Non-equilibrium Localized Structures

Ehud Meron

Localized spatial structures, such as defects in periodic patterns, fronts and vortices, are ubiquitous in non-equilibrium systems. Understanding the mechanisms by which they form, their stability and how to manipulate them, is significant for exploiting them in technological applications.

A localized structure may involve a single mode, e.g. a spiral wave in an oscillating medium (showcasing a Hopf mode), but quite often richer structures appear. This is particularly true when a system is driven far from thermal equilibrium and the number of growing modes increases. The system may still be governed by a single dominant mode that damps all other modes by means of nonlinear mode coupling. However, localized structures of the dominant mode, where its amplitude vanishes or becomes sufficiently small, can host the hidden damped mode, giving rise to multimode structures. We studied structures of this kind in systems that go through dual (Hopf-Turing) instabilities. Among our findings are defect lines acting as self-organized wave-guides for traveling pulses (Fig. 1), breathing defects, and multi-state localized structures, that are potentially significant for data storage applications.


Figure 1: Self-organized waveguide. A pulse of a Hopf mode (amplitude B) propagating along a defect line in a Turing pattern (amplitude A). Time proceeds from top to bottom. Produced by Adam Lampert.

Further reading:

• A. Lampert and E. Meron, "Localized structures as spatial hosts for unstable modes", Europhys. Lett. 78 (2007) 14002.