Velocity fluctuations in cooling granular gases

TL;DR

This paper investigates velocity fluctuations and correlations in cooling granular gases in 1D and 2D, revealing limitations of mean field models and proposing a lattice model that accurately captures the complex dynamics.

Contribution

It introduces an Inelastic Lattice Maxwell Model that reproduces properties of the Homogeneous Cooling State and provides detailed insights into velocity correlation structures.

Findings

Mean field models fail when velocity fluctuations are significant.

The lattice model accurately reproduces the Homogeneous Cooling State.

Velocity field dynamics are compatible with diffusive behavior at large scales.

Abstract

We study the formation and the dynamics of correlations in the velocity field for 1D and 2D cooling granular gases with the assumption of negligible density fluctuations (``Homogeneous Velocity-correlated Cooling State'', HVCS). It is shown that the predictions of mean field models fail when velocity fluctuations become important. The study of correlations is done by means of molecular dynamics and introducing an Inelastic Lattice Maxwell Models. This lattice model is able to reproduce all the properties of the Homogeneous Cooling State and several features of the HVCS. Moreover it allows very precise measurements of structure functions and other crucial statistical indicators. The study suggests that both the 1D and the 2D dynamics of the velocity field are compatible with a diffusive dynamics at large scale with a more complex behavior at small scale. In 2D the issue of scale separation, which is of interest in the context of kinetic theories, is addressed.