Lectures on Random Interfaces

Tadahisa Funaki

ISBN 10: 9811008485 ISBN 13: 9789811008481

Editorial: Springer, 2017

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Sinopsis:

Vershik curves are derived in that limit.A sharp interface limit for the Allen–Cahn equation, that is, a reaction–diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces.

De la contraportada:

Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book.

Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ?f-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers.

Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit.

A sharp interface limit for the Allen–Cahn equation, that is, a reaction–diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg–Landau model, stochastic quantization, or dynamic P(f)-model, is considered. Brief introductions to Brownian motions, martingales, and stochastic integrals are given in an infinite dimensional setting. The regularity property of solutions of stochastic PDEs (SPDEs) of a parabolic type with additive noises is also discussed.

The Kardar–Parisi–Zhang (KPZ) equation , which describes a growing interface with fluctuation, recently has attracted much attention. This is an ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied.

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T�tulo: Lectures on Random Interfaces
Editorial: Springer
A�o de publicaci�n: 2017
Encuadernaci�n: Taschenbuch
Condici�n: Neu

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Lectures on Random Interfaces (eng)

Funaki, Tadahisa

Publicado por Springer, 2017

ISBN 10: 9811008485 ISBN 13: 9789811008481

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Lectures on Random Interfaces

Tadahisa Funaki

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ISBN 10: 9811008485 ISBN 13: 9789811008481

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Condici�n: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. &nbsp &nbsp&nbspInterfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/. N� de ref. del art�culo: 140458812

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Lectures on Random Interfaces

Tadahisa Funaki

Publicado por Springer Nature Singapore Jan 2017, 2017

ISBN 10: 9811008485 ISBN 13: 9789811008481

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Taschenbuch. Condici�n: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book.Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called phi-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers.Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit.A sharp interface limit for the Allen-Cahn equation, that is, a reaction-diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg-Landau model, stochastic quantization, or dynamic P(phi)-model, is considered. Brief introductions to Brownian motions, martingales, and stochastic integrals are given in an infinite dimensional setting. The regularity property of solutions of stochastic PDEs (SPDEs) of a parabolic type with additive noises is also discussed.The Kardar-Parisi-Zhang (KPZ) equation , which describes a growing interface with fluctuation, recently has attracted much attention. This is an ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied. 152 pp. Englisch. N� de ref. del art�culo: 9789811008481

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Lectures on Random Interfaces

Tadahisa Funaki

Publicado por Springer, Springer Jan 2017, 2017

ISBN 10: 9811008485 ISBN 13: 9789811008481

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Taschenbuch. Condici�n: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Shows that the microscopic point of view is useful in choosing a real minimizer of a variational problem that determines an interface shapeSpringer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 152 pp. Englisch. N� de ref. del art�culo: 9789811008481

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Lectures on Random Interfaces

Tadahisa Funaki

Publicado por Springer, Springer, 2017

ISBN 10: 9811008485 ISBN 13: 9789811008481

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Librería: AHA-BUCH GmbH, Einbeck, Alemania

Calificaci�n del vendedor: 5 de 5 estrellas

Taschenbuch. Condici�n: Neu. Druck auf Anfrage Neuware - Printed after ordering - Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book.Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called phi-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers.Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamicsis studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit.A sharp interface limit for the Allen-Cahn equation, that is, a reaction-diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg-Landau model, stochastic quantization, or dynamic P(phi)-model, is considered. Brief introductions to Brownian motions, martingales, and stochastic integrals are given in an infinite dimensional setting. The regularity property of solutions of stochastic PDEs (SPDEs) of a parabolic type with additive noises is also discussed.The Kardar-Parisi-Zhang (KPZ) equation , which describes a growing interface with fluctuation, recently has attracted much attention. This is an ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied. N� de ref. del art�culo: 9789811008481

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