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The objective of this monograph is a numerical analysis of the well-accepted models of Landau, Lifshitz and Gilbert for (electrically conducting) ferromagnets. Part I discusses convergence behavior of different finite element schemes for solving the stationary problem. Part II deals with numerical analyses of different penalization / projection strategies in nonstationary micromagnetism; it closes with a chapter on nematic liquid crystals to show applicability of these new methods to further applications.
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Dr. Andreas Prohl, Universität Kiel
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Ferromagnetic materials are widely used as recording media.
Their magnetic patterns are described by the well-accepted model of Landau and Lifshitz. Over the last years, different strategies habe been developed to tackle the related non-convex minimization problem: direct minimization, convexification, and relaxation by using Young measures. Nonstationary effects are considered in the extended models of Landau, Lifshitz and Gilbert for (electrically conducting) ferromagnets.
The objective of this monograph is a numerical analysis of these models. Part I discusses convergence behavior of different finite element schemes for solving the stationary problem. Part II deals with numerical analyses of different penalization / projection strategies in nonstationary micromagnetism; it closes with a chapter on nematic liquid crystals to show applicability of these new methods to further applications.
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- VerlagVieweg+Teubner Verlag
- Erscheinungsdatum2001
- ISBN 10 3519003589
- ISBN 13 9783519003588
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten324
- Kontakt zum HerstellerNicht verfügbar
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Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Dr. Andreas Prohl, Universitaet KielThe objective of this monograph is a numerical analysis of the well-accepted models of Landau, Lifshitz and Gilbert for (electrically conducting) ferromagnets. Part I discusses convergence behavior of different finit. Bestandsnummer des Verkäufers 4858975
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Computational Micromagnetism
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Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Dez 2001, 2001
ISBN 10: 3519003589
ISBN 13: 9783519003588
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Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -In this work, we study numerical issues related to a common mathematical model which describes ferromagnetic materials, both in a stationary and non stationary context. Electromagnetic effects are accounted for in an extended model to study nonstationary magneto-electronics. The last part deals with the numerical analysis of the commonly used Ericksen-Leslie model to study the fluid flow of nematic liquid crystals which find applications in display technologies, for example. All these mathematical models to describe different microstructural phe nomena share common features like (i) strong nonlinearities, and (ii) non convex side constraints (i.e., I m I = 1, almost everywhere in w C JRd, for the order parameter m : w -+ JRd). One key issue in numerical modeling of such problems is to make sure that the non-convex constraint is fulfilled for computed solutions. We present and analyze different solution strategies to deal with the variational problem of stationary micromagnetism, which builds part I of the book: direct minimization, convexification, and relaxation using Young measure-valued solutions. In particular, we address the following points: ¿ Direct minimization: A spatial triangulation 'generates an artificial exchange energy contribution' in the discretized minimizing problem which may pollute physically relevant exchange energy contributions; its minimizers exhibit multiple scales (with branching structures near the boundary of the ferromagnet) and are difficult to be computed efficiently. We exploit this observation to construct an adaptive scheme which better resolves multiple scale structures (cubic ferromagnets). 324 pp. Englisch. Bestandsnummer des Verkäufers 9783519003588
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Computational Micromagnetism
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - In this work, we study numerical issues related to a common mathematical model which describes ferromagnetic materials, both in a stationary and non stationary context. Electromagnetic effects are accounted for in an extended model to study nonstationary magneto-electronics. The last part deals with the numerical analysis of the commonly used Ericksen-Leslie model to study the fluid flow of nematic liquid crystals which find applications in display technologies, for example. All these mathematical models to describe different microstructural phe nomena share common features like (i) strong nonlinearities, and (ii) non convex side constraints (i.e., I m I = 1, almost everywhere in w C JRd, for the order parameter m : w -+ JRd). One key issue in numerical modeling of such problems is to make sure that the non-convex constraint is fulfilled for computed solutions. We present and analyze different solution strategies to deal with the variational problem of stationary micromagnetism, which builds part I of the book: direct minimization, convexification, and relaxation using Young measure-valued solutions. In particular, we address the following points: - Direct minimization: A spatial triangulation 'generates an artificial exchange energy contribution' in the discretized minimizing problem which may pollute physically relevant exchange energy contributions; its minimizers exhibit multiple scales (with branching structures near the boundary of the ferromagnet) and are difficult to be computed efficiently. We exploit this observation to construct an adaptive scheme which better resolves multiple scale structures (cubic ferromagnets). Bestandsnummer des Verkäufers 9783519003588
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Computational Micromagnetism (Advances in Numerical Mathematics)
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Computational Micromagnetism (Advances in Numerical Mathematics)
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Vieweg+Teubner Verlag 2001-12-11, 2001
ISBN 10: 3519003589
ISBN 13: 9783519003588
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Computational Micromagnetism Advances in Numerical Mathematics Andreas Prohl Informatik Mathe Wahrscheinlichkeit Kombinatorik Technik Advances in Numerical Mathematics Direct Minimization Finite Element Method Wahrscheinlichkeitstheorie Stochastik Mathematische Statistik magnetic material magnetism Magnetismus Micromagnetism Model Nematic Liquid Crystals Numerical Mathematics Numerical Nonstationary Numerical Stationary Relaxed Micromagnetism
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Softcover. Zustand: gut. Auflage: 1 (2001). The objective of this monograph is a numerical analysis of the well-accepted models of Landau, Lifhitz an Gilbert for (electrically conducting) ferromagnets. Part I discusses convergence behavior of different finite element schemes for solving the stationary problem. Part II deals with numerical analyses of different penalization / projection strategies in nonstationary micromagnetism; it closes with a chapter on nematic liquid crystals to show applicability of these new methods to further applications. Content: I: Numerical Stationary Micromagnetism - Direct Minimization - Convexified Micromagnetism - Relaxed Micromagnetism using Young Measures - II: Numerical Nonstationary Micromagnetism - The Landau-Lifshitz-Gilbert Equation - The Maxwell-Landau-Lifshitz-Gilbert Equation - Nematic Liquid Crystals - Summary and Outlook Reihe/Serie Advances in Numerical Mathematics Zusatzinfo XVIII, 304 p. 93 illus. Verlagsort Wiesbaden Sprache englisch Maße 170 x 244 mm Mathematik Informatik Mathe Wahrscheinlichkeit Kombinatorik Technik Advances in Numerical Mathematics Direct Minimization Finite Element Method Wahrscheinlichkeitstheorie Stochastik Mathematische Statistik magnetic material magnetism Magnetismus Micromagnetism Model Nematic Liquid Crystals Numerical Mathematics Numerical Nonstationary Numerical Stationary Relaxed Micromagnetism ISBN-10 3-519-00358-9 / 3519003589 ISBN-13 978-3-519-00358-8 / 9783519003588 Computational Micromagnetism Advances in Numerical Mathematics Andreas Prohl In englischer Sprache. 304 pages. 23,8 x 17 x 1,6 cm. Bestandsnummer des Verkäufers BN4547
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Computational Micromagnetism (Advances in Numerical Mathematics) [Paperback] Prohl, Andreas
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Computational Micromagnetism
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Computational Micromagnetism
Verlag:
Vieweg+Teubner, Vieweg+Teubner Verlag Dez 2001, 2001
ISBN 10: 3519003589
ISBN 13: 9783519003588
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In this work, we study numerical issues related to a common mathematical model which describes ferromagnetic materials, both in a stationary and non stationary context. Electromagnetic effects are accounted for in an extended model to study nonstationary magneto-electronics. The last part deals with the numerical analysis of the commonly used Ericksen-Leslie model to study the fluid flow of nematic liquid crystals which find applications in display technologies, for example. All these mathematical models to describe different microstructural phe nomena share common features like (i) strong nonlinearities, and (ii) non convex side constraints (i.e., I m I = 1, almost everywhere in w C JRd, for the order parameter m : w -+ JRd). One key issue in numerical modeling of such problems is to make sure that the non-convex constraint is fulfilled for computed solutions. We present and analyze different solution strategies to deal with the variational problem of stationary micromagnetism, which builds part I of the book: direct minimization, convexification, and relaxation using Young measure-valued solutions. In particular, we address the following points: - Direct minimization: A spatial triangulation 'generates an artificial exchange energy contribution' in the discretized minimizing problem which may pollute physically relevant exchange energy contributions; its minimizers exhibit multiple scales (with branching structures near the boundary of the ferromagnet) and are difficult to be computed efficiently. We exploit this observation to construct an adaptive scheme which better resolves multiple scale structures (cubic ferromagnets). 304 pp. Englisch. Bestandsnummer des Verkäufers 9783519003588
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Computational Micromagnetism
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