The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

The dynamics of many nonlinear systems gravitate around a few common central themes: intermittency, order/coherence and disorder. These features affect scalings and lead to deviations from Gaussian behaviour. Intermittency may be the universal outcome of a large class of nonlinear systems; however the universality properties of specific nonlinear systems, that is the dependencies of the intermittent structure on initial and boundary conditions, remain open questions. This volume consists of articles by prominent figures who all participated in a workshop held at the Newton Institute in Cambridge. It reflects the aims of the workshop, namely to capture and summarise recent developments, encourage cross-fertilisation of ideas, lay out research directions for the future and provide an overview of our current understanding of the subject.

The ocean is transparent to sound where slight irregularities within the ocean cause sound fluctuations, and thus set limits on the many uses of sound in the ocean, similar to the limits imposed by the atmosphere on ground-based telescopes. This 1979 book attempts to connect the known structure of the ocean volume with experimental results in long-range sound transmission. Theories of wave propagation through irregular media, developed for optical and radio wave transmission are found to be inapplicable in many respects due to the complications of ocean structure, particularly the combination of anisotropy and 'sound channel'. The authors extend wave propagation theory to account for the ocean complications and introduces the path-integral approach to the solution of the strong-scattering regime that solves many long-standing problems. The book is written at the post-graduate level, but has been carefully organised to give experimenters a grasp of important results without undue mathematics.

Many of the significant issues in fluid dynamics occur at interfaces, that is, at the boundaries between differing fluids or between fluids and solids. These issues are important in areas ranging from aircraft flight, to the flow of blood in the heart, to chemical vapour deposition. The subject is an area of active research and development, owing to improved analytical, experimental, and computational techniques. This book describes research and applications in interfacial fluid dynamics and stability. It is organized around five topics: Benard and thermocapillary instabilities, shear and pressure induced instabilities, waves and dispersions, multiphase systems, and complex flows. Chapters have been contributed by internationally recognized experts, both theoreticians and experimentalists. Because of the range and importance of topics discussed, this book will interest a broad audience of graduate students and researchers in mechanical, aerospace, materials, and chemical engineering, as well as in applied mathematics and physics.

The large number of text books on the theory of sound deal principally with periodic disturbances such as harmonic wave trains and standing waves and give scant attention to aperiodic disturbances with clearly defined fronts, conveniently called sound pulses. This monograph attempts to fill this gap by providing an up-to-date description of the theory of sound pulses and its developments. The treatment is based on the thoery of linear partial differential equations of hyperbolic type - a method which is frequently simpler and more effective than the commoner one of resolving the pulse into harmonic components by Fourier analysis; this is especially true of any treatment of pulse fronts as wave fronts in the sense of geometrical optics. The individual chapters deal with the equations of motion, wave fronts and characteristics, geometrical acoustics and their application to reflection problems and the diffraction of a pulse by a wedge, circular cylinder, sphere and other objects. The book will also be of interest to readers concerned with other aspects of wave propagation, such as electromagnetic waves.

Time series with mixed spectra are characterized by hidden periodic components buried in random noise. Despite strong interest in the statistical and signal processing communities, no book offers a comprehensive and up-to-date treatment of the subject. Filling this void, Time Series with Mixed Spectra focuses on the methods and theory for the statistical analysis of time series with mixed spectra. It presents detailed theoretical and empirical analyses of important methods and algorithms. Using both simulated and real-world data to illustrate the analyses, the book discusses periodogram analysis, autoregression, maximum likelihood, and covariance analysis. It considers real- and complex-valued time series, with and without the Gaussian assumption. The author also includes the most recent results on the Laplace and quantile periodograms as extensions of the traditional periodogram. Complete in breadth and depth, this book explains how to perform the spectral analysis of time series data to detect and estimate the hidden periodicities represented by the sinusoidal functions. The book not only extends results from the existing literature but also contains original material, including the asymptotic theory for closely spaced frequencies and the proof of asymptotic normality of the nonlinear least-absolute-deviations frequency estimator.

This volume represents the findings of the first test cases considered by ERCOFTAC (European Research Consortium on Flow Turbulence and Combustion). The workshop, held in Lausanne, Switzerland, in 1990, studied five test cases: boundary layer in an S-shaped duct; periodic array of cylinders; transition in a boundary layer under the influence of free-stream turbulence; axisymmetric confined jet flows. These test cases represented the interests of both the academic and industrial groups in finding out the limits of various models and codes to predict real problems supported by experimental data. The articles summarise the work of each group and point to refinements and further study to perfect the models. As such there will be much of interest to all professionals and researchers concerned with the prediction of flows and turbulence.

Acoustics of Fluid-Structure Interactions addresses an increasingly important branch of fluid mechanics - the absorption of noise and vibration by fluid flow. This subject, which offers numerous challenges to conventional areas of acoustics, is of growing concern in places where the environment is adversely affected by sound. Howe presents useful background material on fluid mechanics and the elementary concepts of classical acoustics and structural vibrations. Using examples, many of which include complete worked solutions, he vividly illustrates the theoretical concepts involved. He provides the basis for all calculations necessary for the determination of sound generation by aircraft, ships, general ventilation and combustion systems, as well as musical instruments. Both a graduate textbook and a reference for researchers, Acoustics of Fluid-Structure Interactions is an important synthesis of information in this field. It will also aid engineers in the theory and practice of noise control.

The study of vibration in physical systems is central to almost all fields in physics and engineering. This work, originally published in two volumes, examines the classical aspects in Part I and the quantum oscillator in Part II. The classical linear vibrator is treated first and the underlying unity of all linear oscillations in electrical, mechanical and acoustic systems is emphasized. The treatment of nonlinear vibrations, a field with which engineers and physicists are generally less familiar, is then examined. Part II then concentrates on quantum systems, looking at the vibrations in atoms and molecules and their interaction with electromagnetic radiation. The similarities of classical and quantum methods are stressed and the limits of the classical treatment are examined. Throughout the book, each phenomenon discussed is well illustrated with many examples; and theory and experiment are compared. This is a useful introduction to the more advanced mathematical treatment of vibrations as it bridges the gap between the basic principles and more specialized concepts.

This highly informative and fascinating book brings together perspectives on sound by leading experts from a wide variety of disciplines. These include anthropology, physiology, zoology, physics, music, phonetics and film. Through crossing disciplinary boundaries, the volume hopes to inspire a richer and more creative approach to the acoustic world. Whilst aiming for a general audience and presented in an accessible style, several chapters also represent important contributions within their own disciplines or will serve as core texts for students. The sequence of nine chapters passes from cultural perspectives on silence, via the physics of sound, physiology of the ear, songs of birds, and sounds of human speech, to music. From the reconstruction of medieval music, via twentieth-century composition and the music of the Kaluli of Papua New Guinea, the volume concludes with the role of sound in film. Life will never sound the same again.

Reactive flows encompass a broad range of physical phenomena, interacting over many different time and space scales. Such flows occur in combustion, chemical lasers, the earth's oceans and atmosphere, and in stars. Because of a similarity in their descriptive equations, procedures for constructing numerical models of these systems are also similar, and these similarities can be exploited. Moreover, using the latest technology, what were once difficult and expensive computations can now be done on desktop computers. This new edition of a highly successful book presents algorithms useful for reactive flow simulations, describes trade-offs involved in their use, and gives guidance for building and using models of complex reactive flows. It takes account of the explosive growth in computer technology and the greatly increased capacity for solving complex reactive-flow problems that has occurred since the previous edition was published more than fifteen years ago. An indispensable guide on how to construct, use, and interpret numerical simulations of reactive flows, this book will be welcomed by advanced undergraduate and graduate students, and a wide range of researchers and practitioners in engineering, physics, and chemistry.

Gravitational radiation has not been positively detected. Over the past two decades an army of extremely sensitive detectors has been built up, so that today its detection appears inevitable. In the opening chapters of this 1991 book David Blair introduces the concepts of gravitational waves within the context of general relativity. The sources of gravitational radiation for which there is direct observational evidence and those of a more speculative nature are described. He then gives a general introduction to the methods of detection. In the subsequent chapters he has drawn together the leading scientists in the field to give a comprehensive practical and theoretical account of the physics and technology of gravitational wave detection. David Blair has extensive knowledge of the subject and has visited most of the gravitational radiation experiments over the world. He has compiled a book which will be of lasting value to specialists, both the postgraduates and researchers in the field.

From Edison's invention of the phonograph through contemporary field recording and sound installation, artists have become attracted to those domains against which music has always defined itself: noise, silence, and environmental sound. Christoph Cox argues that these developments in the sonic arts are not only aesthetically but also philosophically significant, revealing sound to be a continuous material flow to which human expressions contribute but which precedes and exceeds those expressions. Cox shows how, over the course of the twentieth and twenty-first centuries, philosophers and sonic artists have explored this "sonic flux." Through the philosophical analysis of works by John Cage, Maryanne Amacher, Max Neuhaus, Christian Marclay, and many others, Sonic Flux contributes to the development of a materialist metaphysics and poses a challenge to the prevailing positions in cultural theory, proposing a realist and materialist aesthetics able to account not only for sonic art but for artistic production in general.

This is an introduction to the branch of fluid mechanics concerned with the production of sound by hydrodynamic flows. It is designed for a one semester introductory course at the advanced undergraduate or graduate level. Great care is taken to explain underlying fluid mechanical and acoustic concepts, and to describe fully the steps in a complicated derivation. The discussion deals specifically with low Mach number flows, which enables the sound produced by `vortex-surface' interactions to be analyzed using the `compact Green's function'. This provides a routine procedure for estimating the sound, and an easy identification of those parts of a structure that are likely to be important sources of sound.

This book gathers contributions on various aspects of the theory and applications of linear and nonlinear waves and associated phenomena, as well as approaches developed in a global partnership of researchers with the national Centre of Excellence in Nonlinear Studies (CENS) at the Department of Cybernetics of Tallinn University of Technology in Estonia. The papers chiefly focus on the role of mathematics in the analysis of wave phenomena. They highlight the complexity of related topics concerning wave generation, propagation, transformation and impact in solids, gases, fluids and human tissues, while also sharing insights into selected mathematical methods for the analytical and numerical treatment of complex phenomena. In addition, the contributions derive advanced mathematical models, share innovative ideas on computing, and present novel applications for a number of research fields where both linear and nonlinear wave problems play an important role. The papers are written in a tutorial style, intended for non-specialist researchers and students. The authors first describe the basics of a problem that is currently of interest in the scientific community, discuss the state of the art in related research, and then share their own experiences in tackling the problem. Each chapter highlights the importance of applied mathematics for central issues in the study of waves and associated complex phenomena in different media. The topics range from basic principles of wave mechanics up to the mathematics of Planet Earth in the broadest sense, including contemporary challenges in the mathematics of society. In turn, the areas of application range from classic ocean wave mathematics to material science, and to human nerves and tissues. All contributions describe the approaches in a straightforward manner, making them ideal material for educational purposes, e.g. for courses, master class lectures, or seminar presentations.

Interfacial fluid dynamics is important in areas ranging from the flight of an aircraft to the flow of blood in the heart, and an area of active research and development owing to improved analytical, experimental, and computational techniques. This book describes the latest methods and applications in the field. Written by an internationally recognized panel of experts in both theory and experimentation, coverage is organized around five topics: Benard and thermocapillary instabilities, shear and pressure induced instabilities, waves and dispersions, multiphase systems, and complex flows. This comprehensive volume will interest a broad audience of graduate students, faculty, and researchers in mechanical, aerospace, materials, and chemical engineering, as well as in applied mathematics and physics.

The investigation of nonlinear phenomena in acoustics has a rich history stretching back to the mechanical physical sciences in the nineteenth century. The study of nonlinear phenomena, such as explosions and jet engines, prompted the sharp growth of interest in nonlinear acoustic phenomena. The authors consider models of different 'acoustic' media as well as equations and behaviour of finite-amplitude waves. Consideration is given to the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction upon the evolution and interaction of acoustic beams. This book will be of interest not only to specialists in acoustics, but also to a wide audience of mathematicians, physicists, and engineers working on nonlinear waves in various physical systems.

The investigation of nonlinear phenomena in acoustics has a rich history stretching back to the mechanical physical sciences in the nineteenth century. The study of nonlinear phenomena, such as explosions and jet engines, prompted the sharp growth of interest in nonlinear acoustic phenomena. In this book, the authors consider models of different "acoustic" media as well as equations and behavior of finite-amplitude waves. The authors also consider the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction on the evolution and interaction of acoustic beams. This book will be of interest not only to specialists in acoustics, but also to a wide audience of mathematicians, physicists, and engineers working on nonlinear waves in various physical systems.

This book explores the fascinating and intimate relationship between music and physics. Over millennia, the playing of, and listening to music have stimulated creativity and curiosity in people all around the globe. Beginning with the basics, the authors first address the tonal systems of European-type music, comparing them with those of other, distant cultures. They analyze the physical principles of common musical instruments with emphasis on sound creation and particularly charisma. Modern research on the psychology of musical perception - the field known as psychoacoustics - is also described. The sound of orchestras in concert halls is discussed, and its psychoacoustic effects are explained. Finally, the authors touch upon the role of music for our mind and society. Throughout the book, interesting stories and anecdotes give insights into the musical activities of physicists and their interaction with composers and musicians.

Many of the topics in inviscid fluid dynamics are not only vitally important mechanisms in everyday life but they are also readily observable without any need for instrumentation. It is therefore stimulating when the mathematics that emerges when these phenomena are modelled is novel and suggestive of alternative methodologies. This book provides senior undergraduates who are already familiar with inviscid fluid dynamics with some of the basic facts about the modelling and analysis of viscous flows. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be ideal reading for students of applied mathematics who should then be able to delve further into the subject and be well placed to exploit mathematical ideas throughout the whole of applied science.

Many of the topics in inviscid fluid dynamics are not only vitally important mechanisms in everyday life but they are also readily observable without any need for instrumentation. It is therefore stimulating when the mathematics that emerges when these phenomena are modelled is novel and suggestive of alternative methodologies. This book provides senior undergraduates who are already familiar with inviscid fluid dynamics with some of the basic facts about the modelling and analysis of viscous flows. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be ideal reading for students of applied mathematics who should then be able to delve further into the subject and be well placed to exploit mathematical ideas throughout the whole of applied science.

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

This volume represents the findings of the first test cases considered by ERCOFTAC (European Research Consortium on Flow Turbulence and Combustion). The workshop, held in Lausanne, Switzerland, in 1990, studied five test cases: boundary layer in an S-shaped duct; periodic array of cylinders; transition in a boundary layer under the influence of free-stream turbulence; axisymmetric confined jet flows. These test cases represented the interests of both the academic and industrial groups in finding out the limits of various models and codes to predict real problems supported by experimental data. The articles summarise the work of each group and point to refinements and further study to perfect the models. As such there will be much of interest to all professionals and researchers concerned with the prediction of flows and turbulence.