WAVES AND FIELDS IN INHOMOGENEOUS MEDIA

Size: px
Start display at page:

Download "WAVES AND FIELDS IN INHOMOGENEOUS MEDIA"

Transcription

1 WAVES AND FIELDS IN INHOMOGENEOUS MEDIA WENG CHO CHEW UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN IEEE PRESS Series on Electromagnetic Waves Donald G. Dudley, Series Editor IEEE Antennas and Propagation Society, Sponsor IEEE PRESS The Institute of Electrical and Electronics Engineers, Inc., New York

2 PREFACE xvii ACKNOWLEDGMENTS xxi 1 PRELIMINARY BACKGROUND Maxwell's Equations Differential Representations Integral Representations Time Harmonic Forms Constitutive Relations Poynting Theorem and Lossless Conditions Duality Principle Scalar Wave Equations Acoustic Wave Equation Scalar Wave Equation from Electromagnetics Cartesian Coordinates Cylindrical Coordinates Spherical Coordinates Vector Wave Equations Boundary Conditions Reciprocity Theorem Plane Wave in Homogeneous, Anisotropic Media Green's Function Huygens' Principle Scalar Waves Electromagnetic Waves Uniqueness Theorem Scalar Wave Equation Vector Wave Equation 35 Exercises for Chapter 1 37 References for Chapter 1 41 Further Readings for Chapter 1 42

3 viii CONTENTS 2 PLANARLY LAYERED MEDIA One-Dimensional Planar Inhomogeneity Derivation of the Scalar Wave Equations Reflection from a Half-Space Reflection and Transmission in a Multilayered Medium Ricatti Equation for Reflection Coefficients Specific Inhomogeneous Profiles Spectral Representations of Sources A Line Source A Point Source Riemann Sheets and Branch Cuts A Source on Top of a Layered Medium Electric Dipole Fields Magnetic Dipole Fields The Transverse Field Components A Source Embedded in a Layered Medium Asymptotic Expansions of Integrals Method of Stationary Phase Method of Steepest Descent Uniform Asymptotic Expansions Dipole Over Layered Media Asymptotic Expansions Dipole Over Half-Space (VMD) Dipole Over Half-Space (VED) Dipole Over a Slab Example of Uniform Asymptotic Expansion Transmitted Wave in a Half-Space Angular Spectrum Representation Singularities of the Sommerfeld Integrals Absence of Branch Points Bounds on the Locations of Singularities Numerical Integration of Sommerfeld Integrals WKB Method Derivation of the WKB Solution Asymptotic Matching 124

4 ix 2.9 Propagator Matrix Derivation of the State Equation Solution of the State Equation Reflection from a Three-Layer Medium Reflection from an Inhomogeneous Slab Waves in Anisotropic, Layered Media Derivation of the State Equation Solution of the State Equation Reflection from an Interface of Anisotropic Half Spaces Reflection from a Slab Geometrical Optics Series 138 Exercises for Chapter References for Chapter Further Readings for Chapter CYLINDRICALLY AND SPHERICALLY LAYERED MEDIA Cylindrically Layered Media Single Interface Case Vector Wave Equation in Cylindrical Coordinates Reflection and Transmission of an Outgoing Wave Reflection and Transmission of a Standing Wave Cylindrically Layered Media Multi-Interface Case The Outgoing-Wave Case The Standing-Wave Case Source in a Cylindrically Layered Medium Discrete, Angular-Wave-Number Representation Continuum, Angular-Wave-Number Representation Propagator Matrix Cylindrical Layers Isotropic, Layered Media Anisotropic, Layered Media Spherically Layered Media Single Interface Case Vector Wave Equation in Spherical Coordinates Reflection and Transmission of an Outgoing Wave Reflection and Transmission of a Standing Wave Spherically Layered Media Multi-Interface Case 191

5 3.6.1 The Outgoing-Wave Case The Standing-Wave Case Source in a Spherically Layered Medium Propagator Matrix Spherical Layers 197 Exercises for Chapter References for Chapter Further Readings for Chapter TRANSIENTS Causality of Transient Response The Kramers-Kronig Relation Causality and Contour of Integration The Cagniard-de Hoop Method Line Source in Free-Space Two-Dimensional Green's Function Point Source in Free-Space Three-Dimensional Green's Function Line Source Over Half-Space Transient Response Dipole Over Half Space Transient Response Multi-interface Problems Direct Inversion Numerical Integration of Fourier Integrals Direct Field in a Lossy Medium Two- Diemnsional Case Direct Field in a Lossy Medium Three- Dimensional Case Finite-Difference Method The Finite-Difference Approximation Stability Analysis Grid-Dispersion Error The Yee Algorithm Absorbing Boundary Conditions Engquist-Majda Absorbing Boundary Condition Lindman Absorbing Boundary Condition Bayliss-Turkel Absorbing Boundary Condition Liao's Absorbing Boundary Condition 251

6 xi Exercises for Chapter References for Chapter Further Readings for Chapter VARIATIONAL METHODS Review of Linear Vector Space Inner Product Spaces Linear Operators Basis Functions Parseval's Theorem Parseval's Theorem for Complex Vectors Solutions to Operator Equations A Preview The Eigenvalue Problem Variational Expressions for Self-Adjoint Problems General Concepts Rayleigh-Ritz Procedure Self-Adjoint Problems Applications to Scalar Wave Equations Applications to Vector Wave Equations Variational Expressions for Non-Self-Adjoint Problems General Concepts Rayleigh-Ritz Procedure Non-Self-Adjoint Problems Applications to Scalar Wave Equations Applications to Vector Wave Equations Variational Expressions for Eigenvalue Problems General Concepts Applications to Scalar Wave Equations Applications to Electromagnetic Problems Essential and Natural Boundary Conditions The Scalar Wave Equation Case The Electromagnetic Case 312 Exercises for Chapter References for Chapter Further Readings for Chapter 5 323

7 xii CONTENTS 6 MODE MATCHING METHOD Eigenmodes of a Planarly Layered Medium Orthogonality of Eigenmodes in a Layered Medium Guided Modes and Radiation Modes of a Layered Medium Eigenfunction Expansion of a Field Excitation of Modes due to a Line Source The Use of Vector Notation Reflection and Transmission at a Junction Discontinuity Derivation of Reflection and Transmission Operators The Continuum Limit Case A Numerical Method to Find the Eigenmodes The Cylindrically Layered Medium Case Eigenmodes of a Cylindrically Layered Medium Differential Equations of a Cylindrical Structure Numerical Solution of the Eigenmodes Eigenfunction Expansion of a Field Reflection from a Junction Discontinuity The Multiregion Problem The Three-Region Problem The iv-region Problem 362 Exercises for Chapter References for Chapter Further Readings for Chapter DYADIC GREEN'S FUNCTIONS Dyadic Green's Function in a Homogeneous Medium The Spatial Representation The Singularity of the Dyadic Green's Function The Spectral Representation Equivalence of Spectral and Spatial Representations Vector Wave Functions Derivation of Vector Wave Functions Orthogonality Relationships of Vector Wave Functions 388

8 xiii Vector Wave Functions for Unbounded Media Dyadic Green's Function Using Vector Wave Functions The Integral Representations Singularity Extraction Dyadic Green's Functions for Layered Media A General, Isotropic, Inhomogeneous Medium Planarly Layered Media Cylindrically Layered Media Spherically Layered Media Reciprocity Considerations 418 Exercises for Chapter References for Chapter Further Readings for Chapter INTEGRAL EQUATIONS Surface Integral Equations Scalar Wave Equation Vector Wave Equation The Anisotropic, Inhomogeneous Medium Case Two-Dimensional Electromagnetic Case Solutions by the Method of Moments Scalar Wave Case The Electromagnetic Case Problem with Internal Resonances Extended-Boundary-Condition Method The Scalar Wave Case The Electromagnetic Wave Case The Transition and Scattering Matrices The Method of Rayleigh's Hypothesis Scattering by Many Scatterers Two-Scatterer Solution iv-scatterer Solution A Recursive Algorithm Scattering by Multilayered Scatterers One-Interface Problem Many-Interface Problems 471

9 xiv CONTENTS 8.8 Surface Integral Equation with Finite-Element Method Volume Integral Equations Scalar Wave Case The Electromagnetic Wave Case Matrix Representation of the Integral Equation Approximate Solutions of the Scattering Problem Born Approximation Rytov Approximation 487 Exercises for Chapter References for Chapter Further Readings for Chapter INVERSE SCATTERING PROBLEMS Linear Inverse Problems Back-Projection Tomography Radon Transforms Diffraction Tomography Finite-Source Effect Nonuniqueness of the Solution One-Dimensional Inverse Problems The Method of Characteristics Transformation to a Schrodinger-like Equation The Gel'fand-Levitan Integral Equation The Marchenko Integral Equation The Gel'fand-Levitan-Marchenko Integral Equation Higher-Dimensional Inverse Problems Distorted Born Iterative Method Born Iterative Method Operator Forms of the Scattering Equations 554 Exercises for Chapter References for Chapter Further Readings for Chapter APPENDIX A Some Useful Mathematical Formulas 571 A.l Useful Vector Identities 571

10 xv A.2 Gradient, Divergence, Curl, and Laplacian in Rectangular, Cylindrical, Spherical, and General Orthogonal Curvilinear Coordinate Systems 571 A.3 Useful Integral Identities 573 A.4 Integral Transforms 574 APPENDIX B Review of Tensors 577 APPENDIX C Generalized Functions 583 APPENDIX D Addition Theorems 591 References for Appendices 597 Further Readings for Appendices 598 INDEX 599

6 J - vector electric current density (A/m2 )

6 J - vector electric current density (A/m2 ) Determination of Antenna Radiation Fields Using Potential Functions Sources of Antenna Radiation Fields 6 J - vector electric current density (A/m2 ) M - vector magnetic current density (V/m 2 ) Some problems

More information

Mathematical Foundations of Imaging, Tomography and Wavefield Inversion

Mathematical Foundations of Imaging, Tomography and Wavefield Inversion Mathematical Foundations of Imaging, Tomography and Wavefield Inversion Inverse problems are of interest and importance across many branches of physics, mathematics, engineering and medical imaging. In

More information

Asymptotic Analysis of Fields in Multi-Structures

Asymptotic Analysis of Fields in Multi-Structures Asymptotic Analysis of Fields in Multi-Structures VLADIMIR KOZLOV Department of Mathematics, Linkoeping University, Sweden VLADIMIR MAZ'YA Department of Mathematics, Linkoeping University, Sweden ALEXANDER

More information

Introduction to Optics

Introduction to Optics Second Edition Introduction to Optics FRANK L. PEDROTTI, S.J. Marquette University Milwaukee, Wisconsin Vatican Radio, Rome LENO S. PEDROTTI Center for Occupational Research and Development Waco, Texas

More information

Preface Acknowledgments Acronyms

Preface Acknowledgments Acronyms Contents Preface Acknowledgments Acronyms xi xiii xv 1 Introduction 1 1.1 The history of Antennas and Antenna Analysis 1 1.2 Antenna Synthesis 5 1.3 Approximate Antenna Modeling 7 1.4 Organization of the

More information

MATHEMATICAL METHODS OF STATISTICS

MATHEMATICAL METHODS OF STATISTICS MATHEMATICAL METHODS OF STATISTICS By HARALD CRAMER TROFESSOK IN THE UNIVERSITY OF STOCKHOLM Princeton PRINCETON UNIVERSITY PRESS 1946 TABLE OF CONTENTS. First Part. MATHEMATICAL INTRODUCTION. CHAPTERS

More information

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum UNIT I: The Hyperbolic Functions basic calculus concepts, including techniques for curve sketching, exponential and logarithmic

More information

INTEGRAL METHODS IN LOW-FREQUENCY ELECTROMAGNETICS

INTEGRAL METHODS IN LOW-FREQUENCY ELECTROMAGNETICS INTEGRAL METHODS IN LOW-FREQUENCY ELECTROMAGNETICS I. Dolezel Czech Technical University, Praha, Czech Republic P. Karban University of West Bohemia, Plzeft, Czech Republic P. Solin University of Nevada,

More information

Modern Classical Optics

Modern Classical Optics Modern Classical Optics GEOFFREY BROOKER Department of Physics University of Oxford OXPORD UNIVERSITY PRESS Contents 1 Electromagnetism and basic optics 1 1.1 Introduction 1 1.2 The Maxwell equations 1

More information

Signal Processing for Intelligent Sensor Systems with MATLAB 9

Signal Processing for Intelligent Sensor Systems with MATLAB 9 Signal Processing for Intelligent Sensor Systems with MATLAB 9 Second Edition David С Swanson @ CRC Press Taylor & Francis Gro jroup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis

More information

SCHWEITZER ENGINEERING LABORATORIES, COMERCIAL LTDA.

SCHWEITZER ENGINEERING LABORATORIES, COMERCIAL LTDA. Pocket book of Electrical Engineering Formulas Content 1. Elementary Algebra and Geometry 1. Fundamental Properties (real numbers) 1 2. Exponents 2 3. Fractional Exponents 2 4. Irrational Exponents 2 5.

More information

Tentamen i GRUNDLÄGGANDE MATEMATISK FYSIK

Tentamen i GRUNDLÄGGANDE MATEMATISK FYSIK Karlstads Universitet Fysik Tentamen i GRUNDLÄGGANDE MATEMATISK FYSIK [ VT 2008, FYGB05] Datum: 2008-03-26 Tid: 8.15 13.15 Lärare: Jürgen Fuchs c/o Carl Stigner Tel: 054-700 1815 Total poäng: 28 Godkänd:

More information

APPLICATIONS OF TENSOR ANALYSIS

APPLICATIONS OF TENSOR ANALYSIS APPLICATIONS OF TENSOR ANALYSIS (formerly titled: Applications of the Absolute Differential Calculus) by A J McCONNELL Dover Publications, Inc, Neiv York CONTENTS PART I ALGEBRAIC PRELIMINARIES/ CHAPTER

More information

SIO 229 Gravity and Geomagnetism: Class Description and Goals

SIO 229 Gravity and Geomagnetism: Class Description and Goals SIO 229 Gravity and Geomagnetism: Class Description and Goals This graduate class provides an introduction to gravity and geomagnetism at a level suitable for advanced non-specialists in geophysics. Topics

More information

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

MASTER OF SCIENCE IN MECHANICAL ENGINEERING MASTER OF SCIENCE IN MECHANICAL ENGINEERING Introduction There are over 22 schools in Mindanao that offer Bachelor of Science in Mechanical Engineering and majority of their faculty members do not have

More information

DIGITAL IMAGE PROCESSING AND ANALYSIS

DIGITAL IMAGE PROCESSING AND ANALYSIS DIGITAL IMAGE PROCESSING AND ANALYSIS Human and Computer Vision Applications with CVIPtools SECOND EDITION SCOTT E UMBAUGH Uffi\ CRC Press Taylor &. Francis Group Boca Raton London New York CRC Press is

More information

Distinguished Professor George Washington University. Graw Hill

Distinguished Professor George Washington University. Graw Hill Mechanics of Fluids Fourth Edition Irving H. Shames Distinguished Professor George Washington University Graw Hill Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok

More information

Elementary Differential Equations

Elementary Differential Equations Elementary Differential Equations EIGHTH EDITION Earl D. Rainville Late Professor of Mathematics University of Michigan Phillip E. Bedient Professor Emeritus of Mathematics Franklin and Marshall College

More information

Fundamentals of Heat and Mass Transfer

Fundamentals of Heat and Mass Transfer 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. SIXTH EDITION Fundamentals of Heat and Mass Transfer FRANK P. INCROPERA

More information

MATH Mathematics-Nursing. MATH Remedial Mathematics I-Business & Economics. MATH Remedial Mathematics II-Business and Economics

MATH Mathematics-Nursing. MATH Remedial Mathematics I-Business & Economics. MATH Remedial Mathematics II-Business and Economics MATH 090 - Mathematics-Nursing MATH 091 - Remedial Mathematics I-Business & Economics MATH 094 - Remedial Mathematics II-Business and Economics MATH 095 - Remedial Mathematics I-Science (3 CH) MATH 096

More information

ESSENTIAL COMPUTATIONAL FLUID DYNAMICS

ESSENTIAL COMPUTATIONAL FLUID DYNAMICS ESSENTIAL COMPUTATIONAL FLUID DYNAMICS Oleg Zikanov WILEY JOHN WILEY & SONS, INC. CONTENTS PREFACE xv 1 What Is CFD? 1 1.1. Introduction / 1 1.2. Brief History of CFD / 4 1.3. Outline of the Book / 6 References

More information

Teaching Electromagnetic Field Theory Using Differential Forms

Teaching Electromagnetic Field Theory Using Differential Forms IEEE TRANSACTIONS ON EDUCATION, VOL. 40, NO. 1, FEBRUARY 1997 53 Teaching Electromagnetic Field Theory Using Differential Forms Karl F. Warnick, Richard H. Selfridge, Member, IEEE, and David V. Arnold

More information

MASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCES IN PHYSICS (MS PHYS) (LIST OF COURSES BY SEMESTER, THESIS OPTION)

MASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCES IN PHYSICS (MS PHYS) (LIST OF COURSES BY SEMESTER, THESIS OPTION) MASTER OF SCIENCE IN PHYSICS Admission Requirements 1. Possession of a BS degree from a reputable institution or, for non-physics majors, a GPA of 2.5 or better in at least 15 units in the following advanced

More information

Programming the Finite Element Method

Programming the Finite Element Method Programming the Finite Element Method FOURTH EDITION I. M. Smith University of Manchester, UK D. V. Griffiths Colorado School of Mines, USA John Wiley & Sons, Ltd Contents Preface Acknowledgement xv xvii

More information

Optical Metrology. Third Edition. Kjell J. Gasvik Spectra Vision AS, Trondheim, Norway JOHN WILEY & SONS, LTD

Optical Metrology. Third Edition. Kjell J. Gasvik Spectra Vision AS, Trondheim, Norway JOHN WILEY & SONS, LTD 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. Optical Metrology Third Edition Kjell J. Gasvik Spectra Vision AS,

More information

Mean value theorem, Taylors Theorem, Maxima and Minima.

Mean value theorem, Taylors Theorem, Maxima and Minima. MA 001 Preparatory Mathematics I. Complex numbers as ordered pairs. Argand s diagram. Triangle inequality. De Moivre s Theorem. Algebra: Quadratic equations and express-ions. Permutations and Combinations.

More information

Calculation of Eigenmodes in Superconducting Cavities

Calculation of Eigenmodes in Superconducting Cavities Calculation of Eigenmodes in Superconducting Cavities W. Ackermann, C. Liu, W.F.O. Müller, T. Weiland Institut für Theorie Elektromagnetischer Felder, Technische Universität Darmstadt Status Meeting December

More information

FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS

FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS With Mathematica and MATLAB Computations M. ASGHAR BHATTI WILEY JOHN WILEY & SONS, INC. CONTENTS OF THE BOOK WEB SITE PREFACE xi xiii 1 FINITE ELEMENT

More information

3-D WAVEGUIDE MODELING AND SIMULATION USING SBFEM

3-D WAVEGUIDE MODELING AND SIMULATION USING SBFEM 3-D WAVEGUIDE MODELING AND SIMULATION USING SBFEM Fabian Krome, Hauke Gravenkamp BAM Federal Institute for Materials Research and Testing, Unter den Eichen 87, 12205 Berlin, Germany email: Fabian.Krome@BAM.de

More information

The waveguide adapter consists of a rectangular part smoothly transcending into an elliptical part as seen in Figure 1.

The waveguide adapter consists of a rectangular part smoothly transcending into an elliptical part as seen in Figure 1. Waveguide Adapter Introduction This is a model of an adapter for microwave propagation in the transition between a rectangular and an elliptical waveguide. Such waveguide adapters are designed to keep

More information

Numerical Methods for Engineers

Numerical Methods for Engineers Steven C. Chapra Berger Chair in Computing and Engineering Tufts University RaymondP. Canale Professor Emeritus of Civil Engineering University of Michigan Numerical Methods for Engineers With Software

More information

GPR Polarization Simulation with 3D HO FDTD

GPR Polarization Simulation with 3D HO FDTD Progress In Electromagnetics Research Symposium Proceedings, Xi an, China, March 6, 00 999 GPR Polarization Simulation with 3D HO FDTD Jing Li, Zhao-Fa Zeng,, Ling Huang, and Fengshan Liu College of Geoexploration

More information

Coefficient of Potential and Capacitance

Coefficient of Potential and Capacitance Coefficient of Potential and Capacitance Lecture 12: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay We know that inside a conductor there is no electric field and that

More information

Chapter 7: Polarization

Chapter 7: Polarization Chapter 7: Polarization Joaquín Bernal Méndez Group 4 1 Index Introduction Polarization Vector The Electric Displacement Vector Constitutive Laws: Linear Dielectrics Energy in Dielectric Systems Forces

More information

Passive Optical Resonators

Passive Optical Resonators Passive Optical Resonators Optical Cavities and Feedback Back mirror I 0 I 1 Laser medium with gain, G Output mirror I 3 R = 100% R < 100% I 2 Cavities are essential components of the lasers. They provide

More information

The Role of Electric Polarization in Nonlinear optics

The Role of Electric Polarization in Nonlinear optics The Role of Electric Polarization in Nonlinear optics Sumith Doluweera Department of Physics University of Cincinnati Cincinnati, Ohio 45221 Abstract Nonlinear optics became a very active field of research

More information

State of Stress at Point

State of Stress at Point State of Stress at Point Einstein Notation The basic idea of Einstein notation is that a covector and a vector can form a scalar: This is typically written as an explicit sum: According to this convention,

More information

Frequency-dependent underground cable model for electromagnetic transient simulation

Frequency-dependent underground cable model for electromagnetic transient simulation Frequency-dependent underground cable model for electromagnetic transient simulation Vasco José Realista Medeiros Soeiro Abstract A computation method for transients in a three-phase underground power-transmission

More information

FRACTIONAL INTEGRALS AND DERIVATIVES. Theory and Applications

FRACTIONAL INTEGRALS AND DERIVATIVES. Theory and Applications FRACTIONAL INTEGRALS AND DERIVATIVES Theory and Applications Stefan G. Samko Rostov State University, Russia Anatoly A. Kilbas Belorussian State University, Minsk, Belarus Oleg I. Marichev Belorussian

More information

Existence of Rayleigh Waves Over The Heterogeneous Prestressed Medium

Existence of Rayleigh Waves Over The Heterogeneous Prestressed Medium International Journal of New Technology and Research (IJNTR) ISSN:2454-4116 Volume-2 Issue-2 February 2016 Pages 12-18 Existence of Rayleigh Waves Over The Heterogeneous Prestressed Medium Inder Singh

More information

Mathematics (MAT) MAT 061 Basic Euclidean Geometry 3 Hours. MAT 051 Pre-Algebra 4 Hours

Mathematics (MAT) MAT 061 Basic Euclidean Geometry 3 Hours. MAT 051 Pre-Algebra 4 Hours MAT 051 Pre-Algebra Mathematics (MAT) MAT 051 is designed as a review of the basic operations of arithmetic and an introduction to algebra. The student must earn a grade of C or in order to enroll in MAT

More information

DOKUZ EYLUL UNIVERSITY GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES DIRECTORATE COURSE / MODULE / BLOCK DETAILS ACADEMIC YEAR / SEMESTER

DOKUZ EYLUL UNIVERSITY GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES DIRECTORATE COURSE / MODULE / BLOCK DETAILS ACADEMIC YEAR / SEMESTER Offered by: Fen Bilimleri Enstitüsü Course Title: Applied Mathematics Course Org. Title: Applied Mathematics Course Level: Lisansüstü Course Code: MAT 5001 Language of Instruction: İngilizce Form Submitting/Renewal

More information

AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS

AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS Revised Edition James Epperson Mathematical Reviews BICENTENNIAL 0, 1 8 0 7 z ewiley wu 2007 r71 BICENTENNIAL WILEY-INTERSCIENCE A John Wiley & Sons, Inc.,

More information

Vectors and Tensors in Engineering Physics

Vectors and Tensors in Engineering Physics Module Description Vectors and Tensors in Engineering Physics General Information Number of ECTS Credits 3 Abbreviation FTP_Tensors Version 19.02.2015 Responsible of module Christoph Meier, BFH Language

More information

Cortical Source Localization of Human Scalp EEG. Kaushik Majumdar Indian Statistical Institute Bangalore Center

Cortical Source Localization of Human Scalp EEG. Kaushik Majumdar Indian Statistical Institute Bangalore Center Cortical Source Localization of Human Scalp EEG Kaushik Majumdar Indian Statistical Institute Bangalore Center Cortical Basis of Scalp EEG Baillet et al, IEEE Sig Proc Mag, Nov 2001, p 16 Mountcastle,

More information

Lecture 13 Electromagnetic Waves Ch. 33

Lecture 13 Electromagnetic Waves Ch. 33 Lecture 13 Electromagnetic Waves Ch. 33 Cartoon Opening Demo Topics Electromagnetic waves Traveling E/M wave - Induced electric and induced magnetic amplitudes Plane waves and spherical waves Energy transport

More information

Effects of Cell Phone Radiation on the Head. BEE 4530 Computer-Aided Engineering: Applications to Biomedical Processes

Effects of Cell Phone Radiation on the Head. BEE 4530 Computer-Aided Engineering: Applications to Biomedical Processes Effects of Cell Phone Radiation on the Head BEE 4530 Computer-Aided Engineering: Applications to Biomedical Processes Group 3 Angela Cai Youjin Cho Mytien Nguyen Praveen Polamraju Table of Contents I.

More information

A RIGOROUS AND COMPLETED STATEMENT ON HELMHOLTZ THEOREM

A RIGOROUS AND COMPLETED STATEMENT ON HELMHOLTZ THEOREM Progress In Electromagnetics Research, PIER 69, 287 304, 2007 A RIGOROU AND COMPLETED TATEMENT ON HELMHOLTZ THEOREM Y. F. Gui and W. B. Dou tate Key Lab of Millimeter Waves outheast University Nanjing,

More information

INVESTIGATIONS IN ANALYSIS, DIFFERENTIAL EQUATIONS AND APPLICATIONS

INVESTIGATIONS IN ANALYSIS, DIFFERENTIAL EQUATIONS AND APPLICATIONS International Conference Advances and Perspectives of Basic Sciences in Caucasus and Central Asian Region Tbilisi, November 1-3, 2011 MATHEMATICS IN GEORGIA, PART 2: INVESTIGATIONS IN ANALYSIS, DIFFERENTIAL

More information

Progress In Electromagnetics Research, PIER 61, 111 131, 2006

Progress In Electromagnetics Research, PIER 61, 111 131, 2006 Progress In Electromagnetics Research, PIER 61, 111 131, 2006 LOCALIZATION OF THE INVESTIGATION DOMAIN IN INVERSE PROFILING OF BURIED 2-D DIELECTRIC PIPELINES WITH CIRCULAR CROSS SECTION USING ELECTROMAGNETIC

More information

* Magnetic Scalar Potential * Magnetic Vector Potential. PPT No. 19

* Magnetic Scalar Potential * Magnetic Vector Potential. PPT No. 19 * Magnetic Scalar Potential * Magnetic Vector Potential PPT No. 19 Magnetic Potentials The Magnetic Potential is a method of representing the Magnetic field by using a quantity called Potential instead

More information

Fundamentals of Electromagnetic Fields and Waves: I

Fundamentals of Electromagnetic Fields and Waves: I Fundamentals of Electromagnetic Fields and Waves: I Fall 2007, EE 30348, Electrical Engineering, University of Notre Dame Mid Term II: Solutions Please show your steps clearly and sketch figures wherever

More information

A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle

A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle Page 1 of 15 Abstract: The wireless power transfer link between two coils is determined by the properties of the

More information

Towards a Theory for Arbitrarily Shaped Sound Field Reproduction Systems

Towards a Theory for Arbitrarily Shaped Sound Field Reproduction Systems Towards a Theory for Arbitrarily Shaped Sound Field Reproduction Systems Sascha Spors, Matthias Rath and Jens Ahrens Sascha.Spors@telekom.de Acoustics 08, Paris ===!" Laboratories AG Laboratories Aim of

More information

APPLIED MATHEMATICS ADVANCED LEVEL

APPLIED MATHEMATICS ADVANCED LEVEL APPLIED MATHEMATICS ADVANCED LEVEL INTRODUCTION This syllabus serves to examine candidates knowledge and skills in introductory mathematical and statistical methods, and their applications. For applications

More information

Analysis of Multi-Spacecraft Magnetic Field Data

Analysis of Multi-Spacecraft Magnetic Field Data COSPAR Capacity Building Beijing, 5 May 2004 Joachim Vogt Analysis of Multi-Spacecraft Magnetic Field Data 1 Introduction, single-spacecraft vs. multi-spacecraft 2 Single-spacecraft data, minimum variance

More information

Applied Linear Algebra I Review page 1

Applied Linear Algebra I Review page 1 Applied Linear Algebra Review 1 I. Determinants A. Definition of a determinant 1. Using sum a. Permutations i. Sign of a permutation ii. Cycle 2. Uniqueness of the determinant function in terms of properties

More information

Assessment Plan for Learning Outcomes for BA/BS in Physics

Assessment Plan for Learning Outcomes for BA/BS in Physics Department of Physics and Astronomy Goals and Learning Outcomes 1. Students know basic physics principles [BS, BA, MS] 1.1 Students can demonstrate an understanding of Newton s laws 1.2 Students can demonstrate

More information

Numerical Analysis An Introduction

Numerical Analysis An Introduction Walter Gautschi Numerical Analysis An Introduction 1997 Birkhauser Boston Basel Berlin CONTENTS PREFACE xi CHAPTER 0. PROLOGUE 1 0.1. Overview 1 0.2. Numerical analysis software 3 0.3. Textbooks and monographs

More information

Co-simulation of Microwave Networks. Sanghoon Shin, Ph.D. RS Microwave

Co-simulation of Microwave Networks. Sanghoon Shin, Ph.D. RS Microwave Co-simulation of Microwave Networks Sanghoon Shin, Ph.D. RS Microwave Outline Brief review of EM solvers 2D and 3D EM simulators Technical Tips for EM solvers Co-simulated Examples of RF filters and Diplexer

More information

Copyright 2000 IEEE. Reprinted from IEEE MTT-S International Microwave Symposium 2000

Copyright 2000 IEEE. Reprinted from IEEE MTT-S International Microwave Symposium 2000 Copyright 2000 IEEE Reprinted from IEEE MTT-S International Microwave Symposium 2000 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE

More information

The Wave Equation and the Speed of Light

The Wave Equation and the Speed of Light The Wave Equation and the Speed of Light Chapter 1 Physics 208, Electro-optics Peter Beyersdorf Document info Ch 1 Class Outline Maxwell s equations Boundary conditions Poynting s theorem and conservation

More information

The Physics Degree. Graduate Skills Base and the Core of Physics

The Physics Degree. Graduate Skills Base and the Core of Physics The Physics Degree Graduate Skills Base and the Core of Physics Version date: September 2011 THE PHYSICS DEGREE This document details the skills and achievements that graduates of accredited degree programmes

More information

Calculation of Eigenfields for the European XFEL Cavities

Calculation of Eigenfields for the European XFEL Cavities Calculation of Eigenfields for the European XFEL Cavities Wolfgang Ackermann, Erion Gjonaj, Wolfgang F. O. Müller, Thomas Weiland Institut Theorie Elektromagnetischer Felder, TU Darmstadt Status Meeting

More information

Study and improvement of the condition number of the Electric Field Integral Equation

Study and improvement of the condition number of the Electric Field Integral Equation Monografías del Seminario Matemático García de Galdeano. 27: 73 80, (2003). Study and improvement of the condition number of the Electric Field Integral Equation X. Antoine 1, A. Bendali 2 and M. Darbas

More information

The Quantum Harmonic Oscillator Stephen Webb

The Quantum Harmonic Oscillator Stephen Webb The Quantum Harmonic Oscillator Stephen Webb The Importance of the Harmonic Oscillator The quantum harmonic oscillator holds a unique importance in quantum mechanics, as it is both one of the few problems

More information

Microwave Measurements. 3rd Edition. Edited by RJ. Collier and A.D. Skinner. The Institution of Engineering and Technology

Microwave Measurements. 3rd Edition. Edited by RJ. Collier and A.D. Skinner. The Institution of Engineering and Technology Microwave Measurements 3rd Edition Edited by RJ. Collier and A.D. Skinner The Institution of Engineering and Technology Contents List of contributors Preface xvii xix 1 Transmission lines - basic principles

More information

Electromagnetic Wave Simulation Software Poynting

Electromagnetic Wave Simulation Software Poynting Electromagnetic Wave Simulation Software Poynting V Takefumi Namiki V Yoichi Kochibe V Takatoshi Kasano V Yasuhiro Oda (Manuscript received March 19, 28) The analysis of electromagnetic behavior by computer

More information

Finite Element Analysis for Acoustic Behavior of a Refrigeration Compressor

Finite Element Analysis for Acoustic Behavior of a Refrigeration Compressor Finite Element Analysis for Acoustic Behavior of a Refrigeration Compressor Swapan Kumar Nandi Tata Consultancy Services GEDC, 185 LR, Chennai 600086, India Abstract When structures in contact with a fluid

More information

BUCKLING OF BARS, PLATES, AND SHELLS. Virginia Polytechnic Institute and State University Biacksburg, Virginia 24061-0219

BUCKLING OF BARS, PLATES, AND SHELLS. Virginia Polytechnic Institute and State University Biacksburg, Virginia 24061-0219 BUCKLING OF BARS, PLATES, AND SHELLS ROBERT M. JONES Science and Mechanics Professor Emeritus of Engineering Virginia Polytechnic Institute and State University Biacksburg, Virginia 24061-0219 Bull Ridge

More information

Longwave IR focal-plane binary optics

Longwave IR focal-plane binary optics Longwave IR focal-plane binary optics Z. Sikorski, H. Polakowski Institute of Optoelectronics, Military University of Technology, 2 Kaliskiego Str., -98 Warsaw, e-mail: zsikorsk@wat.waw.pl Abstract In

More information

Essential Mathematics for Computer Graphics fast

Essential Mathematics for Computer Graphics fast John Vince Essential Mathematics for Computer Graphics fast Springer Contents 1. MATHEMATICS 1 Is mathematics difficult? 3 Who should read this book? 4 Aims and objectives of this book 4 Assumptions made

More information

Estimated Pre Calculus Pacing Timeline

Estimated Pre Calculus Pacing Timeline Estimated Pre Calculus Pacing Timeline 2010-2011 School Year The timeframes listed on this calendar are estimates based on a fifty-minute class period. You may need to adjust some of them from time to

More information

Nonlinear Iterative Partial Least Squares Method

Nonlinear Iterative Partial Least Squares Method Numerical Methods for Determining Principal Component Analysis Abstract Factors Béchu, S., Richard-Plouet, M., Fernandez, V., Walton, J., and Fairley, N. (2016) Developments in numerical treatments for

More information

Amplification of the Radiation from Two Collocated Cellular System Antennas by the Ground Wave of an AM Broadcast Station

Amplification of the Radiation from Two Collocated Cellular System Antennas by the Ground Wave of an AM Broadcast Station Amplification of the Radiation from Two Collocated Cellular System Antennas by the Ground Wave of an AM Broadcast Station Dr. Bill P. Curry EMSciTek Consulting Co., W101 McCarron Road Glen Ellyn, IL 60137,

More information

Complex Function Theory. Second Edition. Donald Sarason >AMS AMERICAN MATHEMATICAL SOCIETY

Complex Function Theory. Second Edition. Donald Sarason >AMS AMERICAN MATHEMATICAL SOCIETY Complex Function Theory Second Edition Donald Sarason >AMS AMERICAN MATHEMATICAL SOCIETY Contents Preface to the Second Edition Preface to the First Edition ix xi Chapter I. Complex Numbers 1 1.1. Definition

More information

Principles of Digital Communication

Principles of Digital Communication Principles of Digital Communication Robert G. Gallager January 5, 2008 ii Preface: introduction and objectives The digital communication industry is an enormous and rapidly growing industry, roughly comparable

More information

THE GRADUATE COURSE IN ELECTROMAGNETICS: INTEGRATING THE PAST, PRESENT, AND FUTURE

THE GRADUATE COURSE IN ELECTROMAGNETICS: INTEGRATING THE PAST, PRESENT, AND FUTURE THE GRADUATE COURSE IN ELECTROMAGNETICS: INTEGRATING THE PAST, PRESENT, AND FUTURE D. A. ROGERS AND B. D. BRAATEN Department of Electrical and Computer Engineering North Dakota State University Fargo,

More information

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document

More information

PARALLEL PROGRAMMING

PARALLEL PROGRAMMING PARALLEL PROGRAMMING TECHNIQUES AND APPLICATIONS USING NETWORKED WORKSTATIONS AND PARALLEL COMPUTERS 2nd Edition BARRY WILKINSON University of North Carolina at Charlotte Western Carolina University MICHAEL

More information

Physics 235 Chapter 1. Chapter 1 Matrices, Vectors, and Vector Calculus

Physics 235 Chapter 1. Chapter 1 Matrices, Vectors, and Vector Calculus Chapter 1 Matrices, Vectors, and Vector Calculus In this chapter, we will focus on the mathematical tools required for the course. The main concepts that will be covered are: Coordinate transformations

More information

Certificate of Advanced Study in Microwave Engineering

Certificate of Advanced Study in Microwave Engineering Certificate of Advanced Study in Microwave Engineering The Department of Electrical Engineering and Computer Science (EECS) at Syracuse University offers the Certificate of Advanced Study in Microwave

More information

Antenna A mean for radiating and receiving radio waves Transitional structure between free-space and a guiding device. Application: Radiation

Antenna A mean for radiating and receiving radio waves Transitional structure between free-space and a guiding device. Application: Radiation Antenna A mean for radiating and receiving radio waves Transitional structure between free-space and a guiding device Application: adiation Introduction An antenna is designed to radiate or receive electromagnetic

More information

Digital Image Processing

Digital Image Processing Digital Image Processing Using MATLAB Second Edition Rafael C. Gonzalez University of Tennessee Richard E. Woods MedData Interactive Steven L. Eddins The MathWorks, Inc. Gatesmark Publishing A Division

More information

Design of 2D waveguide networks for the study of fundamental properties of Quantum Graphs

Design of 2D waveguide networks for the study of fundamental properties of Quantum Graphs Design of 2D waveguide networks for the study of fundamental properties of Quantum Graphs Introduction: what is a quantum graph? Areas of application of quantum graphs Motivation of our experiment Experimental

More information

Convergence and stability of the inverse scattering series for diffuse waves

Convergence and stability of the inverse scattering series for diffuse waves Convergence and stability of the inverse scattering series for diffuse waves Shari Moskow Department of Mathematics, Drexel University, Philadelphia, PA 19104, USA E-mail: moskow@math.drexel.edu John C.

More information

INTRODUCTION TO FLUID MECHANICS

INTRODUCTION TO FLUID MECHANICS INTRODUCTION TO FLUID MECHANICS SIXTH EDITION ROBERT W. FOX Purdue University ALAN T. MCDONALD Purdue University PHILIP J. PRITCHARD Manhattan College JOHN WILEY & SONS, INC. CONTENTS CHAPTER 1 INTRODUCTION

More information

Nonlinear evolution of unstable fluid interface

Nonlinear evolution of unstable fluid interface Nonlinear evolution of unstable fluid interface S.I. Abarzhi Department of Applied Mathematics and Statistics State University of New-York at Stony Brook LIGHT FLUID ACCELERATES HEAVY FLUID misalignment

More information

MINIMUM USAGE OF FERRITE TILES IN ANECHOIC CHAMBERS

MINIMUM USAGE OF FERRITE TILES IN ANECHOIC CHAMBERS Progress In Electromagnetics Research B, Vol. 19, 367 383, 2010 MINIMUM USAGE OF FERRITE TILES IN ANECHOIC CHAMBERS S. M. J. Razavi, M. Khalaj-Amirhosseini, and A. Cheldavi College of Electrical Engineering

More information

Univariate and Multivariate Methods PEARSON. Addison Wesley

Univariate and Multivariate Methods PEARSON. Addison Wesley Time Series Analysis Univariate and Multivariate Methods SECOND EDITION William W. S. Wei Department of Statistics The Fox School of Business and Management Temple University PEARSON Addison Wesley Boston

More information

Empirical Model-Building and Response Surfaces

Empirical Model-Building and Response Surfaces Empirical Model-Building and Response Surfaces GEORGE E. P. BOX NORMAN R. DRAPER Technische Universitat Darmstadt FACHBEREICH INFORMATIK BIBLIOTHEK Invortar-Nf.-. Sachgsbiete: Standort: New York John Wiley

More information

European Benchmark for Physics Bachelor Degree

European Benchmark for Physics Bachelor Degree European Benchmark for Physics Bachelor Degree 1. Summary This is a proposal to produce a common European Benchmark framework for Bachelor degrees in Physics. The purpose is to help implement the common

More information

Advanced Linear Modeling

Advanced Linear Modeling Ronald Christensen Advanced Linear Modeling Multivariate, Time Series, and Spatial Data; Nonparametric Regression and Response Surface Maximization Second Edition Springer Preface to the Second Edition

More information

EVALUATION OF SAR AND TEMPERATURE ELEVATION IN A MULTI-LAYERED HUMAN HEAD MODEL EXPOSED TO RF RADIATION. By Ayman Ibrahim Sabbah

EVALUATION OF SAR AND TEMPERATURE ELEVATION IN A MULTI-LAYERED HUMAN HEAD MODEL EXPOSED TO RF RADIATION. By Ayman Ibrahim Sabbah EVALUATION OF SAR AND TEMPERATURE ELEVATION IN A MULTI-LAYERED HUMAN HEAD MODEL EXPOSED TO RF RADIATION By Ayman Ibrahim Sabbah Advisor Prof. Nihad Ibrahim Dib Co-Advisor Prof. Moh d Ahmed Al-Nimr Thesis

More information

BACKWARD WAVES AND NEGATIVE REFRACTION IN UNIAXIAL DIELECTRICS WITH NEGATIVE DIELECTRIC PERMITTIVITY ALONG THE ANISOTROPY AXIS

BACKWARD WAVES AND NEGATIVE REFRACTION IN UNIAXIAL DIELECTRICS WITH NEGATIVE DIELECTRIC PERMITTIVITY ALONG THE ANISOTROPY AXIS 2003 Wiley Periodicals, Inc. Reprinted, with permission, from P.A. Belov, Microwave and Optical Technology Letters, Vol. 37, No. 4, pp. 259-263, 2003. mere prototype; the same method can be extended to

More information

AUTOMATED THREE-ANTENNA POLARIZATION MEASUREMENTS USING DIGITAL SIGNAL PROCESSING

AUTOMATED THREE-ANTENNA POLARIZATION MEASUREMENTS USING DIGITAL SIGNAL PROCESSING AUTOMATED THREE-ANTENNA POLARIZATION MEASUREMENTS USING DIGITAL SIGNAL PROCESSING John R. Jones and Doren W. Hess Abstract In this paper we present a three-antenna measurement procedure which yields the

More information

TABLE OF CONTENTS. GENERAL AND HISTORICAL PREFACE iii SIXTH EDITION PREFACE v PART ONE: REVIEW AND BACKGROUND MATERIAL

TABLE OF CONTENTS. GENERAL AND HISTORICAL PREFACE iii SIXTH EDITION PREFACE v PART ONE: REVIEW AND BACKGROUND MATERIAL TABLE OF CONTENTS GENERAL AND HISTORICAL PREFACE iii SIXTH EDITION PREFACE v PART ONE: REVIEW AND BACKGROUND MATERIAL CHAPTER ONE: REVIEW OF INTEREST THEORY 3 1.1 Interest Measures 3 1.2 Level Annuity

More information

Contents. Preface. xiii. Part I 1

Contents. Preface. xiii. Part I 1 Contents Preface xiii Part I 1 Chapter 1 Introduction to Frequency-Modulated Continuous-Wave 3 Radar 1.1 Brief History 3 1.2 Examples of Use of FMCW Radar 5 1.2.1 Radio Altimeters 5 1.2.2 Level-Measuring

More information

Bronx High School of Science Regents Physics

Bronx High School of Science Regents Physics Bronx High School of Science Regents Physics 1. Orange light has a frequency of 5.0 10 14 hertz in a vacuum. What is the wavelength of this light? (A) 1.5 10 23 m (C) 6.0 10 7 m (B) 1.7 10 6 m (D) 2.0

More information

Unit 21 Influence Coefficients

Unit 21 Influence Coefficients Unit 21 Influence Coefficients Readings: Rivello 6.6, 6.13 (again), 10.5 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering Systems Have considered the vibrational behavior of

More information