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Low and High Frequency Asymptotics by V.K. Varadan Pdf
This volume focuses on asymptotic methods in the low and high frequency limits for the solution of scattering and propagation problems. Each chapter is pedagogical in nature, starting with the basic foundations and ending with practical applications. For example, using the Geometrical Theory of Diffraction, the canonical problem of edge diffraction is first solved and then used in solving the problem of diffraction by a finite crack. In recent times, the crack problem has been of much interest for its applications to Non-Destructive Evaluation (NDE) of flaws in structural materials.
Low Frequency Scattering by George Dassios,Ralph Kleinman Pdf
Scattering theory deals with the interactions of waves with obstacles in their path, and low frequency scattering occurs when the obstacles involved are very small. This book gives an overview of the subject for graduates and researchers, for the first time unifying the theories covering acoustic, electromagnetic and elastic waves.
Fast Multipole Methods for the Helmholtz Equation in Three Dimensions by Nail A Gumerov,Ramani Duraiswami Pdf
This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions. The Fast Multipole Method was pioneered by Rokhlin and Greengard in 1987 and has enjoyed a dramatic development and recognition during the past two decades. This method has been described as one of the best 10 algorithms of the 20th century. Thus, it is becoming increasingly important to give a detailed exposition of the Fast Multipole Method that will be accessible to a broad audience of researchers. This is exactly what the authors of this book have accomplished. For this reason, it will be a valuable reference for a broad audience of engineers, physicists and applied mathematicians. The Only book that provides comprehensive coverage of this topic in one location Presents a review of the basic theory of expansions of the Helmholtz equation solutions Comprehensive description of both mathematical and practical aspects of the fast multipole method and it's applications to issues described by the Helmholtz equation
Asymptotic Approximations for the Sound Generated by Aerofoils in Unsteady Subsonic Flows by Lorna Ayton Pdf
This thesis investigates the sound generated by solid bodies in steady subsonic flows with unsteady perturbations, as is typically used when determining the noise generated by turbulent interactions. The focus is predominantly on modelling the sound generated by blades within an aircraft engine, and the solutions are presented as asymptotic approximations. Key analytical techniques, such as the Wiener-Hopf method, and the matched asymptotic expansion method are clearly detailed. The results allow for the effect of variations in the steady flow or blade shape on the noise generated to be analysed much faster than when solving the problem numerically or considering it experimentally.
Asymptotic Waveform Evaluation by Eli Chiprout,Michel S. Nakhla Pdf
The intense drive for signal integrity has been at the forefront ofrapid and new developments in CAD algorithms. Thousands ofengineers, intent on achieving the best design possible, use SPICE on a daily basis for analog simulation and general circuit analysis. But the strained demand for high data speeds, coupled with miniaturizationon an unprecedented scale, has highlighted the previously negligible effects of interconnects; effects which are not always handled appro priately by the present levels of SPICE. Signals at these higher speeds may be degraded by long interconnect lengths compared to the increasingly shorter sig nal rise times. Interconnect structures can be diverse (pins, connectors, leads, microstrips, striplines, etc. ) and present at any of the hierarchical packaging levels: integrated circuits, printed circuit boards, multi-chip modules or sys tem backplanes. Analysis of these effects in any CAD package has become a necessity. Asymptotic waveform evaluation (AWE) and other moment matching tech niques have recently proven useful in the analysis of interconnect structures and various networks containing large linear structures with nonlinear termi nations. Previously, all that was available to the designer was a full SPICE simulation or a quick but uncertain timing estimation. Moment matching, used in linear systems analysis as a method of model reduction, describes a method to extract a small set of dominant poles from a large network. The information is obtained from the Taylor series coefficients (moments) of that system.
Magnetotellurics in the Context of the Theory of Ill-posed Problems by Mark Naumovich Berdichevskiĭ,Vladimir Ivanovich Dmitriev Pdf
This volume serves as an introduction to modern magnetotellurics originating with the pioneering work of Tikhonov and Cagniard. It presents a comprehensive summary of theoretical and methodological aspects of magnetotellurics. It provides a bridge between textbooks on electrical prospecting and numerous papers on magnetotelluric methods scattered among various geophysical journals and collections. The book has been written in the terms of the theory of ill-posed problems and contains a special chapter encouraging readers to master the elements of this theory that defines the philosophy of the physical experiment. The book thus offers the connected and consistent account of the principles of magnetotellurics from that single viewpoint. The book also brings together developments from many sources and involves some little-known results developed in Russia in Tikhonov's magnetotellurics school. Of particular interest are concluding chapters of the book that demonstrate the potential of magnetotellurics in oil and gas surveys, including discovery of the Urengoy gas field in Western Siberia, one of the largest gas fields in the world. This potential also is revealed in studies of the earth's crust and upper mantle.
Asymptotic Approaches in Nonlinear Dynamics by Jan Awrejcewicz,Igor V. Andrianov,Leonid I. Manevitch Pdf
This book covers developments in the theory of oscillations from diverse viewpoints, reflecting the fields multidisciplinary nature. It introduces the state-of-the-art in the theory and various applications of nonlinear dynamics. It also offers the first treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with Pad approximations. With its wealth of interesting examples, this book will prove useful as an introduction to the field for novices and as a reference for specialists.
Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics by John P. Boyd Pdf
This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.
Applied Asymptotic Methods in Nonlinear Oscillations by Yuri A. Mitropolsky,Nguyen Van Dao Pdf
Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted primarily to applied asymptotic methods in nonlinear oscillations which are associated with the names of N. M. Krylov, N. N. Bogoli ubov and Yu. A. Mitropolskii. The advantages of the present methods are their simplicity, especially for computing higher approximations, and their applicability to a large class of quasi-linear problems. In this book, we confine ourselves basi cally to the scheme proposed by Krylov, Bogoliubov as stated in the monographs [6,211. We use these methods, and also develop and improve them for solving new problems and new classes of nonlinear differential equations. Although these methods have many applications in Mechanics, Physics and Technique, we will illustrate them only with examples which clearly show their strength and which are themselves of great interest. A certain amount of more advanced material has also been included, making the book suitable for a senior elective or a beginning graduate course on nonlinear oscillations.
Asymptotic Methods in Nonlinear Wave Phenomena by Tommaso Ruggeri,Antonio M. Greco,Marco Sammartino Pdf
This book brings together several contributions from leading experts in the field of nonlinear wave propagation. This field, which during the last three decades has seen important breakthroughs from the theoretical point of view, has recently acquired increased relevance due to advances in the technology of fluids e.g. at microscale or nanoscale and the recognition of crucial applications to the understanding of biological phenomena. Nonlinear wave theory requires the use of disparate approaches, including formal and rigorous asymptotic methods, Lie group theory, energy methods, numerical analysis, and bifurcation theory. This book presents a unique blend in which different aspects of the theory are enlightened and several real-life applications are investigated. The book will be a valuable resource for applied scientists interested in some of the most recent advances in the theory and in the applications of wave propagation, shock formation, nonequilibrium thermodynamics and energy methods.
Theories of Plates and Shells by Reinhold Kienzler,Holm Altenbach,Ingrid Ott Pdf
Plate and shell theories experienced a renaissance in recent years. The potentials of smart materials, the challenges of adaptive structures, the demands of thin-film technologies and more on the one hand and the availability of newly developed mathematical tools, the tremendous increase in computer facilities and the improvement of commercial software packages on the other caused a reanimation of the scientific interest. In the present book the contributions of the participants of the EUROMECH Colloquium 444 "Critical Review of the Theories of Plates and Shells and New Applications" have been collected. The aim was to discuss the common roots of different plate and shell approaches, to review the current state of the art, and to develop future lines of research. Contributions were written by scientists with civil and mechanical engineering as well as mathematical and physical background.
Principles of Control Engineering by Fred White Pdf
This book provides a basic grounding in the theory of control engineering, without assuming an unrealistic level of mathematical understanding. When control engineering is first approached, no matter what the ultimate application, a certain amount of background theory must be grasped to make sense of the topic. To meet this general need the author presents the basic principles in a clear and accessible way, along with plenty of examples and assessment questions. * Offers control principles without details of instrumentation * Features worked examples, assessment questions and practical tasks * Includes introduction to control engineering software
