Geometrical models of interface evolution. III. Theory of dendritic growth
- 1 March 1985
- journal article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 31 (3), 1712-1717
- https://doi.org/10.1103/physreva.31.1712
Abstract
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.Keywords
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