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
Recommended Citation
Glimm, Tilmann and Hentschel, H. George E., "On Isoconcentration Surfaces of Three Dimensional Turing Patterns" (2008). Mathematics Faculty Publications. 55.
https://cedar.wwu.edu/math_facpubs/55
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