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Titolo:
MOTION BY CURVATURE IN GENERALIZED CAHN-ALLEN MODELS
Autore:
FIFE PC; LACEY AA;
Indirizzi:
UNIV UTAH,DEPT MATH SALT LAKE CITY UT 84112 HERIOT WATT UNIV,DEPT MATH EDINBURGH MIDLOTHIAN SCOTLAND
Titolo Testata:
Journal of statistical physics
fascicolo: 1-2, volume: 77, anno: 1994,
pagine: 173 - 181
SICI:
0022-4715(1994)77:1-2<173:MBCIGC>2.0.ZU;2-E
Fonte:
ISI
Lingua:
ENG
Soggetto:
INTERFACES; DIFFUSION;
Keywords:
GRAIN BOUNDARY; INTERNAL LAYERS; MOTION BY CURVATURE; CAHN-ALLEN MODEL; ALLEN-CAHN MODEL; GINZBURG-LANDAU FUNCTIONAL;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
Science Citation Index Expanded
Citazioni:
14
Recensione:
Indirizzi per estratti:
Citazione:
P.C. Fife e A.A. Lacey, "MOTION BY CURVATURE IN GENERALIZED CAHN-ALLEN MODELS", Journal of statistical physics, 77(1-2), 1994, pp. 173-181

Abstract

The Cahn-Allen model for the motion of phase-antiphase boundaries is generalized to account for nonlinearities in the kinetic coefficient (relaxation velocity) and the coefficient of the gradient free energy. The resulting equation is epsilon(2)u(t) = )(epsilon(2)[kappa(u)](1/2)del.{[kappa(u)](1/2)del u}-f(u))where f is bistable. Here u is an order parameter and kappa and alpha are physical quantities associated with the system's free energy and relaxation speed, respectively. Grain boundaries, away from triple junctions, are modeled by solutions with internal layers when epsilon much less than 1. The classical motion-by-curvature law for solution layers, well known when kappa and alpha areconstant, is shown by formal asymptotic analysis to be unchanged in form under this generalization, the only difference being in the value of the coefficient entering into the relation. The analysis is extended to the case when the relaxation time for the process vanishes for a set of values of u. Then alpha is infinite for those values.

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Documento generato il 30/10/20 alle ore 00:08:08