Geometrical models of interface evolution. III. Theory of dendritic growth

David A. Kessler, Joel Koplik, Herbert Levine

Research output: Contribution to journalArticlepeer-review

107 Scopus citations


We construct a theory of velocity selection and tip stability for dendritic growth in the local evolution model. We show that the growth rate of dendritic patterns is determined by a nonlinear solvability condition for a translating finger. The sidebranching instability is related to a single discrete oscillatory mode about the selected velocity solution, and the existence of a critical anisotropy is shown to be due to the zero crossing of its growth rate. The marginal-stability hypothesis cannot predict the correct dynamics of this model system. We give heuristic arguments that the same ideas will apply to dendritic growth in the full diffusion system.

Original languageEnglish
Pages (from-to)1712-1717
Number of pages6
JournalPhysical Review A
Issue number3
StatePublished - 1985
Externally publishedYes


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