Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chif1ese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Substances possessing heterogeneous microstructure on the nanometer and micron scales are scientifically fascinating and technologically useful. Examples of such substances include liquid crystals, microemulsions, biological matter, polymer mixtures and composites, vycor glasses, and zeolites. In this volume, an interdisciplinary group of researchers report their developments in this field. Topics include statistical mechanical free energy theories which predict the appearance of various microstructures, the topological and geometrical methods needed for a mathematical description of the subparts and dividing surfaces of heterogeneous materials, and modern computer-aided mathematical models and graphics for effective exposition of the salient features of microstructured materials.

During the last half century, the development and testing of prediction models of combustion chamber performance have been an ongoing task at the International Flame Research Foundation (IFRF) in IJmuiden in the Netherlands and at many other research organizations. This task has brought forth a hierarchy of more or less standard numerical models for heat transfer predictions, in particular for the prediction of radiative heat transfer. Unfortunately all the methods developed, which certainly have a good physical foundation, are based on a large number of extreme sim plifications or uncontrolled assumptions. To date, the ever more stringent requirements for efficient production and use of energy and heat from com bustion chambers call for prediction algorithms of higher accuracy and more detailed radiative heat transfer calculations. The driving forces behind this are advanced technology requirements, the costs of large-scale experimen tal work, and the limitation of physical modeling. This interest is growing more acute and has increased the need for the publication of a textbook for more accurate treatment of radiative transfer in enclosures. The writing of a textbook on radiative heat transfer, however, in ad dition to working regularly on other subjects is a rather difficult task for which some years of meditation are necessary. The book must satisfy two requirements which are not easily reconciled. From the mathematical point of view, it must be written in accordance with standards of mathemati cal rigor and precision."

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.

Many novel cooperative phenomena found in a variety of systems studied by scientists can be treated using the uniting principles of synergetics. Examples are frustrated and random systems, polymers, spin glasses, neural networks, chemical and biological systems, and fluids. In this book attention is focused on two main problems. First, how local, topological constraints (frustrations) can cause macroscopic cooperative behavior: related ideas initially developed for spin glasses are shown to play key roles also for optimization and the modeling of neural networks. Second, the dynamical constraints that arise from the nonlinear dynamics of the systems: the discussion covers turbulence in fluids, pattern formation, and conventional 1/f noise. The volume will be of interest to anyone wishing to understand the current development of work on complex systems, which is presently one of the most challenging subjects in statistical and condensed matter physics.

The concept of this book was developed during the Winter Seminar held in the Austrian mountains at the Alpengasthof Zeinisjoch, Tirol-Vorarlberg, from February 27 to March 3, 1988. Leading experts and advanced students in math ematics, physics, chemistry and computer science met to present and discuss their most recent results in an informal seminar. These were the circumstances that led to the idea of compiling some of the essential contributions presented at this seminar together with others describing basic features of "optimal struc tures in heterogeneous reaction systems". The aim of this book is to present the scientific results of the intensive work carried out in each of the specific fields of research. Each contribution therefore presents the current state of the art together with a deeper treatment enabling a more comprehensive understanding of that particular field of work. The common ideas which unite all the different contributions are already ex pressed in the title of this book. The nature of heterogeneous reaction systems is quite varied. An example is provided by the chemical systems such as noble metal particles which may act as heterogeneous catalysts for gaseous chemical compounds. Under these circumstances the metal particles and/or their sur faces may undergo phase transitions during reaction. Imbihl and Plath report on special catalytic systems of this kind, which are of industrial importance.

Is the heat and mass transfer intensification defined as a new paradigm of process engineering, or is it just a common and old idea, renamed and given the current taste? Where might intensification occur? How to achieve intensification? How the shape optimization of thermal and fluidic devices leads to intensified heat and mass transfers? To answer these questions, "Heat & Mass Transfer Intensification and Shape Optimization: A Multi-scale Approach "clarifies the definition of the intensification by highlighting the potential role of the multi-scale structures, the specific interfacial area, the distribution of driving force, the modes of energy supply and the temporal aspects of processes.

A reflection on the methods of process intensification or heat and mass transfer enhancement in multi-scale structures is provided, including porous media, heat exchangers, fluid distributors, mixers and reactors. A multi-scale approach to achieve intensification and shape optimization is developed and clearly explained.

Providing readers with a tool box of reflections, techniques, methods, supported by literature reviews, "Heat & Mass Transfer Intensification and Shape Optimization: A Multi-scale Approach "will be a key guide for students, a teaching aid for lecturers and a source of inspiration for future research subjects.

Providing readers with a tool box of reflections, techniques, methods, supported by literature reviews, "Heat & Mass Transfer Intensification and Shape Optimization: A Multi-scale Approach "will be a key guide for students, a teaching aid for lecturers and a source of inspiration for future research subjects.

Continuing the tradition of the IUTAM Symposia TRANSSONICA, this review of the numerical simulation and physical modelling of transonic flows presents new developments in the fields of computational and experimental aerodynamics. A major topic of the symposium proceedings is the evaluation of present numerical analysis techniques with respect to transonic aerodynamics. In the field of experimental aerodynamics, the high Reynolds number effect and the interference-free testing in transonic wind tunnels are of special interest.

This book brings together data from Czechoslovakia on vapor pressures, data from England on critical properties, and data from America on physical properties of organic and organometallic compounds to provide a basic reference book for engineers and scientists involved with research and design in the chemical and petroleum industries. We would like to acknowledge Jaroslav Dykyj, Milan Repas, and Josef Svo boda of Czechoslovakia for providing the material on Antoine constants and Douglas Ambrose of the University of London for providing the material on critical properties. Stanislaw Malanowski pointed out and made available the sources of data from Eastern Europe. Richard Stephenson translated and correlated the data in tabular form. We would like to thank Dr. Matej Andras of the Slovenska Literarna Agentura for granting permission to use the data from Czechoslovakia and Dr. Marjan Bace of Elsevier Science Publishing Co., Inc., who encouraged preparation of this manuscript and handled the publishing arrangements. Particular thanks go to Mary Stephenson for typing the entire camera-ready copy. Richard M. Stephenson University of Connecticut Storrs, Connecticut Stanislaw Malanowski Institute of Physical Chemistry Warsaw, Poland vii Introduction All scientific and engineering calculations are dependent on the availability of thennodynamic and physical property data for the materials or systems in question. This dependency is particularly true in engineering design, which relies almost exclusively on computers for accurate data to produce meaningful final designs."

This volume comprises a selection of the best papers presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, held in Lisbon in July 1996.
The papers describe novel ideas for instrumentation, instrumentation developments, results of measurements of wall-bounded flows, free flows and flames and flow and combustion in engines. The papers demonstrate the continuing interest in the development of an understanding of new methodologies and implementation in terms of new instrumentation.

At first glance it may seem presumptuous to want to add yet another to the numerous books on Differential Thermal Analysis (DT A). Thermoanalytical methods have been in use for some time, as shown by the more than five thousand publications containing DT A or TG curves listed by SMOTHERS and CHIANG in the bibliography to their handbook and abstracted in the several volumes of Thermal Analysis Abstracts (TAA), edited by J. P. REDFERN for the International Con federation for Thermal Analysis (ICT A). Every three years the proceed ings of ICT A meetings are published, bringing the latest results of thermoanalytic research. There is also the Scifax DT A Data Index, edited by R. C. MACKENZIE (1962) and modeled on the ASTM pattern card index (used for X-ray investigations), a compilation of the DT A data for several hundred minerals, and inorganic and organic materials. The theoretical foundations of thermogravimetry and DT A have been described in detail by LEHMANN, DAS and PAETSCH (1953), R. C. MACKENZIE (1957, 1970), DUVAL (1963), WENDLANDT (1964), GARN (1965), F. PAULIK et al. (1966), SMOTHERS and CHIANG (1966), and KEATTCH (1969). Thermoanalytical results are strongly influenced by various factors relative to preparation and equipment (see 1-2. 4 of this study). This is the reason why we frequently find, in these books as well as in the Scifax-Card catalog, contradictory data on the same substance."

The idea for this book was conceived by the authors some time in 1988, and a first outline of the manuscript was drawn up during a summer school on mathematical physics held in Ravello in September 1988, where all three of us were present as lecturers or organizers. The project was in some sense inherited from our friend Marvin Shinbrot, who had planned a book about recent progress for the Boltzmann equation, but, due to his untimely death in 1987, never got to do it. When we drew up the first outline, we could not anticipate how long the actual writing would stretch out. Our ambitions were high: We wanted to cover the modern mathematical theory of the Boltzmann equation, with rigorous proofs, in a complete and readable volume. As the years progressed, we withdrew to some degree from this first ambition- there was just too much material, too scattered, sometimes incomplete, sometimes not rigor ous enough. However, in the writing process itself, the need for the book became ever more apparent. The last twenty years have seen an amazing number of significant results in the field, many of them published in incom plete form, sometimes in obscure places, and sometimes without technical details. We made it our objective to collect these results, classify them, and present them as best we could. The choice of topics remains, of course, subjective.

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.

This book deals with a subject that has been studied since the beginning of physical chemistry. Despite the thousands of articles and scores of books devoted to solvation thermodynamics, I feel that some fundamen tal and well-established concepts underlying the traditional approach to this subject are not satisfactory and need revision. The main reason for this need is that solvation thermodynamics has traditionally been treated in the context of classical (macroscopic) ther modynamics alone. However, solvation is inherently a molecular pro cess, dependent upon local rather than macroscopic properties of the system. Therefore, the starting point should be based on statistical mechanical methods. For many years it has been believed that certain thermodynamic quantities, such as the standard free energy (or enthalpy or entropy) of solution, may be used as measures of the corresponding functions of solvation of a given solute in a given solvent. I first challenged this notion in a paper published in 1978 based on analysis at the molecular level. During the past ten years, I have introduced several new quantities which, in my opinion, should replace the conventional measures of solvation thermodynamics. To avoid confusing the new quantities with those referred to conventionally in the literature as standard quantities of solvation, I called these "nonconventional," "generalized," and "local" standard quantities and attempted to point out the advantages of these new quantities over the conventional ones."

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.

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.

This work marks a stage in the evolution of a scientific and technical field which has been developed by the Commissariat a l'Energie Atomique (CEA) over several decades. Many members of the staff of the CEA have won re nown in this field, and their work has brought it to the high degree of excel lence for which it is internationally recognized today. These scientists had to consider every aspect of the field, as it concerned: modeling, which has recourse to fluid thermodynamics, molecular phys ics, and chemistry; numerical evaluation, which relies on mathematical analysis and data processing; and experiments in the firing area, which require specific stress generators and instrumentation. Whilst this book is a testament to the activity and success of staff of the CEA, it also reviews a number ofthe advances made in the discipline. How ever, it is not intended to be an exhaustive account of those advances; it is assumed that the reader can, if desired, consult the standard monographs, and more recent, more specialized works (notably W.C. Davis and W. Fickett, and C.L. Mader). The history of the discipline is interesting in itself, and also as an illustra tion of the causes which lead to progress in a coherent body of scientific work. I should like to make some comments on this progress, of which there is a fascinating summary in the introduction, and which will figure largely throughout the work."

Over the years enormous effort was invested in proving ergodicity, but for a number of reasons, con?dence in the fruitfulness of this approach has waned. - Y. Ben-Menahem and I. Pitowsky [1] Abstract The basic motivation behind the present text is threefold: To give a new explanation for the emergence of thermodynamics, to investigate the interplay between quantum mechanics and thermodynamics, and to explore possible ext- sions of the common validity range of thermodynamics. Originally, thermodynamics has been a purely phenomenological science. Early s- entists (Galileo, Santorio, Celsius, Fahrenheit) tried to give de?nitions for quantities which were intuitively obvious to the observer, like pressure or temperature, and studied their interconnections. The idea that these phenomena might be linked to other ?elds of physics, like classical mechanics, e.g., was not common in those days. Such a connection was basically introduced when Joule calculated the heat equ- alent in 1840 showing that heat was a form of energy, just like kinetic or potential energy in the theory of mechanics. At the end of the 19th century, when the atomic theory became popular, researchers began to think of a gas as a huge amount of bouncing balls inside a box.

Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk, were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (:::: ) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (:::: ) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.

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.

The potential of supercritical fluid methods is presented in a comprehensive way. On the basis of a careful discussion of physical and chemical principles, the application of this method in process technology is demonstrated.

`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.

'Why are atoms so small?' asks 'naive physicist' in Erwin Schrodinger's book 'What is Life? The Physical Aspect of the Living Cell'. 'The question is wrong' answers the author, 'the actual problem is why we are built of such an enormous number of these particles'. The idea that everything is built of atoms is quite an old one. It seems that l Democritus himself borrowed it from some obscure Phoenician source . The arguments for the existence of small indivisible units of matter were quite simple. 2 According to Lucretius observable matter would disappear by 'wear and tear' (the world exists for a sufficiently long, if not infinitely long time) unless there are some units which cannot be further split into parts. th However, in the middle of the 19 century any reference to the atomic structure of matter was considered among European physicists as a sign of extremely bad taste and provinciality. The hypothesis of the ancient Greeks (for Lucretius had translated Epicurean philosophy into Latin hexameters) was at that time seen as bringing nothing positive to exact science. The properties of gaseous, liquid and solid bodies, as well as the behaviour of heat and energy, were successfully described by the rapidly developing science of thermodynamics.

In the tradition of its predecessors, this volume comprises a selection of the best papers presented at the Ninth International Symposium on Applications of Laser Techniques to Fluid Mechanics, held in Lisbon in July 2000.
The papers reflect the state-of-the-art in laser applications of laser techniques in fluid mechanics describing novel ideas for instrumentation, instrumentation developments, results of measurements of wall-bounded flows, free flows and flames and flow and combustion in engines. The papers demonstrate the continuing interest in the development of an understanding of new methodologies and implementation in terms of new instrumentation.

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.