Composite Media And Homogenization Theory
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Composite Media and Homogenization Theory
Author: Gianni Dal Maso
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This volume contains the Proceedings of the Workshop on Composite Media and Homogenization Theory held in Trieste, Italy, from January 15 to 26, 1990. The workshop was organized by the International Centre for Theo retical Physics (ICTP); part of the activity was co-sponsored by the Interna tional School for Advanced Studies (SISSA). The workshop covered a broad range of topics in the mathematical the ory of composite materials and homogenization. Among the specific areas of focus were homogenization of periodic and nonperiodic structures, porous me dia, asymptotic analysis for linear and nonlinear problems, optimal bounds for effective moduli, waves in composite materials, optimal design and relaxation, random media. The workshop was actively attended by more than 100 participants from 23 countries. In the afternoon sessions 35 seminars were delivered by the participants. This volume contains research articles corresponding to 14 of the 20 invited talks which were presented. Its content will be of interest both to mathematicians working in the field and to applied mathematicians and engineers interested in modelling the behaviour of composite and random media We are pleased to express here our thanks to the ICTP for having made this workshop possible, to Ms. A. Bergamo for her continuous help during the workshop, and to Ms. C. Parma for her collaboration in editing the proceedings. Gianni Dal Maso Gian Fausto Dell'Antonio SIS SA, Trieste Universita "La Sapienza", Roma v Contents Preface ... v List of Speakers ... ix Contributors ... ... ... ... . xiii ... ... ...
Composite Media And Homogenization Theory: Proceedings Of The Second Workshop
A rigorous mathematical treatment of the properties of composite materials has been made possible by recent mathematical results in the fields of partial differential equations and the calculus of variations. The progress in the mathematical models for composite media has led to a deeper understanding of the overall behaviour of composite structures and to significant applications in physics and engineering, including a new approach to optimal design problems.Many new, relevant results are presented in this volume, which contains 16 invited papers from the Second Workshop on Composite Media and Homogenization Theory held at the International Centre for Theoretical Physics in Trieste, Italy, from September 20 to October 1, 1993. Topics include homogenization of problems singularly depending on small or large parameters, homogenization of nonlinear problems, optimal bounds for effective moduli, asymptotic analysis of problems in perforated domains, laminate structures in phase transitions, optimal design and relaxation. Mathematicians and engineers interested in mathematical models of composite materials will find this book to be an important reference.
Composite Media with Weak Spatial Dispersion
This book presents a modern theory of so-called weak spatial dispersion (WSD) in composite media of optically small inclusions without natural magnetism and optical nonlinearity. WSD manifests in two important phenomena called bianisotropy and artificial magnetism, whose microscopic origin is thoroughly studied in this book. The theory of this book is applicable to the natural media with WSD, such as chiral materials. However, emphasis is given to artificial media, too, with the idea to engineer needed electromagnetic properties. The text describes a homogenization model of effectively continuous media with multipole electromagnetic response, taking into account the interface effects. Another model is developed for so-called metamaterials in which artificial magnetism can be a resonant phenomenon and may result in the violation of Maxwell’s boundary conditions and other challenges. The book will hopefully improve the understanding of WSD and help readers to correctly describe and characterize metamaterials.