Design of Parametrically Forced Patterns and Quasipatterns

DOI10.1137/080719066zbMath1171.35010arXiv0805.0878OpenAlexW3102209191WikidataQ58422053 ScholiaQ58422053MaRDI QIDQ3624510

Mary Silber, Alastair M. Rucklidge

Publication date: 30 April 2009

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

Full work available at URL: https://arxiv.org/abs/0805.0878

zbMATH Keywords

pattern formationmode interactionsFaraday wavesquasipatternssuperlattice patterns

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Bifurcations in context of PDEs (35B32) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Parametric resonances for nonlinear problems in mechanics (70K28)

Related Items (12)

Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems ⋮ Small divisor problems in fluid mechanics ⋮ Localized Patterns in Periodically Forced Systems: II. Patterns with Nonzero Wavenumber ⋮ Existence of quasipattern solutions of the Swift-Hohenberg equation ⋮ Existence of bifurcating quasipatterns in steady Bénard-Rayleigh convection ⋮ Quasipatterns in a parametrically forced horizontal fluid film ⋮ Numerical simulation of Faraday waves ⋮ Understanding Sensory Induced Hallucinations: From Neural Fields to Amplitude Equations ⋮ On the existence of quasipattern solutions of the Swift-Hohenberg equation ⋮ Microstructure reconstruction using entropic descriptors ⋮ A New Resonance Mechanism in the Swift--Hohenberg Equation with Time-Periodic Forcing ⋮ Patterns and Quasipatterns from the Superposition of Two Hexagonal Lattices

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