disks
• Unified description of long-time tails and long-range correlation functions for sheared granular liquids
• A classical long-time tail in a driven granular fluid
• Power-law decay of the velocity autocorrelation function of a granular fluid in the homogeneous cooling state