Growing stripes, with and without wrinkles

M. Avery, R. Goh, O. Goodloe, A. Milewski, A. Scheel

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We present results on stripe formation in the Swift-Hohenberg equation with a directional quenching term. Stripes are "grown" in the wake of a moving parameter step line, and we analyze how the orientation of stripes changes depending on the speed of the quenching line and on a lateral aspect ratio. We observe stripes perpendicular to the quenching line, but also stripes created at oblique angles, as well as periodic wrinkles created in an otherwise oblique stripe pattern. Technically, we study stripe formation as traveling-wave solutions in the Swift-Hohenberg equation and in reduced Cahn-Hilliard and Newell-Whitehead-Segel models, analytically, through numerical continuation, and in direct simulations.

Original languageEnglish (US)
Pages (from-to)1078-1117
Number of pages40
JournalSIAM Journal on Applied Dynamical Systems
Volume18
Issue number2
DOIs
StatePublished - Jan 1 2019

Keywords

  • Cahn-Hilliard
  • Growing domains
  • Stripe selection
  • Swift-Hohenberg
  • Zigzag instabilities

Fingerprint Dive into the research topics of 'Growing stripes, with and without wrinkles'. Together they form a unique fingerprint.

Cite this