English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In pattern-forming systems, localized patterns are states of intermediatecomplexity between fully extended ordered patterns and completely irregularpatterns. They are formed by stationary fronts enclosing an ordered patterninside an homogeneous background. In two dimensions, the ordered pattern ismost often hexagonal and the conditions for fronts to stabilize are stillunknown. In this letter, we show how the locking of these fronts depends ontheir orientation relative to the pattern. The theory rests on generalasymptotic arguments valid when the spatial scale of the front is slow comparedto that of the hexagonal pattern. Our analytical results are confirmed bynumerical simulations with the Swift-Hohenberg equation, relevant tohydrodynamical and buckling instabilities, and a nonlinear optical cavitymodel.

Analytical results for front pinning between an hexagonal pattern and a uniform state in pattern-formation systems