Heterogeneity-stabilized homogeneous states in driven media

TL;DR

This paper demonstrates that introducing specific asymmetries into driven systems can stabilize otherwise unstable homogeneous states, with theoretical and experimental evidence showing potential for controlling instabilities.

Contribution

It introduces the concept of heterogeneity-stabilized homogeneity, showing how asymmetry can preserve symmetric states in driven media, supported by theoretical models and experiments.

Findings

Asymmetry can stabilize homogeneous states against symmetry-breaking instabilities.

Theoretical models of driven pendulum arrays confirm the stabilizing effect.

Experimental Faraday wave studies demonstrate practical realization.

Abstract

Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest. Symmetry-breaking instabilities underlie the formation of important patterns in driven systems, but there are many instances in which such instabilities are undesirable. Using parametric resonance as a model process, here we show that a range of states that would be destabilized by symmetry-breaking instabilities can be preserved and stabilized by the introduction of suitable system asymmetry. Because symmetric states are spatially homogeneous and asymmetric systems are spatially heterogeneous, we refer to this effect as heterogeneity-stabilized homogeneity. We illustrate this effect theoretically using driven pendulum array models and demonstrate it experimentally using Faraday wave instabilities. Our results have potential implications for the mitigation of instabilities in engineered systems and the emergence of homogeneous states in natural systems with inherent heterogeneities.