Universal wavenumber selection laws in apical growth

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.

References in corpus (2)

• Modelling Pattern Formation in Dip-Coating Experiments
• Pattern formation in the wake of triggered pushed fronts

Cited by in corpus (4)

• Pattern-forming fronts in a Swift-Hohenberg equation with directional quenching - parallel and oblique stripes
• Wavenumber selection via spatial parameter jump
• Spectral stability of pattern-forming fronts in the complex Ginzburg-Landau equation with a quenching mechanism
• Strain and defects in oblique stripe growth