Getting Acquainted with Homogenization and Multiscale

1. Auflage 2018
ISBN: 978-3-030-01776-7
Verlag: Springer International Publishing

Buch, Englisch, 178 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 306 g

Reihe: Compact Textbooks in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Rybalko, Volodymyr

Berlyand, Leonid

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

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.

Über Autor(innen)

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.