Universal wave-number selection laws in apical growth.

Phys Rev E

School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA.

Published: August 2016

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.

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http://dx.doi.org/10.1103/PhysRevE.94.022219DOI Listing

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