Lyapunov instability of rough hard-disk fluids

TL;DR

This study investigates the dynamical instability of rough hard-disk fluids in two dimensions, analyzing how rotation influences chaos, phase-space mixing, and Lyapunov spectra across different densities and moments of inertia.

Contribution

It provides a detailed characterization of Lyapunov spectra and chaos measures in rough hard-disk fluids, revealing how rotational degrees of freedom affect dynamical instability.

Findings

Rotation affects the separation of Lyapunov spectrum components.

Phase-space mixing rate decreases with increased rotational influence.

Maximum Lyapunov exponent is enhanced at high densities but reduced at low densities.

Abstract

The dynamical instability of rough hard-disk fluids in two dimensions is characterized through the Lyapunov spectrum and the Kolmogorov-Sinai entropy, $h_{KS}$, for a wide range of densities and moments of inertia $I$. For small $I$ the spectrum separates into translation-dominated and rotation-dominated parts. With increasing $I$ the rotation-dominated part is gradually filled in at the expense of translation, until such a separation becomes meaningless. At any density, the rate of phase-space mixing, given by $h_{KS}$, becomes less and less effective the more the rotation affects the dynamics. However, the degree of dynamical chaos, measured by the maximum Lyapunov exponent, is only enhanced by the rotational degrees of freedom for high-density gases, but is diminished for lower densities. Surprisingly, no traces of Lyapunov modes were found in the spectrum for larger moments of inertia. The spatial localization of the perturbation vector associated with the maximum exponent however persists for any $I$.