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Getting Acquainted with Homogenization and Multiscale

  • Leonid Berlyand
  • Volodymyr Rybalko

Part of the Compact Textbooks in Mathematics book series (CTM)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Leonid Berlyand, Volodymyr Rybalko
    Pages 1-15
  3. Leonid Berlyand, Volodymyr Rybalko
    Pages 17-33
  4. Leonid Berlyand, Volodymyr Rybalko
    Pages 35-43
  5. Leonid Berlyand, Volodymyr Rybalko
    Pages 45-52
  6. Leonid Berlyand, Volodymyr Rybalko
    Pages 53-58
  7. Leonid Berlyand, Volodymyr Rybalko
    Pages 59-74
  8. Leonid Berlyand, Volodymyr Rybalko
    Pages 85-101
  9. Leonid Berlyand, Volodymyr Rybalko
    Pages 103-122
  10. Leonid Berlyand, Volodymyr Rybalko
    Pages 139-168
  11. Back Matter
    Pages 169-178

About this book

Introduction

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.


Keywords

Multiscale Homogenization Effective coefficients Asymptotic expansion Gamma-convergence Two-scale convergence Continuum limit Stochastic homogenizaiton Cell problem Plasticity Composite material Heterogeneous media

Authors and affiliations

  • Leonid Berlyand
    • 1
  • Volodymyr Rybalko
    • 2
  1. 1.Mathematics and Materials Research InstitutePennsylvania State UniversityUniversity ParkUSA
  2. 2.Mathematical DivisionB Verkin Institute for Low Temperature Physics and Engineering of National Academy of Sciences of UkraineKharkivUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-01777-4
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-01776-7
  • Online ISBN 978-3-030-01777-4
  • Series Print ISSN 2296-4568
  • Series Online ISSN 2296-455X
  • Buy this book on publisher's site