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Cover: 9783642051944 | The General Theory of Homogenization | A Personalized Introduction
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The General Theory of Homogenization
A Personalized Introduction
Taschenbuch von Luc Tartar
Sprache: Englisch

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Beschreibung
Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly.

For a better understanding of 20th century science, new mathematical tools must be introduced, like the author's H-measures, variants by Patrick Gérard, and others yet to be discovered.

Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly.

For a better understanding of 20th century science, new mathematical tools must be introduced, like the author's H-measures, variants by Patrick Gérard, and others yet to be discovered.

Inhaltsverzeichnis
Why Do I Write?.- A Personalized Overview of Homogenization I.- A Personalized Overview of Homogenization II.- An Academic Question of Jacques-Louis Lions.- A Useful Generalization by Fran#x00E7;ois Murat.- Homogenization of an Elliptic Equation.- The Div#x2013;Curl Lemma.- Physical Implications of Homogenization.- A Framework with Differential Forms.- Properties of H-Convergence.- Homogenization of Monotone Operators.- Homogenization of Laminated Materials.- Correctors in Linear Homogenization.- Correctors in Nonlinear Homogenization.- Holes with Dirichlet Conditions.- Holes with Neumann Conditions.- Compensated Compactness.- A Lemma for Studying Boundary Layers.- A Model in Hydrodynamics.- Problems in Dimension = 2.- Bounds on Effective Coefficients.- Functions Attached to Geometries.- Memory Effects.- Other Nonlocal Effects.- The Hashin#x2013;Shtrikman Construction.- Confocal Ellipsoids and Spheres.- Laminations Again, and Again.- Wave Front Sets, H-Measures.- Small-Amplitude Homogenization.- H-Measures and Bounds on Effective Coefficients.- H-Measures and Propagation Effects.- Variants of H-Measures.- Relations Between Young Measures and H-Measures.- Conclusion.- Biographical Information.- Abbreviations and Mathematical Notation.
Details
Erscheinungsjahr: 2009
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xxii
471 S.
ISBN-13: 9783642051944
ISBN-10: 3642051944
Sprache: Englisch
Herstellernummer: 978-3-642-05194-4
Autor: Tartar, Luc
Hersteller: Springer
Springer, Berlin
Springer Berlin Heidelberg
Abbildungen: XXII, 471 p.
Maße: 236 x 157 x 27 mm
Von/Mit: Luc Tartar
Erscheinungsdatum: 21.12.2009
Gewicht: 0,745 kg
Artikel-ID: 101462662
Inhaltsverzeichnis
Why Do I Write?.- A Personalized Overview of Homogenization I.- A Personalized Overview of Homogenization II.- An Academic Question of Jacques-Louis Lions.- A Useful Generalization by Fran#x00E7;ois Murat.- Homogenization of an Elliptic Equation.- The Div#x2013;Curl Lemma.- Physical Implications of Homogenization.- A Framework with Differential Forms.- Properties of H-Convergence.- Homogenization of Monotone Operators.- Homogenization of Laminated Materials.- Correctors in Linear Homogenization.- Correctors in Nonlinear Homogenization.- Holes with Dirichlet Conditions.- Holes with Neumann Conditions.- Compensated Compactness.- A Lemma for Studying Boundary Layers.- A Model in Hydrodynamics.- Problems in Dimension = 2.- Bounds on Effective Coefficients.- Functions Attached to Geometries.- Memory Effects.- Other Nonlocal Effects.- The Hashin#x2013;Shtrikman Construction.- Confocal Ellipsoids and Spheres.- Laminations Again, and Again.- Wave Front Sets, H-Measures.- Small-Amplitude Homogenization.- H-Measures and Bounds on Effective Coefficients.- H-Measures and Propagation Effects.- Variants of H-Measures.- Relations Between Young Measures and H-Measures.- Conclusion.- Biographical Information.- Abbreviations and Mathematical Notation.
Details
Erscheinungsjahr: 2009
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xxii
471 S.
ISBN-13: 9783642051944
ISBN-10: 3642051944
Sprache: Englisch
Herstellernummer: 978-3-642-05194-4
Autor: Tartar, Luc
Hersteller: Springer
Springer, Berlin
Springer Berlin Heidelberg
Abbildungen: XXII, 471 p.
Maße: 236 x 157 x 27 mm
Von/Mit: Luc Tartar
Erscheinungsdatum: 21.12.2009
Gewicht: 0,745 kg
Artikel-ID: 101462662
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