Here is a new method for calculating heat transfer in coupled convective-conductive fluid-wall systems under periodical intensity oscillations in fluid flow. The true steady state mean value of the heat transfer coefficient must be multiplied by a newly defined coupling factor, which is always smaller than one and depends on the coupling parameters Biot number, Fourier number as well as dimensionless geometry and oscillation parameters. Includes characteristic solved problems, with tables and diagrams.

Most of the specialists working in this interdisciplinary field of physics, biology, biophysics and medicine are associated with "The International Institute of Biophysics" (IIB), in Neuss, Germany, where basic research and possibilities for applications are coordinated. The growth in this field is indicated by the increase in financial support, interest from the scientific community and frequency of publications.

Audience: The scientists of IIB have presented the most essential background and applications of biophotonics in these lecture notes in biophysics, based on the summer school lectures by this group. This book is devoted to questions of elementary biophysics, as well as current developments and applications. It will be of interest to graduate and postgraduate students, life scientists, and the responsible officials of industries and governments looking for non-invasive methods of investigating biological tissues.

The contents of this book are the result of work performed in the past three years to provide some answers to questions raised by several colleagues wo- inginastrophysics. Examiningseveraltransportprocessesinplasmasrelated to dissipative e?ects in phenomena such as cooling ?ows, propagation of sound waves, thermal conduction in the presence of magnetic ?elds, an- lar momentum transfer in accretion disks, among many, one ?nds a rather common pattern. Indeed when values for transport coe?cients are required the overwhelming majority of authors refer to the classical results obtained by L. Spitzer and S. Braginski over forty years ago. Further, it is also often mentioned that under the prescribed working conditions the values of such coe?cients are usually insu?cient to provide agreement with observations. The methodology followed by these authors is based upon Landau's - oneering idea that collisions in plasmas may be substantially accounted for when viewed as a di?usive process. Consequently the ensuing basic kinetic equation is the Fokker-Planck version of Boltzmann's equation as essentially proposed by Landau himself nearly 70 years ago. Curiously enough the magni?cent work of the late R. Balescu in both Classical and Non-Classical transport in plasmas published in 1988 and also based on the Fokker-Planck equation is hardly known in the astrophysical audience. The previous work of Spitzer and Braginski is analyzed with much more rigorous vision in his two books on the subject.

The first volume of this work is organized in three levels, so that the portion and importance of thermodynamics and mathematics increase from level to level. The ground level shows that basics of phase equilibria can be understood without thermodynamics provided the concept of chemical potential is introduced early. The intermediate level introduces thermodynamics, culminating in the Gibbs energy as the arbiter for equilibrium. At the third level the accent is on binary systems, where one or more phases are solutions of the components. Priority is given throughout to the thermodynamic assessment of experimental data. 200 exercises are included with solutions.

Stratospheric processes play a signi?cant role in regulating the weather and c- mate of the Earth system. Solar radiation, which is the primary source of energy for the tropospheric weather systems, is absorbed by ozone when it passes through the stratosphere, thereby modulating the solar-forcing energy reaching into the t- posphere. The concentrations of the radiatively sensitive greenhouse gases present in the lower atmosphere, such as water vapor, carbon dioxide, and ozone, control the radiation balance of the atmosphere by the two-way interaction between the stratosphere and troposphere. The stratosphere is the transition region which interacts with the weather s- tems in the lower atmosphere and the richly ionized upper atmosphere. Therefore, this part of the atmosphere provides a long list of challenging scienti?c problems of basic nature involving its thermal structure, energetics, composition, dynamics, chemistry, and modeling. The lower stratosphere is very much linked dynamically, radiatively, and chemically with the upper troposphere, even though the temperature characteristics of these regions are different. The stratosphere is a region of high stability, rich in ozone and poor in water - por and temperature increases with altitude. The lower stratospheric ozone absorbs the harmful ultraviolet (UV) radiation from the sun and protects life on the Earth. On the other hand, the troposphere has high concentrations of water vapor, is low in ozone, and temperature decreases with altitude. The convective activity is more in the troposphere than in the stratospher

Modern energetic materials include explosives, blasting powders, pyrotechnic m- tures and rocket propellants [1, 2]. The study of high-temperature decomposition of condensed phases of propellants and their components (liquid, solid and hybrid) is currently of special importance for the development of space-system engineering [3, 4]. To better understand the burning mechanisms (stationary, nonstationary, - steady) of composite solid propellants and their components, information about the macrokinetics of their high-temperature decomposition is required [5]. To be able to evaluate the ignition parameters and conditions of safe handling of heat-affected explosives, one needs to know the kinetic constants of their high-temperature - composition. The development of new composite solid propellants characterized by high performance characteristics (high burning rates, high thermal stability, stability to intrachamber perturbations, and other aspects) is not possible without quanti- tive data on the high-temperature decomposition of composite solid propellants and their components [6]. The same reasons have resulted in signi?cant theoretical and practical interest in the high-temperature decomposition of components of hybrid propellants. It is known that hybrid propellants have not been used very widely due to the low bu- ing (pyrolysis) rates of the polymer blocks in the combustion chambers of hybrid rocket engines. To increase the burning rates it is necessary to obtain information about their relationships to the corresponding kinetic and thermophysical prop- ties of the fuels.

The book constitutes a particularly complete and original collection of ideas, models, numerical methods and experimental tools which will prove invaluable in the study of microscale and nanoscale heat transfer. It should be of interest to research scientists and thermal engineers who wish to carry out theoretical research or metrology in this field, but also to physicists concerned with the problems of heat transfer, or teachers requiring a solid foundation for an undergraduate university course in this area.

Presents experiment, theory and technology in a unified manner.

Contains numerous illustrations, tables and references as well as carefully selected problems for students.

Surveys the fascinating historical development of the field.

Although the solution of Partial Differential Equations by numerical methods is the standard practice in industries, analytical methods are still important for the critical assessment of results derived from advanced computer simulations and the improvement of the underlying numerical techniques. Literature devoted to analytical methods, however, often focuses on theoretical and mathematical aspects and is therefore useless to most engineers. Analytical Methods for Heat Transfer and Fluid Flow Problems addresses engineers and engineering students. It describes useful analytical methods by applying them to real-world problems rather than solving the usual over-simplified classroom problems. The book demonstrates the applicability of analytical methods even for complex problems and guides the reader to a more intuitive understanding of approaches and solutions.

Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions.

It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution).

The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions.

Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.

The methods of statistical physics have become increasingly important in recent years for the treatment of a variety of diverse physical problems. Of principal interest is the microscopic description of the dynamics of dissipative systems. Although a unified theoretical description has at present not yet been achieved, we have assumed the task of writing a textbook which summarizes those of the most important methods which are self-contained and complete in themselves. We cannot, of course, claim to have treated the field exhaustively. A microscopic description of physical phenomena must necessarily be based upon quantum theory, and we have therefore carried out the treatment of dynamic processes strictly within a quantum-theoretical framework. For this reason alone it was necessary to omit a number of extremely important theories which have up to now been formulated only in terms of classical statistics. The goal of this book is, on the one hand, to give an introduction to the general principles of the quantum statistics of dynamical processes, and, on the other, to provide readers who are interested in the treatment of particular phenomena with methods for solving specific problems. The theory is for the most part formulated within the calculational frame work of Liouville space, which, together with projector formalism, has become an expedient mathematical tool in statistical physics."

Many phenomena in social, natural and engineering fields are governed by wave, potential, parabolic heat-conduction, hyperbolic heat-conduction and dual-phase-lagging heat-conduction equations. This monograph examines these equations: their solution structures, methods of finding their solutions under various supplementary conditions, as well as the physical implication and applications of their solutions.

This monograph develops a unified microscopic basis for phases and phase changes of bulk matter and small systems, based on classical physics. It describes the thermodynamics of ensembles of particles and explains phase transition in gaseous and liquid systems. The origins are derived from simple but physically relevant models of how transitions occur between rigid and fluid states, of how phase equilibria arise, and how they differ for small and large systems.

J-B. J. FOURIER'S immensely influential treatise Theorie Analytique de la Chaleur [21J, and the subsequent developments and refinements of FOURIER's ideas and methods at the hands of many authors, provide a highly successful theory of heat conduction. According to that theory, the growth or decay of the temperature e in a conducting body is governed by the heat equation, that is, by the parabolic partial differential equation Such has been the influence of FOURIER'S theory, which must forever remain the classical theory in that it sets the standard against which all other theories are to be measured, that the mathematical investigation of heat conduction has come to be regarded as being almost identicalt with the study of the heat equation, and the reader will not need to be reminded that intensive analytical study has t But not entirely; witness, for example, those theories which would replace the heat equation by an equation which implies a finite speed of propagation for the temperature. The reader is referred to the article [9] of COLEMAN, FABRIZIO, and OWEN for the derivation of such an equation from modern Continuum Thermody namics and for references to earlier work in this direction. viii Introduction amply demonstrated that the heat equation enjoys many properties of great interest and elegance.

The approach to plasticity theory developed here is firmly rooted in thermodynamics. Emphasis is placed on the use of potentials and the derivation of incremental response, necessary for numerical analysis. The derivation of constitutive models for irreversible behaviour entirely from two scalar potentials is shown.

The use of potentials allows models to be very simply defined, classified and, if necessary, developed and it permits dependent and independent variables to be interchanged, making possible different forms of a model for different applications.

The theory is extended to include treatment of rate-dependent materials and a powerful concept, in which a single plastic strain is replaced by a plastic strain function, allowing smooth transitions between elastic and plastic behaviour is introduced.

This monograph will benefit academic researchers in mechanics, civil engineering and geomechanics and practising geotechnical engineers; it will also interest numerical analysts in engineering mechanics.

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."

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.

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."