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Electromagnetic homogenization is the process of estimating the effective electromagnetic properties of composite materials in the long-wavelength regime, wherein the length scales of nonhomogeneities are much smaller than the wavelengths involved. This is a bird’s-eye view of currently available homogenization formalisms for particulate composite materials. It presents analytical methods only, with focus on the general settings of anisotropy and bianisotropy. The authors largely concentrate on ‘effective’ materials as opposed to ‘equivalent’ materials, and emphasize the fundamental (but sometimes overlooked) differences between these two categories of homogenized composite materials. The properties of an ‘effective’ material represents those of its composite material, regardless of the geometry and dimensions of the bulk materials and regardless of the orientations and polarization states of the illuminating electromagnetic fields. In contrast, the properties of ‘equivalent’ materials only represent those of their corresponding composite materials under certain restrictive circumstances.
This book is an overview of state-of-the-art analytical homogenization formalisms used to estimate the effective electromagnetic properties of complex composite materials. Beginning with an introduction to homogenization, the book progresses to cover both constitutive and depolarization dyadics. The homogenization formalisms for linear and non-linear materials are examined, followed by their applications and multiple examples using Mathematica code. This text is a valuable reference for PhD students and researchers working on the electromagnetic theory of complex composite materials.
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Composites have been studied for more than 150 years, and interest in their properties has been growing. This classic volume provides the foundations for understanding a broad range of composite properties, including electrical, magnetic, electromagnetic, elastic and viscoelastic, piezoelectric, thermal, fluid flow through porous materials, thermoelectric, pyroelectric, magnetoelectric, and conduction in the presence of a magnetic field (Hall effect). Exact solutions of the PDEs in model geometries provide one avenue of understanding composites; other avenues include microstructure-independent exact relations satisfied by effective moduli, for which the general theory is reviewed; approximation formulae for effective moduli; and series expansions for the fields and effective moduli that are the basis of numerical methods for computing these fields and moduli. The range of properties that composites can exhibit can be explored either through the model geometries or through microstructure-independent bounds on the properties. These bounds are obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. The Theory of Composites surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. This book is intended for applied mathematicians, physicists, and electrical and mechanical engineers. It will also be of interest to graduate students.
The topics of anisotropy and bianisotropy are fundamental to electromagnetics from both theoretical and experimental perspectives. These properties underpin a host of complex and exotic electromagnetic phenomenons in naturally occurring materials and in relativistic scenarios, as well as in artificially produced metamaterials. As a unique guide to this rapidly developing field, the book provides a unified presentation of key classic and recent results on the studies of constitutive relations, spacetime symmetries, planewave propagation, dyadic Green functions, and homogenization of composite materials. This book also offers an up-to-date extension to standard treatments of crystal optics with coverage on both linear and weakly nonlinear regimes.
This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author`s modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).
Sculptured thin films (STFs) are a class of nanoengineered materials with properties that can be designed and realized in a controllable manner using physical vapor deposition. This text, presented as a course at the SPIE Optical Science and Technology Symposium, couples detailed knowledge of thin-film morphology with the optical response characteristics of STF devices. An accompanying CD contains Mathematica programs for use with the presented formalisms. Thus, readers will learn to design and engineer STF materials and devices for future applications, particularly with optical applications. Graduate students in optics and practicing optical engineers will find the text valuable, as well as those interested in emerging nanotechnologies for optical devices.
For decades, the surface-plasmon-polariton wave guided by the interface of simple isotropic materials dominated the scene. However, in recent times research on electromagnetic surface waves guided by planar interfaces has expanded into new and exciting areas. In the 1990's research focused on advancing knowledge of the newly discovered Dyakonov wave. More recently, much of the surface wave research is motivated by the proliferation of nanotechnology and the growing number of materials available with novel properties. This book leads the reader from the relatively simple surface-plasmon-polariton wave with isotropic materials to the latest research on various types of electromagnetic surface waves guided by the interfaces of complex materials enabled by recent developments in nanotechnology. This includes: Dyakonov waves guided by interfaces formed with columnar thin films, Dyakonov-Tamm waves guided by interfaces formed with sculptured thin films, and multiple modes of surface-plasmon-polariton waves guided by the interface of a metal and a periodically varying dielectric material. - Gathers research from the past 5 years in a single comprehensive view of electromagnetic surface waves. - Written by the foremost experts and researchers in the field. - Layered presentation explains topics with an introductory overview level up to a highly technical level.
A large part of the research currently being conducted in the fields of materials science and engineering mechanics is devoted to carbon nanotubes and their applications. In this process, modeling is a very attractive investigation tool due to the difficulties in manufacturing and testing of nanomaterials. Continuum modeling offers significant advantages over atomistic modeling. Furthermore, the lack of accuracy in continuum methods can be overtaken by incorporating input data either from experiments or atomistic methods. This book reviews the recent progress in continuum modeling of carbon nanotubes and their composites. The advantages and disadvantages of continuum methods over atomistic methods are comprehensively discussed. Numerical models, mainly based on the finite element method, as well as analytical models are presented in a comparative way starting from the simulation of isolated pristine and defected nanotubes and proceeding to nanotube-based composites. The ability of continuum methods to bridge different scales is emphasized. Recommendations for future research are given by focusing on what still continuum methods have to learn from the nano-scale. The scope of the book is to provide current knowledge aiming to support researchers entering the scientific area of carbon nanotubes to choose the appropriate modeling tool for accomplishing their study and place their efforts to further improve continuum methods.
As the generic pharmaceutical industry continues to grow and thrive, so does the need to conduct efficient and successful bioequivalence studies. In recent years, there have been significant changes to the statistical models for evaluating bioequivalence, and advances in the analytical technology used to detect drug and metabolite levels have made bioequivalence testing more difficult to conduct and summarize. The Handbook of Bioequivalence Testing offers a complete description of every aspect of bioequivalence testing. Features: Describes the current analytical methods used in bioequivalence testing, as well as their respective strengths and limitations Discusses worldwide regulatory requirements for filing for approval of generic drugs Covers GLP, GCP, and 21 CFR compliance requirements for qualifying studies for regulatory submission and facility certification Includes actual examples of reports approved by regulatory authorities to illustrate various scientific, regulatory, and formatting aspects Provides a list of vendors for the software used to analyze bioequivalence studies and recommendations Explains how to apply for a waiver, how to secure regulatory approval of reports, and how to obtain regulatory certification of facilities conducting bioequivalence studies