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arXiv · 1602.02281

Universal wavenumber selection laws in apical growth

Ryan Goh·Rajendra Beekie·Daniel Matthias·Joshua Nunley·Arnd Scheel
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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.

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Ryan Goh, Rajendra Beekie, Daniel Matthias, Joshua Nunley, Arnd Scheel. 2016-02-06. Universal wavenumber selection laws in apical growth. https://doi.org/10.1103/physreve.94.022219

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