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Getting acquainted with homogenizati...

Berlyand, Leonid.

Getting acquainted with homogenization and multiscale

Record Type:	Electronic resources : Monograph/item
Title/Author:	Getting acquainted with homogenization and multiscaleby Leonid Berlyand, Volodymyr Rybalko.
Author:	Berlyand, Leonid.
other author:	Rybalko, Volodymyr.
Published:	Cham :Springer International Publishing :2018.
Description:	xviii, 178 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Homogenization (Differential equations)
Online resource:	https://doi.org/10.1007/978-3-030-01777-4
ISBN:	9783030017774$q(electronic bk.)

Getting acquainted with homogenization and multiscale
Berlyand, Leonid.

Getting acquainted with homogenization and multiscale[electronic resource] /by Leonid Berlyand, Volodymyr Rybalko. - Cham :Springer International Publishing :2018. - xviii, 178 p. :ill. (some col.), digital ;24 cm. - Compact textbooks in mathematics,2296-4568. - Compact textbooks in mathematics..

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.

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.

ISBN: 9783030017774$q(electronic bk.)

Standard No.: 10.1007/978-3-030-01777-4doiSubjects--Topical Terms:

308616
Homogenization (Differential equations)

LC Class. No.: QA377 / .B475 2018

Dewey Class. No.: 515.35

Getting acquainted with homogenization and multiscale
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505 0 $a 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.
520 $a 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.
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