Inhomogeneous frozen states in the Swift-Hohenberg equation: hexagonal patterns vs. localized structures

Simple item page
dc.creatorBoyer, Denis
dc.creatorMondragón-Palomino, Octavio
dc.date2003-06-20
dc.date.accessioned2026-07-07T02:51:58Z
dc.date.available2026-07-07T02:51:58Z
dc.descriptionWe revisit the Swift-Hohenberg model for two-dimensional hexagonal patterns in the bistability region where hexagons coexist with the uniform quiescent state. We both analyze the law of motion of planar interfaces (separating hexagons and uniform regions), and the stability of localized structures. Interfaces exhibit properties analogous to that of interfaces in crystals, such as faceting, grooving and activated growth or " melting". In the nonlinear regime, some spatially disordered heterogeneous configurations do not evolve in time. Frozen states are essentially composed of extended polygonal domains of hexagons with pinned interfaces, that may coexist with isolated localized structures randomly distributed in the quiescent background. Localized structures become metastable at the pinning/depinning transition of interfaces. In some region of the parameter space, localized structures shrink meanwhile interfaces are still pinned. The region where localized structures have an infinite life-time is relatively limited.
dc.description12 pages, 11 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0306535
dc.identifierhttp://arxiv.org/abs/cond-mat/0306535
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/21666
dc.subjectSoft Condensed Matter
dc.titleInhomogeneous frozen states in the Swift-Hohenberg equation: hexagonal patterns vs. localized structures
dc.typetext

Files

Collections

arXiv