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An Introduction To The Mathematical Theory Of Dynamic Materials动力材料的数学理论概论

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An Introduction To The Mathematical Theory Of Dynamic Materials动力材料的数学理论概论

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作 者:Konstantin A. Lurie 著

出 版 社:

出版时间:2007-4-1

I S B N:9780387382784

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内容简介

“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。”
  “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。”
  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 Maxwells 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。

作者简介

目录

1 A General Concept of Dynamic Materials.
 1.1 The idea and definition of dynamic materials
 1.2 Two types of dynamic materials-
 1.3 Implementation of dynamic materials in electronics
  1.3.1 Ferroelectric and ferromagnetic materials
  1.3.2 Nonlinear optics
 1.4 Some applications of dynamic materials
 1.5 Dynamic materials and vibrational mechanics
References
2 An Activated Elastic Bar:Efiective Properties
 2.1 Longitudinal vibrations of activated elastic bar
 2.2 The effective parameters of activated Iaminate
 2.3 The effective parameters:homogenization
 2.4 T11e effective parameters:the Floquet theory.
 2.5 The effective parameters:discussion
 2.6 Balance of energy in longitudinal wave propagation through all activated elastic bar
References
3 Dynamic Materials in Eleetrodynamics of Moving Dielectrics
3.1 Preliminary remarks.
3.2 The basics of electrodynamics of moving dielectrics
3.3 Relativistic form of Maxwell’S system.
3.4 Material tensor s:discussion.Two types of dynamic materials
3.5 An activated dielectric 1aminate:one—dimensional wave propagation
 3.6 A spatio—temporal polycrystallic laminate:one dimensional wave propagation
 3.7 A spatio—temporal polycrystallic laminate the bounds
 3.8 An activated dielectric laminate:negative effective material properties
 3.9 An activated dielectric laminate:the energy considerations Waves of negative energy
 3.10 Numerical examples and discussion
 3.11 Effective properties of activated laminates calculated via Lorentz transform.Case of spacelike interface
Refefences
4 G.Closures of a Set of Isotropic Dielectrics with Respect to One.Dimensional Wave Propagation
 4.1 Preliminary considerations.Terminology
 4.2 Conservation of the wave impedance through one.dimensional wave propagation.A stable G—closure of a single isotropic dielectric 4.3 A stable G.closure of a set U of two isotropic dielectrics with respect to one—dimensional wave propagation
 4.4 The second invariant* as an affine function;a stable G—closure of an arbitrary set U of isotropic dielectrics
 4.5 A stable Gm—closure of a set U of two isotropic dielectrics.
 4.6 Comparison with an elliptic case
References
5 Rectangular Microstructures in Space.Time
 5.1 Introductorv remarks
 5.2 Statement of a problem
 5.3 Case of separation of variables
 5.4 Checkerboard assemblage of materials with equal wave impedance。
 5.5 Energy transformation in the presence of limit cycles
 5.6 Numerical analysis of energy accumulation
 5.7 Some remarks about discontinuous solutions for Iaminates
References
6 Some Applications of Dynamic Materials in Electrical Engineering and Optimal Design
References
Appendix:1
Appendix:2
Appendix:3
Appendix:4
Index

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