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Many inhomogeneous systems involve domains of well-de?ned phases se- rated by a distinct interface. If they are driven out of equilibrium one phase will grow at the cost of the other. Examples are phase separation by sp- odal decomposition or nucleation and subsequent growth of the nucleus in the nourishing phase [139]. Another example which has often been discussed as a paradigmatic problem is that of dendritic solidi?cation [29, 64, 79, 199]. The phenomenological description of these phenomena involves the de?- tion of a precisely located interfacial surface on which boundary conditions are imposed. One of those boundary conditions typically yields a normal - locity at which the interface is moving. This is the so-calledsharp interface approach, adopted both in analytical and numerical studies for a variety of contexts involving a moving boundary. The origin of such a description is - ten transparent, being obtained by symmetry arguments and common sense.

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What Is an Interface? Interfaces in Materials Science and Beyond.- Equilibrium Thermodynamics of Multiphase Systems: Thermodynamic Potentials and Phase Diagrams.- Thermodynamic Concepts of Phase-Field Modeling.- Asymptotic Analysis.- Application of Diffuse Interface Modeling to Hydrodynamically Driven Growth.- Application to Epitaxial Growth Involving Elasticity.- Conclusions and Perspectives.

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From the reviews:

"In total, this very interesting book gives a modern understanding of the problems of phase-field modeling, and may be useful for students and specialists working in this and in related scientific fields." (Zentralblatt MATH 2004, vol. 1039, page 51)

"This book is devoted to an application of the diffuse interface approach to different interfacial growth phenomena, as a whole, and to a discussion of the difference between the sharp interface limit and diffuse interface limit of a phase-field model, in particular. ... In total, this very interesting book gives a modern understanding of the problems of phase-field modeling, and may be useful for students and specialists working in this and in related scientific fields." (I. A. Parinov, Zentralblatt MATH, Vol. 1039 (8), 2004)

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