03958nam 22006255 450 991030011670332120200703131434.03-030-01777-X10.1007/978-3-030-01777-4(CKB)4100000007158903(DE-He213)978-3-030-01777-4(MiAaPQ)EBC6312528(PPN)232472173(EXLCZ)99410000000715890320181122d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierGetting Acquainted with Homogenization and Multiscale /by Leonid Berlyand, Volodymyr Rybalko1st ed. 2018.Cham :Springer International Publishing :Imprint: Birkhäuser,2018.1 online resource (XVIII, 178 p. 42 illus., 14 illus. in color.) Compact Textbooks in Mathematics,2296-45683-030-01776-1 Includes bibliographical references and index.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.Compact Textbooks in Mathematics,2296-4568Computer mathematicsApplied mathematicsEngineering mathematicsPartial differential equationsComputational Science and Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/M14026Mathematical and Computational Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/T11006Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Computer mathematics.Applied mathematics.Engineering mathematics.Partial differential equations.Computational Science and Engineering.Mathematical and Computational Engineering.Partial Differential Equations.515.353515.35Berlyand Leonidauthttp://id.loc.gov/vocabulary/relators/aut768261Rybalko Volodymyrauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910300116703321Getting Acquainted with Homogenization and Multiscale2266035UNINA