The result of two decades spent developing and refining the phase-integral method to a high level of precision, the authors have applied this method to problems in various fields of theoretical physics. The problems treated are of a mathematical nature, but have important physical applications. This book will thus be of great use to research workers in various branches of theoretical physics, where the problems can be reduced to one-dimensional second-order differential equations of the Schrodinger type for which phase-integral solutions are required. Includes contributions from notable scientists who have already made use of the authors'technique."

It seemed appropriate to arrange a meeting of teachers of thermodynamics in the United Kingdom, a meeting held in the pleasant surroundings of Emmanuel College, Cambridge, in Sept mber, 1984. This volume records the ideas put forward by authors, the discussion generated and an account of the action that discussion has initiated. Emphasis was placed on the Teaching of Thermodynamics to degree-level students in their first and second years. The meeting, a workshop for practitioners in which all were expected to take part, was remarkably well supported. This was notable in the representation of essentially every UK university and polytechnic engaged in teaching engineering thermodynamics and has led to a stimulating spread of ideas. By intention, the emphasis for attendance was put on teachers of engineering concerned with thermodynamics, both mechanical and chemical engineering disciplines. Attendance from others was encouraged but limited as follows: non-engineering acad emics, 10%, industrialists, 10%. The record of attendance, which will also provide addresses for direct correspondance, will show the broad cover achieved. I am indeed grateful for the attendance of those outside the engineering departments who in many cases brought a refreshing approach to discussions of the 'how' and 'why' of teaching thermodynamics. It was also notable that many of those speaking from the polytechnics had a more original approach to the teaching of thermodynamics than those from conventional universities. The Open University however brought their own special experience to bear."

One of the major achievements in computational fluid dynamics has been the development of numerical methods for simulating compressible flows, combining higher-order accuracy in smooth regions with a sharp, oscillation-free representation of embedded shocks methods and now known as "high-resolution schemes." Together with introductions from the editors written from the modern vantage point this volume collects in one place many of the most significant papers in the development of high-resolution schemes as occured at ICASE.

Fluid flows that transfer heat and mass often involve drops and bubbles, particularly if there are changes of phase in the fluid in the formation or condensation of steam, for example. Such flows pose problems for the chemical and mechanical engineer significantly different from those posed by single-phase flows. This book reviews the current state of the field and will serve as a reference for researchers, engineers, teachers, and students concerned with transport phenomena. It begins with a review of the basics of fluid flow and a discussion of the shapes and sizes of fluid particles and the factors that determine these. The discussion then turns to flows at low Reynolds numbers, including effects due to phase changes or to large radial inertia. Flows at intermediate and high Reynolds numbers are treated from a numerical perspective, with reference to experimental results. The next chapter considers the effects of solid walls on fluid particles, treating both the statics and dynamics of the particle-wall interaction and the effects of phase changes at a solid wall. This is followed by a discussion of the formation and breakup of drops and bubbles, both with and without phase changes. The last two chapters discuss compound drops and bubbles, primarily in three-phase systems, and special topics, such as transport in an electric field.

In the decades the of the formation of structures past subject spontaneous in far from has into a branch of - systems equilibrium major physics grown search with ties to It has become evident that strong neighboring disciplines. a diverse of can be understood within a common mat- phenomena range matical framework which has been called nonlinear of continuous dynamics This name the close to the field of nonlinear systems. emphasizes relationship of with few of freedom which has evolved into a dynamics systems degrees mature in the recent features mathematically subject past. Many dynamical of continuous be described reduction few can a to a systems actually through of freedom and of the latter of continue to degrees properties type systems of continuous the inspire study systems. The of this book is to demonstrate the numerous goal through examples that exist for the of nonlinear the opportunities study phenomena through tools of mathematical and use of common analyses dynamical interpretations. Instead of overview of the a providing comprehensive rapidly evolving field, the contributors to this book are to communicate to a wide scientific trying audience the of what have learnt about the formation of essence they spon- neous structures in continuous and about the dissipative systems competition between order and chaos that characterizes these It is that systems. hoped the book will be even to those scientists whose not helpful are disciplines the authors.

Imaging Heat and Mass Transfer Processes: Visualization and Analysis applies Schlieren and shadowgraph techniques to complex heat and mass transfer processes. Several applications are considered where thermal and concentration fields play a central role. These include vortex shedding and suppression from stationary and oscillating bluff bodies such as cylinders, convection around crystals growing from solution, and buoyant jets. Many of these processes are unsteady and three dimensional. The interpretation and analysis of images recorded are discussed in the text.

This volume contains the proceedings of the Seventh International Conference on Phonon Scattering in Condensed Matter held August 3-7, 1992, at Cornell University in Ithaca, NY, USA. The preceding conferences were held at: St. Maxime and Paris (France) 1972, Nottingham (UK) 1975, Providence (USA) 1979, Stuttgart (Germany) 1983, Urbana (USA) 1986, and Heidelberg (Germany) 1989. The Heidelberg conference was held jointly with the Third International Con ference on Phonon Physics. The next conference, to be held in August, 1995, in Sapporo, Japan, and hosted by Professor T. Nakayama and his colleagues, will also be such a joint conference. This conference was attended by 227 scientists from 27 countries, and covered all aspects of phonon scattering in condensed matter, ranging from the more traditional topics of thermal conductivity, Kapitza resistance, and ballistic phonon propagation to the recently added topics, such as electron-phonon interaction in high-T c superconductors, the use of phonons in particle detection, and phonons in confined geometries. The 207 papers arranged in 11 chapters in this volume are a cross section of the present activities in the quite obviously vibrant field of phonons and their interactions."

`Non-equilibrium Thermodynamics and Statistical Mechanics: Foundations and Applications' builds from basic principles to advanced techniques, and covers the major phenomena, methods, and results of time-dependent systems. It is a pedagogic introduction, a comprehensive reference manual, and an original research monograph. Uniquely, the book treats time-dependent systems by close analogy with their static counterparts, with most of the familiar results of equilibrium thermodynamics and statistical mechanics being generalized and applied to the non-equilibrium case. The book is notable for its unified treatment of thermodynamics, hydrodynamics, stochastic processes, and statistical mechanics, for its self-contained, coherent derivation of a variety of non-equilibrium theorems, and for its quantitative tests against experimental measurements and computer simulations. Systems that evolve in time are more common than static systems, and yet until recently they lacked any over-arching theory. 'Non-equilibrium Thermodynamics and Statistical Mechanics' is unique in its unified presentation of the theory of non-equilibrium systems, which has now reached the stage of quantitative experimental and computational verification. The novel perspective and deep understanding that this book brings offers the opportunity for new direction and growth in the study of time-dependent phenomena. 'Non-equilibrium Thermodynamics and Statistical Mechanics' is an invaluable reference manual for experts already working in the field. Research scientists from different disciplines will find the overview of time-dependent systems stimulating and thought-provoking. Lecturers in physics and chemistry will be excited by many fresh ideas and topics, insightful explanations, and new approaches. Graduate students will benefit from its lucid reasoning and its coherent approach, as well as from the chem12physof mathematical techniques, derivations, and computer algorithms.

This book takes the topic of H-infinity control as a point of departure, and pursues an improved controller design suggested in the mainstream of robust control. Using stochastic methods, the book is important to the circuits and systems community, alongside researchers in networking systems, operator theory and linear multivariable control.

Macroscopic physics provides us with a great variety of pattern-forming systems displaying propagation phenomena, from reactive fronts in combustion, to wavy structures in convection and to shear flow instabilities in hydrodynamics. These proceedings record progress in this rapidly expanding field. The contributions have the following major themes: - The problems of velocity selection and front morphology of propagating interfaces in multiphase media, with emphasis on recent theoretical and experimental results on dendritic crystal growth, Saffman-Taylor fingering, directional solidification and chemical waves. - The "unfolding" of large-scale, low-frequency behavior in weakly confined homogeneous systems driven far from equilibrium, and more specifically, the envelope approach to the mathematical description of textures in different cases: steady cells, propagating waves, structural defects, and phase instabilities. - The implications of the presence of global downstream transport in open flows for the nature, convective or absolute, of shear flow instabilities, with applications to real boundary layer flows or shear layers, as reported in contributions covering experimental situations of fundamental and/or engineering interest.

This IMA Volume in Mathematics and its Applications DYNAMICAL ISSUES IN COMBUSTION THEORY is based on the proceedings of a workshop which was an integral part of the 1989-90 IMA program on "Dynamical Systems and their Applications." The aim of this workshop was to cross-fertilize research groups working in topics of current interest in combustion dynamics and mathematical methods applicable thereto. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, George R. Sell, Paul Fife, Amable Liiian and Foreman Williams for organizing the meeting. We especially thank Paul Fife, Amable Liiilin and Foreman Williams for editing the proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, the National Science Foundation and the Office of Naval Research. Avner Friedman Willard Miller, Jr. ix PREFACE The world ofcombustion phenomena is rich in problems intriguing to the math ematical scientist. They offer challenges on several fronts: (1) modeling, which involves the elucidation of the essential features of a given phenomenon through physical insight and knowledge of experimental results, (2) devising appropriate asymptotic and computational methods, and (3) developing sound mathematical theories. Papers in the present volume, which are based on talks given at the Workshop on Dynamical Issues in Combustion Theory in November, 1989, describe how all of these challenges have been met for particular examples within a number of common combustion scenarios: reactiveshocks, low Mach number premixed reactive flow, nonpremixed phenomena, and solid propellants."

B. Coleman, M.E. Gurtin: Thermodynamics and wave propagation in Elastic and Viscoelastic media.- L. De Vito: Sui fondamenti della meccanica di sistemi continui (II).- G. Fichera: Problemi elastostatici con ambigue condizioni al contorno.- G. Grioli: Sistemi a trasformazioni reversibili.- W. Noll: the foundations of mechanics.- R.A. Toupin: Elasticity and electromagnetic.- C.C. Wang: Subfluids.

Mon but n'a jamais be de m'occuper des ces matieres comme physicien, mais seulement comme /ogicien ... F. REECH, 1856 I do not think it possible to write the history of a science until that science itself shall have been understood, thanks to a clear, explicit, and decent logical structure. The exuberance of dim, involute, and undisciplined his torical essays upon classical thermodynamics reflects the confusion of the theory itself. Thermodynamics, despite its long history, has never had the benefit of a magisterial synthesis like that which EULER gave to hydro dynamics in 1757 or that which MAXWELL gave to electromagnetism in 1873; the expositions in the works of discovery in thermodynamics stand a pole apart from the pellucid directness of the notes in which CAUCHY presented his creation and development of the theory of elasticity from 1822 to 1845. Thermodynamics was born in obscurity and disorder, not to say confusion, and there the common presentations of it have remained. With this tractate I aim to provide a simple logical structure for the classical thermodynamics of homogeneous fluid bodies. Like any logical structure, it is only one of many possible ones. I think it is as simple and pretty as can be."

Shock wave research covers important inderdisciplinary areas which range from basic topics on gasdynamics, combustion and detonation, physico-chemistry of high temperature gases, plasma physics, astro and geophysics, materials science, astronautics and space technology to medical and industrial applications. This book includes 202 papers presented at the 18th the International Symposium on Shock Waves which describe the research frontier of shock wave phenopmena and 14 plenary lectures which show the state of the art of various fields of shock wave research. This proceedings is a unique collection of most important and updated shock wave research.

This book summarizes the most recent theoretical, computational and experimental results dealing with homogeneous turbulence dynamics. A large class of flows is covered: flows governed by anisotropic production mechanisms (e.g. shear flows) and flows without production but dominated by waves (e.g. homogeneous rotating or stratified turbulence). Compressible turbulent flows are also considered. In each case, main trends are illustrated using computational and experimental results, while both linear and nonlinear theories and closures are discussed. Details about linear theories (e.g. Rapid Distortion Theory and variants) and nonlinear closures (e.g. EDQNM) are provided in dedicated chapters, following a fully unified approach. The emphasis is on homogeneous flows, including several interactions (rotation, stratification, shear, shock waves, acoustic waves, and more) which are pertinent to many applications fields - from aerospace engineering to astrophysics and Earth sciences.

The Eurotherm Committee was created in 1986 from member countries of the European Community. It has the purpose of organising and coordinating scientific events such as seminars and conferences in the thermal sciences. The series of Eurotherm Seminars established by the Committee has become a popular forum for high-level scientific and technical interchange of ideas in a wide range of specialist topics. While the presentation and publication of papers at the Seminars are encouraged, the primary aim is to stimulate discussion and liaison between specialist groups. The present Chairman of Eurotherm is Professor C.J. Hoogendoorn of the Technical University, Delft (Fax [NL] 15, 783251). Information on Mure Seminars is available from the Secretary, Keith Cornwell, Heriot-Watt University, Edinburgh (Fax [UK] 31, 451, 3129). This particular Seminar No. 18 on the Design and Operation of Heat Exchangers was the first one on this topic and was held at the Universitat der Bundeswehr Hamburg (University of the Federal Armed Forces Hamburg) from February 27 to March 1 in 1991. The seminar was an international event and was attended by more than 60 scientists not only from countries of the European Community such as Belgium, France, Germany, Great Britain, and the Netherlands but also from other countries such as Canada, China, India, Israel, Romania, Soviet Union, Sweden and the United States of America.

This volume consists of edited papers presented at the International Symposion Gas Phase Chemical Reaction Systems: Experiments and Models 100 Years After Max Bodenslein, held at the Internationales Wissenschaftsforum Heidelberg (IWH) in Heidelberg during July 25-28, 1995. The intention of this symposion was to bring together leading researchers from the fields of reaction dynamics, kinetics, catalysis and reactive flow model ling to discuss and review the advances in the understanding of chemical kinetics about 100 years after Max Bodenstein's pioneering work on the "hydrogen iodine reaction", which he carried out at the Chemistry Institute of the University of Heidelberg. The idea to focus in his doctoral thesis [1] on this reaction was brought up by his supervisor Victor Meyer (successor of Robert Bunsen at the Chemistry Institute of the University of Heidelberg) and originated from the non reproducible behaviour found by Bunsen and Roscoe in their early photochemical investigations of the H2/Cl2 system [2] and by van't Hoff [3], and V. Meyer and co-workers [4] in their experiments on the slow combustion of H2/02 mixtures.

The Symposium on "The Influence of Polymer Additives on Veloc- ity and Temperature Fields" was proposed to the General Assem- bly of the International Union of Theoretical and Applied Me- chanics (IUTAM) by the "Gesellschaft fur Angewandte Mathematik und Mechanik" (GAMM). The Symposium was held under the auspices of IUTAM in association with the "Deutsche Rheologische Ge- sellschaft" (DRG) with responsibility for the organization ly- ing with B. Gampert (Universitat-GH-Essen). The main aim of this IUTAM Symposium was to consider the funda- mental aspects of the phenomena that occur when small amounts of polymers are added to turbulent flows (turbulent drag re- duction) and laminar porous media flows. In particular atten- tion was devoted to - the influence of molecular parameters of the polymers and solution properties, especially the elongational viscosity, on turbulent flow and laminar porous media flow; the influence of polymers on the turbulence structure in polymer drag reduction.

The renormalization-group approach is largely responsible for the considerable success which has been achieved in the last ten years in developing a complete quantitative theory of phase transitions. Before, there was a useful physical picture of phase transitions, but a general method for making accurate quantitative predictions was lacking. Existent theories, such as the mean-field theory of Landau, sometimes reproduce phase diagrams reliably but were known to fail qualitatively near critical points, where the critical behavior is particularly interesting be cause of its universal character. In the mid 1960's Widom found that the singularities in thermodynamic quanti ties were well described by homogeneous functions. Kadanoff extended the homogeneity hypothesis to correlation functions and linked it to the idea of scale invariance. In the early 1970's Wilson showed how Kadanoff's rescaling could be explicitly carried out near the fixed point of a flow in Hamiltonian space. He made the first practical renormalization-group calculation of the flow induced by the elimination of short-wave-length Fourier components of the order-parameter field. The univer sality of the critical behavior emerges in a natural way in this approach, with a different fixed point for each universality class. The discovery by Wilson and Fisher of a systematic expansion procedure in E for a system in d = 4 - E dimen sions was followed by a cascade of calculations of critical quantities as a function of d and of the order-parameter dimensionality n."

Covers a wide spectrum of applications and contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The new edition reflects new developments and contains a new chapter on the interplay between hydrodynamics and thermodynamics.

This unique book provides a fundamental introduction to all aspects of modern plasma chemistry. The book describes mechanisms and kinetics of chemical processes in plasma, plasma statistics, thermodynamics, fluid mechanics, and electrodynamics, as well as all major electric discharges applied in plasma chemistry. The book considers most of the major applications of plasma chemistry from electronics to thermal coatings, from treatment of polymers to fuel conversion and hydrogen production, and from plasma metallurgy to plasma medicine. The book can be helpful to engineers, scientists, and students interested in plasma physics, plasma chemistry, plasma engineering, and combustion, as well as in chemical physics, lasers, energy systems, and environmental control. The book contains an extensive database on plasma kinetics and thermodynamics as well as a lot of convenient numerical formulas for practical calculations related to specific plasma-chemical processes and applications. The book contains a large number of problems and concept questions that are helpful in university courses related to plasma, lasers, combustion, chemical kinetics, statistics and thermodynamics, and high-temperature and high-energy fluid mechanics.

Advances through carefully conducted quantitative work on well designed, high quality materials characterize the present state of high-temperature superconductivity research. The contributions to this volume present a theoretical and experimental overview of electronic structure and physical properties, including anisotropic features, of high-temperative materials, with a focus on cuprates. In order to enhance the understanding of the mechanisms of superconductivity at high temperatures, this volume is divided into theoretical and experimental parts. The contributions to the two parts correspond to each other, giving readers involved in either area of research activity a reference to findingsof the other. On the other hand, this book gives young physicists high-level information on the present state of research, enhanced by tutorial contributions of leading physicists in the field.

This text on the statistical theory of nonequilibrium phenomena grew out of lecture notes for courses on advanced statistical mechanics that were held more or less regularly at the Physics Department of the Technical University in Munich. My aim in these lectures was to incorporate various developments of many-body theory made during the last 20-30 years, in particular the correlation function approach, not just as an "extra" alongside the more "classical" results; I tried to use this approach as a unifying concept for the presentation of older as well as more recent results. I think that after so many excellent review articles and advanced treatments, correlation functions and memory kernels are as much a matter of course in nonequilibrium statistical physics as partition functions are in equilibrium theory, and should be used as such in regular courses and textbooks. The relations between correlation functions and earlier vehicles for the formulation of nonequilibrium theory such as kinetic equations, master equations, Onsager's theory, etc. , are discussed in detail in this volume. Since today there is growing interest in nonlinear phenomena I have included several chapters on related problems. There is some nonlinear response theory, some results on phenomenological nonlinear equations and some microscopic applications of the nonlinear response formalism. The main focus, however, is on the linear regime.

The 2002 Pan-American Advanced Studies Institute School on Quantum Gravity was held at the Centro de Estudios Cientificos (CECS), Valdivia, Chile, January 4-14, 2002. The school featured lectures by ten speakers, and was attended by nearly 70 students from over 14 countries. A primary goal was to foster interaction and communication between participants from different cultures, both in the layman 's sense of the term and in terms of approaches to quantum gravity. We hope that the links formed by students and the school will persist throughout their professional lives, continuing to promote interaction and the essential exchange of ideas that drives research forward.

This volume contains improved and updated versions of the lectures given at the School. It has been prepared both as a reminder for the participants, and so that these pedagogical introductions can be made available to others who were unable to attend. We expect them to serve students of all ages well.

The development of the modern theory of metals and alloys has coincided with great advances in quantum-mechanical many-body theory, in electronic structure calculations, in theories of lattice dynamics and of the configura tional thermodynamics of crystals, in liquid-state theory, and in the theory of phase transformations. For a long time all these different fields expanded quite independently, but now their overlap has become sufficiently large that they are beginning to form the basis of a comprehensive first-principles the ory of the cohesive, structural, and thermodynamical properties of metals and alloys in the crystalline as well as in the liquid state. Today, we can set out from the quantum-mechanical many-body Hamiltonian of the system of electrons and ions, and, following the path laid out by generations of the oreticians, we can progress far enough to calculate a pressure-temperature phase diagram of a metal or a composition-temperature phase diagram of a binary alloy by methods which are essentially rigorous and from first prin ciples. This book was written with the intention of confronting the materials scientist, the metallurgist, the physical chemist, but also the experimen tal and theoretical condensed-matter physicist, with this new and exciting possibility. Of course there are limitations to such a vast undertaking as this. The selection of the theories and techniques to be discussed, as well as the way in which they are presented, are necessarily biased by personal inclination and personal expertise."