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Velocity selection at large undercooling in a two-dimensional nonlocal model of solidificationThe formation of needle-crystal dendrites from an undercooled melt is investigated analytically, applying the method of Caroli et al. (1986) to Langer's (1980) symmetric two-dimensional nonlocal model of solidification with finite anisotropy in the limit of large undercooling. A solution based on the WKB approximation is obtained, and a saddle-point evaluation is performed. It is shown that needle-crystal solutions exist only if the capillary anisotropy is nonzero, in which case a particular value of the growth velocity can be selected. This finding and the expression for the dependence of the selected velocity on the singular perturbation parameter and the strength of the anisotropy are found to be in complete agreement with the results of a boundary-layer model (Langer and Hong, 1986).
Document ID
19880033962
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Barbieri, Angelo
(California, University Santa Barbara, United States)
Date Acquired
August 13, 2013
Publication Date
December 1, 1987
Publication Information
Publication: Physical Review A - General Physics, 3rd Series
Volume: 36
ISSN: 0556-2791
Subject Category
Solid-State Physics
Accession Number
88A21189
Funding Number(s)
CONTRACT_GRANT: NSF PHY-82-17853
CONTRACT_GRANT: DE-FG03-84ER-45108
Distribution Limits
Public
Copyright
Other

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