This monograph is concerned with the fundamentals of up-to-date geo metrical optics treated as an approximate method of wave theory. Geometrical optics has changed dramatically over the last two decades. Primarily, it has acquired a number of novel disciplines: space-time geo metrical optics, the quasi-isotropic approximation, the modern theory of caustics related to catastrophe theory, and perturbation techniques for rays, to name only a few. Another acquisition is the reliable boundaries of appli cability for geometrical optics, based upon the concept of the Fresnel volume for a ray. These recent additions to the field are the focus of dis cussion in the book. We did not attempt to separate study-oriented and illustrative material from that intended for professionals, but rather we spread it throughout the text to facilitate for the reader the mastering of this attractive, intuitively appealing and efficient ray method. In preparing the manuscript we used a set of lecture notes devised for All-Union Schools on Diffraction and Wave Propagation, published in Rus sian. Sections 2.1-4,6 and 10 result from joint efforts of both authors. The other material of the book we wrote separately. I contributed Sects. 2.5,9 and 3.17 and Chap.4; Yu.l. Orlov prepared the rest. Unfortunately, he could not take part in the preparation of the English edition, as he died in 1982 at the age of 41, on the verge of what would have been great achieve ments considering his strong and original talent."

The topic of surface waves lies at the interface between a number of disci plines - physics, theoretical and applied mechanics, electroacoustics, ap plied mathematics, surface science and seismology. This volume, based on papers delivered at European Mechanics Colloquium 226, reflects this diversity in approach and background, while showing strong links between phenomena arising from different fields. The emphasis is on recent de velopments such as nonlinear and other nonclassical effects, which have great importance for both pure science and for applications such as signal processing, nondestructive evaluation and seismic studies. In recent years there has been considerable progress in the mathe matical treatment of nonlinear effects, of viscoelastic and of more novel constitutive effects which modify the predictions of linear elastic and piezo electric theory for surface acoustic wave (SAW) propagation. A number of these themes serve to group the contents of this volume. Part I contains recent advances in the rigorous mathematical treatment of nonlinearity, together with a paper giving experimental results showing the need for further theoretical development. Part II deals with anisotropic elasticity, showing that even the linear theory presents many possible behaviours, which are still not fully categorized."

Symposia in the areas of fluid mechanics and hydraulics are, in many cases, strongly oriented toward the researcher, with only peripheral participation of the practicing engineer. The possible danger therein is an increased emphasis on those problems that are theoretically or experimentally attractive, rather than those that would most effectively lead to improved design criteria. To bring the practical aspects of flow-induced vibrations to the forefront, and to enhance in terchange of information on shortcomings of design criteria, it was decided to extend invitations to fielrl engineers, designers and researchers. The leading theme of the Symposium would be experiences from practice, encompassing informa tion on failures, fatigue, and wear; and wherever possible, the associated cures would be addressed as well. Moreover, to promote interaction between disciplines, a variety of specialities, ranging from tall structures to heat exchanger and re actor components, was included; but to keep the undertaking within a reasonable scope, topics dealing with slender body aerodynamics, and high-speed internal and external flow, were not incorporated. During this planning phase, many of our colleagues encouraged us to follow through with the spirit of the Symposium, and provided a number of helpful suggestions. It was gratifying to receive the en dorsement of the International Association for Hydraulic Research and the Inter national Union for Theoretical and Applied Mechanics, as the variety of interests represented by these organizations enhanced the theme of the Symposium.

This book comprises some of the lecture notes I developed for various one-or two-semester courses I taught at the Colorado School of Mines. The main objective of all the courses was to introduce students to the mathematical aspects of wave theory with a focus on the solution of some specific fundamental problems. These fundamental solutions would then serve as a basis for more complex wave propagation and scattering problems. Although the courses were taught in the mathematics department, the audience was mainly not mathematicians. It consisted of gradu ate science and engineering majors with a varied background in both mathematics and wave theory in general. I believed it was necessary to start from fundamental principles of both advanced applied math ematics as well as wave theory and to develop them both in some detail. The notes reflect this type of development, and I have kept this detail in the text. I believe it essential in technical careers to see this detailed development at least once. This volume consists of five chapters. The first two on Scalar Wave Theory (Chapter 1) and Green's Functions (Chapter 2) are mainly mathematical although in Chapter 1 the wave equation is derived from fundamental physical principles. More complicated problems involving spatially and even temporally varying media are briefly introduced."

The call for papers for the rUTAM-Symposium on Mechanics of Passive and Active Flow Control brought an overwhelming response of applications for contributions. Fi nally 12 invited lectures, 48 papers and 23 posters were selected by thc Scientific Com mittee to be presented in the conference. 58 papers are published in this volume. Due to the limited number of pages available, poster presentations could not be considered for publication. The editors would like to thank all the members of the Scientific Committee for their very valuable assistance. The papers presented at the rUT AM Symposium were classified under three groups de voted to * Passive Control Methods, * Active Control Methods and * Control Concepts. This was done to contrast at first between the passive techniques where the control power is mainly supplied by the flow itself and the active techniques where the power is pro vided by external sources; the third group was devoted to control concepts for presenting methods of control theory and new techniques of flow control.

In recent years substantial progress has been made in the detection of surface phonons owing to considerable improvements in inelastic rare gas scattering tech niques and electron energy loss spectroscopy. With these methods it has become possible to measure surface vibrations in a wide energy range for all wave vectors in the two-dimensional Brillouin zone and thus to deduce the complete surface phonon dispersion curves. Inelastic atomic beam scattering and electron energy loss spectroscopy have started to play a role in the study of surface phonons similar to the one played by inelastic neutron scattering in the investigation of bulk phonons in the last thirty years. Detailed comparison between experimen tal results and theoretical studies of inelastic surface scattering and of surface phonons has now become feasible. It is therefore possible to test and to improve the details of interaction models which have been worked out theoretically in the last few decades. At this point we felt that a concise, coherent and self-contained guide to the rapidly growing field of surface phonons was needed."

After many years of sterile arms control negotiations between the super powers, which did not produce a single genuine disarmament measure - and sometimes had the opposite effect of stimulating the development of new weapons to serve as bargaining chips - an agreement to abolish completely two categories of nu clear weapons, the INF Treaty, was signed and is now being implemented. This historical event, the first actual destruction of deployed nuclear missiles (although not of their warheads) became possible largely because of the radical changes in the policies of the Soviet Union, the "new way of thinking," ad vanced by its leader Mikhail Gorbachev. The relaxation of tension that resulted from this policy was one of the factors contributing to the successful conclu sion of the INF Treaty. Another, no less important factor, was the acceptance by the Soviet Union of on-site inspections as a basic element of a verification system essential to ensure compliance with the Treaty. This breakthrough led to the mutual acceptance of an elaborate and precise verification regime, and thus made possible the signing of the INF Treaty, which in tum contributed to the further lessening of tension between East and West. But perhaps the most important factor, one which carries much promise for the future, was the changed approach to security problems."

In the 1950s the direct observation of dislocations became possible, stimulat ing the interest of many research workers in the dynamics of dislocations. This led to major contributions to the understanding of the plasticity of various crys talline materials. During this time the study of metals and alloys of fcc and hcp structures developed remarkably. In particular, the discovery of the so-called in ertial effect caused by the electron and phonon frictional forces greatly influenced the quantitative understanding of the strength of these metallic materials. Statis tical studies of dislocations moving through random arrays of point obstacles played an important role in the above advances. These topics are described in Chaps. 2-4. Metals and alloys with bcc structure have large Peierls forces compared to those with fcc structure. The reasons for the delay in studying substances with bcc structure were mostly difficulties connected with the purification techniques and with microscopic studies of the dislocation core. In the 1970s, these difficulties were largely overcome by developments in experimental techniques and computer physics. Studies of dislocations in ionic and covalent bonding materials with large Peierls forces provided infonnation about the core structures of dislocations and their electronic interactions with charged particles. These are the main subjects in Chaps. 5-7."

This Topics volume is devoted to a study of sound propagation in the ocean. The effect of the interior of the ocean on underwater sound is analogous to the effect of a lens on light. The oceanic lens is related, as in light propagation, to the index of refraction of the medium. The latter is giv n by the ratio of the sound frequency to the speed of sound in water, typi ca lly about 1500 m s -1. It is the vari ation of the sound speed due to changing temperature, density, salinity, and pres sure in the complex ocean environment which creates the lens effect. Many oceanic processes such as currents, tides, eddies (circulating, translating regions of wa ter), and internal waves (the wave-like structure of the oceanic density variabil ity) contri bute in turn to the changes in sound speed'. The net effect of the ocean lens is to trap and guide sound waves in a channel created by the lens. The trapped sound can then propagate thousands of miles in this oceanic waveguide. In addition to the propagation in the interior of the ocean, sound can propagate into and back out of the ocean bottom as well as scatter from the ocean surface. Just as the sound produced by a loudspeaker in a room is affected by the walls of the room, so the ocean boundaries and the material properties below the ocean bottom are essential ingredients in the problem."

Materials that can mold the ?ow of elastic waves of certain energy in certain directions are called phononic materials. The present thesis deals essentially with such phononic systems, which are structured in the mesoscale (\1 lm), and with their individual components. Such systems show interesting phononic properties in the hypersonic region, i.e., at frequencies in the GHz range. It is shown that colloidal systems are excellent model systems for the realization of such phononic materials. Therefore, different structures and particle architectures are investigated by Brillouin light scattering, the inelastic scattering of light by phonons. Both the mechanical properties of the individual colloidal particles, which manifest in their resonance vibrations (eigenmodes), as well as the acoustic propagation in colloidal structures have been investigated. The measurement of the eigenmodes allows for new insights into physical properties at the mesoscale, e.g., con?nement effects, copolymer behavior, or the non-destructive determination of nanomechanical properties of core-shell particles, supporting the working groups aim to achieve a deeper understanding of 'soft mechanics' at small length scales. Another novel contribution assigned to this thesis is the ?rst experimental rea- zation of a phononic band gap arising from the interaction of these particle - genmodes with the effective medium band (hybridization gap). This ?nding already gave new impulses to the whole ?eld of phononics.

Radar Array Processing presents modern techniques and methods for processingradar signals received by an array of antenna elements. With the recent rapid growth of the technology of hardware for digital signal processing, itis now possible to apply this to radar signals and thus to enlist the full power of sophisticated computational algorithms. Topics covered in detail here include: super-resolution methods of array signal processing as applied to radar, adaptive beam forming for radar, and radar imaging. This book will be of interest to researchers and studentsin the radar community and also in related fields such as sonar, seismology, acoustics and radio astronomy.

Quantum mechanics and the Schrodinger equation are the basis for the de scription of the properties of atoms, molecules, and nuclei. The development of reliable, meaningful solutions for the energy eigenfunctions of these many is a formidable problem. The usual approach for obtaining particle systems the eigenfunctions is based on their variational extremum property of the expectation values of the energy. However the complexity of these variational solutions does not allow a transparent, compact description of the physical structure. There are some properties of the wave functions in some specific, spatial domains, which depend on the general structure of the Schrodinger equation and the electromagnetic potential. These properties provide very useful guidelines in developing simple and accurate solutions for the wave functions of these systems, and provide significant insight into their physical structure. This point, though of considerable importance, has not received adequate attention. Here we present a description of the local properties of the wave functions of a collection of particles, in particular the asymptotic properties when one of the particles is far away from the others. The asymptotic behaviour of this wave function depends primarily on the separation energy of the outmost particle. The universal significance of the asymptotic behaviour of the wave functions should be appreciated at both research and pedagogic levels. This is the main aim of our presentation here."

This book had its conception when Dr. Gudkov visited me in Austin in the Fall of 1995 and urged me to join him in writing a review of the field of magnetoacoustic polarization phenomena. I protested that, although my students and I had done some early work on this topic, most of the later work was done by researchers at the Institute for Metal Physics and by other investigators in the former Soviet Union. He eventually persuaded me that my initial contribution and general experience with magnetoacoustic phenomena qualified me to serve as a co-author. When I considered the fact that the extensive exploration of magnetoacoustic phenomena in the former Soviet Union was relatively unknown to Western scientists, I agreed to work with him on this project. In order to make the material more accessible to nonspecialists, we have adopted consistent notation throughout the text and redrawn the figures from published papers in a consistent fashion. Because our two institutions lie on opposite sides of the world, we needed some financial support to bring the book to fruition. We are very grateful to the Science Program for International Collaboration of the North Atlantic Treaty Organization for financial support through Grant No. HTECH. CRG 951549. I have dedicated this book to my wife, Janie, in recognition of the support she has given me throughout my professional career. J. D.

Vibration and noise reduce the perceived quality, productivity, and efficiency of many and limit production speeds electromechanical systems. Vibration can cause defects during manufacturing and produce premature failure of finished products due to fa tigue. Potential contact with a vibrating system or hearing darnage from a noisy machine can produce a dangerous, unhealthy, and uncomfortable operating environ ment. Recent advances in computer technology have allowed the development of so phisticated electromechanical systems for the control of vibration and noise. The demanding specifications of many modern systems require higher performance than possible with the traditional, purely mechanical approaches of increasing system stiff ness or damping. Mechatronic systems that integrate computer software and hard ware with electromechanical sensors and actuators to control complex mechanical systems have been demonstrated to provide outstanding vibration and noise reduc tion. The current trends toward higher speed computation and lower cost, higher performance sensors and actuators indicate the continuing possibilities for this con trol approach in future applications."

My first encounter with the theory of harmony was during my last year at school (1975). This fascinating system of rules crystallized the intuitive knowledge of harmony I had acquired from years of piano playing, and facilitated memorization, transcription, arrangement and composition. For the next five years, I studied music (piano) and science (Physics) at the Univer sity of Melbourne. This "strange combination" started me wondering about the origins of those music theory "rules." To what extent were they determined or influenced by physics? mathematics? physiology? conditioning? In 1981, the supervisor of my honours project in musical acoustics, Neville Fletcher, showed me an article entitled "Pitch, consonance, and harmony," by a certain Ernst Terhardt of the Technical University of Munich. By that stage, I had devoured a considerable amount of (largely unsatisfactory) material on the nature and origins of harmony, which enabled me to recognize the significance of Terhardt's article. But it was not until I arrived in Munich the following year (on Terhardt's invitation) that I began to appreciate the conse quences of his "psychoacoustical" approach for the theory of harmony. That is what this book is about. The book presents Terhardt's work against the broad context of music perception research, past and present. Music perception is a multidisciplinary mixture of physics, psychology and music. Where different theoretical ap proaches appear contradictory, I try to show instead that they complement and enrich one another."

Thirty years ago pattern recognition was dominated by the learning machine concept: that one could automate the process of going from the raw data to a classifier. The derivation of numerical features from the input image was not considered an important step. One could present all possible features to a program which in turn could find which ones would be useful for pattern recognition. In spite of significant improvements in statistical inference techniques, progress was slow. It became clear that feature derivation was a very complex process that could not be automated and that features could be symbolic as well as numerical. Furthennore the spatial relationship amongst features might be important. It appeared that pattern recognition might resemble language analysis since features could play the role of symbols strung together to form a word. This led. to the genesis of syntactic pattern recognition, pioneered in the middle and late 1960's by Russel Kirsch, Robert Ledley, Nararimhan, and Allan Shaw. However the thorough investigation of the area was left to King-Sun Fu and his students who, until his untimely death, produced most of the significant papers in this area. One of these papers (syntactic recognition of fingerprints) received the distinction of being selected as the best paper published that year in the IEEE Transaction on Computers. Therefore syntactic pattern recognition has a long history of active research and has been used in industrial applications.

Principles of Statistical Radiophysics is concerned with the theory of random func tions (processes and fields) treated in close association with a number of applications in physics. Primarily, the book deals with radiophysics in its broadest sense, i.e., l viewed as a general theory of oscillations and waves of any physical nature * This translation is based on the second (two-volume) Russian edition. It appears in four volumes: 1. Elements of Random Process Theory 2. Correlation Theory of Random Processes 3. Elements of Random Fields 4. Wave Propagation Through Random Media. The four volumes are, naturally, to a large extent conceptually interconnected (being linked, for instance, by cross-references); yet for the advanced reader each of them might be of interest on its own. This motivated the division of the Principles into four separate volumes. The text is designed for graduate and postgraduate students majoring in radio physics, radio engineering, or other branches of physics and technology dealing with oscillations and waves (e.g., acoustics and optics). As a rule, early in their career these students face problems involving the use of random functions. The book pro vides a sound basis from which to understand and solve problems at this level. In addition, it paves the way for a more profound study of the mathematical theory, should it be necessary2. The reader is assumed to be familiar with probability theory.

In this volume, the shock compression technology of materials is described in parallel with the latest research results and their background. In the past, this type of technology was developed in connection with military techniques by certain particular research organizations. For this reason, researchers of materials in general have had less opportunity to make use of the technology. The conventional technology of shock compression has now been established, and is recognized as being remarkably useful as a means of materials science study. The feasibility of shock compression technology is dealt with in this book, as well as the latest research results for general material scientists. The shock synthesis of ceramics and intermetallic compounds, as well as shock compression behavior, are also described. In contrast to conventional works of this kind, this book describes shock compression studies performed by material scientists.

The increasing prevalence of musical stimulation in our everyday environment makes studies of musical listening, comprehension and memory important. Music has simply become a pervasive aspect of the experienced environment for most of us; along with enhanced levels of machine sounds, musical sound sources are contributing to a virtual transformation of contemporary soundscapes occurring in many industrial countries. In spite of such trends, arguably the mainstream research in psychology and related fields has been slow to devote concentrated attention to this phenomenon and what it might mean. As a result, with respect to more established fields of research (e.g., visual perception, speech perception, attention and memory etc.), less is known about how people perceive and respond to complex, non-random, acoustic signals found in musical events. Although these topics reside in the domain of music research, this field is a relatively new one, with a history that dates back only about 25 years. Nevertheless, it is now a vibrant and rapidly growing field that draws from multiple disciplines (psychology, psychoacoustics, computer science, music theory, and so forth) to seek answers to questions about how we listen to musical events in our world. It tackles questions about pitch perception in complex patterns, about the role of tonal schemes as well as effects of metrical and rhythmic schemes on musical listening behaviors. It also examines abilities of children and adults to perceive and comprehend dynamic sound patterns. Emotional responses to music are also studied; and overarching all of this are exciting new neuroscience findings concerned with neural responses to musical events.

Music Perception introduces its audience to these and related basic issues concerned with listening to music. It also illustrates how knowledge about music perception may ultimately lead to a broader understanding of conventional concepts regarding perception, attention and memory.

In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the meth ods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those pUblications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections."

Recently, there have been significant advances in the fields of high-enthalpy hypersonic flows, high-temperature gas physics, and chemistry shock propagation in various media, industrial and medical applications of shock waves, and shock-tube technology. This series contains all the papers and lectures of the 19th International Symposium on Shock Waves held in Marseille in 1993. They are published in four topical volumes, each containing papers on related topics, and preceded by an overview written by a leading international expert. The volumes may be purchased independently.

In the past fi fteen years there has been a growi ng interest in the development of children's awareness of language as an object in itself -- a phenomenon now generally referred to as metal inguistic awareness. Until the publication of an earlier volume in the Springer Series in Language and Communication, The Chitd's Conoeption oi Language, edited by A. Sinclair, R. J. Jarvella, and W. J. M. Levelt, there had been no systematic treatment of metalinguistic awareness. The major goal of that volume was to map out the field of study by describing the phenomenon of interest and defining major theoretical issues. The aim of the present volume is to present an overview of metalinguistic awareness in children which reflects the current state of research and theory. The volume is divided into three major sections. The first considers various conceptual and methodological issues that have arisen from efforts to study metalinguistic awareness. It addresses such questions as what is metalinguistic awareness, when does it begin to emerge, and what tasks and procedures can be employed to assess its development in young children. The second sect ion cri ti ca 11y revi ews the research that has been conducted i nto the four general types of metalinguistic awareness -- phonologieal, word, syntactic, and pragmatic awareness. In the final section the development of metalinguistic awareness is examined in relation to general cognitive development, reading acquisition, bilingualism, and early childhood education.

For four decades, information theory has been viewed almost exclusively as a theory based upon the Shannon measure of uncertainty and information, usually referred to as Shannon entropy. Since the publication of Shannon's seminal paper in 1948, the theory has grown extremely rapidly and has been applied with varied success in almost all areas of human endeavor. At this time, the Shannon information theory is a well established and developed body of knowledge. Among its most significant recent contributions have been the use of the complementary principles of minimum and maximum entropy in dealing with a variety of fundamental systems problems such as predic tive systems modelling, pattern recognition, image reconstruction, and the like. Since its inception in 1948, the Shannon theory has been viewed as a restricted information theory. It has often been argued that the theory is capable of dealing only with syntactic aspects of information, but not with its semantic and pragmatic aspects. This restriction was considered a v~rtue by some experts and a vice by others. More recently, however, various arguments have been made that the theory can be appropriately modified to account for semantic aspects of in formation as well. Some of the most convincing arguments in this regard are in cluded in Fred Dretske's Know/edge & Flow of Information (The M.LT. Press, Cambridge, Mass., 1981) and in this book by Guy lumarie.

This book studies language behaviour in the larger context of modelling or ganismic behaviour more generally. It starts out from the basic premise that what is characteristic of organismic behaviour is that an organism uses its behavioural acts to accomplish something in its interactions with the world in which it finds itself. These two features, that an organism has a behav ioural repertoire and that it deploys specific behavioural acts from its repertoire in an intentional way, define the agentive nature of an organism. The study of organismic behaviour, then, must primarily concern itself with this agentive aspect of an organism and determine what structures and proces ses underlie these intentional organismic acts. We should be able to say what primitive structures and what primitive processes put together in what ways can give rise to the kinds of behavioural acts an organism engages in. Any explanation of behaviour that we formulate in terms of underlying structures and processes must be testable and must be consonant with the observed pheno menological aspects of such behaviour."

For a system consisting of a random medium with rough boundaries, the governing (Bethe-Salpeter) equation for boundary-value transport problems can be written in a form such that the medium and the boundaries are treatedon an equal footing. This enables several expressions for the solution to be obtained by interchanging the roles of the medium and the boundaries, thus allowing the most convenient one to be selected according to the specific situation and the information required. This book presents a unified theory based on the Bethe-Salpeter equation with particular attention being paid to: boundary-value problems of transport, layer problems, a fixed scatterer imbedded in a bounded random medium, construction of an optical scattering matrix for a complete system, and optical wave propagation in a turbulent medium. The last topic is treated in terms of first moment equations combined with the cluster expansion and, second, the two-scale method based on the Lagrange variational principle.