Bifurcation analysis of cellular interfaces in unidirectional solidification of a dilute binary mixture
Impey, M.D., Riley, D.S. and Wheeler, A.A. (1993) Bifurcation analysis of cellular interfaces in unidirectional solidification of a dilute binary mixture. SIAM Journal on Applied Mathematics, 53, (1), 78-95.
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Analytical bifurcation theory is used to study interface patterns in the unidirectional solidification of a dilute binary mixture. Armbruster and Dangelmayr's classification of bifurcation equations equivariant under the diagonal action in ℂ2 of the symmetry group O(2) is used to show that the local bifurcation structure of the model long-wave evolution equation derived by Riley and Davis is equivalent to that of a codimension-one normal form. Examination of the bifurcation structure of the normal form then leads to a description of the development of three-dimensional interface patterns during unidirectional solidification. The general methodology underlying this study is also discussed, and conditions under which the method can be applied to other evolution equations are derived and clearly stated.
|Subjects:||Q Science > QA Mathematics|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
|Date Deposited:||26 Mar 2004|
|Last Modified:||01 Jun 2011 15:50|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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