Multiple Front Propagation Into Unstable States

TL;DR

This paper investigates how multiple fronts propagate into unstable states in nonequilibrium systems, revealing mechanisms for pattern decay and providing analytical tools for understanding front speeds and periodicities.

Contribution

It introduces a generalized marginal stability formalism to analytically predict the behavior of fronts propagating into unstable periodic states.

Findings

Decay of unstable states occurs via a second propagating front.

Analytical expressions for front speed and periodicity are derived.

Numerical simulations confirm the theoretical predictions.

Abstract

The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable periodic pattern. It is found by a numerical solution of a model of the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of decay of such periodic unstable states is the propagation of a second front which replaces the unstable pattern by a another unstable periodic state with larger wavelength. The speed of this second front and the periodicity of the new state are analytically calculated with a generalization of the marginal stability formalism suited to the study of front propagation into periodic unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+r