MODELS OF PATTERN FORMATION IN FIRST-ORDER PHASE TRANSITIONS
1986; World Scientific; Linguagem: Inglês
10.1142/9789814415309_0005
ISSN1793-1444
Autores Tópico(s)Metallurgy and Material Forming
ResumoSeries on Directions in Condensed Matter PhysicsDirections in Condensed Matter Physics, pp. 165-186 (1986) No AccessMODELS OF PATTERN FORMATION IN FIRST-ORDER PHASE TRANSITIONSJ. S. LangerJ. S. LangerInstitute for Theoretical Physics, University of California, Santa Barbara, California 93106, USAhttps://doi.org/10.1142/9789814415309_0005Cited by:169 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The study of simplified theoretical models is an important part of the search for a more general and systematic theory of natural pattern formation. Three qualitatively different kinds of models are considered here, each pertaining to the special class of situations in which patterns are formed during first-order phase transformations. The first of these models is the basic thermodynamic description of a solidifying system controlled by thermal diffusion and interfacial attachment kinetics. The second is a continuum model which is the deterministic limit of "Model C" of Hohenberg, Halperin and Ma. The third is a contour dynamical, boundary-layer model that recently has proven useful for probing the fully nonlinear development of morphological instabilities. Insights concerning the mathematical mechanism for pattern selection in the relatively tractable boundary-layer model appear to be useful clues for understanding the behavior of the more complex and realistic models. 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Wheeler, B.T. Murray and S.R. Coriell et al.1 Nov 1993 | Physica D: Nonlinear Phenomena, Vol. 69, No. 1-2Continuum theory of thermally induced phase transitions based on an order parameterEliot Fried and Morton E. Gurtin1 Oct 1993 | Physica D: Nonlinear Phenomena, Vol. 68, No. 3-4Critical Behavior of Crystal Growth VelocityH Löwen and J Bechhoefer25 July 2007 | Europhysics Letters (EPL), Vol. 16, No. 2Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarseningPeter W. Bates and Paul C. Fife1 Jul 1990 | Physica D: Nonlinear Phenomena, Vol. 43, No. 2-3Thermodynamically consistent models of phase-field type for the kinetic of phase transitionsOliver Penrose and Paul C. Fife1 May 1990 | Physica D: Nonlinear Phenomena, Vol. 43, No. 1 Directions in Condensed Matter PhysicsMetrics History PDF download
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