The study of incompressible ?ows is vital to many areas of science and te- nology. This includes most of the ?uid dynamics that one ?nds in everyday life from the ?ow of air in a room to most weather phenomena. Inundertakingthesimulationofincompressible?uid?ows, oneoftentakes many issues for granted. As these ?ows become more realistic, the problems encountered become more vexing from a computational point-of-view. These range from the benign to the profound. At once, one must contend with the basic character of incompressible ?ows where sound waves have been analytically removed from the ?ow. As a consequence vortical ?ows have been analytically "preconditioned," but the ?ow has a certain non-physical character (sound waves of in?nite velocity). At low speeds the ?ow will be deterministic and ordered, i.e., laminar. Laminar ?ows are governed by a balance between the inertial and viscous forces in the ?ow that provides the stability. Flows are often characterized by a dimensionless number known as the Reynolds number, which is the ratio of inertial to viscous forces in a ?ow. Laminar ?ows correspond to smaller Reynolds numbers. Even though laminar ?ows are organized in an orderly manner, the ?ows may exhibit instabilities and bifurcation phenomena which may eventually lead to transition and turbulence. Numerical modelling of suchphenomenarequireshighaccuracyandmostimportantlytogaingreater insight into the relationship of the numerical methods with the ?ow physics.

This IMA Volume in Mathematics and its Applications AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS We are grateful to the Scientific Committee: Haim Brezis Constantine Dafermos Jerry Ericksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface Experiences with amorphous polymers have supplied much of the motivation for developing novel kinds of molecular theory, to try to deal with the more significant features of systems involving very large molecules with many degrees offreedom. Similarly, the observations of many unusual macroscopic phenomena has stimulated efforts to develop linear and nonlinear theories of viscoelasticity to describe them. In either event, we are confronted not with a well-established, specific set of equations, but with a variety of equations, conforming to a loose pattern and suggested by general kinds of reasoning. One challenge is to devise techniques for finding equations capable of delivering definite and reliable predictions. Related to this is the issue of discovering ways to better grasp the nature of solutions ofthose equations showing some promise."

Intended for self-study, this second volume presents a systematic approach for deriving model equations of planar and spatial mechanisms. The necessary theoretical foundations have been laid in the first volume. The focus is on the application of the modeling methodology to various examples of rigid-body mechanisms, simple planar ones as well as more challenging spatial problems. A rich variety of joint models, active constraints, as well as active and passive force elements is treated. The book is intended for self-study by working engineers and students concerned with the control of mechanical systems, i.e. robotics, mechatronics, vehicles, and machine tools. Its examples can be used as models for university lectures.

* Offers a rigorous mathematical treatment of mechanics as a text or reference

* Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles

* Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries

This short but complicated book is very demanding of any reader. The scope and style employed preserve the nature of its subject: the turbulence phe nomena in gas and liquid flows which are believed to occur at sufficiently high Reynolds numbers. Since at first glance the field of interest is chaotic, time-dependent and three-dimensional, spread over a wide range of scales, sta tistical treatment is convenient rather than a description of fine details which are not of importance in the first place. When coupled to the basic conserva tion laws of fluid flow, such treatment, however, leads to an unclosed system of equations: a consequence termed, in the scientific community, the closure problem. This is the central and still unresolved issue of turbulence which emphasizes its chief peculiarity: our inability to do reliable predictions even on the global flow behavior. The book attempts to cope with this difficult task by introducing promising mathematical tools which permit an insight into the basic mechanisms involved. The prime objective is to shed enough light, but not necessarily the entire truth, on the turbulence closure problem. For many applications it is sufficient to know the direction in which to go and what to do in order to arrive at a fast and practical solution at minimum cost. The book is not written for easy and attractive reading."

Foreword Looking back the past 30 years. we have seen steady progress made in the area of speech science and technology. I still remember the excitement in the late seventies when Texas Instruments came up with a toy named "Speak-and-Spell" which was based on a VLSI chip containing the state-of-the-art linear prediction synthesizer. This caused a speech technology fever among the electronics industry. Particularly. applications of automatic speech recognition were rigorously attempt ed by many companies. some of which were start-ups founded just for this purpose. Unfortunately. it did not take long before they realized that automatic speech rec ognition technology was not mature enough to satisfy the need of customers. The fever gradually faded away. In the meantime. constant efforts have been made by many researchers and engi neers to improve the automatic speech recognition technology. Hardware capabilities have advanced impressively since that time. In the past few years. we have been witnessing and experiencing the advent of the "Information Revolution." What might be called the second surge of interest to com mercialize speech technology as a natural interface for man-machine communication began in much better shape than the first one. With computers much more powerful and faster. many applications look realistic this time. However. there are still tremendous practical issues to be overcome in order for speech to be truly the most natural interface between humans and machines."

This book is based on the author's 50+ years experience in the power and distribution transformer industry. The first few chapters of the book provide a step-by-step procedures of transformer design. Engineers without prior knowledge or exposure to design can follow the procedures and calculation methods to acquire reasonable proficiency necessary to designing a transformer. Although the transformer is a mature product, engineers working in the industry need to understand its fundamentals oand design to enable them to offer products to meet the challenging demands of the power system and the customer. This book can function as a useful guide for practicing engineers to undertake new designs, cost optimization, design automation etc., without the need for external help or consultancy. The book extensively covers the design processes with necessary data and calculations from a wide variety of transformers, including dry-type cast resin transformers, amorphous core transformers, earthing transformers, rectifier transformers, auto transformers, transformers for explosive atmospheres, and solid-state transformers. The other subjects covered include, carbon footprint salculation of transformers, condition monitoring of transformers and design optimization techniques. In addition to being useful for the transformer industry, this book can serve as a reference for power utility engineers, consultants, research scholars, and teaching faculty at universities.

In the signal-processing research community, a great deal of progress in higher-order statistics (HOS) began in the mid-1980s. These last fifteen years have witnessed a large number of theoretical developments as well as real applications. Blind Estimation Using Higher-Order Statistics focuses on the blind estimation area and records some of the major developments in this field. Blind Estimation Using Higher-Order Statistics is a welcome addition to the few books on the subject of HOS and is the first major publication devoted to covering blind estimation using HOS. The book provides the reader with an introduction to HOS and goes on to illustrate its use in blind signal equalisation (which has many applications including (mobile) communications), blind system identification, and blind sources separation (a generic problem in signal processing with many applications including radar, sonar and communications). There is also a chapter devoted to robust cumulant estimation, an important problem where HOS results have been encouraging. Blind Estimation Using Higher-Order Statistics is an invaluable reference for researchers, professionals and graduate students working in signal processing and related areas.

Whatdoasupernovaexplosioninouterspace, ?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite di?erent. So are the motivations for studying them scienti?cally. The super- 8 nova is a thermo-nuclear explosion on a scale of 10 cm. Astrophysicists try to understand them in order to get insight into fundamental properties of the universe. In ?ows around airfoils of commercial airliners at the scale of 3 10 cm shock waves occur that in?uence the stability of the wings as well as fuel consumption in ?ight. This requires appropriate design of the shape and structure of airfoils by engineers. Knocking occurs in combustion, a chemical 1 process, and must be avoided since it damages motors. The scale is 10 cm and these processes must be optimized for e?ciency and environmental conside- tions. The common thread is that the underlying ?uid ?ows may at a certain scale of observation be described by basically the same type of hyperbolic s- tems of partial di?erential equations in divergence form, called conservation laws. Astrophysicists, engineers and mathematicians share a common interest in scienti?c progress on theory for these equations and the development of computational methods for solutions of the equations. Due to their wide applicability in modeling of continua, partial di?erential equationsareamajor?eldofresearchinmathematics. Asubstantialportionof mathematical research is related to the analysis and numerical approximation of solutions to such equations. Hyperbolic conservation laws in two or more spacedimensionsstillposeoneofthemainchallengestomodernmathematics

This book is intended for first year physics graduate students who wish to learn about analytical mechanics. Lagrangians and Hamiltonians are extensively treated following chapters where particle motion, oscillations, coordinate systems, and rigid bodies are dealt with in far greater detail than in most undergraduate textbooks. Perturbation theory, relativistic mechanics, and two case studies of continuous systems are presented.Each subject is approached at progressively higher levels of abstraction. Lagrangians and Hamiltonians are first presented in an inductive way, leading up to general proofs. Hamiltonian mechanics is expressed in Cartan's notation not too early; there is a self-contained account of the traditional formulation.Numerous problems with detailed solutions are provided. Graduate students studying for the qualifying examination will find them very useful.

This book presents tensors and tensor analysis as primary mathematical tools for engineering and engineering science students and researchers. The discussion is based on the concepts of vectors and vector analysis in three-dimensional Euclidean space, and although it takes the subject matter to an advanced level, the book starts with elementary geometrical vector algebra so that it is suitable as a first introduction to tensors and tensor analysis. Each chapter includes a number of problems for readers to solve, and solutions are provided in an Appendix at the end of the text. Chapter 1 introduces the necessary mathematical foundations for the chapters that follow, while Chapter 2 presents the equations of motions for bodies of continuous material. Chapter 3 offers a general definition of tensors and tensor fields in three-dimensional Euclidean space. Chapter 4 discusses a new family of tensors related to the deformation of continuous material. Chapter 5 then addresses constitutive equations for elastic materials and viscous fluids, which are presented as tensor equations relating the tensor concept of stress to the tensors describing deformation, rate of deformation and rotation. Chapter 6 investigates general coordinate systems in three-dimensional Euclidean space and Chapter 7 shows how the tensor equations discussed in chapters 4 and 5 are presented in general coordinates. Chapter 8 describes surface geometry in three-dimensional Euclidean space, Chapter 9 includes the most common integral theorems in two- and three-dimensional Euclidean space applied in continuum mechanics and mathematical physics.

The scientists and engineers of today are relentless in their continuing study and analysis of the world about us from the microcosm to the macrocosm. A central purpose of this study is to gain sufficient scientific information and insight to enable the development of both representative and useful models of the superabundance of physical processes that surround us. The engineers need these models and the associated insight in order to build the information processing systems and control systems that comprise these new and emerging technologies. Much of the early modeling work that has been done on these systems has been based on the linear time-invariant system theory and its extensive use of Fourier transform theory for both continuous and discrete systems and signals. However many of the signals arising in nature and real systems are neither stationary nor linear but tend to be concentrated in both time and frequency. Hence a new methodology is needed to take these factors properly into account.

This work focuses on computational methods in continuum thermomechanics. The text is based on the author's lectures, which ensures a didactical and coherent buildup.The main emphasis is put on the presentation of ideas and qualitative considerations, illustrated by specific examples and applications. Conditions and explanations that are essential for the practical application of methods are discussed thoroughly.

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

The book presents an updated state-of-the-art overview of the general aspects and practical applications of the theories of thin structures, through the interaction of several topics, ranging from non-linear thin-films, shells, junctions, beams of different materials and in different contexts (elasticity, plasticity, etc.). Advanced problems like the optimal design and the modeling of thin films made of brittle or phase-transforming materials will be presented as well.

Bivectors occur naturally in the description of elliptically polarized homogeneous and inhomogeneous plane waves. The description of a homogeneous plane wave generally involves a vector (the unit vector along the propagation direction) and a bivbector (the complex amplitude of the wave). Inhomogeneous plane waves are described in terms of two bivectors - the complex amplitude and the complex slowness. The use of bivectors and their associated ellipses is essential for the presentation of the 'directional ellipse' method given in this book, in deriving all possible inhomogeneous plane wave solutions in a given context.
The purpose of this book is to give an extensive treatment of the properties of bivectors and to show how these may be applied to the theory of homogeneous and inhomogeneous plane waves. For each chapter there are exercises with answers, many of which present further useful properties which are referred to afterwards. The material in this book is suitable for senior undergraduate and first year graduate students. It will also prove useful for researchers interested in homogeneous and inhomogeneous plane waves.

The rationale for publishing a second edition of this monograph is that this area of research continues to show remarkable advancement. The new generation of synthetic aperture radar satellites has provided unprecedented spatial resolution of sea surface features. In addition, satellites to measure sea surface salinity have been launched. Computational fluid dynamics models open new opportunities in understanding the processes in the near-surface layer of the ocean and their visibility from space. Passive acoustic methods for monitoring short surface waves have significantly progressed. Of importance for climate research, processes in the near-surface layer of the ocean contribute to errors in satellite estimates of sea surface temperature trends. Due to growing applications of near-surface science, it is anticipated that more students will be trained in this area of research. Therefore this second edition of the monograph is closer to a textbook format.

The near-field region within an order of 100 nm from the solid interface is an exciting and crucial arena where many important multiscale transport phenomena are physically characterized, such as flow mixing and drag, heat and mass transfer, near-wall behavior of nanoparticles, binding of bio-molecules, crystallization, surface deposition processes, just naming a few. This monograph presents a number of label-free experimental techniques developed and tested for near-field fluid flow characterization. Namely, these include Total Internal Reflection Microscopy (TIRM), Optical Serial Sectioning Microscopy (OSSM), Surface Plasmon Resonance Microscopy (SPRM), Interference Reflection Contrast Microscopy (IRCM), Thermal Near-Field Anemometry, Scanning Thermal Microscopy (STM), and Micro-Cantilever Near-Field Thermometry. Presentation on each of these is laid out for the working principle, how to implement the system, and its example applications, to promote the readers understanding and knowledge of the specific technique that can be applied for their own research interests.

New edition of the popular textbook, comprehensively updated throughout and now includes a new dedicated website for gas dynamic calculations The thoroughly revised and updated third edition of Fundamentals of Gas Dynamics maintains the focus on gas flows below hypersonic. This targeted approach provides a cohesive and rigorous examination of most practical engineering problems in this gas dynamics flow regime. The conventional one-dimensional flow approach together with the role of temperature-entropy diagrams are highlighted throughout. The authors--noted experts in the field--include a modern computational aid, illustrative charts and tables, and myriad examples of varying degrees of difficulty to aid in the understanding of the material presented. The updated edition of Fundamentals of Gas Dynamics includes new sections on the shock tube, the aerospike nozzle, and the gas dynamic laser. The book contains all equations, tables, and charts necessary to work the problems and exercises in each chapter. This book's accessible but rigorous style: Offers a comprehensively updated edition that includes new problems and examples Covers fundamentals of gas flows targeting those below hypersonic Presents the one-dimensional flow approach and highlights the role of temperature-entropy diagrams Contains new sections that examine the shock tube, the aerospike nozzle, the gas dynamic laser, and an expanded coverage of rocket propulsion Explores applications of gas dynamics to aircraft and rocket engines Includes behavioral objectives, summaries, and check tests to aid with learning Written for students in mechanical and aerospace engineering and professionals and researchers in the field, the third edition of Fundamentals of Gas Dynamics has been updated to include recent developments in the field and retains all its learning aids. The calculator for gas dynamics calculations is available at https: //www.oscarbiblarz.com/gascalculator gas dynamics calculations