A color time-varying image can be described as a three-dimensional vector (representing the colors in an appropriate color space) defined on a three-dimensional spatiotemporal space. In conventional analog television a one-dimensional signal suitable for transmission over a communication channel is obtained by sampling the scene in the vertical and tem poral directions and by frequency-multiplexing the luminance and chrominance informa tion. In digital processing and transmission systems, sampling is applied in the horizontal direction, too, on a signal which has been already scanned in the vertical and temporal directions or directly in three dimensions when using some solid-state sensor. As a conse quence, in recent years it has been considered quite natural to assess the potential advan tages arising from an entire multidimensional approach to the processing of video signals. As a simple but significant example, a composite color video signal, such as the conven tional PAL or NTSC signal, possesses a three-dimensional spectrum which, by using suitable three-dimensional filters, permits horizontal sampling at a rate which is less than that re quired for correctly sampling the equivalent one-dimensional signal. More recently it has been widely recognized that the improvement of the picture quality in current and advanced television systems requires well-chosen signal processing algorithms which are multidimen sional in nature within the demanding constraints of a real-time implementation."

Writing a new book on the classic subject of Special Relativity, on which numerous important physicists have contributed and many books have already been written, can be like adding another epicycle to the Ptolemaic cosmology. Furthermore, it is our belief that if a book has no new elements, but simply repeats what is written in the existing literature, perhaps with a different style, then this is not enough to justify its publication. However, after having spent a number of years, both in class and research with relativity, I have come to the conclusion that there exists a place for a new book. Since it appears that somewhere along the way, mathem- ics may have obscured and prevailed to the degree that we tend to teach relativity (and I believe, theoretical physics) simply using "heavier" mathematics without the inspiration and the mastery of the classic physicists of the last century. Moreover current trends encourage the application of techniques in producing quick results and not tedious conceptual approaches resulting in long-lasting reasoning. On the other hand, physics cannot be done a la carte stripped from philosophy, or, to put it in a simple but dramatic context A building is not an accumulation of stones As a result of the above, a major aim in the writing of this book has been the distinction between the mathematics of Minkowski space and the physics of r- ativity."

This book gives a systematic investigation of convection in systems comprised of liquid layers with deformatable interfaces.

This new edition includes completely updated and new material on flows in ultra thin films and brings up to date progress made in the technology on micro and nano scales. Also, this revised edition will reflect progress in thedynamics of complex fluids."

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.

Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D."

Written for an interdisciplinary readership of physicists, engineers, and chemists, this book is a practical guide to the fascinating world of solitons. These waves of large amplitude propagate over long distances without dispersing and therefore show one of the most striking aspects of nonlinearity. The author addresses students, practitioners, and researchers, approaching the subject from the standpoint of applications in optics, hydrodynamics, and electrical and chemical engineering. The book also encourages readers to perform their own experiments. Since the printing of the second edition of this book, there has been a large growth in the literature on nonlinear waves and so has the wide applicability of the subject to the physical, chemical and biological sciences. This third edition has been thoroughly revised. Some of the topics are brought up to date with pertinent references. Furthermore, the book now includes a completely new chapter on solitary waves in diffuse systems.

Turbulence and the associated turbulent transport of scalar and vector fields is a classical physics problem that has dazzled scientists for over a century, yet many fundamental questions remain. Igor Rogachevskii, in this concise book, systematically applies various analytical methods to the turbulent transfer of temperature, particles and magnetic field. Introducing key concepts in turbulent transport including essential physics principles and statistical tools, this interdisciplinary book is suitable for a range of readers such as theoretical physicists, astrophysicists, geophysicists, plasma physicists, and researchers in fluid mechanics and related topics in engineering. With an overview to various analytical methods such as mean-field approach, dimensional analysis, multi-scale approach, quasi-linear approach, spectral tau approach, path-integral approach and analysis based on budget equations, it is also an accessible reference tool for advanced graduates, PhD students and researchers.

Condensing 40 years of teaching experience, this unique textbook will provide students with an unrivalled understanding of the fundamentals of fluid mechanics, and enable them to place that understanding firmly within a biological context. Each chapter introduces, explains, and expands a core concept in biofluid mechanics, establishing a firm theoretical framework for students to build upon in further study. Practical biofluid applications, clinical correlations, and worked examples throughout the book provide real-world scenarios to help students quickly master key theoretical topics. Examples are drawn from biology, medicine, and biotechnology with applications to normal function, disease, and devices, accompanied by over 500 figures to reinforce student understanding. Featuring over 120 multicomponent end-of-chapter problems, flexible teaching pathways to enable tailor-made course structures, and extensive Matlab and Maple code examples, this is the definitive textbook for advanced undergraduate and graduate students studying a biologically-grounded course in fluid mechanics.

This technical book considers the application side of LDA techniques. Starting from the basic theories that are crucial for each LDA user, the main subject of the book is focused on diverse application methods. In details, it deals with universal methodical techniques that have been mostly developed in the last 15 years. The book thus gives for the first time an application reference for LDA users in improving the optical conditions and enhancing the measurement accuracies. It also provides the guidelines for simplifying the measurements and correcting measurement errors as well as for clarifying the application limits and extending the application areas of LDA techniques. Beside the treatments of some traditional optical and flow mechanical features influencing the measurement accuracies, the book shows a broad spectrum of LDA application methods in the manner of measuring the flow turbulence, resolving the secondary flow structures, and quantifying the optical aberrations at measurements of internal flows etc.. Thus, it also supports the further developments of both the hard- and software of LDA instrumentations.

The book unifies classical continuum mechanics and turbulence modeling, i.e. the same fundamental concepts are used to derive model equations for material behaviour and turbulence closure and complements these with methods of dimensional analysis. The intention is to equip the reader with the ability to understand the complex nonlinear modeling in material behaviour and turbulence closure as well as to derive or invent his own models. Examples are mostly taken from environmental physics and geophysics.

This open access book provides a view into the state-of-the-art research on aviation noise and related annoyance. The book will primarily focus on the achievements of the ANIMA project (Aviation Noise Impact Management through Novel Approaches), but not exclusively. The content has a broader theme in order to encompass. regulation issues, the ICAO (International Civil Aviation Organization) balanced approach, progresses made on technologies and reduction of noise at source, impact of possible future civil supersonic aircraft, land-use planning issues, as well as the core topics of the ANIMA project, i.e. impact on human beings, annoyance, quality of life, health and findings of the project in this respect. This book differs from traditional research programmes on aviation noise as the authors endeavour, not to lower noise at source, but to reduce the annoyance. This book examines these non-acoustic factors in an effort to help those most affected by aviation noise - communities living close to airports, and also help airport managers, policy-makers, local authorities and researchers to deal with this issue holistically. The book concludes with some recommendations for EU, national and local policy-makers, airport and aviation authorities, and more broadly a scientifically literate audience. These recommendations may help to identify gaps for progress in terms of research but also genuine implementation actions for political and regulatory authorities.

Dynamics of Ice Sheets and Glaciers presents an introduction to the dynamics and thermodynamics of flowing ice masses on Earth. Based on an outline of general continuum mechanics, the different initial-boundary-value problems for the flow of ice sheets, ice shelves, ice caps and glaciers are systematically derived. Special emphasis is put on developing hierarchies of approximations for the different systems, and suitable numerical solution techniques are discussed. A separate chapter is devoted to glacial isostasy. The book is appropriate for graduate courses in glaciology, cryospheric sciences, environmental sciences, geophysics and related fields. Standard undergraduate knowledge of mathematics (calculus, linear algebra) and physics (classical mechanics, thermodynamics) provide a sufficient background for successfully studying the text.

This concise textbook develops step by step the fundamental principles of continuum mechanics. Emphasis is on mathematical clarity, and an extended appendix provides the required background knowledge in linear algebra and tensor calculus. After introducing the basic notions about general kinematics, balance equations, material objectivity and constitutive functions, the book turns to the presentation of rational thermodynamics by stressing the role of Lagrange multipliers in deriving constitutive funcitions from the underlying entropy principle. A brief lecture on extended thermodynamics closes the book. Many examples and exercises round off the material presented in the chapters. The book addresses primarily advanced undergraduate students in theoretical physics, applied mathematics and materials sciences.

Crystal growth, casting, soldering, welding, high-energy surface treatment, nuclear safety systems and geophysical flows are just a few examples where solidification and convection occur together. These processes are interactive on micro- and macroscales: flow affects the distribution of heat and species and hence the freezing process, while solidification evolves flow boundaries, as in crusting, for example, and hence can radically alter the convection. Mathematical modellers, experimentalists and applied scientists were invited to this colloquium with the aim of consolidating our understanding of such interactions, of identifying key outstanding issues, and of developing new approaches in this important area of fundamental research. Both invited and contributed papers focus on both fundamental and technologically relevant problems.

This book presents problems and solutions of the mathematical theories of thermoelasticity and magnetothermoelasticity. The classical, coupled and generalized theories are solved using the eigenvalue methodology. Different methods of numerical inversion of the Laplace transform are presented and their direct applications are illustrated. The book is very useful to those interested in continuum mechanics.

This book addresses supergravity and supergravity-motivated effective field theories in the context of cosmological model building. Extracting information about quintessence from string theory has attracted much attention in the past few years. The question became more urgent very recently after the possibility of obtaining de Sitter space was called into question. Therefore, there is an interesting debate as to whether de Sitter space or, even, quintessence can be derived from a fundamental theory, string theory or otherwise. This is a very active field of research, and the topics covered in the book render this work very timely. Throughout the book, special care has been taken in demonstrating historical relevance of the field and describing the set of open questions motivating the state-of-the-art research. The first few chapters in each part provide a detailed review of standard perturbative and non-perturbative techniques in supergravity model building, as a way to prepare the reader for the more technical and original subsequent chapters. These early chapters also represent a self-contained review that would be useful for anyone planning to enter this challenging area of study. The subsequent chapters detail research in supergravity-motivated effective field theories, in the first part, and supergravity models, in the second part. One of the important conclusions in this book is that modelling quintessence in perturbative string theory is at least as challenging as modelling de Sitter, placing the wider programme on a collision course with observations.

This book grew out of lectures on geophysical fluid dynamics delivered over many years at the Moscow Institute of Physics and Technology by the author (and, with regard to some parts of the book, by his colleagues). During these lectures the students were advised to read many books, and sometimes individual articles, in order to acquaint themselves with the necessary material, since there was no single book available which provided a sufficiently complete and systematic account (except, perhaps, the volumes on Hydrophysics of the Ocean, Hydrodynamics of the Ocean, and Geodynamics in the ten-volume Oceanology series published by Nauka Press in 1978-1979; these refer, however, specifically to the ocean, and anyway they are much too massive to be convenient for study by students). As far as we know, no text corresponding to our understanding of geophysical fluid dynamics has as yet been published outside the Soviet Union. The present book is designed to fill this gap. Since it is customary to write the preface after the entire book has been completed, the author has an opportunity there to raise some points of possible criticism by the reviewers and readers. First of all, note that this work presents the theoretical fundamentals of geophysical fluid dynamics, and that observational and experimental data (which in the natural sciences are always very copious) are referred to only rarely and briefly.

foundations of duct acoustics to the acoustic design of duct systems, through practical modeling, optimization and measurement techniques. Discover in-depth analyses of one- and three-dimensional models of sound generation, propagation and radiation, as techniques for assembling acoustic models of duct systems from simpler components are described. Identify the weaknesses of mathematical models in use and improve them by measurement when needed. Cope with challenges in acoustic design, and improve understanding of the underlying physics, by using the tools described. An essential reference for engineers and researchers who work on the acoustics of fluid machinery ductworks.

The thesis tackles two distinct problems of great interest in gravitational mechanics - one relativistic and one Newtonian. The relativistic one is concerned with the "first law of binary mechanics", a remarkably simple variational relation that plays a crucial role in the modern understanding of the gravitational two-body problem, thereby contributing to the effort to detect gravitational-wave signals from binary systems of black holes and neutron stars. The work reported in the thesis provides a mathematically elegant extension of previous results to compact objects that carry spin angular momentum and quadrupolar deformations, which more accurately represent astrophysical bodies than mere point particles. The Newtonian problem is concerned with the isochrone problem of celestial mechanics, namely the determination of the set of radial potentials whose bounded orbits have a radial period independent of the angular momentum. The thesis solves this problem completely in a geometrical way and explores its consequence on a variety of levels, in particular with a complete characterisation of isochrone orbits. The thesis is exceptional in the breadth of its scope and achievements. It is clearly and eloquently written, makes excellent use of images, provides careful explanations of the concepts and calculations, and it conveys the author's personality in a way that is rare in scientific writing, while never sacrificing academic rigor.

A description of the theoretical foundations of inelasticity, its numerical formulation and implementation, constituting a representative sample of state-of-the-art methodology currently used in inelastic calculations. Among the numerous topics covered are small deformation plasticity and viscoplasticity, convex optimisation theory, integration algorithms for the constitutive equation of plasticity and viscoplasticity, the variational setting of boundary value problems and discretization by finite element methods. Also addressed are the generalisation of the theory to non-smooth yield surface, mathematical numerical analysis issues of general return mapping algorithms, the generalisation to finite-strain inelasticity theory, objective integration algorithms for rate constitutive equations, the theory of hyperelastic-based plasticity models and small and large deformation viscoelasticity. Of great interest to researchers and graduate students in various branches of engineering, especially civil, aeronautical and mechanical, and applied mathematics.

One of the fundamental aspects of petroleum exploitation and production is that of petroleum engineering, ie the assessment and recovery of oil from the various types of oil 'reservoirs'. The importance of effective petroleum engineering has increased dramatically due to a number or of varying reasons. Firstly, recoverable oil reserves should be capable of extended life by application of efficient reservoir depletion methods. Secondly, the average recovery factor does not appear to have increased over the last three decades. Thirdly, the behaviour of reservoirs is still unpredictable in spite of the fact that the principles of oil recovery are better understood. Finally, there has been an enormous growth in the number of computer-based analysis techniques available to the engineer. These factors, taken in conjunction with the fact that many developments have been presented as unpublished papers, have highlighted the need for a series of volumes which will give the engineer a starting point for the collection of up-to-date information. This new series of volumes, Developments in Petroleum Engineering, is intended to fill this gap and will contain reviews of recent developments. The chapters are written by specialists at a level which summarises the progress, but does not necessarily cover every facet and detail, of a particular subject. Rather, they direct the reader to the most useful of the original sources.

Intended for a two-semester course. Chapters discuss linear, time invariant, continuous-time systems and discrete-time systems; the Fourier transform; the Laplace transform; analog filters; the discrete Fourier transform; the z-transform; and digital filters. Worked examples and exercises are includ

This book contains the papers that were accepted for presentation at the 1988 NATO Advanced Study Institute on Underwater Acoustic Data Processing, held at the Royal Military College of Canada from 18 to 29 July, 1988. Approximately 110 participants from various NATO countries were in attendance during this two week period. Their research interests range from underwater acoustics to signal processing and computer science; some are renowned scientists and some are recent Ph.D. graduates. The purpose of the ASI was to provide an authoritative summing up of the various research activities related to sonar technology. The exposition on each subject began with one or two tutorials prepared by invited lecturers, followed by research papers which provided indications of the state of development in that specific area. I have broadly classified the papers into three sections under the titles of I. Propagation and Noise, II. Signal Processing and III. Post Processing. The reader will find in Section I papers on low frequency acoustic sources and effects of the medium on underwater acoustic propagation. Problems such as coherence loss due to boundary interaction, wavefront distortion and multipath transmission were addressed. Besides the medium, corrupting noise sources also have a strong influence on the performance of a sonar system and several researchers described methods of modeling these sources.