The aim of this book is to comment on, and clarify, the mathematical aspects of the theory of thermodynamics. The standard presentations of the subject are often beset by a number of obscurities associated with the words "state", "reversible", "irreversible", and "quasi-static". This book is written in the belief that such obscurities are best removed not by the formal axiomatization of thermodynamics, but by setting the theory in the wider context of a genuine field theory which incorporates the effects of heat conduction and intertia, and proving appropriate results about the governing differential equations of this field theory. Even in the simplest one-dimensional case it is a nontrivial task to carry through the details of this program, and many challenging problems remain open.

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."

One of the most spectacular consequences of the description of the superfluid condensate in superfluid He or in superconductors as a single macroscopic quantum state is the quantization of circulation, resulting in quantized vortex lines. This book draws no distinction between superfluid He3 and He4 and superconductors. The reader will find the essential introductory chapters and the most recent theoretical and experimental progress in our understanding of the vortex state in both superconductors and superfluids, from lectures given by leading experts in the field, both experimentalists and theoreticians, who gathered in Cargese for a NATO ASI. The peculiar features related to short coherence lengths, 2D geometry, high temperatures, disorder, and pinning are thoroughly discussed. "

We have classified the articles presented here in two Sections according to their general content. In Part I we have included papers which deal with statistical mechanics, math ematical aspects of dynamical systems and sthochastic effects in nonequilibrium systems. Part II is devoted mainly to instabilities and self-organization in extended nonequilibrium systems. The study of partial differential equations by numerical and analytic methods plays a great role here and many works are related to this subject. Most recent developments in this fascinating and rapidly growing area are discussed. PART I STATISTICAL MECHANICS AND RELATED TOPICS NONEQUILIBRIUM POTENTIALS FOR PERIOD DOUBLING R. Graham and A. Hamm Fachbereich Physik, Universitiit Gesamthochschule Essen D4300 Essen 1 Germany ABSTRACT. In this lecture we consider the influence of weak stochastic perturbations on period doubling using nonequilibrium potentials, a concept which is explained in section 1 and formulated for the case of maps in section 2. In section 3 nonequilibrium potentials are considered for the family of quadratic maps (a) at the Feigenbaum 'attractor' with Gaussian noise, (b) for more general non Gaussian noise, and (c) for the case of a strange repeller. Our discussion will be informal. A more detailed account of this and related material can be found in our papers [1-3] and in the reviews [4, 5], where further references to related work are also given. 1.

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.

Deeply rooted in fundamental research in Mathematics and Computer Science, Cellular Automata (CA) are recognized as an intuitive modeling paradigm for Complex Systems. Already very basic CA, with extremely simple micro dynamics such as the Game of Life, show an almost endless display of complex emergent behavior. Conversely, CA can also be designed to produce a desired emergent behavior, using either theoretical methodologies or evolutionary techniques. Meanwhile, beyond the original realm of applications - Physics, Computer Science, and Mathematics - CA have also become work horses in very different disciplines such as epidemiology, immunology, sociology, and finance. In this context of fast and impressive progress, spurred further by the enormous attraction these topics have on students, this book emerges as a welcome overview of the field for its practitioners, as well as a good starting point for detailed study on the graduate and post-graduate level. The book contains three parts, two major parts on theory and applications, and a smaller part on software. The theory part contains fundamental chapters on how to design and/or apply CA for many different areas. In the applications part a number of representative examples of really using CA in a broad range of disciplines is provided - this part will give the reader a good idea of the real strength of this kind of modeling as well as the incentive to apply CA in their own field of study. Finally, we included a smaller section on software, to highlight the important work that has been done to create high quality problem solving environments that allow to quickly and relatively easily implement a CA model and run simulations, both on the desktop and if needed, on High Performance Computing infrastructures.

Adaptive Resonance Theory Microchips describes circuit strategies resulting in efficient and functional adaptive resonance theory (ART) hardware systems. While ART algorithms have been developed in software by their creators, this is the first book that addresses efficient VLSI design of ART systems. All systems described in the book have been designed and fabricated (or are nearing completion) as VLSI microchips in anticipation of the impending proliferation of ART applications to autonomous intelligent systems. To accommodate these systems, the book not only provides circuit design techniques, but also validates them through experimental measurements. The book also includes a chapter tutorially describing four ART architectures (ART1, ARTMAP, Fuzzy-ART and Fuzzy-ARTMAP) while providing easily understandable MATLAB code examples to implement these four algorithms in software. In addition, an entire chapter is devoted to other potential applications for real-time data clustering and category learning.

It is our pleasure to contribute the forewordto this book on symbiotic mul- robot organisms, which is largely based on the scienti?c ?ndings and exp- rations of two major EU research projects, Symbrion and Replicator, funded under the Seventh Framework Programme for Research and Technological 1 development (FP7) . FP7 emphasises consortia of European partners, tra- national collaboration, open coordination, ?exibility and excellence of - search and plays a leading role in multidisciplinary research and cooperative activities in Europe and beyond. Its impact is major in terms of integrating and structuring research communities across national borders to achieve a critical mass, providing the leverage for high-potential ?elds to take o?, and encouraging healthy competition at European level while avoiding unn- essary duplication of research capacities. Research proposals are evaluated through a demanding peer-review process and only the best are selected to be funded bythe EuropeanCommission(EC). The InformationandCom- nication Technologies(ICT) theme has set out a number of challengeswithin this context, which cover topics such as cognitive systems, modular robotics, adaptive systems and societies of artefacts. * Symbrion was selected following the Call "Pervasive Adaptation" of the 2 "Future and Emerging Technologies (FET)" programme area. Itstarted on 1 February 2008 and will run for 5 years. FET Proactive addresses evolutionary and revolutionary approaches through multidisciplinary - operation and investigates new future technology options in response to emerging societal and industrial needs and identi?es new drivers for - search.

Computational intelligence encompasses a wide variety of techniques that allow computation to learn, to adapt, and to seek. That is, they may be designed to learn information without explicit programming regarding the nature of the content to be retained, they may be imbued with the functionality to adapt to maintain their course within a complex and unpredictably changing environment, and they may help us seek out truths about our own dynamics and lives through their inclusion in complex system modeling. These capabilities place our ability to compute in a category apart from our ability to erect suspension bridges, although both are products of technological advancement and reflect an increased understanding of our world. In this book, we show how to unify aspects of learning and adaptation within the computational intelligence framework. While a number of algorithms exist that fall under the umbrella of computational intelligence, with new ones added every year, all of them focus on the capabilities of learning, adapting, and helping us seek. So, the term unified computational intelligence relates not to the individual algorithms but to the underlying goals driving them. This book focuses on the computational intelligence areas of neural networks and dynamic programming, showing how to unify aspects of these areas to create new, more powerful, computational intelligence architectures to apply to new problem domains.

This sixth Volume of the International Workshop on Instabilities and Nonequilibrium Structures is dedicated to the memory of my friend Walter Zeller, Professor of the Universidad C'at6lica df' Valparaiso and Vice-Director of the Workshop. Walter Zeller was much more than an organizer of this meeting: his enthusiasm, dedication and critical views were many times the essential ingredients to continue with a task which in occasions faced difficulties and incomprehensiolls. It is in great part due to him that the workshop has adquired to-day tradition. maturity and international recognition. This Volume should have been coedited by Walter and it is with df'ep emotion that I learned that his disciples Javier Martinez and Rolando Tiemann wanted as a last hommage to their Professor and friend to coedit tfus book. No me seria posible terminal' estas lineas sin pensar en la senora Adriana Gamonal de Zelln. qUf' ella encuentre en este libro la admiraci6n y reconocimiento hacia su marido de quiPIlf's [l\Prall sus discipulos, colegas y amigos.

Hybrid Neural Network and Expert Systems presents the basics of expert systems and neural networks, and the important characteristics relevant to the integration of these two technologies. Through case studies of actual working systems, the author demonstrates the use of these hybrid systems in practical situations. Guidelines and models are described to help those who want to develop their own hybrid systems. Neural networks and expert systems together represent two major aspects of human intelligence and therefore are appropriate for integration. Neural networks represent the visual, pattern-recognition types of intelligence, while expert systems represent the logical, reasoning processes. Together, these technologies allow applications to be developed that are more powerful than when each technique is used individually. Hybrid Neural Network and Expert Systems provides frameworks for understanding how the combination of neural networks and expert systems can produce useful hybrid systems, and illustrates the issues and opportunities in this dynamic field.

An Analog VLSI System for Stereoscopic Vision investigates the interaction of the physical medium and the computation in both biological and analog VLSI systems by synthesizing a functional neuromorphic system in silicon. In both the synthesis and analysis of the system, a point of view from within the system is adopted rather than that of an omniscient designer drawing a blueprint. This perspective projects the design and the designer into a living landscape. The motivation for a machine-centered perspective is explained in the first chapter. The second chapter describes the evolution of the silicon retina. The retina accurately encodes visual information over orders of magnitude of ambient illumination, using mismatched components that are calibrated as part of the encoding process. The visual abstraction created by the retina is suitable for transmission through a limited bandwidth channel. The third chapter introduces a general method for interchip communication, the address-event representation, which is used for transmission of retinal data. The address-event representation takes advantage of the speed of CMOS relative to biological neurons to preserve the information of biological action potentials using digital circuitry in place of axons. The fourth chapter describes a collective circuit that computes stereodisparity. In this circuit, the processing that corrects for imperfections in the hardware compensates for inherent ambiguity in the environment. The fifth chapter demonstrates a primitive working stereovision system. An Analog VLSI System for Stereoscopic Vision contributes to both computer engineering and neuroscience at a concrete level. Through the construction of a working analog of biological vision subsystems, new circuits for building brain-style analog computers have been developed. Specific neuropysiological and psychophysical results in terms of underlying electronic mechanisms are explained. These examples demonstrate the utility of using biological principles for building brain-style computers and the significance of building brain-style computers for understanding the nervous system.

Deng Feng Wang was born February 8, 1965 in Chongqing City, China and died August 15, 1999 while swimming with friends in the Atlantic Ocean off Island Beach State Park, New Jersey. In his brief life, he was to have an influence far beyond his years. On August 12th 2000, The Deng Feng Wang Memorial Conference was held at his alma mater, Princeton University, during which Deng Feng's mentors, collaborators and friends presented scientific talks in a testimonial to his tremendous influence on their work and careers. The first part of this volume contains proceedings contributions from the conference, with plenary talks by Nobel Laureate Professor Phil Anderson of Princeton University and leading Condensed Matter Theorists Professor Piers Coleman of Rutgers University and Professor Christian Gruber of the University of Lausanne. Other talks, given by collaborators, friends and classmates testify to the great breadth of Deng Feng Wang's influence, with remarkable connections shown between seemingly unrelated areas in physics such as Condensed Matter Physics, Superconductivity, One-Dimensional Models, Statistical Physics, Mathematical Physics, Quantum Field Theory, High Energy Theory, Nuclear Magnetic Resonance, Supersymmetry, M-Theory and String Theory, in addition to such varied fields outside of physics such as Oil Drilling, Mixed Signal Circuits and Neurology. The second part of the volume consists of reprints of some of Deng Feng Wang's most important papers in the areas of Condensed Matter Physics, Statistical Physics, Magnetism, Mathematical Physics and Mathematical Finance. This volume represents a fascinating synthesis of a wide variety of topics, and ultimately points to the universality of physics and of science as a whole. As such, it represents a fitting tribute to a remarkable individual, whose tragic death will never erase his enduring influence.

Human Face Recognition Using Third-Order Synthetic Neural Networks explores the viability of the application of High-order synthetic neural network technology to transformation-invariant recognition of complex visual patterns. High-order networks require little training data (hence, short training times) and have been used to perform transformation-invariant recognition of relatively simple visual patterns, achieving very high recognition rates. The successful results of these methods provided inspiration to address more practical problems which have grayscale as opposed to binary patterns (e.g., alphanumeric characters, aircraft silhouettes) and are also more complex in nature as opposed to purely edge-extracted images - human face recognition is such a problem. Human Face Recognition Using Third-Order Synthetic Neural Networks serves as an excellent reference for researchers and professionals working on applying neural network technology to the recognition of complex visual patterns.

This volume contains the proceedings of a NATO Advanced study Institute held at Geilo, Norway between 2 - 12 april 1991. This institute was the eleventh in a series held biannually at Geilo on the subject of phase transitions. It was intended to capture the latest ideas on selforgan ized patterns and criticality. The Institute brought together many lecturers, students and active re searchers in the field from a wide range of NATO and non-NATO countries. The main financial support came from the NATO scientific Affairs Divi sion, but additional support was obtained from the Norwegian Research Council for Science and the Humanities (NAVF) and Institutt for energi teknikk. The organizers would like to thank all these contributors for their help in promoting an exciting and rewarding meeting, and in doing so are confident that they echo the appreciation of all the parti cipants. In cooperative, equilibrium systems, physical states are described by spatio-temporal correlation functions. The intimate connection between space and time correlations is especially apparent at the critical point, the second order phase transition, where the spatial range and the decay time of the correlation function both become infinite. The salient features of critical phenomena and the history of the devel opment of this field of science are treated in the first chapter of this book.

In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution."

This volume contains twenty contributions of work, conducted since 1996 in the French- German Research Programme "Numerical Flow Simulation" of the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). The main purpose of this publication is to give an overview over the work conducted in this programme, and to make the results obtained available to the pUblic. The reports are grouped under the four headings "Development of Solution Techniques", "Crystal Growth and Melts", "Flows of Reacting Gases" and "Turbulent Flows". AIl contributions to this publica- tion were reviewed by a board consisting of T. Alziary de Roquefort (Poitiers, France), P. Bontoux (Marseille, France), JA Desideri (Sophia-Antipolis, France), W. Kordulla (G6t- tingen, Germany), R. Peyret (Nice, France), R. Rannacher (Heidelberg, Germany), G. War- necke (Magdeburg, ,Germany), and the editor. The responsibility for the contents of the reports nevertheless lies with the authors. E. H. Hirschel Editor Preface The Colloquium on "Numerical Simulation of Flows", Marseille, November 21 and 22, th 1997, was the 6 Joint CNRS-DFG Colloquium organized in the frame of the French- German Research Collaboration on Computational Fluid Dynamics. This Collaborative Program was elaborated progressively since 1991, when the two major research groups were brought together: the Priority Program "Flow Simulation with Super Computers" from the DFG in Germany and the Groupement de Recherche de "Mecanique des Fluides NumCrique" (GDR MFN) from the CNRS in France.

Observation, Prediction and Simulation of Phase Transitions in Complex Fluids presents an overview of the phase transitions that occur in a variety of soft-matter systems: colloidal suspensions of spherical or rod-like particles and their mixtures, directed polymers and polymer blends, colloid--polymer mixtures, and liquid-forming mesogens. This modern and fascinating branch of condensed matter physics is presented from three complementary viewpoints. The first section, written by experimentalists, emphasises the observation of basic phenomena (by light scattering, for example). The second section, written by theoreticians, focuses on the necessary theoretical tools (density functional theory, path integrals, free energy expansions). The third section is devoted to the results of modern simulation techniques (Gibbs ensemble, free energy calculations, configurational bias Monte Carlo). The interplay between the disciplines is clearly illustrated. For all those interested in modern research in equilibrium statistical mechanics.

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.

As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily provides the required justification. However things are not so easy, if we take a step forward and consider a gas is not in equilibrium, as is, e.g., the case for air around a flying vehicle. Questions of this kind have been asked since the dawn of the kinetic theory of gases, especially when certain results appeared to lead to paradoxical conclu sions. Today this matter is rather well understood and a rigorous kinetic theory is emerging. The importance of these developments stems not only from the need of providing a careful foundation of such a basic physical theory, but also to exhibit a prototype of a mathematical construct central to the theory of non-equilibrium phenomena of macroscopic size."

Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.

Polymers are substances made of macromolecules formed by thousands of atoms organized in one (homopolymers) or more (copolymers) groups that repeat themselves to form linear or branched chains, or lattice structures. The concept of polymer traces back to the years 1920's and is one of the most significant ideas of last century. It has given great impulse to indus try but also to fundamental research, including life sciences. Macromolecules are made of sm all molecules known as monomers. The process that brings monomers into polymers is known as polymerization. A fundamental contri bution to the industrial production of polymers, particularly polypropylene and polyethylene, is due to the Nobel prize winners Giulio Natta and Karl Ziegler. The ideas of Ziegler and Natta date back to 1954, and the process has been improved continuously over the years, particularly concerning the design and shaping of the catalysts. Chapter 1 (due to A. Fasano ) is devoted to a review of some results concerning the modelling of the Ziegler- Natta polymerization. The specific ex am pie is the production of polypropilene. The process is extremely complex and all studies with relevant mathematical contents are fairly recent, and several problems are still open.

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.

Neural Networks in Telecommunications consists of a carefully edited collection of chapters that provides an overview of a wide range of telecommunications tasks being addressed with neural networks. These tasks range from the design and control of the underlying transport network to the filtering, interpretation and manipulation of the transported media. The chapters focus on specific applications, describe specific solutions and demonstrate the benefits that neural networks can provide. By doing this, the authors demonstrate that neural networks should be another tool in the telecommunications engineer's toolbox. Neural networks offer the computational power of nonlinear techniques, while providing a natural path to efficient massively-parallel hardware implementations. In addition, the ability of neural networks to learn allows them to be used on problems where straightforward heuristic or rule-based solutions do not exist. Together these capabilities mean that neural networks offer unique solutions to problems in telecommunications. For engineers and managers in telecommunications, Neural Networks in Telecommunications provides a single point of access to the work being done by leading researchers in this field, and furnishes an in-depth description of neural network applications.

Neural Information Processing and VLSI provides a unified treatment of this important subject for use in classrooms, industry, and research laboratories, in order to develop advanced artificial and biologically-inspired neural networks using compact analog and digital VLSI parallel processing techniques. Neural Information Processing and VLSI systematically presents various neural network paradigms, computing architectures, and the associated electronic/optical implementations using efficient VLSI design methodologies. Conventional digital machines cannot perform computationally-intensive tasks with satisfactory performance in such areas as intelligent perception, including visual and auditory signal processing, recognition, understanding, and logical reasoning (where the human being and even a small living animal can do a superb job). Recent research advances in artificial and biological neural networks have established an important foundation for high-performance information processing with more efficient use of computing resources. The secret lies in the design optimization at various levels of computing and communication of intelligent machines. Each neural network system consists of massively paralleled and distributed signal processors with every processor performing very simple operations, thus consuming little power. Large computational capabilities of these systems in the range of some hundred giga to several tera operations per second are derived from collectively parallel processing and efficient data routing, through well-structured interconnection networks. Deep-submicron very large-scale integration (VLSI) technologies can integrate tens of millions of transistors in a single silicon chip for complex signal processing and information manipulation. The book is suitable for those interested in efficient neurocomputing as well as those curious about neural network system applications. It has been especially prepared for use as a text for advanced undergraduate and first year graduate students, and is an excellent reference book for researchers and scientists working in the fields covered.