2003/06/20 by Denis Boyer, Boyer, Denis, Octavio Mondragón-Palomino +1
Computer Science · Materials Science · Physics and Astronomy · #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Soft Condensed Matter (cond-mat.soft) #Solidification and crystal growth phenomena #Theoretical and Computational Physics #cond-mat.soft
paper · pdf · doi:10.48550/arxiv.cond-mat/0306535
12 pages, 11 figures
arxiv created 2003/06/20 · openalex publication_date 2003/06/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We 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.