Addressing graduate students and researchers in physics and mathematics, this book fills a gap in the literature. It is an introduction into modern constructive physics, field theory and statistical mechanics and a survey on the most recent research in this field. It presents the main technical tools such as cluster expansion and their implementation in the rigorous renormalization group, and studies physical models in some detail. The reader will find a study of the ultraviolet limit of the Gross-Neveu model, of continuous symmetry breaking and of self-avoiding random walks in statistical mechanics, as well as applications to solid-state physics. Mathematicians will find constructive methods useful for studies in partial differential equations.

The study of chaotic behaviour of dynamical systems has triggered new efforts to reconcile deterministic and stochastic processes as well as classical and quantum physics. New efforts are made to understand complex and unpredictable behaviour. The papers collected in this volume give a broad overview of these activities. Readers will get a glimpse of the growing importance of Levy processes for physics. They will find new views on fundamental concepts of quantum physics and will see many applications of chaotic and essentially random phenomena to a number of physical problems."

Quantum effects may be modelled by means of stochastic perturbation of non-linear partial differential (field) equations. Contributions to this field of research are collected in this volume. Finite dimensional stochastically perturbed Hamiltonian systems and infinite dimensional white noise analysis are treated. The main part concerns problems encountered in deterministic equations. Papers treat the existence of solutions for given initial data, the existence of non-linear bound states or solitary waves including a thorough discussion of various approaches to stability, and global properties (e.g. time decay properties) for non-linear wave equations. This volume provides a good survey of present-day research in non-linear problems of quantum theory for researchers and graduate students.

Foundations of Information Technology in the Era of Network and Mobile Computing is presented in two distinct but interrelated tracks: -Algorithms, Complexity and Models of Computation; -Logic, Semantics, Specification and Verification. This volume contains 45 original and significant contributions addressing these foundational questions, as well as 4 papers by outstanding invited speakers. These papers were presented at the 2nd IFIP International Conference on Theoretical Computer Science (TCS 2002), which was held in conjunction with the 17th World Computer Congress, sponsored by the International Federation for Information Processing (IFIP), and which convened in Montreal, Quebec, Canada in August 2002.

Broadband communications is widely recognized as one of the key technologies for building the next generation global network infrastructure to support ever-increasing multimedia applications. This book contains a collection of timely leading-edge research papers that address some of the important issues of providing such a broadband network infrastructure. Broadband Communications represents the selected proceedings of the Fifth International Conference on Broadband Communications, sponsored by the International Federation for Information Processing (IFIP) and held in Hong Kong in November 1999. The book is organized according to the eighteen technical sessions of the conference. The topics covered include internet services, traffic modeling, internet traffic control, performance evaluation, billing, pricing, admission policy, mobile network protocols, TCP/IP performance, mobile network performance, bandwidth allocation, switching systems, traffic flow control, routing, congestion and admission control, multicast protocols, network management, and quality of service. It will serve as an essential reference for computer scientists and practitioners.

This is a collection of papers on a variety of topics of current interest in mathematical physics: integrable systems, quantum groups, topological quantum theory, string theory. Some of the contributions are lengthy reviews of lasting value on subjects like symplectic geometry of the Chern-Simons theory or on mirror symmetry. The book addresses graduate students as well as researchers in mathematical physics.

Written for researchers and advanced students the book exhibits a combination of various methods and tools required to describe the complexity of the chemical and physical behaviour of fluid surfaces. The common denominator for all the contributions presented here is the simultaneous use of concepts from surface chemistry and physics and from hydrodynamics where external force fields can be introduced. Theoretical and experimental work is equally represented. Most of the basic problems in the area of nonequilibrium multiphase systems have not yet received extensive treatment. This volume should be a reference for physicists, physico-chemists, and chemical engineers and will serve as a jumping-off point for new directions and new points of view.

The book covers the basics and some generalizations of Monte Carlo methods and its applications to discrete and field theoretic models. It covers the study of nonequilibrium models of granular media by computer simulation and pattern formation. Furthermore, the lectures deal with details of phenomena such as chaos, segregation, pattern formation and phase transitions, convection, fluidification, density waves, surface reaction and growth, spread of epidemics, acoustics, deformation, etc. The book addresses students in physics and scientific computation. It should be a valuable reference work for researchers as well.

It is man's ongoing hope that a machine could somehow adapt to its environment by reorganizing itself. This is what the notion of self-organizing robots is based on. The theme of this book is to examine the feasibility of creating such robots within the limitations of current mechanical engineering. The topics comprise the following aspects of such a pursuit: the philosophy of design of self-organizing mechanical systems; self-organization in biological systems; the history of self-organizing mechanical systems; a case study of a self-assembling/self-repairing system as an autonomous distributed system; a self-organizing robot that can create its own shape and robotic motion; implementation and instrumentation of self-organizing robots; and the future of self-organizing robots. All topics are illustrated with many up-to-date examples, including those from the authors' own work. The book does not require advanced knowledge of mathematics to be understood, and will be of great benefit to students in the robotics discipline, including in the areas of mechanics, control, electronics, and computer science. It is also an important source for researchers who wish to investigate the field of robotics or who have an interest in the application of self-organizing phenomena.

This monograph describes and discusses the properties of heterogeneous materials, including conductivity, elastic moduli, and dielectrical constant. The book outlines typical experimental methods, and compares the experimental data and the theoretical predictions. This multidisciplinary book will appeal to applied physicists, materials scientists, chemical and mechanical engineers, chemists, and applied mathematicians.

Neuromorphic Systems Engineering: Neural Networks in Silicon emphasizes three important aspects of this exciting new research field. The term neuromorphic expresses relations to computational models found in biological neural systems, which are used as inspiration for building large electronic systems in silicon. By adequate engineering, these silicon systems are made useful to mankind. Neuromorphic Systems Engineering: Neural Networks in Silicon provides the reader with a snapshot of neuromorphic engineering today. It is organized into five parts viewing state-of-the-art developments within neuromorphic engineering from different perspectives. Neuromorphic Systems Engineering: Neural Networks in Silicon provides the first collection of neuromorphic systems descriptions with firm foundations in silicon.Topics presented include: * large scale analog systems in silicon * neuromorphic silicon * auditory (ear) and vision (eye) systems in silicon * learning and adaptation in silicon * merging biology and technology * micropower analog circuit design * analog memory * analog interchipcommunication on digital buses GBP/LISTGBP Neuromorphic Systems Engineering: Neural Networks in Silicon serves as an excellent resource for scientists, researchers and engineers in this emerging field, and may also be used as a text for advanced courses on the subject.

Dynamics of Topological Magnetic Solitons gives a theoretical and experimental review of the dynamics of high-speed domain walls and Bloch lines. After the introduction of magnetic solitons, experimental methods for the observation of the dynamics of domain walls are presented. Further chapters discuss main features of the stimulated motion of domain walls, their magnetoelastic interaction, stability and relaxation. Finally, the dynamics of domain walls in weak ferromagnets with more than one dimension is treated. The last chapter presents the dynamics of Bloch lines and their clusters. More than 230 references guide the reader to the literature. Physicists will gain new insights in interesting applications of soliton theory in condensed matter physics. Engineers will find new information on magnetooptical effects for further applications.

This IMA Volume in ~athematics and its Applications PERCOLATION THEORY AND ERGODIC THEORY OF INFINITE PARTICLE SYSTEMS represents the proceedings of a workshop which was an integral part of the 19R4-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: naniel Stroock (Chairman) Wendell Fleming Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaoo for planning and implementing an exciting and stimulating year-long program. We especially thank the Workshop Organizing Committee, Harry Kesten (Chairman), Richard Holley, and Thomas Liggett for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinherger PREFACE Percolation theory and interacting particle systems both have seen an explosive growth in the last decade. These suhfields of probability theory are closely related to statistical mechanics and many of the publications on these suhjects (especially on the former) appear in physics journals, wit~ a great variahility in the level of rigour. There is a certain similarity and overlap hetween the methods used in these two areas and, not surprisingly, they tend to attract the same probabilists. It seemed a good idea to organize a workshop on "Percolation Theory and Ergodic Theory of Infinite Particle Systems" in the framework of the special probahility year at the Institute for Mathematics and its Applications in 1985-86. Such a workshop, dealing largely with rigorous results, was indeed held in February 1986.

Predicting thermodynamic quantities for chemically realistic systems on the basis of atomistic calculations is still, even today, a nontrivial task. Nonetheless, accurate treatment of inter-particle interactions, in terms of quantum chemical first principles methods, is a prerequisite for many applications, because of the complexity of both reactants and solvents in modern molecular sciences. Currently, a straightforward calculation of thermodynamic properties from these methods is only possible for high-temperature and low- density systems. Although the enthalpy of a system can often be predicted to a good level of precision with this ideal gas approach, calculating the entropy contribution to the free energy is problematic, especially as the density of the system increases. This thesis contains a compact and coherent introduction of basic theoretical features. The foundations are then laid for the development of approaches suitable for calculation of condensed phase entropies on the basis of well-established quantum chemical methods. The main emphasis of this work is on realistic systems in solution, which is the most important environment for chemical synthesis. The presented results demonstrate how isolated molecular concepts typically employed in modern quantum chemistry can be extended for the accurate determination of thermodynamic properties by means of scale- transferring approaches.

Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.

This book introduces 'functional networks', a novel neural-based paradigm, and shows that functional network architectures can be efficiently applied to solve many interesting practical problems. Included is an introduction to neural networks, a description of functional networks, examples of applications, and computer programs in Mathematica and Java languages implementing the various algorithms and methodologies. Special emphasis is given to applications in several areas such as: * Box-Jenkins AR(p), MA(q), ARMA(p, q), and ARIMA (p, d, q) models with application to real-life economic problems such as the consumer price index, electric power consumption and international airlines' passenger data. Random time series and chaotic series are considered in relation to the Henon, Lozi, Holmes and Burger maps, as well as the problems of noise reduction and information masking. * Learning differential equations from data and deriving the corresponding equivalent difference and functional equations. Examples of a mass supported by two springs and a viscous damper or dashpot, and a loaded beam, are used to illustrate the concepts.* The problem of obtaining the most general family of implicit, explicit and parametric surfaces as used in Computer Aided Design (CAD). * Applications of functional networks to obtain general nonlinear regression models are given and compared with standard techniques. Functional Networks with Applications: A Neural-Based Paradigm will be of interest to individuals who work in computer science, physics, engineering, applied mathematics, statistics, economics, and other neural networks and data analysis related fiel

From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation. The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established "continuum" approach typical of macroscopic laws of physics.The author sheds light on a new method-using invariant manifolds-which addresses a functional equation for the nonequilibrium single-particle distribution function. This method allows one to find exact and thermodynamically consistent expressions for: hydrodynamic modes; transport coefficient expressions for hydrodynamic modes; and transport coefficients of a fluid beyond the traditional hydrodynamic limit. The invariant manifold method paves the way to establish a needed bridge between Boltzmann equation theory and a particle-based theory of hydrodynamics. Finally, the author explores the ambitious and longstanding task of obtaining hydrodynamic constitutive equations from their kinetic counterparts. The work is intended for specialists in kinetic theory-or more generally statistical mechanics-and will provide a bridge between a physical and mathematical approach to solve real-world problems.

Initially a subfield of solid state physics, the study of mesoscopic systems has evolved over the years into a vast field of research in its own right. Keeping track its rapid progress, this book provides a broad survey of the latest developments in the field. The focus is on statistics and dynamics of mesoscopic systems with special emphasis on topics like quantum chaos, localization, noise and fluctuations, mesoscopic optics and quantum transport in nanostructures. Written with nonspecialists in mind, this book will also be useful to graduate students wishing to familiarize themselves with this field of research.

This IMA Volume in Mathematics and its Applications NONLINEAR PHENOMENA IN ATMOSPHERIC AND OCEANIC SCIENCES is based on the proceedings of a workshop which was an integral part of the 1989-90 IMA program on "Dynamical Systems and their Applications". The aim of this workshop was to promote cross-fertilization of ideas between investigators who are using nonlinear dynamical systems and numerical simulations to study the earth's atmosphere and oceans. We thank George F. Carnevale, Shui-Nee Chow, Martin Golubitsky, Richard McGehee, Raymond Pierrehumbert and George R. Sell for organizing the meeting. We especially thank George F. Carnevale and Raymond Pierrehumbert for editing the proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, the Minnesota Supercom puter Institute, the National Science Foundation, and the Office of Naval Research. A vner Friedman Willard Miller, Jr. PREFACE When we took on this project, we did not realize we were organizing a workshop on two-dimensional fluid dynamics. The participants who were invited had been working on a broad range of mathematically challenging problems related to atmo spheric and oceanic phenomena, and they were given carte blanche to talk about their current interests. With few exceptions, the favored subject involved one or another aspect of fluid flow in two dimensions.

The Handbook of Feynman Path Integrals appears just fifty years after Richard Feynman published his pioneering paper in 1948 entitled "Space-Time Approach to Non-Relativistic Quantum Mechanics", in which he introduced his new formulation of quantum mechanics in terms of path integrals. The book presents for the first time a comprehensive table of Feynman path integrals together with an extensive list of references; it will serve the reader as a thorough introduction to the theory of path integrals. As a reference book, it is unique in its scope and will be essential for many physicists, chemists and mathematicians working in different areas of research.

Small-scale structures in turbulent flows appear as a subtle mixture of order and chaos that could play an important role in the energetics. The aim here is a better understanding of the similarities and differences between vortex and current dynamics, and of the influence of these structures on the statistical and transport properties of hydrodynamic and magnetohydrodynamic turbulence, with special concern for fusion plasmas, and solar or magnetospheric environments. Special emphasis is given to the intermittency at inertial scales and to the coherent structures at small scales. Magnetic reconnection and the dynamo effect are also discussed, together with the effect of stratification and inhomogeneity. The impact of hydrodynamic concepts on astro and geophysical observations are reviewed.

"Fundamental Aspects of Plasma Chemical Physics - Thermodynamics" develops basic and advanced concepts of plasma thermodynamics from both classical and statistical points of view.

After a refreshment of classical thermodynamics applied to the dissociation and ionization regimes, the book invites the reader to discover the role of electronic excitation in affecting the properties of plasmas, a topic often overlooked by the thermal plasma community.

Particular attention is devoted to the problem of the divergence of the partition function of atomic species and the state-to-state approach for calculating the partition function of diatomic and polyatomic molecules. The limit of ideal gas approximation is also discussed, by introducing Debye-Huckel and virial corrections.

Throughout the book, worked examples are given in order to clarify concepts and mathematical approaches.

This book is a first of a series of three books to be published by the authors on fundamental aspects of plasma chemical physics. The next books will discuss transport and kinetics.

"

This book deals with the theory and the applications of a new time domain, termed natural time domain, that has been forwarded by the authors almost a decade ago (P.A. Varotsos, N.V. Sarlis and E.S. Skordas, Practica of Athens Academy 76, 294-321, 2001; Physical Review E 66, 011902, 2002). In particular, it has been found that novel dynamical features hidden behind time series in complex systems can emerge upon analyzing them in this new time domain, which conforms to the desire to reduce uncertainty and extract signal information as much as possible. The analysis in natural time enables the study of the dynamical evolution of a complex system and identifies when the system enters a critical stage. Hence, natural time plays a key role in predicting impending catastrophic events in general. Relevant examples of data analysis in this new time domain have been published during the last decade in a large variety of fields, e.g., Earth Sciences, Biology and Physics. The book explains in detail a series of such examples including the identification of the sudden cardiac death risk in Cardiology, the recognition of electric signals that precede earthquakes, the determination of the time of an impending major mainshock in Seismology, and the analysis of the avalanches of the penetration of magnetic flux into thin films of type II superconductors in Condensed Matter Physics. In general, this book is concerned with the time-series analysis of signals emitted from complex systems by means of the new time domain and provides advanced students and research workers in diverse fields with a sound grounding in the fundamentals of current research work on detecting (long-range) correlations in complex time series. Furthermore, the modern techniques of Statistical Physics in time series analysis, for example Hurst analysis, the detrended fluctuation analysis, the wavelet transform etc., are presented along with their advantages when natural time domain is employed.

This is a collection of outstanding review papers on integrable systems. It gives the algebraic geometric aspects of the subject, describes integrability techniques e.g. for the modified KdV equation, integrability of Hamiltonian systems, hierarchies of equations, probability distribution of eigenvalues, and modern aspects of quantum groups. It addresses researchers in mathematics and mathematical physics.

Molecularly small confined phases play an important role in many scientific and engineering disciplines. For instance, the confining membrane of a living cell is known to affect the structure and transport of cellular water, which mediates the cell's metabolism and other biochemical processes. Transport of hazardous waste through the soil is strongly influenced by the adsorption of bulk phase molecules on the confining mineral _surfaces. Finally, molecularly thin confined fluid films play a prominent part in lubrication. These examples illustrate the broad range of natural and commercial processes to which the present subject pertains. Much experimental effort has been devoted to molecularly small confined phases, revealing the intriguing nature of such systems. Several sections of this book are therefore devoted to descriptions of experimental techniques. To date even the most refined experiments do not yield direct information about structure and processes on the molecular scale. Computer simulations, on the other hand, do give such information and therefore complement real laboratory experiments. Several sections of this book discuss the link between experiments and the corre sponding simulations."