Irreversibility and self-organisation in hydrodynamic echo experiments

TL;DR

This paper investigates the transition from reversible to irreversible behavior in low-Reynolds hydrodynamic systems under cyclic driving, identifying regimes with exponential noise amplification and cooperative particle movement without spatial organization.

Contribution

It introduces models that demonstrate a sharp crossover between Lyapunov and diffusive regimes, highlighting the absence of auto-organization despite cooperative particle motion.

Findings

Exponential amplification of noise in the Lyapunov regime

Cooperative particle movement without spatial organization in the diffusive regime

Identification of a sharp crossover between regimes

Abstract

We discuss the reversible-irreversible transition in low-Reynolds hydrodynamic systems driven by external cycling actuation. We introduce a set of models with no auto-organisation, and show that a sharp crossover is obtained between a Lyapunov regime in which any noise source, such as thermal noise, is amplified exponentially, and a diffusive regime where this no longer holds. In the latter regime, groups of particles are seen to move cooperatively, yet no spatial organization occurs.