Issue
EPL
Volume 81, Number 5, March 2008
Article Number 54004
Number of page(s) 6
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
DOI http://dx.doi.org/10.1209/0295-5075/81/54004
Published online 12 February 2008
EPL, 81 (2008) 54004
DOI: 10.1209/0295-5075/81/54004

Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition

T. 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

Abstract
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.

PACS
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.


© EPLA 2008