Coexistence of Stable Branched Patterns in Anisotropic Inhomogeneous Systems

TL;DR

This paper introduces a new class of pattern-forming systems characterized by anisotropy and spatial inhomogeneity, revealing stable branched stripe patterns that coexist with unbranched patterns over certain parameter ranges.

Contribution

It identifies and analyzes a novel class of anisotropic, inhomogeneous systems, demonstrating the emergence and stability of branched stripe patterns through amplitude equations and model studies.

Findings

Branched stripe patterns are stable within a band of wavenumbers.

Coexistence of branched and unbranched patterns over finite parameter ranges.

Potential experimental systems include surface wrinkling and electroconvection in nematic liquid crystals.

Abstract

A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class and a model equation, we show that branched stripe patterns emerge, which for a given parameter set are stable within a band of different wavenumbers and different numbers of branching points (defects). Moreover, the branched patterns and unbranched ones (defect-free stripes) coexist over a finite parameter range. We propose two systems where this generic scenario can be found experimentally, surface wrinkling on elastic substrates and electroconvection in nematic liquid crystals, and relate them to the findings from the amplitude equation.