Patterns and Quasipatterns from the Superposition of Two Hexagonal Lattices

DOI10.1137/20M1372780zbMath1498.35052arXiv2010.09274MaRDI QIDQ5864061

Gérard Iooss, Alastair M. Rucklidge

Publication date: 3 June 2022

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.09274

zbMATH Keywords

Swift-Hohenberg equationquasipatternssuperlattice patternssmall-divisor techniques

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to PDEs (35B15) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Higher-order elliptic equations (35J30) Semilinear elliptic equations (35J61) Pattern formations in context of PDEs (35B36)

Cites Work

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• Quasipatterns in a parametrically forced horizontal fluid film
• Proof of quasipatterns for the Swift-Hohenberg equation
• On the existence of quasipattern solutions of the Swift-Hohenberg equation
• Applications of centre manifold theory
• Singularities and groups in bifurcation theory. Volume II
• Neural fields: localised states with piece-wise constant interactions
• Existence of bifurcating quasipatterns in steady Bénard-Rayleigh convection
• Superlattice patterns in surface waves
• Convergence properties of the 8, 10 and 12 mode representations of quasipatterns
• Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems
• Exploring critical points of energy landscapes: from low-dimensional examples to phase field crystal PDEs
• Pattern Formation
• Design of Parametrically Forced Patterns and Quasipatterns
• Stability results for steady, spatially periodic planforms
• D₄+T²mode interactions and hidden rotational symmetry
• Pattern formation in weakly damped parametric surface waves driven by two frequency components
• Reducible actions ofD₄ T²: superlattice patterns and hidden symmetries
• Transcritical bifurcation withO(3) symmetry
• What are the possible moiré patterns of graphene on hexagonally packed surfaces? Universal solution for hexagonal coincidence lattices, derived by a geometric construction
• Existence of quasipatterns in the superposition of two hexagonal patterns
• Turbulent crystals in macroscopic systems
• Pattern Selection for Faraday Waves in an Incompressible Viscous Fluid
• Sideband instabilities and defects of quasipatterns

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