Hydrogen can behave as an alkaline metal or a halogen and can react with nearly all elements of the periodic table. This explains the large number of metal hydrides. Since T. Graham's first observation of the absorption of hydrogen in palladium in 1866 the behaviour of hydrogen in metals has been studied very extensively. The interest was motivated by the possible application of metal-hydrogen systems in new technologies (e.g., moderator material in nuclear fission reactors, reversible storage material for thermal energy and large amounts of hydrogen) and by the fact that metal hydrides show very exciting physical properties (e.g., superconductivity, quantum diffusion, order-disorder transitions, phase diagrams, etc.). Many of these properties have been determined for the stable hydrogen isotopes Hand D in various metals. In comparison, very little is known about the behaviour of the ra dioactive isotope tritium in metals. This book is a first attempt to summarize part of the knowledge of tritium gained in the last few years. In addition to the task of presenting the properties of tritium in metals, I have tried to compare these data with those of protium and deuterium. Furthermore, helium-3 is connected inse parably with tritium via the tritium decay. Therefore one chapter of this book is solely devoted to the curious properties of helium in metals caused mainly by its negligible solubility."

A IUTAM symposium on "Measuring Techniques in Gas-Liquid Two Phase Flows" was held on July 5-8, 1983 in Nancy, France. This topic in cluded instrumentation for steam-water and liquid-vapor flows but strictly excluded measuring techniques for gas or liquid flows with solid particles. The top priority in the paper selection was given to presentations of new methods which had been substantiated by theoretical modeling, calibration tests and comparison tests with other techniques. Examples of experimental resul ts obtained with the proposed instrumentation had to be displayed. However the interpretation of these results in terms of two-phase flow or heat transfer modeling did not fall wi thin the scope of the meeting. Thirty four papers were presented during the Symposium and 79 participants coming from Canada, European countries, Japan and the United States attended the sessions. They represented not only Universities but also state agencies and private companies. After the meeting each paper was peer-reviewed by at least three referees. The Editors of this Procee dings Volume are pleased to extend their deep gratitude to the following reviewers: J.L. Achard, R.J. Adrian, B. Azzopardi, J.A. Boure, G. Costigan, M. Courtaud, A.E. Dukler, F. Durst, J.R. Fincke, G. Gouesbet, P. Griffith, T.J. Hanratty, A. Hawighorst, T.R. Heidrick, G. Hetsroni, Y.Y. Hsu, M."

The Compendium of Theoretical Physics contains the canonical curriculum of theoretical physics. From classical mechanics over electrodynamics, quantum mechanics and statistical physics/thermodynamics, all topics are treated axiomatic-deductively and confimed by exercises, solutions and short summaries.

The last two decades have witnessed an intensifying effort in learning how to manage flow turbulence: it has in fact now become one of the most challenging and prized techno logical goals in fluid dynamics. The goal itself is of course not new. More than a hundred years ago, Reynolds already listed factors conducive to laminar and to turbulent flow (including among them curvature and acceleration). Further more, it is in retrospect clear that there were several early instances ot successful turbulence management. Examples are the reduction in drag achieved with a ring-trip placed on the front of a sphere or the insertion of a splitter-plate behind a circular cylinder; by the early 1950s there were numerous exercises at boundary layer control. Although many of these studies were interesting and suggestive, they led . to no spectacularly successful practical application, and the effort petered out in the late 1950s. The revival of interest in these problems in recent years can be attributed to the emergence of several new factors. First of all, fresh scientific insight into the structure of turbulence, in particular the accumulated evidence for the presence of significant order in turbulent flow, has been seen to point to new methods of managing turbulence. A second major reason has been the growing realisation that the rate at which the world is consuming its reserves of fossil fuels is no longer negligible; the economic value of greater energy effi ciency and lower drag has gone up significantly."

Open nonlinear systems are capable of self-organization in space and time. This realization constitutes a major breakthrough of modern science, and is currently at the origin of explosive developments in chemistry, physics and biology. Observations and numerical computations of nonlinear systems surprise us by their inexhaustible and sometimes nonintuitive variety of structures with different shapes and functions. But as well as variety one finds on closer inspection that nonlinear phenomena share universal aspects of pattern formation in time and space. These similarities make it possible to bridge the gap between inanimate and living matter at various levels of complexity, in both theory and experiment. This book is an account of different approaches to the study of this pattern formation. The universality of kinetic, thermodynamic and dimensional approaches is documented through their application to purely mathematical, physical and chemical systems, as well as to systems in nature: biochemical, cellular, multicellular, physiological, neurophysiological, ecological and economic systems. Hints given throughout the book allow the reader to discover how to make use of the principles and methods in different fields of research, including those not treated explicitly in the book.

The Third European Turbulence Conference was held at the Royal Institute of Technology, Sweden, from the 3rd to the 6th of July 1990 under the auspices of the European Mechanics Committee. This series of conferences is primarily devoted to fundamental aspects of turbulence and aimed at bringing together engineers, physicists and mathematicians. The scientific committee - serving also as the European Turbulence Con ference Committee - consisted of the following members: G. Comte-Bellot (Lyon), H.H. Fernholz (Berlin), H. Fiedler (Berlin), U. Frisch (Nice), J.c.R. Hunt (Cambridge), J. Jimenez (Madrid), A.V. Johansson (Stockholm), E. Krause (Aachen), G. Ooms (Amsterdam), and 1. Rhyming (Lausanne). The local organizing committee consisted of A.V. Johansson and P.H. Alfredsson. The conference programme comprised six invited lectures, given by D. Bechert, Y. Gagne, J. Jimenez, M.T. Landahl, C.H. Priddin and G.M. Za slavsky, and 96 contributions given as either oral or poster presentations.There were 172 participants from 17 countries. The members of this scientific com mittee acted as referees for the selection and scrutiny of the papers published in these proceedings. The main topics of this meeting were turbulence structure; transition and dynamical systems; turbulent combustion and mixing; turbulence affected by body forces; turbulence modelling; drag reduction and turbulence control; and novel experimental techniques. During the first evening of the conference the new MTL low-speed, low-turbulence wind-tunnel at KTH was inaugurated. The wind-tunnel outline, also acting as decoration for the "official conference cakes," is shown below."

th This volume contains the proceedings of the X Congress of the Interna- tional Association of Mathematical Physics, held at the University of Leipzig from 30 July until 9 August 1991. There were more than 400 participants, from 29 countries, making it a truly international gathering. The congress had the support of the Deutsche Forschungsgemeinschaft, the European Economic Community, the International Association of Math- ematical Physics, the International Mathematical Union and the Interna- tional Union of Pure and Applied Physics. There were also sponsors from in- dustry and commerce: ATC Mann, Deutsche Bank AG, Miele & Cie GmbH, NEC Deutschland GmbH, Rank Xerox, Siemens AG and Stiftungsfonds IBM Deutschland. On behalf of the congress participants and the members of the International Association of Mathematical Physics, I would like to thank all these organisations for their very generous support. The congress took place under the auspices of the Ministerp6isident des Freistaates Sachsen, K. Biedenkopf. The conference began with an address by A. Uhlmann, Chairman of the Local Organizing Committee. This was followed by speeches of welcome from F. Magirius, City President of Leipzig; C. Weiss, Rector of the Uni- versity of Leipzig; and A. Jaffe, President of the International Association of Mathematical Physics.

An international workshop on Elementary Excitations and Fluctuations in Magnetic Systems was held in Turin for five days beginning 25 May, 1987. The workshop followed much the same format as the one with the same title held in San Miniato in 1984 (proceedings: Springer Series in-Solid-State Sciences, Vol. 54), that most participants contributed talks and provided papers for the proceedings. While many of the participants had attended the first workshop, 15 of the 40 invited review papers were presented by scientists who had not. The majority of the talks reported theoretical work concerned with the introduction of new techniques. However, experimental work was also well represented, not least because many of the reported theoretical studies were motivated by experimental findings, and a highlight of the workshop was an extremely stimulating session devoted to recent neutron scattering measure- ments, on various systems, that exploited polarization analysis. The fine venue of the workshop, Villa Gualino, with its excellent facili- ties and spacious accommodation, helped to produce a delightful relaxed and friendly atmosphere. For the use of Villa Gualino and significant financial support we are indebted to our host organization, the Institute for Scien- tific Interchange (lSI). Additional financial support came from the Consiglio Nazionale delle Ricerche (CNR), Centro Interuniversitario di Struttura della Material del Ministero della Pubblica Istruzione (CISM-MPI) and Gruppo Nazionale di Struttura della Materia (GNSM-CNR).

The Second European Turbulence Conference was held at the Technische Univer sitat Berlin, Federal Republic of Germany, from August 30th to September 2nd 1988 under the auspices of the European Mechanics Committee. It was primar ily devoted to fundamental aspects of turbulence, and aimed at bringing together engineers, physicists, and mathematicians. The scientific committee - serving also as Sub-committee of the European Turbulence Conference - consisted of the following members: G. Comte-Bellot (Lyon), H.-H. Fernholz and H.E. Fiedler (both from Berlin) as co-chairmen of the conference, U. Frisch (Nice), J.C.R. Hunt (Cambridge), E. Krause (Aachen), M. Landahl (Stockholm), A.M. Obukhov (Moscow), and G. Ooms (Amsterdam). The conference programme comprised 6 invited lectures and 94 contributions, presented either orally or at poster sessions. There were 165 participants from 18 countries. All papers published in these conference proceedings were, with the exception of the invited ones, again refereed by the members of the scientific committee. The main research topics discussed at this meeting were stability and gener ation of turbulence, effects of rotation, stratification and buoyancy forces, novel instrumentation, manipulation and control, boundary layers with separation and reattachment, computer simulation, turbulent diffusion, image analysis and flow visualization, vorticity dynamics and turbulence, and large-scale structures. We have taken the liberty of regrouping some papers following the submitted final versions for this volume. Authors may therefore find their paper under a different heading from that in the conference programme."

What is thermodynamics? What does statistical physics teach us? In the pages of this slim book, we confront the answers. The reader will discover that where thermodynami cs provi des a 1 arge scal e, macroscopi c theory of the ef fects of temperature on physical systems, statistical mechanics provides the microscopic analysis of these effects which, invariably, are the results of thermal disorder. A number of systems in nature undergo dramatic changes in aspect and in their properties when subjected to changes in ambient temperature or pres sure, or when electric or magnetic fields are applied. The ancients already knew that a liquid, a solid, or a gas can represent different states of the same matter. But what is meant by "state"? It is here that the systematic study of magnetic materials has provided one of the best ways of examining this question, which is one of the principal concerns of statistical physics (alias "statistical mechanics") and of modern thermodynamics."

Rhythms are a basic phenomenon in all physiological systems. They cover an enormous range of frequencies with periods from the order of milliseconds up to some years. They are described by many disciplines and are investigated usually in the context of the physiology of the respective function or organ. The importance given to the research on rhythmicity is quite different in different systems. In some cases where the functional significance is obvious rhythms are at the center of interest, as in the case of respiration or locomotion. In other fields they are considered more or less as interesting epiphenomena or at best as indicators without essential functional significance, as in the case of cardiovascular or EEG rhythms. Recently the study of physiological rhythms has attracted growing interest in several fields, especially with respect to rhythm research in humans and its rapidly spreading applications in basic behavioral research, and as a diagnostic tool in clinical medicine. This development was favored by two methodological and conceptual ad vances: on the one hand, the availability of non-invasive methods of continu ous recording of physiological parameters and their computer-assisted evaluation, and on the other, the rapid development of theoretical analyses, for example, the understanding of dynamic systems, the generation of coordinated macroscopic pro cesses in systems comprising many single elements, and the mathematical tools for treating nonlinear oscillators and their mutual coupling.

Fundamentals of Continuum Mechanics of Soils provides a long-needed general scheme for the study of the important yet problematic material of soil. It closes the gap between two disciplines, soil mechanics and con- tinuum mechanics, showing that the familiar concepts of soil mechanics evolve directly from continuum mechanics. It confirms concepts such as pore pressures, cohesion and dependence of the shear stress on consolidation, and rejects the view that continuum mechanics cannot be applied to a material such as soil. The general concepts of continuum mechanics, field equations and constitutive equations are discussed. It is shown how the theory of mixtures evolves from these equations and how, along with energetics and irrevers- ible thermodynamics, it can be applied to soils. The discussion also sheds light on some aspects of mechanics of materials, especially compressible materials. Examples are the introduction of the Hencky measure of strain, the requirement of dual constitutive equations, and the dependence of the spent internal energy on the stored internal energy. Researchers in engineering mechanics and material sciences may find that the results of experiments on soils can be generalized and extended to other materials. The book is a reference text for students familiar with the fundamentals of mechanics, for scholars of soil engineering, and for soil scientists. It is also suitable as an advanced undergraduate course in soil mechanics.

This monograph treats, for the first time, major aspects of gas dynamics of nozzles from a general point of view. Its outstanding feature is the pre- sentation of the modern theory of gas flows and modern analytical and nu- merical methods, together with numerous examples of practical applications. At the same time, quite diverse physico-chemical processes, such as disso- ciation and recombination, relaxation of vibrational degrees of freedom, two-phase flows wi th phase trans formati ons and e 1 ectromagneti c i nf1 uences, are considered. The material is presented in such a way as to help the reader to use numer- ous methods and approaches, not only for the study of gas flows in nozzles, but also for the investigation of a wide variety of problems of physical gas dynamics in different areas of application. The number of applications which may benefit from the use of the methods and results presented in this book is constantly growing. Theoretical, numerical and analytical methods of physical gas dynamics of internal flows may be, and are nowadays, ap- plied to solving the problem of preventing pollution of the air basin with toxic substances. These methods make it possible to describe the formation and transformation of toxic components in the vapour generators of thermal power plants, internal combustion engines and various metallurgical instal- lations. The methods of physical gas dynamics may be used in meteorology and powder metallurgy to create ultradispersed media and predict their proper- ties.

Convective heat tranfer is the result of fluid flowing between objects of different temperatures. Thus it may be the objective of a process (as in refrigeration) or it may be an incidental aspect of other processes. This monograph reviews in a concise and unified manner recent contributions to the principles of convective heat transfer for single- and multi-phase systems: It summarizes the role of the fundamental mechanism, discusses the governing differential equations, describes approximation schemes and phenomenological models, and examines their solutions and applications. After a review of the basic physics and thermodynamics, the book divides the subject into three parts. Part 1 deals with single-medium transfer, specifically with intraphase transfers in single-phase flows and with intramedium transfers in two-phase flows. Part 2 deals with fluid-solid transfer processes, both in cases where the interface is small and in cases where it is large, as well as liquid-liquid transfer processes. Part 3 considers three media, addressing both liquid-solid-solid and gas-liquid-solid systems.

This book is based on research carried out by the author in close collabora- tion with a number of colleagues. In particular, I wish to thank Per Bak, A. John Berlinsky, Hans C. Fogedby, Barry Frank, S. 1. Knak Jensen, David Mukamel, David Pink, and Martin Zuckermann for fruitful and extremely stimulating cooperation. It is a pleasure for me to note that active interaction with most of these colleagues is still continuing. The work has been performed at several different institutions, notably the Department of Chemistry, Aarhus University, Denmark, and the Depart- ment of Physics, University of British Columb~a, Canada. I wish to thank the Department of Chemistry at Aarhus University for providing me with splen- did research facilities over the years. From May 1980 to August 1981, I visited the Department of Physics at the University of British Columbia and I would like to express my sincere gratitude to members ofthe department for provi- ding me with excellent working conditions. My special thanks are due to Professor Myer Bloom who introduced me to the field of phase transitions in biological membranes and in whose biomembrane group I found an extre- mely stimulating scientific atmosphere happily married with a most agreeable social climate. During the last two years when a major part ofthis work was carried out, I was supported by AlS De Danske Spritfabrikker through their Jubilreumsle- gat of 1981. Their support is gratefully acknowledged.

Statistical thermodynamics and the related domains of statistical physics and quantum mechanics are very important in many fields of research, including plasmas, rarefied gas dynamics, nuclear systems, lasers, semiconductors, superconductivity, ortho- and para-hydrogen, liquid helium, and so on. Statistical Thermodynamics: Understanding the Properties of Macroscopic Systems provides a detailed overview of how to apply statistical principles to obtain the physical and thermodynamic properties of macroscopic systems. Intended for physics, chemistry, and other science students at the graduate level, the book starts with fundamental principles of statistical physics, before diving into thermodynamics. Going further than many advanced textbooks, it includes Bose-Einstein, Fermi-Dirac statistics, and Lattice dynamics as well as applications in polaron theory, electronic gas in a magnetic field, thermodynamics of dielectrics, and magnetic materials in a magnetic field. The book concludes with an examination of statistical thermodynamics using functional integration and Feynman path integrals, and includes a wide range of problems with solutions that explain the theory.

This book is an introduction to the physics of elementary excitations in condensed matter with emphasis on basic concepts and their mathematical representations. The nature of the book is mainly determined by the fact that it was originally written, in Japanese, as one volume of Iwanami Series of Fundamental Physics supervised by Professor H. Yukawa. Our task was to portray the theory of condensed matter from a unified point of view for the student looking for his own research field and also for more senior readers interested in fundamentals of contemporary physics. As our point of view, we chose the concept of elementary excitation, which we believe to be one of the most fruitful concepts discovered by the quantum theory of matter. The present English edition has been translated by the authors themselves from the second, revised Japanese edition published in 1978, six years after publication of the first edition. In translating, we have introduced no major modifications; only the list of references has been made more suitable to overseas readers. In the English as well as in the Japanese editions, Chaps. 1,4, and part of 6 were written by Nakajima, Chaps. 2, 5, and 7 by Toyozawa, and Chaps. 3 and part of 6 by Abe. Finally we should like to thank Professor P. Fulde for kind help and Dr. H. Lotsch, SpriIiger-Verlag, for patient cooperation in making this English edition a reality.

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."

The core of ths book presents a theory developed by the author to combine the recent insight into empirical data with mathematical models in freeway traffic research based on dynamical non-linear processes.

The utilisation of renewable energies is not at all new; in the history of mankind renewable energies have for a long time been the primary possibility of generating energy. This only changed with industrial revolution when lignite and hard coal became increasingly more important. Later on, also crude oil gained importance. Offering the advantages of easy transportation and processing also as a raw material, crude oil has become one of the prime energy carriers applied today. Moreover, natural gas used for space heating and power provision as well as a transportation fuel has become increasingly important, as it is abundantly available and only requires low investments in terms of energy conversion facilities. As fossil energy carriers were increasingly used for energy generation, at least by the industrialised countries, the application of renewable energies decreased in absolute and relative terms; besides a few exceptions, renewable energies are of secondary importance with regard to overall energy generation.

Combustion of Two-Phase Reactive Media addresses the complex phenomena involved in the burning of solid and liquid fuels. In fact, the multiplicity of phenomena characteristic of combustion of two-phase media determine the contents. The three parts deal with: the dynamics of a single particle; combustion wave propagation in two-phase reactive media; and thermal regimes of combustion reactors. The book generalizes the results of numerous investigations into the ignition and combustion of solid particles, droplets and bubbles, combustion wave propagation in heterogeneous reactive media, the stability of combustion of two-phase media, as well as the thermal regimes of high-temperature combustion reactors. It merges findings from the authors investigations into problems of two-phase flows and material from graduate-level courses they teach at Technion-Israel Institute of Technology.

This concise and unified text reviews recent contributions to the principles of convective heat transfer for single and multi-phase systems. This valuable new edition has been updated throughout and contains new examples and problems.

The subject of the book is uid dynamics and heat transfer in micro-channels. This problem is important for understanding the complex phenomena associated with single- and two-phase ows in heated micro-channels. The challenge posed by high heat uxes in electronic chips makes thermal management a key factor in the development of these systems. Cooling of mic- electronic components by new cooling technologies, as well as improvement of the existing ones, is becoming a necessity as the power dissipation levels of integrated circuits increases and their sizes decrease. Miniature heat sinks with liquid ows in silicon wafers could signi cantly improve the performance and reliability of se- conductor devices. The improvements are made by increasing the effective thermal conductivity, by reducing the temperature gradient across the wafer, by reducing the maximum wafer temperature, and also by reducing the number and intensity of localized hot spots. A possible way to enhance heat transfer in systems with high power density is to change the phase in the micro-channels embedded in the device. This has motivated a number of theoretical and experimental investigations covering various aspects of heat transfer in micro-channel heat sinks with phase change. The ow and heat transfer in heated micro-channels are accompanied by a n- ber of thermohydrodynamic processes, such as liquid heating and vaporization, bo- ing, formation of two-phase mixtures with a very complicated inner structure, etc., which affect signi cantly the hydrodynamic and thermal characteristics of the co- ing systems.

This book provides a comprehensive presentation of the basics of statistical physics. The first part explains the essence of statistical physics and how it provides a bridge between microscopic and macroscopic phenomena, allowing one to derive quantities such as entropy. Here the author avoids going into details such as Liouville's theorem or the ergodic theorem, which are difficult for beginners and unnecessary for the actual application of the statistical mechanics. In the second part, statistical mechanics is applied to various systems which, although they look different, share the same mathematical structure. In this way readers can deepen their understanding of statistical physics. The book also features applications to quantum dynamics, thermodynamics, the Ising model and the statistical dynamics of free spins.