Universal wavenumber selection laws in apical growth

TL;DR

This paper derives universal laws governing wavenumber selection in pattern-forming systems on growing domains, providing a unified framework applicable across various models and validated through simulations.

Contribution

It introduces universal scaling laws for wavenumber selection in dissipative systems with growth, based on boundary conditions and strain-displacement relations.

Findings

Universal wavenumber scaling laws derived for growing domains.

Predictions validated through simulations of multiple pattern-forming equations.

Boundary conditions critically influence defect-free growth patterns.

Abstract

We study pattern-forming dissipative systems in growing domains. We characterize classes of boundary conditions that allow for defect-free growth and derive universal scaling laws for the wavenumber in the bulk of the domain. Scalings are based on a description of striped patterns in semi-bounded domains via strain-displacement relations. We compare predictions with direct simulations in the Swift-Hohenberg, the Complex Ginzburg-Landau, the Cahn-Hilliard, and reaction-diffusion equations.