Synopses & Reviews
This book gives a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials--that is, material substances whose properties are variable in space and time. Unlike conventional composites that are often found in nature, dynamic materials are mostly the products of modern technology developed to maintain the most effective control over dynamic processes. These materials have diverse applications: tunable left-handed dielectrics, optical pumping with high-energy pulse compression, and electromagnetic stealth technology, to name a few. Of special significance is the participation of dynamic materials in almost every optimal material design in dynamics. The book discusses some general features of dynamic materials as thermodynamically open systems; it gives their adequate tensor description in the context of Maxwell's theory of moving dielectrics and makes a special emphasis on the theoretical analysis of spatio-temporal material composites (such as laminates and checkerboard structures). Some unusual applications are listed along with the discussion of some typical optimization problems in space-time via dynamic materials. Audience This book is intended for applied mathematicians interested in optimal problems of material design for systems governed by hyperbolic differential equations. It will also be useful for researchers in the field of smart metamaterials and their applications to optimal material design in dynamics.
Review
From the reviews: "The author introduces the concept of dynamic or time-dependent materials in mechanical and electromagnetic context in order to study varying environmental conditions and changing properties, structures or compositions of materials both in space and time. ... In total, the monograph seems to be a pioneering step in establishing the mathematical theory of dynamic materials, and without chapter problems, computer programs and design projects, which is desirable for normal classroom use, it may basically be of interest to researchers and engineers." (M. Cengiz Dökmeci, Zentralblatt MATH, Vol. 1125 (2), 2008) "Lurie proposes to consider in a dynamical framework materials that present inhomogeneties in both space and time. ... an introduction to a field of continuum physics that may find unexpected developments in some of the newly designed materials that involve small sizes and short wavelength dynamical phenomena. ... It is highly recommended to all those wondering what is new in the field. It should also open new horizons to most of its readers." (Gérard A. Maugin, Mathematical Reviews, Issue 2008 b)
Synopsis
This book has emerged from the study of a new concept in material science that has been realized about a decade ago. Before that, I had been working for more than 20 years on conventional composites assembled in space and therefore adjusted to optimal material design in statics. The reason for that adjustmentisthatsuchcompositesappearedtobecomenecessaryparticipants in almost any optimal material design related to a state of equilibrium. A theoretical study of conventional composites has been very extensive over a long period of time. It received stimulation through many engineering applications, and some of the results have become a part of modern industrial technology. But again, the ordinary composites are all about statics, or, at the utmost, are related to control over the free vibration modes, a situation conceptually close to a static equilibrium. The world of dynamics appears to be quite di?erent in this aspect. When it comes to motion, the immovable material formations distributed in space alone become insu?cient as the elements of design because they are incapable of getting fully adjusted to the temporal variation in the environment. To be able to adequately handle dynamics, especially the wave motion, the material medium must itself be time dependent, i.e. its material properties should vary in space and time alike. Any substance demonstrating such variation has been termed a dynamic material 1].
Synopsis
This book describes a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials---material substances whose properties are variable in space and time. The book discusses some general features of dynamic materials as thermodynamically open systems; it gives their adequate tensor description in the context of Maxwell's theory of moving dielectrics and makes a special emphasis on the theoretical analysis of spatio-temporal material composites (such as laminates and checkerboard structures). Some unusual applications are listed along with the discussion of some typical optimization problems in space-time via dynamic materials. This book will interest applied mathematicians interested in optimal problems of material design for systems governed by hyperbolic differential equations; researchers in the field of smart metamaterials and their applications to optimal material design in dynamics.
Synopsis
This fascinating book is a treatise on real space-age materials. It is a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials--that is, material substances whose properties are variable in space and time. Unlike conventional composites that are often found in nature, dynamic materials are mostly the products of modern technology developed to maintain the most effective control over dynamic processes.
Table of Contents
Preface.- A General Concept of Dynamic Materials.- An Activated Elastic Bar: Effective Properties.- Dynamic Materials in Electrodynamics of Moving Dialectrics.- G-Closures of a Set of Isotropic Dielectrics with Respect to One-Dimensional Wave Propagation.- Rectangular Microstructures in Space-Time.- Some Applications of Dynamic Materials in Electrical Engineering and Optimal Design.- Appendix 1.- Appendix 2.- Appendix 3.- Appendix 4.- Index.