title: Universal wave-number 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 wave number in the bulk of the domain. Scalings are based on a description of striped patterns in semibounded 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.
authors.affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA.
authors.forename: Ryan
authors.initials: R
authors.lastname: Goh
authors.affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA.
authors.forename: Rajendra
authors.initials: R
authors.lastname: Beekie
authors.affiliation: Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80305, USA.
authors.forename: Daniel
authors.initials: D
authors.lastname: Matthias
authors.affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA.
authors.forename: Joshua
authors.initials: J
authors.lastname: Nunley
authors.affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA.
authors.forename: Arnd
authors.initials: A
authors.lastname: Scheel