The effect of impurities on striped phases

Gabriela Jaramillo, Arnd Scheel, Qiliang Wu

Research output: Contribution to journalArticlepeer-review

Abstract

We study the effect of algebraically localized impurities on striped phases in one spatial dimension. We therefore develop a functional-analytic framework that allows us to cast the perturbation problem as a regular Fredholm problem despite the presence of the essential spectrum, caused by the soft translational mode. Our results establish the selection of jumps in wavenumber and phase, depending on the location of the impurity and the average wavenumber in the system. We also show that, for select locations, the jump in the wavenumber vanishes.

Original languageEnglish (US)
Pages (from-to)131-168
Number of pages38
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume149
Issue number1
DOIs
StatePublished - Feb 1 2019

Bibliographical note

Publisher Copyright:
© 2018 Royal Society of Edinburgh.

Keywords

  • Fredholm operator
  • Turing patterns
  • essential spectrum
  • inhomogeneities

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