Phase separation patterns from directional quenching

Abstract

We study the effect of directional quenching on patterns formed in simple bistable systems such as the Allen-Cahn and the Cahn-Hilliard equation on the plane. We model directional quenching as an externally triggered change in system parameters, changing the system from monostable to bistable across an interface. We are then interested in patterns forming in the bistable region, in particular as the trigger progresses and increases the bistable region. We find existence and non-existence results of single interfaces and striped patterns.

31 pages

References in corpus (5)

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• Helices in the wake of precipitation fronts
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Cited by in corpus (7)

• Pattern-forming fronts in a Swift-Hohenberg equation with directional quenching - parallel and oblique stripes
• Self-organised dip-coating patterns of simple, partially wetting, nonvolatile liquids
• Bifurcations of front motion in passive and active Allen-Cahn-type equations
• Wavenumber selection via spatial parameter jump
• Spectral stability of pattern-forming fronts in the complex Ginzburg-Landau equation with a quenching mechanism
• Contact angle selection for interfaces in growing domains
• The Swift-Hohenberg Equation under directional-quenching: finding heteroclinic connections using spatial and spectral decompositions