Steady-State Bifurcations in Euclidean Equivariant Systems
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Many pattern-forming phenomena are modeled by partial differential equations that are invariant under translations, rotations, and reflections on an infinite plane. Lateral boundaries are deemed unimportant when describing these phenomena. Examples include certain kinds of reaction-diffusion models, convection, NavierStokes flow, geometric hallucination patterns in the visual cortex, the appearance of stripes and spots on animal skins, and nematic liquid crystals.
KeywordsRayleigh Number Dispersion Curve Nematic Liquid Crystal Hexagonal Lattice Isotropy Subgroup
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