Phys. Rev. A 35, 1802–1808 (1987)Velocity selection in the symmetric model of dendritic crystal growthReceived 8 July 1986; published in the issue dated February 1987 We present an analytic solution of the problem of velocity selection in a fully nonlocal model of dendritic crystal growth. Our analysis uses a WKB technique to derive and evaluate a solvability condition for the existence of steady-state needlelike solidification fronts in the limit of small undercooling Δ. For the two-dimensional symmetric model with a capillary anisotropy of strength α, we find that the velocity is proportional to Δ4α7/4. We also describe the application of our method in three dimensions. © 1987 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.35.1802
DOI:
10.1103/PhysRevA.35.1802
PACS:
61.50.Cj, 05.70.Ln, 68.70.+w, 81.30.Fb
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