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The current use of complex materials in nanotechnology and industrial engineering has led to a number of intricate problems in mechanics, and the macroscopic behavior of such materials often depends critically on their substructures. This work, written by leading mathematicians and engineers, features a broad range of topics that offer both experimental results and clear, detailed answers to fundamental questions about the general formulation of multifield theories within the context of modeling material substructures. Applied mathematicians, mechanical and structural engineers, material scientists, graduate students, and researchers in the above areas will benefit from the work and may find suggestions for further research in its rich collection of open problems.
Toachieve design, implementation,and servicing ofcomplex systems and struc tures in an efficient and cost-effective way,a deeper knowledge and understanding of the subtle cast and detailed evolution of materials is needed. The analysis in demand borders with the molecular and atomic one, spanning all the way down from classical continua. The study of the behavior of complex materials in sophisticated devices also opens intricate questions about the applicability of primary axioms ofcontinuum mechanics such as the ultimate nature of the material element itselfand the possibility ofidentifying itperfectly. So it is necessary to develop tools that allow usto formulate both theoretical models and methods of numerical approximation for the analysis of material substructures. Multifield theories in continuum mechanics, which bridge classical materials science and modern continuum mechanics, provide precisely these tools. Multifield theories not only address problems of material substructures, but also encompass well-recognized approaches to the study of soft condensed matter and allow one to model disparate conditions in various states ofmatter. However, research inmultifield theories is vast, and there is little in the way of a comprehensive distillation of the subject from an engineer's perspective. Therefore, the papers in the present volume, 1 which grew out of our experience as editors for an engineeringjournal, tackle some fundamental questions,suggest solutions of concrete problems, and strive to interpret a host of experimental evidence. In this spirit, each of the authors has contributed original results having in mind their wider applicability.
Toachieve design, implementation,and servicing ofcomplex systems and struc tures in an efficient and cost-effective way,a deeper knowledge and understanding of the subtle cast and detailed evolution of materials is needed. The analysis in demand borders with the molecular and atomic one, spanning all the way down from classical continua. The study of the behavior of complex materials in sophisticated devices also opens intricate questions about the applicability of primary axioms ofcontinuum mechanics such as the ultimate nature of the material element itselfand the possibility ofidentifying itperfectly. So it is necessary to develop tools that allow usto formulate both theoretical models and methods of numerical approximation for the analysis of material substructures. Multifield theories in continuum mechanics, which bridge classical materials science and modern continuum mechanics, provide precisely these tools. Multifield theories not only address problems of material substructures, but also encompass well-recognized approaches to the study of soft condensed matter and allow one to model disparate conditions in various states ofmatter. However, research inmultifield theories is vast, and there is little in the way of a comprehensive distillation of the subject from an engineer's perspective. Therefore, the papers in the present volume, 1 which grew out of our experience as editors for an engineeringjournal, tackle some fundamental questions,suggest solutions of concrete problems, and strive to interpret a host of experimental evidence. In this spirit, each of the authors has contributed original results having in mind their wider applicability.
"As an outgrowth of a symposium held in Taormina, Italy, in 2001, ten invited papers on multifield theories for continua with substructure are presented here. Multifield theories aim to bridge the area between materials science and continuum mechanics. From the standpoint of material constituents, the simplest model is considered in the contribution of I. Müller: a monatomic gas.... Other contributions deal with the interaction of polymer chains and the turbulent state of a fluid...with topological properties of defects, of shape memory and others. The perhaps most theoretical article is by Cendra, Marsden and Ratiu on...extended...Poisson brackets with cocycles. The articles, though dealing with nontrivial matters, are quite readable and informative even for the nonspecialist."
-Monatshefte für Mathematik
"...This compendium is extremely diverse ...The individual contributions in this compendium are certainly quite interesting and worth reading."
-Rezensionen
-Monatshefte für Mathematik
"...This compendium is extremely diverse ...The individual contributions in this compendium are certainly quite interesting and worth reading."
-Rezensionen