Getting acquainted with homogenization and multiscale /
General Material Designation
[Book]
First Statement of Responsibility
Leonid Berlyand, Volodymyr Rybalko.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Cham, Switzerland :
Name of Publisher, Distributor, etc.
Birkhäuser,
Date of Publication, Distribution, etc.
2018.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource (xviii, 178 pages) :
Other Physical Details
illustrations (some color)
SERIES
Series Title
Compact textbooks in mathematics,
ISSN of Series
2296-4568
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
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.
0
SUMMARY OR ABSTRACT
Text of Note
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.--