Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decompositionT. Fischaleck and K. Kassner
Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg Postfach 4120, D-39016 Magdeburg, Germany
received 25 October 2007; accepted in final form 11 January 2008; published March 2008
published online 12 February 2008
Successful applications of the Kruskal-Segur approach to interfacial pattern formation have remained limited due to the necessity of an integral formulation of the problem. This excludes nonlinear bulk equations, rendering convection intractable. Combining the method with Zauderer's asymptotic decomposition scheme, we are able to strongly extend its scope of applicability and solve selection problems based on free boundary formulations in terms of partial differential equations alone. To demonstrate the technique, we give the first analytic solution of the problem of velocity selection for dendritic growth in a forced potential flow.
47.54.-r - Pattern selection; pattern formation.
11.10.Jj - Asymptotic problems and properties.
81.10.Aj - Theory and models of crystal growth; physics of crystal growth, crystal morphology, and orientation.
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