This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone ad dresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the relation of these results to Leray's weak solutions and backward self-similar solutions, (iv) the extension of the results to further nonlinear evolutionary problems. Particular attention is paid to the critical spaces that are invariant under the self-similar transform. For sufficiently small Reynolds numbers, the conditional stability in the sense of Lyapunov is also studied. The article is endowed by interesting personal and historical comments and an exhaustive bibliography that gives the reader a complete picture about available literature. The papers "The dynamical system approach to the Navier-Stokes equa tions for compressible fluids" by Eduard Feireisl, and "Asymptotic problems and compressible-incompressible limits" by Nader Masmoudi are devoted to the global (in time) properties of solutions to the Navier-Stokes equa and three tions for compressible fluids. The global (in time) analysis of two dimensional motions of compressible fluids were left open for many years."

The subject of the book is directly related to environmental noise and vibration phenomena (sound emission by vibrating structures, prediction and reduction, ...). Transportation noise is one of the main applications. The book presents an overview of the most recent knowledge on interaction phenomena between a structure and a fluid, including nonlinear aspects. It covers all aspects of the phenomena, from the mathematical modeling up to the applications to automotive industrial problems. The aim is to provide readers with a good understanding of the physical phenomena as well as the most recent knowledge of predictive methods.

The aim of this book is to bring together classical and recent developments in the particular field of Newtonian flow at low Reynolds numbers. The methods are developed from first principles, alternative formulations are compared, a variety of configurations are addressed, the proper mathematical framework is discussed in the context of functional analysis and integral-equation-theory, and procedures of numerical solution in the context of the boundary element method are introduced. The text contains a fair amount of original material pertaining, in particular, to the properties and explicit form of the Green's functions, and the theory of the integral equations that arise from boundary integral representations.

The aim of this book is to bring together classical and recent developments in the particular field of Newtonian flow at low Reynolds numbers. The methods are developed from first principles, alternative formulations are compared, a variety of configurations are addressed, the proper mathematical framework is discussed in the context of functional analysis and integral-equation-theory, and procedures of numerical solution in the context of the boundary element method are introduced. The text contains a fair amount of original material pertaining, in particular, to the properties and explicit form of the Green's functions, and the theory of the integral equations that arise from boundary integral representations.

Das Buch stellt spezielle Kenntnisse und Daten aus der Praxis zu Turboverdichtern in Flugtriebwerken zusammen. Damit enthalt es das notwendige Wissen fur die praktische technische Entwicklung, Auslegung und Konstruktion. Der Autor erlautert die Entwicklung der Auslegungs- und Betriebsparameter, die gegenseitigen Abhangigkeiten und die geeigneten Kombinationen der Auslegungsparameter. Grundlage dafur sind umfassende Daten aus der industriellen Entwicklung. Alle Arten von Verdichterkomponenten und Verdichterbauweisen werden berucksichtigt."

This book collects the lecture notes concerning th IUTAM School on Advanced Turbulent Flow Computations held at CISM in Udine September 7-11, 1998. The course was intended for scientists, engineers and post-graduate students interested in the application of advanced numerical techniques for simulating turbulent flows. The topic comprises two closely connected main subjects: modelling and computation, mesh pionts necessary to simulate complex turbulent flow.

In recent years there has been a considerable growth in interest in Monte Carlo methods, and quantum Monte Carlo methods in particlular. Clearly, the ever-increasing computational power available to researchers, has stimulated the development of improved algorithms, and almost all fields in computational physics and chemistry are affected by their applications. Here we just mention some fields that are covered in the lecture notes contained in this volume, viz. electronic structure studies of atoms, molecules and solids, nuclear structure, and low- or zero-temperature studies of strongly-correlated quantum systems, both of the continuum and lattice variety, and cooperative phenomena in classical systems. Although each area of application may have its own peculiarities, requiring specialized solutions, all share the same basic methodology. It was with the intention of bringing together researchers and students from these various areas that the NATO Advanced Study Institute on Quantum Monte Carlo Methods in Physics and Chemistry was held at Cornell University from 12 to 24 July, 1998. This book contains material presented at the Institute in a series of mini courses in quantum Monte Carlo methods. The program consisted of lectures predominantly of a pedagogical nature, and of more specialized seminars. The levels varied from introductory to advanced, and from basic methods to applications; the program was intended for an audience working towards the Ph.D. level and above. Despite the essentially pedagogic nature of the Institute, several of the lectures and seminars contained in this volume present recent developments not previously published.

The book covers selected problems in free surface flows. The topics range from linear and nonlinear gravity and capillary waves, thin film dynamics, equilibrium shape, stability, and dynamics of capillary surfaces to thermal Marangoni effects in several geometries. The fluid dynamical problems are supplemented by a review Eulerian based computational methods.

These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.

Theory of Dislocations provides unparalleled coverage of the fundamentals of dislocation theory, with applications to specific metal and ionic crystals. Rather than citing final results, step-by-step developments are provided to offer an in-depth understanding of the topic. The text provides the solid theoretical foundation for researchers to develop modeling and computational approaches to discrete dislocation plasticity, yet it covers important experimental observations related to the effects of crystal structure, temperature, nucleation mechanisms, and specific systems. This new edition incorporates significant advances in theory, experimental observations of dislocations, and new findings from first principles and atomistic treatments of dislocations. Also included are new discussions on thin films, deformation in nanostructured systems, and connection to crystal plasticity and strain gradient continuum formulations. Several new computer programs and worked problems allow the reader to understand, visualize, and implement dislocation theory concepts.

The Taylor-Couette system is one of the most studied examples of fluid flow exhibiting the spontaneous formation of dynamical structures. In this book, the variety of time independent solutions with periodic spatial structure is numerically investigated by solution of the Navier-Stokes equations.

From the reviews: "The book has a broad and general coverage of both the mathematics and the numerical methods well suited for graduate students." Applied Mechanics Reviews #1 "This is a very well written book. The topics are developed with separate headings making the matter easily understandable. Computer programs are also included for many problems together with a separate chapter dealing with the application of computer programs to heat transfer problems. This enhances the utility of the book." Zentralblatt fur Mathematik #1

Numerical large-eddy simulation techniques are booming at present and will have a decisive impact on industrial modeling and flow control. The book represents the general framework in physical and spectral space. It also gives the recent subgrid-scale models. Topics treated include compressible turbulence research, turbulent combustion, acoustic predictions, vortex dynamics in non-trivial geometries, flows in nuclear reactors and problems in atmospheric and geophysical sciences. The book addresses numerical analysts, physicists, and engineers.

A comprehensive overview of the basic principles of vortex dynamics in superfluids, this book addresses the problems of vortex dynamics in all three superfluids available in laboratories (4He, 3He, and BEC of cold atoms) alongside discussions of the elasticity of vortices, forces on vortices, and vortex mass. Beginning with a summary of classical hydrodynamics, the book guides the reader through examinations of vortex dynamics from large scales to the microscopic scale. Topics such as vortex arrays in rotating superfluids, bound states in vortex cores and interaction of vortices with quasiparticles are discussed. The final chapter of the book considers implications of vortex dynamics to superfluid turbulence using simple scaling and symmetry arguments. Written from a unified point of view that avoids complicated mathematical approaches, this text is ideal for students and researchers working with vortex dynamics in superfluids, superconductors, magnetically ordered materials, neutron stars and cosmological models.

Thermal convection is often encountered by scientists and engineers while designing or analyzing flows involving exchange of energy. Fundamentals of Convective Heat Transfer is a unified text that captures the physical insight into convective heat transfer and thorough, analytical, and numerical treatments. It also focuses on the latest developments in the theory of convective energy and mass transport. Aimed at graduates, senior undergraduates, and engineers involved in research and development activities, the book provides new material on boiling, including nuances of physical processes. In all the derivations, step-by-step and systematic approaches have been followed.

This up-to-date and comprehensive account of theory and experiment on wave-interaction phenomena covers fluids both at rest and in their shear flows. It includes, on the one hand, water waves, internal waves, and their evolution, interaction, and associated wave-driven means flow and, on the other hand, phenomena on nonlinear hydrodynamic stability, especially those leading to the onset of turbulence. This study provide a particularly valuable bridge between these two similar, yet different, classes of phenomena. It will be of value to oceanographers, meteorologists, and those working in fluid mechanics, atmospheric and planetary physics, plasma physics, aeronautics, and geophysical and astrophysical fluid dynamics.

These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.

This volume contributes to one of the most important topics of Fluid Mechanics in future and presents recent research results on control theory and applied control methods. Understanding and handling of control methods of nonlinear systems, typical of Fluid Mechanics, is the key to reduce losses and to improve the efficiency and safety of technical processes.

This well-known 2-volume textbook provides senior undergraduate and postgraduate engineers, scientists and applied mathematicians with the specific techniques, and the framework to develop skills in using the techniques in the various branches of computational fluid dynamics. In Volume 2 specific techniques are described for inviscid, compressible, boundary layer and separating flow. Grid generation and the use of generalized coordinates for complex geometric domains are dealt with in detail. The most modern methods (including many computer programs) are described in connection with real problems in the field of fluid dynamics. For the the second edition the author also compiled a separately available manual of solutions to the many exercises to be found in the main text.

Modern Methods in Analytical Acoustics considers topics fundamental to the understanding of noise, vibration and fluid mechanisms. The series of lectures on which this material is based began by some twenty five years ago and has been developed and expanded ever since. Acknowledged experts in the field have given this course many times in Europe and the USA. Although the scope of the course has widened considerably, the primary aim of teaching analytical techniques of acoustics alongside specific areas of wave motion and unsteady fluid mechanisms remains. The distinguished authors of this volume are drawn from Departments of Acoustics, Engineering of Applied Mathematics in Berlin, Cambridge and London. Their intention is to reach a wider audience of all those concerned with acoustic analysis than has been able to attend the course.

Nanofluids: Mathematical, Numerical and Experimental Analysis provides a combined treatment of the numerical and experimental aspects of this crucial topic. Mathematical methods such as the weighted residual method and perturbation techniques, as well as numerical methods such as Finite Element and Lattice-Boltzmann are addressed, along with experimental methods in nanofluid analysis. The effects of magnetic field, electric field and solar radiation on the optical properties and synthesis of nanofluid flow are examined and discussed as well. This book also functions as a comprehensive review of recent progress in nanofluids analysis and its application in different engineering sciences. This book is ideal for all readers in industry or academia, along with anyone interested in nanofluids for theoretical or experimental design reasons.

Das Buch fuhrt in die CAE-Methoden ein und behandelt die spezifischen Fragestellungen von CAE-Methoden in der Fahrzeugtechnik. Zunachst werden Grundlagen zur Modellbildung und zu Diskretisierungsverfahren fur partielle Differentialgleichungen dargestellt. Die anschliessenden Kapitel beschreiben die Inhalte Temperaturausgleich, Mehrkorpersimulationen sowie Statik und Dynamik elastischer Korper. Es folgt ein Kapitel uber Finite-Elemente. Anschliessend werden die fahrzeugspezifischen Themen Crash- und Insassensimulation, Akustik, Statik und Dynamik von Rohkarosserien, Mehrkorpersimulationen und Lebensdauer, Stromungssimulation und Reifen-Fahrbahn-Wechselwirkungen behandelt. Erganzt werden die Inhalte durch Kapitel uber nichtlineare Phanomene und Optimierungsverfahren."

This volume contains contributions to the BRI-TE/EURAM, Area 5, Pilot phase programme on the validation of computational fluid dynamics (CFD) codes, EUROVAL. Two- and three-dimensional flows are investigated with particular emphasis on precise comparison against measurements, with special attention paid to the validation of turbulence models investigated by the 16 project partners. The main part of this volume is designated to the validation of turbulence models on a boundary layer and Navier-Stokes basis, presented in an application-oriented structure for single- and two-element aerofoils, internal flow over bumps, wind-tunnel-interference problems and a vortex breakdown study.

This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use."

Modern continuum mechanics is the topic of this book. After its introduction it will be applied to a few typical systems arising in the environmental sciences and in geophysics. In large lake/ocean dynamics peculiar effects of the rotation of the Earth will be analyzed in linear/nonlinear processes of a homogenous and inhomogenous water body. Strong thermomechanical coupling paired with nonlinear rheology affects the flow of large ice sheets (such as Antarctica and Greenland) and ice shelves. Its response to the climatic forcing in an environmental of greenhouse warming may significantly affect the life of future generations. The mechanical behavior of granular materials under quasistatic loadings requires non-classical mixture concepts and encounters generally complicated elastic-plastic-type constitutive behavior. Creeping flow of soils, consolidation processes and ground water flow are described by such theories. Rapid shearing flow of granular materials lead to constitutive relations for the stresses which incorporate rate independent behavior of Mohr-Coulomb type together with dispersive stress contributions due to particle collisions. Rockfalls, sturzstroms, snow and ice avalanches, but also debris flow and sea ice drifting can be described with such formulations.