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Existence of needle crystals in local models of solidificationThe way in which surface tension acts as a singular perturbation to destroy the continuous family of needle-crystal solutions of the steady-state growth equations is analyzed in detail for two local models of solidification. All calculations are performed in the limit of small surface tension or, equivalently, small velocity. The basic mathematical ideas are introduced in connection with a quasilinear, isotropic version of the geometrical model of Brower et al., in which case the continuous family of solutions dissappears completely. The formalism is then applied to a simplified boundary-layer model with an anisotropic kinetic attachment coefficient. In the latter case, the solvability condition for the existence of needle crystals can be satisfied whenever the coefficient of anisotropy is arbitrarily small but nonzero.
Document ID
19860035524
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Langer, J. S.
(California, University Santa Barbara, United States)
Date Acquired
August 12, 2013
Publication Date
January 1, 1986
Publication Information
Publication: Physical Review A - General Physics, 3rd Series
Volume: 33
ISSN: 0556-2791
Subject Category
Solid-State Physics
Accession Number
86A20262
Funding Number(s)
CONTRACT_GRANT: NSF PHY-82-17853
CONTRACT_GRANT: DE-FG03-84ER-45108
Distribution Limits
Public
Copyright
Other

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