Abstract

New modulation equations for hexagonal patterns in reaction-diffusion systems are derived for parameter régimes corresponding to the onset of patterns. These systems include additional nonlinearities which are not present in Rayleigh-Bénard convection or Swift-Hohenberg type models. The dynamics of hexagonal and roll patterns are studied using a combination of analytical and computational approaches which exploit the hexagonal structure of the modulation equations. The investigation demonstrates instabilities and new phenomena not found in other systems, and is applied to patterns of flame fronts in a certain model of burner stabilized flames.

Original languageEnglish
Pages (from-to)157-184
Number of pages28
JournalEuropean Journal of Applied Mathematics
Volume10
Issue number2
DOIs
Publication statusPublished - 1 Apr 1999

Fingerprint

Reaction-diffusion System
Modulation
Hexagon
Modulation Equations
Flame
Fuel burners
Rayleigh-Bénard Convection
Nonlinearity
Model
Demonstrate
Convection

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Modulated two-dimensional patterns in reaction-diffusion systems. / Kuske, R.; Milewski, P.

In: European Journal of Applied Mathematics, Vol. 10, No. 2, 01.04.1999, p. 157-184.

Research output: Contribution to journalArticle

@article{565af2cfc6c146fd94d4b65d95eb62f9,
title = "Modulated two-dimensional patterns in reaction-diffusion systems",
abstract = "New modulation equations for hexagonal patterns in reaction-diffusion systems are derived for parameter r{\'e}gimes corresponding to the onset of patterns. These systems include additional nonlinearities which are not present in Rayleigh-B{\'e}nard convection or Swift-Hohenberg type models. The dynamics of hexagonal and roll patterns are studied using a combination of analytical and computational approaches which exploit the hexagonal structure of the modulation equations. The investigation demonstrates instabilities and new phenomena not found in other systems, and is applied to patterns of flame fronts in a certain model of burner stabilized flames.",
author = "R. Kuske and P. Milewski",
year = "1999",
month = "4",
day = "1",
doi = "10.1017/S095679259800360X",
language = "English",
volume = "10",
pages = "157--184",
journal = "European Journal of Applied Mathematics",
issn = "0956-7925",
publisher = "Cambridge University Press",
number = "2",

}

TY - JOUR

T1 - Modulated two-dimensional patterns in reaction-diffusion systems

AU - Kuske, R.

AU - Milewski, P.

PY - 1999/4/1

Y1 - 1999/4/1

N2 - New modulation equations for hexagonal patterns in reaction-diffusion systems are derived for parameter régimes corresponding to the onset of patterns. These systems include additional nonlinearities which are not present in Rayleigh-Bénard convection or Swift-Hohenberg type models. The dynamics of hexagonal and roll patterns are studied using a combination of analytical and computational approaches which exploit the hexagonal structure of the modulation equations. The investigation demonstrates instabilities and new phenomena not found in other systems, and is applied to patterns of flame fronts in a certain model of burner stabilized flames.

AB - New modulation equations for hexagonal patterns in reaction-diffusion systems are derived for parameter régimes corresponding to the onset of patterns. These systems include additional nonlinearities which are not present in Rayleigh-Bénard convection or Swift-Hohenberg type models. The dynamics of hexagonal and roll patterns are studied using a combination of analytical and computational approaches which exploit the hexagonal structure of the modulation equations. The investigation demonstrates instabilities and new phenomena not found in other systems, and is applied to patterns of flame fronts in a certain model of burner stabilized flames.

UR - http://www.scopus.com/inward/record.url?scp=0033462661&partnerID=8YFLogxK

U2 - 10.1017/S095679259800360X

DO - 10.1017/S095679259800360X

M3 - Article

VL - 10

SP - 157

EP - 184

JO - European Journal of Applied Mathematics

JF - European Journal of Applied Mathematics

SN - 0956-7925

IS - 2

ER -