Stable regimes for hard disks in a channel with twisting walls

TL;DR

This paper investigates how a gas of hard disks in a semi-periodic box exhibits stable regimes under small perturbations that twist velocities at collisions, revealing tendencies towards regime collapse.

Contribution

It introduces a novel analysis of the stability of gas dynamics under boundary velocity perturbations in a hyperbolic, ergodic system.

Findings

Dynamics tend to collapse to stable regimes under perturbations

Hyperbolic and ergodic properties are established for N=2 disks

Perturbations influence long-term behavior of the system

Abstract

We study a gas of $N$ hard disks in a box with semi-periodic boundary conditions. The unperturbed gas is hyperbolic and ergodic (these facts are proved for N=2 and expected to be true for all $N\geq 2$). We study various perturbations by twisting the outgoing velocity at collisions with the walls. We show that the dynamics tends to collapse to various stable regimes, however we define the perturbations and however small they are.