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Cahn–Hoffman ?-Vector and its relation to diffuse interface models of phase transitions

Cahn–Hoffman ?-Vector and its relation to diffuse interface models of phase transitions
Cahn–Hoffman ?-Vector and its relation to diffuse interface models of phase transitions
In this paper we review two important theoretical areas to which J. W. Cahn has made major contributions: (i) The theory of the ?-vector developed by Hoffman and Cahn, which provides an elegant setting for the description of the equilibrium shapes of sharp interfaces in the presence of anisotropic surface energy. (ii) Diffuse interface theories of phase transitions. We describe recent work which connects these two complementary facets of models of interfaces by the development of a generalized ?-vector for diffuse interface models with anisotropic surface energy. We show that the generalized ?-vector plays a central role in both the mathematical and physical aspects of a wide range of diffuse interface theories of interfaces with either anisotropic surface energy or attachment kinetics.
Anisotropy, surface energy, diffuse interface model, phase-field model, stress tensor, equilibrium shapes
0022-4715
1245 -1280
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73

Wheeler, A.A. (1999) Cahn–Hoffman ?-Vector and its relation to diffuse interface models of phase transitions. Journal of Statistical Physics, 95 (5-6), 1245 -1280. (doi:10.1023/A:1004575022280).

Record type: Article

Abstract

In this paper we review two important theoretical areas to which J. W. Cahn has made major contributions: (i) The theory of the ?-vector developed by Hoffman and Cahn, which provides an elegant setting for the description of the equilibrium shapes of sharp interfaces in the presence of anisotropic surface energy. (ii) Diffuse interface theories of phase transitions. We describe recent work which connects these two complementary facets of models of interfaces by the development of a generalized ?-vector for diffuse interface models with anisotropic surface energy. We show that the generalized ?-vector plays a central role in both the mathematical and physical aspects of a wide range of diffuse interface theories of interfaces with either anisotropic surface energy or attachment kinetics.

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Published date: 1999
Keywords: Anisotropy, surface energy, diffuse interface model, phase-field model, stress tensor, equilibrium shapes

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Local EPrints ID: 384
URI: http://eprints.soton.ac.uk/id/eprint/384
ISSN: 0022-4715
PURE UUID: 1b6ee385-4957-4581-94bf-23dd09d00949

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Date deposited: 12 Mar 2004
Last modified: 08 Jan 2022 09:46

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Author: A.A. Wheeler

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