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Zusatztext This very good book! presents a study of the dynamics of two-phase systems within the framework of modern continuum thermodynamics ... a detailed account of a number of important results in a field to which the author has made substantial contributions ..! Special problems and exercises are included. This monograph is a very useful work. Klappentext This is one of the few books on the subject of mathematical materials science. It discusses the dynamics of two-phase systems within the framework of modern continuum thermodynamics, stressing fundamentals. Two general theories are discussed: a mechanical theory that leads to a generalization of the classical curve-shortening equation and a theory of heat conduction that broadly generalizes the classical Stefan theory. This original survey includes simple solutions that demonstrate the instabilities inherent in two-phase problems. The free-boundary problems that form the basis of the subject should be of great interest to mathematicians and physical scientists. Zusammenfassung This book is one of the very first on the subject of mathematical materials science and presents a view different from that prevalent in the physical literature. Issues foundational in nature are stressed with the emphasis on the interplay between mathematics and physics. It discusses the dynamics of two-phase systems within the framework of modern continuum thermodynamics. Two general theories are considered and the resulting equations exhibit unstable growth patterns. The free boundary problems that form the basis of the subject should be of great interest to mathematicians and physical scientists. Inhaltsverzeichnis Introduction Part I: Kinematics 1: Curves 1.1: Preliminary definitions 1.2: Convex curves 1.3: Integrals 1.4: Piecewise-smooth curves 1.5: Infinitesimally wrinkled curves 2: Evolving curves 2.1: Definitions 2.2: Transport identities 2.3: Integral identities 2.4: Steadily evolving interfaces 2.5: Piecewise-smooth evolving curves 2.6: Variational lemmas 3: Phase regions, control volumes, and inflows 3.1: Phase regions and control volumes 3.2: Inflows, the pillbox lemma, and infinitesimally thin evolving control volumes Part II: Mechanical theory of interfacial evolution 4: Balance of forces 4.1: Balances of forces 4.2: The power identity 5: Energetics and the dissipation inequality 6: Constitutive theory 6.1: Constitutive equations and the compatibility theorem 6.2: Balance of capillary forces revisited; corners 7: Digression: Statistical theory of interfacial stability; convexity, the Frank diagram, and corners; Wulff regions 7.1: Preliminaries; Polar diagrams 7.2: Convexity; the extended and convexified energies, and the Frank diagram 7.3: Stability 7.4: Instability of the total energy 7.5: Equilibria of the total energy; Wulff regions 7.6: Wulff's theorem 8: Evolution equations for the interface: basic assumptions 8.1: Isotropic interface 8.2: Anisotropic interface 8.2.1: Basic equations 8.2.2.: Equations when the interface is the graph of a function 8.2.3: Equations when the interface is a level set 8.3: Plan of the next few chapters 9: Stationary interfaces and steadily evolving interfaces 9.1: Stationary interfaces 9.2: Steadily evolving facets 9.3: Steadily evolving interfaces that are not flat 10: Global behaviour for an interface with stable energy 10.1: Existence of evolving interfaces from a prescribed initial curve 10.2: Growth and decay of the interface 10.3: Evolution of curvature; fingers 11: Unstable interfacial energies and interfaces with corners 11.1: Admissibility; corner conditions 11.2: The initial-value problem 11.3: Facets and wrinklings that connect evolving curves 11.4: Equations near a corner when the cu...
