Energy decay in three-dimensional freely cooling granular gas

Abstract

The kinetic energy of a freely cooling granular gas decreases as a power law $t^{-\theta }$ at large times $t$. Two theoretical conjectures exist for the exponent $\theta$. One based on ballistic aggregation of compact spherical aggregates predicts $\theta =2d/(d+2)$ in $d$ dimensions. The other based on Burgers equation describing anisotropic, extended clusters predicts $\theta =d/2$ when $2\le d\le 4$. We do extensive simulations in three dimensions to find that while $\theta$ is as predicted by ballistic aggregation, the cluster statistics and velocity distribution differ from it. Thus, the freely cooling granular gas fits to neither the ballistic aggregation or a Burgers equation description.

5 pages, 5 figures

References in corpus (7)

• Dynamics of Freely Cooling Granular Gases
• Experimental investigation of the freely cooling granular gas
• Violation of Porod law in a freely cooling granular gas in one dimension
• Statistical Properties of the Final State in One-dimensional Ballistic Aggregation
• On the equivalence of the freely cooling granular gas to the sticky gas
• Shock Propagation in Granular Flow Subjected to an External Impact
• Lattice models for ballistic aggregation in one-dimension

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• Inhomogeneous Cooling of the Rough Granular Gas in Two Dimensions
• A universal scaling law for the evolution of granular gases
• Shock propagation in locally driven granular systems
• Velocity Distribution of Driven Inelastic One-component Maxwell gas
• A Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation
• Driven inelastic Maxwell gases
• High-energy velocity tails in uniformly heated granular materials
• Asymptotic behavior of the velocity distribution of driven inelastic gas with scalar velocities: analytical results
• Asymptotic velocity distribution of a driven one dimensional binary granular Maxwell gas
• Inelastic Maxwell models for monodisperse gas-solid flows
• Enhanced collective vibrations in granular materials