Green's Functions for an Anisotropic Medium: Part 1. Unbounded Case


Book Description

Dyadic Green's Function (DGF) for layered anisotropic media is essential for the electromagnetic field analysis of several problems. With the goal of deriving the DGF of a two-layer biaxially anisotropic medium we derive in this report the DGF of a corresponding unbounded problem. Using the Fourier transform method, an auxiliary dyadic Green's (ADGF) is first derived. The DGF is then obtained by performing a simple linear transformation on the ADGF. It is expressed in a compact dyadic form in terms of two characteristic waves, viz., the a-wave and the b-wave. Some features of the DGF are discussed by comparing our results with those of a corresponding uniaxial problem. Green's function, Electromagnetic waves, Anisotropic medium.




Static Green's Functions in Anisotropic Media


Book Description

This book presents basic theory on static Green's functions in general anisotropic magnetoelectroelastic media including detailed derivations based on the complex variable method, potential method, and integral transforms. Green's functions corresponding to the reduced cases are also presented including those in anisotropic and transversely isotropic piezoelectric and piezomagnetic media, and in purely anisotropic elastic, transversely isotropic elastic and isotropic elastic media. Problems include those in three-dimensional, (two-dimensional) infinite, half, and biomaterial spaces (planes). While the emphasis is on the Green's functions related to the line and point force, those corresponding to the important line and point dislocation are also provided and discussed. This book provides a comprehensive derivation and collection of the Green's functions in the concerned media, and as such, it is an ideal reference book for researchers and engineers, and a textbook for both students in engineering and applied mathematics.




Waves and Fields in Inhomogenous Media


Book Description

Electrical Engineering/Electromagnetics Waves and Fields in Inhomogeneous Media A Volume in the IEEE Press Series on Electromagnetic Waves Donald G. Dudley, Series Editor ".it is one of the best wave propagation treatments to appear in many years." Gerardo G. Tango, CPG, Consulting Seismologist-Acoustician, Covington, LA This comprehensive text thoroughly covers fundamental wave propagation behaviors and computational techniques for waves in inhomogeneous media. The author describes powerful and sophisticated analytic and numerical methods to solve electromagnetic problems for complex media and geometry as well. Problems are presented as realistic models of actual situations which arise in the areas of optics, radio wave propagation, geophysical prospecting, nondestructive testing, biological sensing, and remote sensing. Key topics covered include: * Analytical methods for planarly, cylindrically and spherically layered media * Transient waves, including the Cagniard-de Hoop method * Variational methods for the scalar wave equation and the electromagnetic wave equation * Mode-matching techniques for inhomogeneous media * The Dyadic Green's function and its role in simplifying problem-solving in inhomogeneous media * Integral equation formulations and inverse problems * Time domain techniques for inhomogeneous media This book will be of interest to electromagnetics and remote sensing engineers, physicists, scientists, and geophysicists. This IEEE Press reprinting of the 1990 version published by Van Nostrand Reinhold incorporates corrections and minor updating. Also in the series. Mathematical Foundations for Electromagnetic Theory by Donald G. Dudley, University of Arizona at Tucson This volume in the series lays the mathematical foundations for the study of advanced topics in electromagnetic theory. Important subjects covered include linear spaces, Green's functions, spectral expansions, electromagnetic source representations, and electromagnetic boundary value problems. 1994 Hardcover 264 pp ISBN 0-7803-1022-5 IEEE Order No. PC3715 About the Series The IEEE Press Series on Electromagnetic Waves consists of new titles as well as reprints and revisions of recognized classics that maintain long-term archival significance in electromagnetic waves and applications. Designed specifically for graduate students, practicing engineers, and researchers, this series provides affordable volumes that explore electromagnetic waves and applications beyond the undergraduate level.




Green's Functions and Boundary Element Analysis for Modeling of Mechanical Behavior of Advanced Materials


Book Description

Demonstrates the potential of Green's functions & boundary element methods in solving a broad range of practical materials science problems. Papers include: Accurate Discretization of Integral Operators, Boundary Element Analysis of Bimaterials Using Anisotropic Elastic Green's Functions, Mechanical Properties of Metal-Matrix Composites, Approximate Operators for Boundary Integral Equations in Transient Elastodynamics, Simulation of the Electrochemical Machining Process Using a 2D Fundamental Singular Solution, Elastic Green's Functions for Anisotropic Solids, & more. Charts & tables.




Green's Functions with Applications


Book Description

Since its introduction in 1828, using Green's functions has become a fundamental mathematical technique for solving boundary value problems. Most treatments, however, focus on its theory and classical applications in physics rather than the practical means of finding Green's functions for applications in engineering and the sciences. Green's







Green's Functions of the Rytov Equation


Book Description

The Green's functions are calculated for the Rytov equation that governs the propagation of plane monochromatic waves in a random medium. The diverging as well as the converging wave solutions of the Green's functions are obtained for the two situations in which the Laplacian operator in the equation is either fully three-dimensional or only two-dimensional in the variables that describe the plane normal to the direction of wave propagation. The solutions found by Chernov and by Tatarski are compared with solutions that can be given in terms of the Green's functions thus obtained. (Author).




Green's Functions and Infinite Products


Book Description

Green's Functions and Infinite Products provides a thorough introduction to the classical subjects of the construction of Green's functions for the two-dimensional Laplace equation and the infinite product representation of elementary functions. Every chapter begins with a review guide, outlining the basic concepts covered. A set of carefully designed challenging exercises is available at the end of each chapter to provide the reader with the opportunity to explore the concepts in more detail. Hints, comments, and answers to most of those exercises can be found at the end of the text. In addition, several illustrative examples are offered at the end of most sections. This text is intended for an elective graduate course or seminar within the scope of either pure or applied mathematics.




Green's Functions for an Anisotropic Medium. Part 2. Two-Layer Case


Book Description

The Dyadic Green's Functions (DGF) of a two-layer biaxially anisotropic medium are derived. The principal coordinate system of the anisotropic medium is allowed to have arbitrary orientation with respect to the layer geometry. The formulation is based on the unbounded Dyadic Green's Function derived in Part I of the sequel. Using the matrix method the coefficients of the two-layer DGF are expressed in terms of half-space Fresnel reflection and transmission coefficients. To complete this procedure the various relevant half-space Fresnel coefficients are derived. The form in which the results are presented has a physically meaningful and compact structure. A numerical example is provided where we have computed the reflectivities.