Radial localization of planar patterns

Paper Title:

Radial amplitude equations for fully localised planar patterns

Published on:

5 March 2024

Primary Category:

Dynamical Systems

Paper Authors:

Dan J. Hill,

David J. B. Lloyd

Bullets

Key Details

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Method formally derives radial amplitude equations for planar patterns

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Uses multiple scales analysis and Bessel function identities

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Predicts fully localized hexagons, stripes and 12-fold quasipatterns

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Applies method to Swift-Hohenberg PDE and reaction-diffusion systems

Explore the topics in this paper

bessel functions

planar patterns

radial localization

reaction-diffusion systems

swift-hohenberg equation

AI generated summary

Radial localization of planar patterns

This paper provides a method to derive equations describing the radial localization of planar patterns, like hexagons or stripes, using special mathematical functions called Bessel functions. The approach allows prediction of fully localized patches surrounded by a uniform state. Equations are derived for patterns with different rotational symmetries. The method is applied to a model PDE called the Swift-Hohenberg equation and to general reaction-diffusion systems.