Pattern orientation in finite domains without boundaries

TL;DR

This paper studies how stripe patterns orient themselves in finite domains with varying control parameters, revealing a transition from perpendicular to parallel alignment due to non-adiabatic effects.

Contribution

It introduces a novel boundary condition approach using a control parameter drop, demonstrating orientation transitions in stripe patterns without traditional boundary constraints.

Findings

Stripes align perpendicular to shallow control parameter drops.

Steeper drops induce a transition to parallel stripe orientation.

The effect is demonstrated using the Brusselator model and amplitude equations.

Abstract

We investigate the orientation of nonlinear stripe patterns in finite domains. Motivated by recent experiments, we introduce a control parameter drop from supercritical inside a domain to subcritical outside without boundary conditions at the domain border. As a result, stripes align perpendicular to shallow control parameter drops. For steeper drops, non-adiabatic effects lead to a surprising orientational transition to parallel stripes with respect to the borders. We demonstrate this effect in terms of the Brusselator model and generic amplitude equations.