The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organises seminars on subjects concerning the algorithmic treatment of par tial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various types of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such seminars was continued in 1994, January 14-16, with the 10th Kiel-Seminar on the special topic Fast Solvers for Flow Problems at the Christian-Albrechts-University of Kiel. The seminar was attended by 100 scientist from 9 countries. 23 lectures were given, including two invited survey lectures. The central topic of most of the contributions are the Navier-Stokes equations. The authors discuss robust methods, parallel implementations, defect correction techniques, adaptive methods including error estimators, domain decompositions and FEM-BEM coupling. The invited lectures concern the hierarchical multigrid method for unstruc tured grids and structured adaptive finite-volume multigrid for compressible flows."

Some years ago we set out to write a detailed book about the basic physics of musical instruments. There have been many admirable books published about the history of the development of musical instruments, about their construction as a master craft, and about their employment in musical perfor mance; several excellent books have treated the acoustics of musical instru ments in a semiquantitative way; but none to our knowledge had then at tempted to assemble the hard acoustic information available in the research literature and to make it available to a wider readership. Our book The Physics of Musical Instruments, published by Springer-Verlag in 1991 and subsequently reprinted several times with only minor corrections, was the outcome of our labor. Because it was our aim to make our discussion of musical instruments as complete and rigorous as possible, our book began with a careful introduction to vibrating and radiating systems important in that field. We treated simple linear oscillators, both in isolation and coupled together, and extended that to a discussion of some aspects of driven and autonomous nonlinear oscilla tors. Because musical instruments are necessarily extended structures, we then went on to discuss the vibrations of strings, bars, membranes, plates, and shells, paying particular attention to the mode structures and characteristic frequencies, for it is these that are musically important."

This book presents the contents of a CISM Course on waves and instabilities in plasmas. For beginners and for advanced scientists a review is given on the state of knowledge in the field. Customers can obtain a broad survey.

This book covers a wide range of technical issues relating to lightwave technologies using high coherence lightwaves. Electromagnetic wave communication started when the first wireless system was invented by Marconi in 1895. However, we had to wait about one hundred years to realize a similar technology in the lightwave frequency region. The invention of lasers in 1960 and two technology innovations in 1970 -low loss silica fiber and semiconductor lasers operating at room temperature - promoted the development of fiber-optic transmission systems. The deployment of high-speed long-haul fiber-optic transmission systems has led to the formation of domestic and international trunk networks. The installed fiber cables in local loop plants provide multimedia communication services including broadband video. However, present lightwave communication systems do not fully utilize the fruitful potential oflightwaves, namely the capacity of extremely high frequency electromagnetic information carrier waves. The frequency oflightwaves used for fiber-optic transmission is about 200 THz 14 (2 x 10 Hz), and the frequency bandwidth of the fiber low loss region is about 13 20 THz (2 x 10 Hz). Recent developments of narrow spectrum width semiconduc tor laser and planar optical waveguide devices offer us the possibilities for a new generation of lightwave-based communication systems. This book focuses on system aspects ofthe new generation lightwave communi cation technologies such as optical frequency division multiplexing and coherent detection. Chapter 1 overviews lightwave communication system technology."

Introduces Systematic Formulations for Use in Acoustic Applications Acoustics in Moving Inhomogeneous Media, Second Edition offers a uniquely complete and rigorous study of sound propagation and scattering in moving media with deterministic and random inhomogeneities. This study is of great importance in many fields including atmospheric and oceanic acoustics, aeroacoustics, acoustics of turbulent flows, remote sensing of the atmosphere and ocean, noise pollution in the atmosphere, and wave propagation. Provides Sensible Explanations Using Step-by-Step Practice The book begins by considering sound propagation through moving media with deterministic inhomogeneities such as vertical profiles of temperature and wind velocity in the atmosphere. It moves on to a new study of sound propagation and scattering in media with random inhomogeneities in adiabatic sound speed, density, and medium velocity. Then this second edition newly sets out state-of-the-art numerical methods for calculating the sound field and its statistical characteristics in moving inhomogeneous media, which is particularly useful for those working in atmospheric acoustics and studying noise pollution. Numerical codes are provided on the book's website www.crcpress.com/product/isbn/9780415564168 Covered in three parts, this second edition: Incorporates new results developed since the previous edition Rewrites and extends the text with formulations of sound propagation and scattering in random moving media Describes numerical methods for performing calculations involving equations from the first two parts Acoustics in Moving Inhomogeneous Media, Second Edition serves as the basis of a graduate course in atmospheric and oceanic acoustics or as a rigorous reference work

Travelling wave processes and wave motion are of great importance in many areas of mechanics, and nonlinearity also plays a decisive role there. The basic mathematical models in this area involve nonlinear partial differential equations, and predictability of behaviour of wave phenomena is of great importance. Beside fluid dynamics and gas dynamics, which have long been the traditional nonlinear scienes, solid mechanics is now taking an ever increasing account of nonlinear effects. Apart from plasticity and fracture mechanics, nonlinear elastic waves have been shown to be of great importance in many areas, such as the study of impact, nondestructive testing and seismology. These lectures offer a thorough account of the fundamental theory of nonlinear deformation waves, and in the process offer an up to date account of the current state of research in the theory and practice of nonlinear waves in solids.

The book provides an introduction to digital signal processing for intermediate level students of electronic and/or electrical engineering and is also relevant to other disciplines which deal with time-series analysis: these include acoustics, mathematics, statistics, psychology and economics.

This volume offers a wide range of theoretical, numerical and experimental research papers on fluid dynamics. The major fields of research - fundamentals of fluid mechanics as well as their applications - are treated: - stability phenomena: convective flow, thermal and hydrodynamic systems - transition, turbulence and separation: boundary-layer, turbulent combustion, rarefied gasdynamics, near wall and off wall flow fields, energy dissipation - transonic flow: homogeneous condensation, shock-waves, effects at Mach number unity - hypersonic flow: flow over spheres, aerothermodynamics, relaxation - fluid machinery: axial fans, compressor cascades, fluid couplings - computational fluid dynamics: passive shock control, zonal computation, cylinderflow, flow over wings - miscellaneous problems.

This book contains original papers presented at the Fourth International Conference on Hyperbolic Problems which was held on April 3-8, 1992 in Taormina (Sicily), Italy. The aim of the Conferences in this cycle is to bring together scientists with interest in theo retical, applied and computational aspects of hyperbolic partial differential equations. The contributions, well balanced among these three aspects, deal with: mathematical theory of wave propagation, kinetic theory, existence, uniqueness and stabil ity of solutions, mathematical modeling of physical phenomena, stability and convergence of numerical schemes, multidimensional computational applications, etc. The papers are printed in the authors' alphabetic order following the idea both of mixing together topics of interest to different areas and of considering either theoretical results connected with applied problems or new applications with an essential mathemat ical approach. The Proceedings from the previous Conferences held in St. Etienne (1986), Aachen (1988) and Uppsala (1990) appeared respectively as: Lecture Notes in Mathematics, 1270, P. Carasso, P. A. Raviart & D. Serre (Eds.), Springer-Verlag (1987) Notes on Numerical Fluid Mechanics, 24, J. Ballmann & R. Jeltsch (Eds.), Vieweg (1989 ) Third International Conference on Hyperbolic Problems, B. Engquist & B. Gustafs son (Eds.), Vol. I, II, Studentlitteratur, Uppsala University (1991). The organizers and the editors of the Conference would like to thank the Scientific Committee for the generous support, for suggesting the invited lectures, and for selecting the contributed papers."

Mechanics of Continua and Wave Dynamics is a textbook for a course on the mechanics of solids and fluids with the emphasis on wave theory. The material is presented with simplicity and clarity but also with mathematical rigor. Many wave phenomena, especially those of geophysical nature (different types of waves in the ocean, seismic waves in the earth crust, wave propagation in the atmosphere, etc.), are considered. Each subject is introduced with simple physical concepts using numerical examples and models. The treatment then goes into depth and complicated aspects are illustrated by appropriate generalizations. Numerous exercises with solutions will help students to comprehend and assimilate the ideas.

In the early 1950s microseisms, with characteristic amplitudes of several micro meters, were considered insignificant relative to powerful destructive earthquakes. They were understood to be noise, as natural fluctuations, not carrying any in formation and distorting recordings on seismograms. Intensive investigations over subsequent decades have shown, however, that microseisins are only a single facet of a huge complex of phenomena comprising cyclone movement over oceans, sea roughness, infrasound, geomagnetic micropulsations, terrestial of these phenomena proved to be confined in time currents, etc. The source and space, whereas their effects propagated over global distances. This could be interpreted as a case of natural "remote sensing." It should be mentioned that all of the evidence gathered in the last few decades supports the theory of M. S. Longuet-Higgins published in 1950. The author has been engaged in problems of microseisms since 1955 and is deeply convinced that these phenomena are not only of theoretical interest but may also find practical application in meteorology, oceanology, navigation and other areas. She hopes. that this book will stimulate further research as well as new approaches to practical problems."

This text considers the problem of the dynamic fluid-structure interaction between a finite elastic structure and the acoustic field in an unbounded fluid-filled exterior domain. The exterior acoustic field is modelled through a boundary integral equation over the structure surface. However, the classical boundary integral equation formulations of this problem either have no solutions or do not have unique solutions at certain characteristic frequencies (which depend on the surface geometry) and it is necessary to employ modified boundary integral equation formulations which are valid for all frequencies. The particular approach adopted here involves an arbitrary coupling parameter and the effect that this parameter has on the stability and accuracy of the numerical method used to solve the integral equation is examined. The boundary integral analysis of the exterior acoustic problem is coupled with a finite element analysis of the elastic structure in order to investigate the interaction between the dynamic behaviour of the structure and the associated acoustic field. Recently there has been some controversy over whether or not the coupled problem also suffers from the non-uniqueness problems associated with the classical integral equation formulations of the exterior acoustic problem. This question is resolved by demonstrating that .the solution to the coupled problem is not unique at the characteristic frequencies and that it is necessary to employ an integral equation formulation valid for all frequencies.

The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree course in which transform techniques will have a significant application. In other disciplines the readership will be past the second year undergraduate stage. In either case, the text is also intended for earlier graduates whose degree courses did not include this type of material and who now find themselves, in a professional capacity, requiring a knowledge of discrete transform methods."

This book is a practical guide for researchers and advanced graduate students in biology and biophysics who need a quantitative understanding of acoustical systems such as hearing, sound production, and vibration detection in animals at the physiological level. It begins with an introduction to physical acoustics, covering the fundamental concepts and showing how they can be applied quantitatively to understand auditory and sound-producing systems in animals. Only after the relatively simple mechanical part of the system is explained does the author focus his attention on the underlying physiological processes. The book is written on three levels. For those wanting a brief survey of the field, each chapter begins with a nonmathematical synopsis which summarizes the content and refers to the figures, all of which are designed to be understood apart from the main text. At the next level, the reader can follow the main text, but need not give close attention to anything but the general concepts and techniques involved. At the third level, the reader should follow the mathematical arguments in detail and attempt the discussion of questions at the end of each chapter. The author has provided detailed solutions which serve to expand the discussions of particular cases.

The study of materials which exhibit new and unconventional properties is of central importance for the devel- opment of advanced and refined technologies in many fields of engineering science. In this connection there has been a rapidly growing interest in real fluid effects on wave phenomena in the past few years. A prominent example is provided by Bethe-Zel'dovich-Thompson (BZT) fluids which have the distinguishing feature that they exhibit negative nonlinearity over a finite range of temperature and pressures in the pure vapour phase. However, two phase flows with and without phase change are an even richer source of new unexpected and previously thought impossible phenomena. Topics covered by this volume include waves in gases near the critical point, waves in retrograde fluids, temperature waves in superfluid helium and density waves in suspensions of particles in liquids. Clearly, the aim of the various contributions is twofold. First, they are intended to provide scientists and engineers working in these and related areas with an overview of various new physical phenomena as for example expansion shocks, sonic shocks, shock splitting, evaporation and liquafaction shocks and the experimental techniques needed to study these phenomena. Second, an attempt is made to discuss aspects of their mathematical modeling with special emphasis on properties which these phenomena have in common.

S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.

The last two subjects mentioned in the title "Wavelets, Time Frequency Methods and Phase Space" are so well established that they do not need any explanations. The first is related to them, but a short introduction is appropriate since the concept of wavelets emerged fairly recently. Roughly speaking, a wavelet decomposition is an expansion of an arbitrary function into smooth localized contributions labeled by a scale and a position pa rameter. Many of the ideas and techniques related to such expansions have existed for a long time and are widely used in mathematical analysis, theoretical physics and engineering. However, the rate of progress increased significantly when it was realized that these ideas could give rise to straightforward calculational methods applicable to different fields. The interdisciplinary structure (R.C.P. "Ondelettes") of the C.N.R.S. and help from the Societe Nationale Elf-Aquitaine greatly fostered these developments. The conference, the proceedings of which are contained in this volume, was held at the Centre National de Rencontres Mathematiques (C.N.R.M) in Marseille from December 14-18, 1987 and bought together an interdisciplinary mix of par ticipants. We hope that these proceedings will convey to the reader some of the excitement and flavor of the meeting.

Smectic and lamellar liquid crystals are three-dimensional layered structures in which each layer behaves as a two-dimensional fluid. Because of their reduced dimensionality they have unique physical properties and challenging theoretical descriptions, and are the subject of much current research. One- and Two-Dimensional Fluids: Properties of Smectic, Lamellar and Columnar Liquid Crystals offers a comprehensive review of these phases and their applications. The book details the basic structures and properties of one- and two-dimensional fluids and the nature of phase transitions. The later chapters consider the optical, magnetic, and electrical properties of special structures, including uniformly and non-uniformly aligned anisotropic films, lyotropic lamellar systems, helical and chiral structures, and organic anisotropic materials. Topics also include typical and defective features, magnetic susceptibility, and electrical conductivity. The book concludes with a review of current and potential applications in the displays, materials science, and biomedical industries. Rather than focusing on one aspect of liquid crystal research, this book provides a cohesive summary of the properties and applications of smectic, lamellar, and columnar liquid crystals. One- and Two-Dimensional Fluids is a valuable resource for those working with liquid crystals every day and an effective foundation for newcomers to the field.

TIlis volume contains the contributions to the Euromech Colloquium No. 241 on Nonlinear Waves in Active Media at the Institute of Cybernetics of the Estonian Academy of Sciences, Tallinn, Estonia, USSR, September 27-30, 1988. The Co-chairmen of the Euromech Colloquium felt that it would be a good service to the community to publish these proceedings. First, the topic itself dealing with various wave processes with energy influx is extremely interesting and attracted a much larger number of participants than usual - a clear sign of its importance to the scientific community. Second, Euromech No. 241 was actually the first Euromech Colloquium held in the Soviet Union and could thus be viewed as a milestone in the extending scientific contacts between East and West. At the colloquium 50 researchers working in very different branches of sci ence met to lecture on their results and to discuss problems of common interest. An introductory paper by I. Engelbrecht presents the common motivation and background of the topics covered. Altogether 36 speakers presented their lectures, of which 30 are gathered here. The remaining six papers which will appear elsewhere are listed on page X. In addition, three contributions by authors who could not attend the colloquium are included. The two lectures given by A.S. Mikhailov, V.S. Davydov and V.S. Zykov are here published as one long paper.

The papers included in this proceedings volume are mostly original research papers, dealing with life-span of waves, nonlinear interaction of waves, and various applications to fluid mechanics.

This new book leads readers step-by-step through the complexities encountered as moving objects approach and cross the sound barrier. The problems of transonic flight were apparent with the very first experimental flights of scale-model rockets when the disastrous impact of shock waves and flow separations caused the aircraft to spin wildly out of control. Today many of these problems have been overcome, and this book offers an introduction to the transonic theory that has made possible many of these advances. The emphasis is on the most important basic approaches to the solution of transonic problems. The book also includes explanations of common pitfalls that must be avoided. An effort has been made to derive the most important equations of inviscid and viscous transonic flow in sufficient detail so that even novices may feel confident in their problem-solving ability. The use of computer approaches is reviewed, with references to the extensive literature in this area, while the critical shortcomings of an exclusive reliance on computational methods are also described. The book will be valuable to anyone who needs to acquire an understanding of transonic flow, including practicing engineers as well as students of fluid mechanics.

Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet scientists working in this field. Instead of producing for the first time English proceedings it has been decided to present a good cross section of nonlinear physics in the USSR. Thus the participants at the last School were invited to provide English reviews and research papers for these two volumes (which in the years to come will be followed by the proceedings of forthcoming schools). "The first volume" starts with a historical overview of nonlinear dynamics from Poincare to the present day and touches topics like attractors, nonlinear oscillators and waves, turbulence, pattern formation, and dynamics of structures in nonequilibrium dissipative media. It then deals with structures, bistabilities, instabilities, chaos, dynamics of defects in 1d systems, self-organizations, solitons, spatio-temporal structures and wave collapse in optical systems, lasers, plasmas, reaction-diffusion systems and solids."

This anthology was originally planned in connection with a symposium "Language in Primates: Implications for Linguistics, Anthropology, Psychology, and Philosophy," at Miami University, Oxford, Ohio. Publication of the book would not have been possible without the support given to the Symposium by many individuals and groups. The Editors thank everyone involved for their kind and generous assistance. Specifi cally, we thank the invited speakers at the Symposium, Thomas A. Sebeok, H. Lyn Miles, Roger S. Fouts, and Thomas Simon. The chapters in this book by Miles, Fouts, and Simon are revised versions of their lectures at the Symposium. We thank Edward Simmel for his encouragement, his patience with our efforts, and his help in planning and directing the Symposium. For their financial assistance, we thank the co-sponsors of the Symposium: the Sigma Chi Foundation/William P. Huffman Scholar-in Residence Program at Miami University, as well as the Departments of Classics, Philosophy, Psychology, and Sociology and Anthropology at Miami. We thank Barbara Johnson, Polly J. Harris and Brenda Shaw for their secretarial and editorial help, and Shirley Gallimore for her patience, care, good humor, and hard work in typing the manuscript. Finally, we thank the contributors to this volume."

VI The idea to hold such a meeting in Germany for the first time was due to Prof. H. Pelzl. Its realization was greatly supported by financial help of the Stiftung Volkswagenwerk and the Deutsche Physikalische Gesellschaft, which is gratefully acknowledged. The Editors VII Contents 1. Basic Principles Photoacoustic Effect in Condensed Matter - Historical Development E. LUscher 1 Opto-Acoustic Spectroscopy - A Tool for the Study of Optical Spectra of very Transparent Materials 21 C. K. N. Patel Thermodynamic r ode 1 s of the Photoacousti c Effect P. Korpiun 40 Frequency Dependent Photoacous tic Spectroscopy of Condensed t latter J. Pelzl 52 Photoacoustic Spectroscopies D. Fournier and A. C. Boccara so Comparison Between Photoacoustic and Other Spectroscopies 94 R. Til gner Generation of Acoustic Waves in Liquids by Pulsed Lasers lOS H. W. Sigrist Piezoelectric Detection in Photoacoustic Spectroscopy. Theory and Application 115 H. D. Breuer Photothermal Radiometry P. -E. Nordal and S. O. Kanstad 129 Contents VIII 2. Spectroscopic Applications Applications of Resonant Photoacoustic Spectroscopy 139 J. Roper, K. Frank, and P. Hess Photoacoustic Fourier Transform Spectroscopy for the Visible and the Near Infrared D. uebarre, A. C. Boccara and D. Fournier 147 Photoacoustic Spectra of Biliverdin Dimethyl Ester S. E. Braslavsky, R. Ellul, S. Culshaw, I. -M. Tegmo-larsson, and K. Schaffner 154 Quantitative Photoacoustic Spectroscopy of Phenolred Potassium Salt in Polyvinalalcohol W. Gortz and H. -H. Perkampus 163 In Situ Photoacoustic Spectroscopy of Copper Electrodes in Solution U. Sander, J. K. Dohrmann, and H. -H."