Cahn–Hoffman ξ-Vector and Its Relation to Diffuse Interface Models of Phase Transitions

作者: A. A. Wheeler

DOI: 10.1023/A:1004575022280

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

参考文章(42)
J. S. Langer, Models of Pattern Formation in First-Order Phase Transitions Directions in Concensed Matter Physics: Memorial Volume in Honor of Shang-Keng Ma. Edited by GRINSTEIN S ET AL. Published by World Scientific Publishing Co. Pte. Ltd. ,vol. 1, pp. 165- 186 ,(1986) , 10.1142/9789814415309_0005
John Shipley Rowlinson, Molecular theory of capillarity ,(1982)
C. Charach, P. C. Fife, On Thermodynamically Consistent Schemes for Phase Field Equations Open Systems & Information Dynamics. ,vol. 5, pp. 99- 123 ,(1998) , 10.1023/A:1009652531731
Richard Courant, David Hilbert, Methods of Mathematical Physics ,(1947)
Gunduz Caginalp, Paul Fife, Phase-field methods for interfacial boundaries Physical Review B. ,vol. 33, pp. 7792- 7794 ,(1986) , 10.1103/PHYSREVB.33.7792
B. Nestler, A. Wheeler, Anisotropic multi-phase-field model: Interfaces and junctions Physical Review E. ,vol. 57, pp. 2602- 2609 ,(1998) , 10.1103/PHYSREVE.57.2602
Eliot Fried, Morton E. Gurtin, Continuum theory of thermally induced phase transitions based on an order parameter Physica D: Nonlinear Phenomena. ,vol. 68, pp. 326- 343 ,(1993) , 10.1016/0167-2789(93)90128-N
Ryo Kobayashi, Modeling and numerical simulations of dendritic crystal growth Physica D: Nonlinear Phenomena. ,vol. 63, pp. 410- 423 ,(1993) , 10.1016/0167-2789(93)90120-P
E. Fried, M.E. Gurtin, Dynamic solid-solid transitions with phase characterized by an order parameter Physica D: Nonlinear Phenomena. ,vol. 72, pp. 287- 308 ,(1994) , 10.1016/0167-2789(94)90234-8