Selected Asymptotic Methods with Applications to Electromagnetics and Antennas

Selected Asymptotic Methods with Applications to Electromagnetics and Antennas
Title Selected Asymptotic Methods with Applications to Electromagnetics and Antennas PDF eBook
Author George Fikioris
Publisher Springer Nature
Pages 187
Release 2022-06-01
Genre Technology & Engineering
ISBN 3031017161

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This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include some recent, direct applications to antennas and computational electromagnetics. Then, specific methods are discussed. These include integration by parts and the Riemann-Lebesgue lemma, the use of contour integration in conjunction with other methods, techniques related to Laplace's method and Watson's lemma, the asymptotic behavior of certain Fourier sine and cosine transforms, and the Poisson summation formula (including its version for finite sums). Often underutilized in the literature are asymptotic techniques based on the Mellin transform; our treatment of this subject complements the techniques presented in our recent Synthesis Lecture on the exact (not asymptotic) evaluation of integrals.

Selected Asymptotic Methods with Applications to Electromagnetics and Antennas

Selected Asymptotic Methods with Applications to Electromagnetics and Antennas
Title Selected Asymptotic Methods with Applications to Electromagnetics and Antennas PDF eBook
Author George J. Fikioris
Publisher Morgan & Claypool
Pages 0
Release 2014
Genre Antennas (Electronics)
ISBN 9781627050395

Download Selected Asymptotic Methods with Applications to Electromagnetics and Antennas Book in PDF, Epub and Kindle

This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include some recent, direct applications to antennas and computational electromagnetics. Then, specific methods are discussed. These include integration by parts and the Riemann-Lebesgue lemma, the use of contour integration in conjunction with other methods, techniques related to Laplace's method and Watson's lemma, the asymptotic behavior of certain Fourier sine and cosine transforms, and the Poisson summation formula (including its version for finite sums). Often underutilized in the literature are asymptotic techniques based on the Mellin transform; our treatment of this subject complements the techniques presented in our recent Synthesis Lecture on the exact (not asymptotic) evaluation of integrals. Throughout, we provide illustrative examples. Some of them are applications to special functions of mathematical physics. Others, taken from our published research, include the application of elementary methods to develop certain simple formulas for transmission lines, examples illustrating the difficulties in solving fundamental integral equations of antenna theory, an examination of the fundamentals of the Method of Auxiliary Sources (MAS), and a study of the near fields of certain unusual types of radiators. Table of Contents: Preface / Introduction: Simple Asymptotic Approximations / Asymptotic Approximations Defined / Concepts from Complex Variables / Laplace's Method and Watson's Lemma / Integration by Parts and Asymptotics of Some Fourier Transforms / Poisson Summation Formula and Applications / Mellin-Transform Method for Asymptotic Evaluation of Integrals / More Applications to Wire Antennas / Authors' Biographies / Index

Accurate Computation of Mathieu Functions

Accurate Computation of Mathieu Functions
Title Accurate Computation of Mathieu Functions PDF eBook
Author Andrew Peterson
Publisher Springer Nature
Pages 123
Release 2022-06-01
Genre Technology & Engineering
ISBN 303101717X

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This lecture presents a modern approach for the computation of Mathieu functions. These functions find application in boundary value analysis such as electromagnetic scattering from elliptic cylinders and flat strips, as well as the analogous acoustic and optical problems, and many other applications in science and engineering. The authors review the traditional approach used for these functions, show its limitations, and provide an alternative "tuned" approach enabling improved accuracy and convergence. The performance of this approach is investigated for a wide range of parameters and machine precision. Examples from electromagnetic scattering are provided for illustration and to show the convergence of the typical series that employ Mathieu functions for boundary value analysis.

Asymptotic Multiple Scale Method in Time Domain

Asymptotic Multiple Scale Method in Time Domain
Title Asymptotic Multiple Scale Method in Time Domain PDF eBook
Author Jan Awrejcewicz
Publisher CRC Press
Pages 506
Release 2022-05-10
Genre Mathematics
ISBN 1000581276

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This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics. Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions. It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.

Wavelet Applications in Engineering Electromagnetics

Wavelet Applications in Engineering Electromagnetics
Title Wavelet Applications in Engineering Electromagnetics PDF eBook
Author Tapan K. Sarkar
Publisher Artech House
Pages 367
Release 2002
Genre Mathematics
ISBN 1580532675

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Written from an engineering perspective, this unique resource describes the practical application of wavelets to the solution of electromagnetic field problems and in signal analysis with an even-handed treatment of the pros and cons. A key feature of this book is that the wavelet concepts have been described from the filter theory point of view that is familiar to researchers with an electrical engineering background. The book shows you how to design novel algorithms that enable you to solve electrically, large electromagnetic field problems using modest computational resources. It also provides you with new ideas in the design and development of unique waveforms for reliable target identification and practical radar signal analysis. The book includes more then 500 equations, and covers a wide range of topics, from numerical methods to signal processing aspects.

Chaos Theory

Chaos Theory
Title Chaos Theory PDF eBook
Author Mykhaylo Andriychuk
Publisher BoD – Books on Demand
Pages 92
Release 2024-05-22
Genre Mathematics
ISBN 1837681228

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Chaos Theory – Recent Advances, New Perspectives and Applications provides a comprehensive overview of chaos theory. It includes five chapters that discuss the history and development of chaos theory, the effectiveness of a chaos auto-associated model based on the Chebyshev-type activation function, neurite morphology, chemical self-replication, and the use of chaotic small particles to create materials with specific refractive index and magnetic permeability.

Geometrical Theory of Diffraction for Electromagnetic Waves

Geometrical Theory of Diffraction for Electromagnetic Waves
Title Geometrical Theory of Diffraction for Electromagnetic Waves PDF eBook
Author Graeme L. James
Publisher IET
Pages 312
Release 1986
Genre Science
ISBN 9780863410628

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The purpose of the book, apart from expounding the Geometrical Theory of Diffraction (GTD) method, is to present useful formulations that can be readily applied to solve practical engineering problems.