Regensburg 2007 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Growth processes and surface properties

DY 10.5: Talk

Monday, March 26, 2007, 17:30–17:45, H5

Rigorous selection theory for crystal growth with nonlinear transport — •Thomas Fischaleck and Klaus Kassner — Institut für Theoretische Physik, Otto von Guericke Universität Magdeburg, Postfach 4120, D-39016 Magdeburg

Asymptotic matching in the complex plane is a strategy for calculating exponentially small terms that has been pioneered for nonlinear equations by Kruskal and Segur. The method has been successfully applied to pattern-forming systems that could be cast into the form of a single ordinary differential or differential-integral equation. Examples are viscous fingering, dendritic crystal growth, or capillary water waves. Interestig problems that are modeled by nonlinear field equations with free boundaries, however, remained untractable.

We show how to combine asymptotic matching in the complex plane with Zauderer’s decomposition scheme of nonlinear partial differential equations to study this class of problems. The method is exemplified by dendritic growth limited by nonlinear heat transport.