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Wave Propagation in Materials for Modern Applications Wave Propagation in Materials for Modern Applications Edited by Andrey Petrin Intech IV Published by Intech Intech Olajnica 19/2, 32000 Vukovar, Croatia Abstracting and non-profit use of the material is permitted with credit to the source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. Publisher assumes no responsibility liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained inside. After this work has been published by the Intech, authors have the right to republish it, in whole or part, in any publication of which they are an author or editor, and the make other personal use of the work. © 2010 Intech Free online edition of this book you can find under www.sciyo.com Additional copies can be obtained from: publication@sciyo.com First published January 2010 Printed in India Technical Editor: Teodora Smiljanic Wave Propagation in Materials for Modern Applications, Edited by Andrey Petrin p. cm. ISBN 978-953-7619-65-7 Preface In the recent decades, there has been growing interest in micro- and nanotechnology. The advances in nanotechnology give rise new applications and new types of materials with unique electromagnetic and mechanical properties. This book is devoted to the modern methods in electrodynamics and acoustics which have been developed to describe wave propagation in these modern materials and nanodevices. The book consists of original works of the leading scientists in the field of wave propagation which produced new theoretical and experimental methods in this field of research and obtained new and important results. The first part of the book consists of chapters with general mathematical methods and approaches to the problem of wave propagation. A special attention is attracted to the advanced numerical methods fruitfully applied in the field of wave propagation. The next chapters of the book are combined in several parts according to the materials in which the considering waves propagate. So, the second part of the book is devoted to the problems of wave propagation in newly developed metamaterials, micro- and nanostructures and porous media. In this part the interested reader find important and fundamental results on electromagnetic wave propagation in media with negative refraction index and electromagnetic imaging in devices based on the materials. The third part of the book is devoted to the problems of wave propagation in elastic and piezoelectric media. In the forth part the works on the problems of wave propagation in plasma are collected. The fifth, sixth and seventh parts are devoted to the problems of wave propagation in media with chemical reactions, in nonlinear and disperse media, respectively. And finally, in the eighth part of the book some experimental methods in wave propagations are considered. It is necessary to emphasis that this book is not a textbook. It is important that the results combined in it are taken “from the desks of researchers“. So, I am sure that in this book the interested and actively working readers (scientists, engineers and students) find many interesting results and new ideas. Editor Andrey Petrin Joint Institute for High Temperatures of Russian Academy of Science, Russia a_petrin@mail.ru Contents Preface V I Wave Propagation. Fundamental Approaches to the Problem. 1. A Volume Integral Equation Method for the Direct/Inverse Problem in Elastic Wave Scattering Phenomena 001 Terumi Touhei 2. Uniform Asymptotic Physical Optics Solutions for a Set of Diffraction Problems 033 Giovanni Riccio 3. Differential Electromagnetic Forms in Rotating Frames 055 Pierre Hillion 4. Iterative Operator-Splitting with Time Overlapping Algorithms: Theory and Application to Constant and Time-Dependent Wave Equations. 065 Jürgen Geiser 5. Comparison Between Reverberation-Ray Matrix, Reverberation-Transfer Matrix, and Generalized Reverberation Matrix 091 Jiayong Tian 6. Accelerating Radio Wave Propagation Algorithms by Implementation on Graphics Hardware 103 Tobias Rick and Torsten Kuhlen II Wave Propagation in Metamaterials, Micro/nanostructures and Porous Media. 7. Application of Media with Negative Refraction Index to Electromagnetic Imaging. Fundamental Aspects. 123 Andrey Petrin 8. Electromagnetic Wave Propagation in Multilayered Structures with Negative Index Material 149 Mariya Golovkina VIII 9. The Nature of Electromagnetic Waves in Metamaterials and Metamaterial-inspired Configurations 163 Rui Yang and Yongjun Xie 10. Electromagnetic Propagation Characteristics in One Dimensional Photonic Crystal 193 Arafa H Aly 11. Wave Propagation in Elastic Media with Micro/Nano-Structures 201 G. L. Huang, C.T. Sun and F. Song 12. Wave Propagation in Carbon Nanotubes 225 Lifeng Wang, Haiyan Hu and Wanlin Guo 13. Differential Quadrature Method for Linear Long Wave Propagation in Open Channels 253 Birol Kaya and Yalcin Arisoy 14. A Parabolic Equation for Wave Propagation over Porous Structures 267 Tai-Wen Hsu and Jen-Yi Chang III Wave Propagation in Elastic and Piezoelectric Media. 15. Propagation of Ultrasonic Waves in Viscous Fluids 293 Oudina Assia and Djelouah Hakim 16. A Multiplicative Method and A Correlation Method for Acoustic Testing of Large-Size Compact Concrete Building Constructions 307 Vladimir K. Kachanov, Igor V. Sokolov, and Sergei L. Avramenko 17. Analysis of Axisymmetric and Non-Axisymmetric Wave Propagation in a Homogeneous Piezoelectric Solid Circular Cylinder of Transversely Isotropic Material 335 Michael Yu. Shatalov 18. Propagation of Thickness-Twist Waves in an Infinite Piezoelectric Plate 359 Zheng-Hua Qian, Feng Jin, Jiashi Yang and Sohichi Hirose IV Wave Propagation in Plasma. 19. Interplay of Kinetic Plasma Instabilities 375 M. Lazar , S. Poedts and R. Schlickeiser IX 20. Plasma Wave Propagation with Light Emission in a Long Positive Column Discharge 389 Guangsup Cho and John V. Verboncoeur V Wave Propagation in Media with Chemical Reactions. 21. Influence of Heavy Water on Waves and Oscillations in the Belousov-Zhabotinsky Reaction 409 Oliver Klink, Wolfgang Hanke, Edeltraud Gerbershagen and Vera Maura Fernandes de Lima VI Wave Propagation in Nonlinear Media. 22. Wave Propagation and Dynamic Fracture in Laser Shock-Loaded Solid Materials 419 Thibaut De Rességuier, Jean-Paul Cuq-Lelandais, Michel Boustie, Emilien Lescoute and Laurent Berthe 23. Nonlinear Waves in Transmission Lines Periodically Loaded with Tunneling Diodes 437 Koichi Narahara VII Wave Propagation in Disperse Media. 24. Wave Velocity Dispersion and Attenuation in Media Exhibiting Internal Oscillations 455 Marcel Frehner, Holger Steeb and Stefan M. Schmalholz 25. Pulse Wave Propagation in Bistable Oscillator Array 477 Kuniyasu Shimizu, Motomasa Komuro and Tetsuro Endo 26. Circuit Analogs for Wave Propagation in Stratified Structures 489 Daniel Sjöberg VIII Some Experimental Methods in Wave Propagation. 27. Field Experiments on Wave Propagation and Vibration Isolation by Using Wave Barriers 509 Seyhan Fırat, Erkan Çelebi, Günay Beyhan, İlyas Çankaya, Osman Kırtel and İsa Vural [...]... following: Lemma 1 The operator is symmetric and non-negative [Proof] Let ui, vi ∈ D( ) Then, is carried out in the sense of 18 Wave Propagation in Materials for Modern Applications (10 0) (10 1) □ Next, the following function is defined: (10 2) together with the boundary condition (10 3) where C is a set of complex numbers The solution of Eq (10 2) for for η ∈ C \ B has the following properties: (10 4) where... scattered waves can be observed in the far field range of regions of the fluctuation (a) Fluctuations of Lamé constants λ and μ (b) Fluctuations of Lamé constants λ and μ in the x 1 – x 2 plane Fig 2 Analyzed model of smooth fluctuations in the x 1 – x 3 plane 14 Wave Propagation in Materials for Modern Applications (a) Amplitudes of scattered waves in the x 1 – x 2 plane (b) Amplitudes of the scattered waves... 3) As a result, the intervals of the grid in the wavenumber space become Δξj = 2π/(Nj ×Δxj) ≈ 0.098 km 1 In addition, ε for the Green’s function in the wavenumber domain shown in Eq ( 21) is set to 0.2 Figures 3(a) and 3(b) show the amplitudes of the scattered waves in the x 1 − x 2 and x 1 − x 3 planes, respectively According to Fig 3(a), the scattered waves are prominent in the regions in which fluctuations...I Wave Propagation Fundamental Approaches to the Problem 1 A Volume Integral Equation Method for the Direct/Inverse Problem in Elastic Wave Scattering Phenomena Terumi Touhei Department of Civil Engineering, Tokyo University of Science, Japan 1 Introduction The analysis of elastic wave propagation and scattering is an important issue in fields... Equation (19 ) yields (20) where (ξ) is expressed by 6 Wave Propagation in Materials for Modern Applications ( 21) In Eq ( 21) , ν0 is the Poisson ratio obtained from the back ground Lamé constants λ0 and μ0, kL, and kT are the wavenumber of the P and S waves obtained from (22) |ξ|2 is given by (23) and ε is an infinitesimally small positive number Note that cT and cL in Eq (22) are the S and P wave velocities,... are 2 and 1 km/s, respectively The analyzed frequency is f = 1 Hz, and the amplitude of the potential for the incident P wave is a = 1. 0 × 10 5 cm2 The intervals of the grids in the space domain for the discrete Fourier transform are set by Δxj = 0.25(km), (j = 1, 2, 3), and the number of intervals of the grids in the space domain for the discrete Fourier transform are set by Nj = 256, (j = 1, 2, 3)... Definition 1 The forward scattering problem is to determine the scattered wave field from information about the regions of fluctuation, the background structure of the wave field, and the plane incident wave Definition 2 The inverse scattering problem involves reconstructing the fluctuating areas from information about the scattered waves, the background structure of the wave field, and the plane incident wave. .. Since there is no point source in the wave field shown in Fig 1( a), the solution of Eq (7) is expressed by the following volume integral equation: (12 ) where Fi and Gij are the plane incident wave and the Green’s function, respectively, which satisfy the following equations: (13 ) (14 ) A Volume Integral Equation Method for the Direct/Inverse Problem in Elastic Wave Scattering Phenomena 5 It is convenient... equation in the wavenumber domain should also be investigated In this chapter, basic equations for elastic wave propagation are first presented in order to prepare the formulation After clarifying the properties of the volume integral equation in the wavenumber domain, a method for solving the volume integral equation is developed 2 Basic equations for elastic wave propagation Figures 1( a) and (b) show... of this section, a method for dealing with Eq (16 ) is described 3.2 The Fourier transform and its application to the volume integral equation The following Fourier integral and its inverse transforms: (17 ) play an important role in the formulation, where ξ = ( 1, ξ2, ξ3) ∈ R3 is a point in the wavenumber space, x · ξ is the scalar product defined by (18 ) 1 are the operators for the Fourier transform . Configurations 16 3 Rui Yang and Yongjun Xie 10 . Electromagnetic Propagation Characteristics in One Dimensional Photonic Crystal 19 3 Arafa H Aly 11 . Wave Propagation in. piezoelectric media. In the forth part the works on the problems of wave propagation in plasma are collected. The fifth, sixth and seventh parts are devoted to the problems of wave propagation in media. Chang III Wave Propagation in Elastic and Piezoelectric Media. 15 . Propagation of Ultrasonic Waves in Viscous Fluids 293 Oudina Assia and Djelouah Hakim 16 . A Multiplicative