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Selection theory of free dendritic growth in a potential flow

Martin von Kurnatowski1,*, Thomas Grillenbeck2,3, and Klaus Kassner1

  • 1Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, Germany
  • 2Hochschule für angewandte Wissenschaften, Fachhochschule Rosenheim, Fakultät für Angewandte Natur-und Geisteswissenschaften, Rosenheim, Germany
  • 3Ignaz-Günther-Gymnasium, Rosenheim, Germany

  • *klaus.kassner@ovgu.de
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Phys. Rev. E 87, 042405 – Published 15 April, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.042405

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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Phys. Rev. E 87, 042405– Published 15 April, 2013
  • Received 31 December 2012

©2013 American Physical Society

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