ON ISOCONCENTRATION SURFACES OF THREE-DIMENSIONAL TURING PATTERNS

Autor:	Tilmann Glimm, H. G. E. Hentschel
Rok vydání:	2008
Předmět:	Combinatorics Pure mathematics Turing patterns Applied Mathematics Modeling and Simulation Engineering (miscellaneous) Mathematics
Zdroj:	International Journal of Bifurcation and Chaos. 18:391-406
ISSN:	1793-6551 0218-1274
Popis:	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].
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::029078bfe1084b38a7a9571fc47e0e73 https://doi.org/10.1142/s0218127408020355 Zobrazit plný text záznamu