Getting Acquainted with Homogenization and...

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Beschreibung

The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.

Über den Autor

Leonid Berlyand is a Professor of Mathematics, and a member of the Materials Research Institute and Huck Institutes for Life Sciences at the Pennsylvania State University (USA) as well as an Honorary Professor (Professoris Honoris Cavza) at the Moscow State University. Leonid Berlyand is an internationally recognized expert in applied mathematics. He has made fundamental contributions to homogenization theory, mathematical Ginzburg-Landau theory, and mathematical biology.

Volodymyr Rybalko works as a senior research fellow in Mathematical Division, B.Verkin Institute for Low Temperature Physics and Engineering of National Academy of Sciences of Ukraine. He is an expert in the area of PDEs, he is known, in particular, for his contributions in homogenization theory.

Zusammenfassung

Development of an intuitive understanding that complements rigorous mathematics

Makes advanced mathematical tools and concepts accessible to non-experts

Presentations in all Chapters is supplied with exercises

Inhaltsverzeichnis

Chapter 1- Preliminaries.- Chapter 2- What is Homogenization and Multiscale? First Examples.- Chapter 3- Brief History and Surprising Examples in Homogenization.- Chapter 4- Formal Two-scale Asymptotic Expansions and the Corrector Problem.- Chapter 5- Compensated Compactness and Oscillating Test-functions.- Chapter 6- Two-scale Convergence.- Chapter 7- Examples of Explicit Effective Coefficients: Laminated Structures and 2D Checkerboards.- Chapter 8- Introduction to Stochastic Homogenization.- Chapter 9- G-Convergence in Nonlinear Homogenization Problems.- Chapter 10- An Example of a Nonlinear Problem: Homogenization of Plasticity and Limit Loads.- Chapter 11- Continuum Limits for Discrete Problems with Fine Scales.- References.- Appendix: Regular and Singular Perturbations and Boundary Layers.- Index.

Details

Erscheinungsjahr:	2018
Fachbereich:	EDV
Genre:	Informatik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
Seiten:	196
Reihe:	Compact Textbooks in Mathematics
Inhalt:	xviii 178 S. 28 s/w Illustr. 14 farbige Illustr. 178 p. 42 illus. 14 illus. in color.
ISBN-13:	9783030017767
ISBN-10:	3030017761
Sprache:	Englisch
Herstellernummer:	978-3-030-01776-7
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Rybalko, Volodymyr Berlyand, Leonid
Auflage:	1st ed. 2018
Hersteller:	Springer International Publishing Compact Textbooks in Mathematics
Maße:	235 x 155 x 11 mm
Von/Mit:	Volodymyr Rybalko (u. a.)
Erscheinungsdatum:	29.11.2018
Gewicht:	0,306 kg

preigu-id: 114334691