Document Type

Article

Publication Date

2-2008

Keywords

Isoconcentration surfaces, Turing patterns

Abstract

We consider three-dimensional Turing patterns and their isoconcentration surfaces corresponding to the equilibrium concentration of the reaction kinetics. We call these surfaces equilibrium concentration surfaces (EC surfaces). They are the interfaces between the regions of "high" and "low" concentrations in Turing patterns. We give alternate characterizations of EC surfaces by means of two variational principles, one of them being that they are optimal for diffusive transport. Several examples of EC surfaces are considered. Remarkably, they are often very well approximated by certain minimal surfaces. We give a dynamical explanation for the emergence of Scherk's surface in certain cases, a structure that has been observed numerically previously in [De Wit et al., 1997].

Publication Title

International Journal of Bifurcation & Chaos in Applied Sciences & Engineering

Volume

18

Issue

2

First Page

391

Last Page

406

DOI

http://dx.doi.org/10.1142/S0218127408020355

Required Publisher's Statement

Electronic version of an article published as International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Feb2008, Vol. 18 Issue 2, p391-406. DOI: 10.1142/S0218127408020355, © World Scientific Publishing Company, http://www.worldscientific.com/loi/ijbc


Subjects - Topical (LCSH)

Surfaces; Functions; Mappings (Mathematics)

Genre/Form

articles

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

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Included in

Mathematics Commons

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