Patterns and Quasipatterns from the Superposition of Two Hexagonal Lattices

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

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 equation quasipatterns superlattice patterns small-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

Unnamed Item
Unnamed Item
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

This page was built for publication: Patterns and Quasipatterns from the Superposition of Two Hexagonal Lattices