Stationary circular target patterns in a surface burning reaction

Forbes L.K. (1996) Stationary circular target patterns in a surface burning reaction. Journal of Engineering Mathematics, 30 4: 471-486.

Author Forbes L.K.
Title Stationary circular target patterns in a surface burning reaction
Journal name Journal of Engineering Mathematics   Check publisher's open access policy
ISSN 0022-0833
Publication date 1996-01-01
Sub-type Article (original research)
Volume 30
Issue 4
Start page 471
End page 486
Total pages 16
Subject 2201 Applied Ethics
2604 Applied Mathematics
Abstract A simple model for burning on the circular face of a substrate is analyzed. It is shown that spatial patterns can form, in which the temperature develops hot and cold regions arranged in concentric circular rings. A linearized study shows the parameter values for which small amplitude patterns are stable. The fully non-linear equations are then solved using an efficient shooting method in the spatial variable, and an extremely complicated bifurcation diagram is obtained, from which it follows that multiple solutions occur at the same values of the defining parameters. The effect of heat leakage at the edges of the circular region is considered, and complicated non-linear behaviour occurs in this case also. Seven different temperature patterns, all co-existing at the same parameter values, are presented in a particular instance.
Keyword Bifurcation diagrams
Exothermic reaction
Multiple solutions
Pattern formation
Shooting method
Q-Index Code C1
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
 
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Created: Tue, 13 Sep 2016, 10:25:10 EST by System User