Ordered and disordered dynamics in monolayers of rolling particles

TL;DR

This paper studies the complex behaviors of monolayers of rolling particles, revealing stable ordered states, chaotic vibrations, and a robust velocity-temperature relationship in both lattice and gas configurations.

Contribution

It introduces a novel model of rolling particles with non-isotropic inertia and offset centers, analyzing ordered and disordered dynamics beyond traditional statistical mechanics.

Findings

Existence and stability of ordered lattice states.

Chaotic vibrations and disturbance propagation in ordered states.

Linear velocity distribution relationship enabling temperature definition.

Abstract

We consider the ordered and disordered dynamics for monolayers of rolling self-interacting particles with an offset center of mass and a non-isotropic inertia tensor. The rolling constraint is considered as a simplified model of a very strong, but rapidly decaying bond with the surface, preventing application of the standard tools of statistical mechanics. We show the existence and nonlinear stability of ordered lattice states, as well as disturbance propagation through and chaotic vibrations of these states. We also investigate the dynamics of disordered gas states and show that there is a surprising and robust linear connection between distributions of angular and linear velocity for both lattice and gas states, allowing to define the concept of temperature.