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Published on: May 18, 2020
Selection theory of free dendritic growth in a potential flow
Martin von Kurnatowski1, Thomas Grillenbeck, Klaus Kassner
1Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Germany. klaus.kassner@ovgu.de
Abstract:
The Kruskal-Segur approach to selection theory in diffusion-limited or Laplacian growth is extended via combination with the Zauderer decomposition scheme. This way nonlinear bulk equations become tractable. To demonstrate the method, we apply it to two-dimensional crystal growth in a potential flow. We omit the simplifying approximations used in a preliminary calculation for the same system [Fischaleck, Kassner, Europhys. Lett. 81, 54004 (2008)], thus exhibiting the capability of the method to extend mathematical rigor to more complex problems than hitherto accessible.
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