Vortex flow is one of the fundamental types of fluid and gas motion. These flows are the most spectacular in the form of concentrated vortices, characterized by the localization of vorticity (curl of velocity) in bounded regions of a space, beyond which the vorticity is either absent or rapidly falls down to zero. Concentrated vortices are often observed in nature, exemplified by atmospheric cyclones, whirlwinds and tornados, oceanic vortices, whirlpools on a water s- face, and ring vortices caused by explosive outburst of volcanoes. In technical - vices concentrated vortices form when flow separates from sharp edges of flying vehicles and ships. Among these are vortices flowing off the ends of airplane wings, and intentionally generated vortices for intensification of burning in c- bustion chambers, vortices in cyclonic devices used for mixing or separation of impurities in fluids and gases. One such remarkable and frequent type of conc- trated vortices is a vortex ring which constitutes a vortex tube closed into a t- oidal ring moving in a surrounding fluid like an isolated body out of contact with solid boundaries of the flow region if such boundaries exist. Formation and motion of vortex rings are important part of the dynamics of a continuum medium and have been studied for more than a century.

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.

This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flows in clear and elementary terms. It begins with an introduction to the fundamentals of spectral methods and then moves on to cover, in particular, the Fourier and Chebyshev methods. Examples are included. Chapters 6 and 7 handle streamfunction-vorticity and velocity-pressure fomulations of the Navier-Stokes equations. Chapter 8 and 9 address special topics such as self- adaptive coordinate transform, treatment of singularities, and domain decomposition. The work will be useful to those teaching in the field at the graduate level, as well as to researchers working in the area.

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.

The main idea of the present study is to demonstrate that the qualitative theory of diffe rential equations, when applied to problems in fluid-and gasdynamics, will contribute to the understanding of qualitative aspects of fluid flows, in particular those concerned with geometrical properties of flow fields such as shape and stability of its streamline patterns. It is obvious that insight into the qualitative structure of flow fields is of great importance and appears as an ultimate aim of flow research. Qualitative insight fashions our know ledge and serves as a good guide for further quantitative investigations. Moreover, quali tative information can become very useful, especially when it is applied in close corres pondence with numerical methods, in order to interpret and value numerical results. A qualitative analysis may be crucial for the investigation of the flow in the neighbourhood of singularities where a numerical method is not reliable anymore due to discretisation er rors being unacceptable. Up till now, familiar research methods -frequently based on rigorous analyses, careful nu merical procedures and sophisticated experimental techniques -have increased considera bly our qualitative knowledge of flows, albeit that the information is often obtained indirectly by a process of a careful but cumbersome examination of quantitative data. In the past decade, new methods are under development that yield the qualitative infor mation more directly. These methods, make use of the knowledge available in the qualitative theory of differen tial equations and in the theory of bifurcations."

Thin shells are three-dimensional structures with a dimension (the thickness) small with respect to the two others.Such thin structures are widely used in automobileandaviation industries,or in civil engineering, because they provide animportantsti?ness, due to theircurvature,with a small weight. Fig. 0.1. Airbus A380 Fig. 0.2. Hemispherical roof (Marseille, France) One ofthechallenges is often to reduce the weight (andconsequently the thickness)oftheshells, preservingtheirsti?ness.So that it is essential to have 1 accuratemodelsforthinandevenverythinshells ,andtobeabletocomputethe displacements resultingfromagivenloading.In particular, singularities leading to fractures in some cases must be absolutely predicted a priori and ofcourse avoided (see Fig.0.3 forexample). Since the pioneeringmodels of Novozhilov-Donnell [81] and Koiter [65][66], numerous works havebeen devoted to establish linear and non linear elastic shell model usingdirect orsurfacic approaches [18][25][100]. More recently, the asymptoticmethods [87] havebeen used, to try tojustify rigorously, fromthe three-dimensional equations, the shell models obtained by direct approaches - lying onapriori assumption, andto construct new models [54][55]. This way, 1 Very thin shells are present in certain domains of industry, as plastic ?lms for pa- aging or for electronics, streched sails, or even very thin metal sheets obtained by drawing. E. Sanchez-Palencia et al.: Singular Problems in Shell Theory, LNACM 54, pp. 1-11.

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."

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."

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.

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 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.

The aim of this book is to impart a sound understanding, both physical and mathematical, of the fundamental theory of vibration and its applications. The book presents in a simple and systematic manner techniques that can easily be applied to the analysis of vibration of mechanical and structural systems. Unlike other texts on vibrations, the approach is general, based on the conservation of energy and Lagrangian dynamics, and develops specific techniques from these foundations in clearly understandable stages. Suitable for a one-semester course on vibrations, the book presents new concepts in simple terms and explains procedures for solving problems in considerable detail.

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.

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.

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.

This open access textbook, like Rayleigh's classic Theory of Sound, focuses on experiments and on approximation techniques rather than mathematical rigor. The second edition has benefited from comments and corrections provided by many acousticians, in particular those who have used the first edition in undergraduate and graduate courses. For example, phasor notation has been added to clearly distinguish complex variables, and there is a new section on radiation from an unbaffled piston. Drawing on over 40 years of teaching experience at UCLA, the Naval Postgraduate School, and Penn State, the author presents a uniform methodology, based on hydrodynamic fundamentals for analysis of lumped-element systems and wave propagation that can accommodate dissipative mechanisms and geometrically-complex media. Five chapters on vibration and elastic waves highlight modern applications, including viscoelasticity and resonance techniques for measurement of elastic moduli, while introducing analytical techniques and approximation strategies that are revisited in nine subsequent chapters describing all aspects of generation, transmission, scattering, and reception of waves in fluids. Problems integrate multiple concepts, and several include experimental data to provide experience in choosing optimal strategies for extraction of experimental results and their uncertainties. Fundamental physical principles that do not ordinarily appear in other acoustics textbooks, like adiabatic invariance, similitude, the Kramers-Kronig relations, and the equipartition theorem, are shown to provide independent tests of results obtained from numerical solutions, commercial software, and simulations. Thanks to the Veneklasen Research Foundation, this popular textbook is now open access, making the e-book available for free download worldwide. Provides graduate-level treatment of acoustics and vibration suitable for use in courses, for self-study, and as a reference Highlights fundamental physical principles that can provide independent tests of the validity of numerical solutions, commercial software, and computer simulations Demonstrates approximation techniques that greatly simplify the mathematics without a substantial decrease in accuracy Incorporates a hydrodynamic approach to the acoustics of sound in fluids that provides a uniform methodology for analysis of lumped-element systems and wave propagation Emphasizes actual applications as examples of topics explained in the text Includes realistic end-of-chapter problems, some including experimental data, as well as a Solutions Manual for instructors. Features "Talk Like an Acoustician" boxes to highlight key terms introduced in the text.

This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book.

This textbook provides an introduction to energy analysis for those students who want to specialise in this challenging field. In comparison to other textbooks, this book provides a balanced treatment of complete energy systems, covering the demand side, the supply side, and the energy markets that connect these. The emphasis is very much on presenting a range of tools and methodologies that will help students find their way in analysing real world problems in energy systems. This new edition has been updated throughout and contains additional content on energy transitions and improvements in the treatment of several energy systems analysis approaches. Featuring learning objectives, further readings and practical exercises in each chapter, Introduction to Energy Analysis will be essential reading for upper-level undergraduate and postgraduate students with a background in the natural sciences and engineering. This book may also be useful for professionals dealing with energy issues, as a first introduction into the field.

This textbook provides an introduction to energy analysis for those students who want to specialise in this challenging field. In comparison to other textbooks, this book provides a balanced treatment of complete energy systems, covering the demand side, the supply side, and the energy markets that connect these. The emphasis is very much on presenting a range of tools and methodologies that will help students find their way in analysing real world problems in energy systems. This new edition has been updated throughout and contains additional content on energy transitions and improvements in the treatment of several energy systems analysis approaches. Featuring learning objectives, further readings and practical exercises in each chapter, Introduction to Energy Analysis will be essential reading for upper-level undergraduate and postgraduate students with a background in the natural sciences and engineering. This book may also be useful for professionals dealing with energy issues, as a first introduction into the field.

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.

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 book addresses the hydrostatics and stability of ships and other floating marine structures - a fundamental aspect of naval architecture and offshore engineering for naval architects and marine engineers. It starts from the most basic concepts, assuming that the reader has no prior knowledge of the subject. By presenting the topic in a methodical and step-by-step manner, the book helps students to enhance their understanding, while also providing valuable guidelines for lecturers teaching related courses.