Drift instabilities in localised Faraday patterns

TL;DR

This paper combines theoretical and experimental approaches to demonstrate how heterogeneities induce drift instabilities in localized Faraday patterns, revealing new symmetry-breaking dynamics and phase behaviors in nonlinear systems.

Contribution

It introduces a minimal model for localized Faraday patterns under heterogeneity, uncovering symmetry-breaking nonlinear gradients and convective instabilities.

Findings

Heterogeneities generate convection in localized patterns.

A minimal theoretical model explains the growth of Faraday patterns.

Patterns exhibit phase dynamics with convective instabilities at bifurcation points.

Abstract

Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the understanding of the underlying symmetry-breaking instabilities has been of longstanding scientific interest. In this article, we provide theoretical and experimental evidence that heterogeneities can generate convection (drift instabilities) in the amplitude of localised patterns. We derive a minimal theoretical model describing the growth of localised Faraday patterns under heterogeneous parametric drive, unveiling the presence of symmetry-breaking nonlinear gradients. The model reveals new dynamics in the phase of the underlying patterns, exhibiting convective instabilities when the system crosses a secondary bifurcation point. We discuss the impact of our results in the understanding of convective instabilities induced by heterogeneities in generic nonlinear extended systems far from equilibrium.