Anomalous self-diffusion in a freely evolving granular gas near the shearing instability

TL;DR

This paper investigates how the self-diffusion coefficient in a granular gas diverges logarithmically near the shearing instability, revealing unique behavior absent in elastic gases, supported by theoretical and simulation evidence.

Contribution

It introduces a mode-coupling theory predicting divergence of the diffusion coefficient near instability, confirmed by molecular dynamics simulations in two dimensions.

Findings

Self-diffusion coefficient diverges logarithmically near shearing instability.

Divergence is due to coupling with shear modes and is absent in elastic gases.

Theoretical predictions are validated by molecular dynamics simulations.

Abstract

The self-diffusion coefficient of a granular gas in the homogeneous cooling state is analyzed near the shearing instability. Using mode-coupling theory, it is shown that the coefficient diverges logarithmically as the instability is approached, due to the coupling of the diffusion process with the shear modes. The divergent behavior, which is peculiar of granular gases and disappears in the elastic limit, does not depend on any other transport coefficient. The theoretical prediction is confirmed by molecular dynamics simulation results for two-dimensional systems.