In Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices the contributions of the International Conference on Nonlinear Dynamics and Pattern Formation in the Natural Environment (ICPF '94) in Noordwijkerhout, held by many internationally reknown experts, are compiled. To connect the field of semiconductor physics with the theory of nonequilibrium dissipative systems, the emphasis lies on the study of localized structures, their stability and bifurcation behaviour. A point of special interest is the evolution of dynamic structures and the investigation of more complex structures arising from interactions between these structures. Possible applications of nonlinear effects and self-organization phenomena with respect to signal processing are discussed.

This book goes beyond the scope of other works in the field with its thorough treatment of applications in a wide variety of disciplines. The third edition features a new section on constants of motion and symmetry and a new appendix on the Lorentz-Legendre expansion.

Principles of Statistical Radiophysics is concerned with the theory of random func tions (processes and fields) treated in close association with a number of applications in physics. Primarily, the book deals with radiophysics in its broadest sense, i.e., l viewed as a general theory of oscillations and waves of any physical nature * This translation is based on the second (two-volume) Russian edition. It appears in four volumes: 1. Elements of Random Process Theory 2. Correlation Theory of Random Processes 3. Elements of Random Fields 4. Wave Propagation Through Random Media. The four volumes are, naturally, to a large extent conceptually interconnected (being linked, for instance, by cross-references); yet for the advanced reader each of them might be of interest on its own. This motivated the division of the Principles into four separate volumes. The text is designed for graduate and postgraduate students majoring in radio physics, radio engineering, or other branches of physics and technology dealing with oscillations and waves (e.g., acoustics and optics). As a rule, early in their career these students face problems involving the use of random functions. The book pro vides a sound basis from which to understand and solve problems at this level. In addition, it paves the way for a more profound study of the mathematical theory, should it be necessary2. The reader is assumed to be familiar with probability theory.

An international workshop on Elementary Excitations and Fluctuations in Magnetic Systems was held in San Miniato, Italy, for five days beginning 28 May, 1984. The workshop comprised eight working sessions that contai- ned a total of 43 invited talks, and 58 scientists were in attendance from 14 countries. Our aim was to review some topics of current interest in the statistical physics of magnetic materials and models, with an emphasis on theoretical studies and confrontations between these and experimental and computer simulation data. book contains summary papers written by the invited speakers, and This the material will be of immediate interest to graduate students and resear- chers engaged in studies of magnetic properties. There is, perhaps, no ef- fective way to record and convey the benefit of the numerous discussions between the participants that are a significant integral feature of a work- shop. The magnificent .venue of the workshop, I Cappuccini, was made availa- ble to us by the.Cassa di Risparmio San Miniato. Financial support for the workshop was received from Consiglio Nazionale delle Ricerche, Universita degli Studi di Firenze and the Gruppo Nazionale Struttura,della Materia. Our administrative load and the burden of preparing the proceedings for publication was made light by the talents of Carla Pardini (CNR, Florence), and Caroline Monypenny and Jane Warren (Rutherford Appleton Laboratory). Fina 11y, we wish to thank all the participants for their attendance and individual contributions to the success of the workshop.

The theory of foliations and contact forms have experienced such great de velopment recently that it is natural they have implications in the field of mechanics. They form part of the framework of what Jean Dieudonne calls "Elie Cartan's great theory ofthe Pfaffian systems", and which even nowa days is still far from being exhausted. The major reference work is. without any doubt that of Elie Cartan on Pfaffian systems with five variables. In it one discovers there the bases of an algebraic classification of these systems, their methods of reduction, and the highlighting ofthe first fundamental in variants. This work opens to us, even today, a colossal field of investigation and the mystery of a ternary form containing the differential invariants of the systems with five variables always deligthts anyone who wishes to find out about them. One of the goals of this memorandum is to present this work of Cartan - which was treated even more analytically by Goursat in its lectures on Pfaffian systems - in order to expound the classifications currently known. The theory offoliations and contact forms appear in the study ofcompletely integrable Pfaffian systems of rank one. In each of these situations there is a local model described either by Frobenius' theorem, or by Darboux' theorem. It is this type of theorem which it would be desirable to have for a non-integrable Pfaffian system which may also be of rank greater than one.

STATISTICAL PHYSICS AND ECONOMICS covers systematically and in simple language the physical foundations of evolution equations, stochastic processes, and generalized Master equations applied to complex economic systems. Strong emphasis is placed on concepts, methods, and techniques for modeling, assessment, and solving or estimation of economic problems in an attempt to understand the large variability of financial markets, trading and communication networks, barriers and acceleration of the economic growth as well as the kinetics of product and money flows. The main focus of the book is a clear physical understanding of the self-organizing principles in social and economic systems. This modern introduction will be a useful tool for researchers, engineers, as well as graduate and post-graduate students in econophysics and related topics.

The second edition of this volume has been extensively revised. A different version of Chap. 7, reflecting recent significant progress in understanding of spatiotempo ral chaos, is now provided. Much new material has been included in the sections dealing with intermittency in birth-death models and noise-induced phase transi tions. A new section on control of chaotic behavior has been added to Chap. 6. The subtitle of the volume has been changed to better reflect its contents. We acknowledge stimulating discussions with H. Haken and E. Scholl and are grateful to our colleagues M. Bar, D. Battogtokh, M. Eiswirth, M. Hildebrand, K. Krischer, and V. Tereshko for their comments and assistance. We thank M. Lubke for her help in producing new figures for this volume. Berlin and Moscow A. s. Mikhailov April 1996 A. Yu. Loskutov Preface to the First Edition This textbook is based on a lecture course in synergetics given at the University of Moscow. In this second of two volumes, we discuss the emergence and properties of complex chaotic patterns in distributed active systems. Such patterns can be produced autonomously by a system, or can result from selective amplification of fluctuations caused by external weak noise."

Neural nets offer a fascinating new strategy for spatial analysis, and their application holds enormous potential for the geographic sciences. However, the number of studies that have utilized these techniques is limited. This lack of interest can be attributed, in part, to lack of exposure, to the use of extensive and often confusing jargon, and to the misapprehension that, without an underlying statistical model, the explanatory power of the neural net is very low. Neural Nets: Applications for Geography attacks all three issues; the text demonstrates a wide variety of neural net applications in geography in a simple manner, with minimal jargon. The volume presents an introduction to neural nets that describes some of the basic concepts, as well as providing a more mathematical treatise for those wishing further details on neural net architecture. The bulk of the text, however, is devoted to descriptions of neural net applications in such broad-ranging fields as census analysis, predicting the spread of AIDS, describing synoptic controls on mountain snowfall, examining the relationships between atmospheric circulation and tropical rainfall, and the remote sensing of polar cloud and sea ice characteristics. The text illustrates neural nets employed in modes analogous to multiple regression analysis, cluster analysis, and maximum likelihood classification. Not only are the neural nets shown to be equal or superior to these more conventional methods, particularly where the relationships have a strong nonlinear component, but they are also shown to contain significant explanatory power. Several chapters demonstrate that the nets themselves can be decomposed to illuminate causative linkages between different events in both the physical and human environments.

In March 1997, we launched the Japan Association for Evolutionary Economics {JAFEE) to gather the academic minds that, out of dissatisfaction with established dynamic approaches, were separately searching for new approaches to economics. To our surprise and joy, as many as 500members, including graduate students, joined us. Later that year Prof. Horst Hanusch, then President of the International oseph A. Schumpeter Society, remarked that such a start would take a couple of decades in Europe to prepare for. Since then we have been developing our activities incessantly not only in terms of the number of members, but also in terms of the intensity of international academic exchange. Originally the planning of this book came about as the successful outcome of our fourth annual conference organized as an international one, JAFEE 2000.Incorporat ing other international contributions related to our preceding conferences, this book has eventually turned out to be one of the most enterprising anthologies on evolu tionary economics ever published. Specifically, it contains excellent papers on such topics as streams of evolutionary economics, evolutionary nonlinear dynamics, experimental economics and evolution, multiagent systems and complexity, new frontiers for evolutionary economics, and economic heresies. In short, this book will provide a vivid and full-fledged picture of up-to-date evolutionary economics."

One service mathematics has rendered the Et moi, .... si j'avait su comment en revenir, je human race. It has put common sense back n'y serais point aile.' where it belongs, on the topmost shelf next to Jules Verne the dusty canister labelled 'discarded nonsense'. Eric T. Bell The series is divergent; therefore we may be able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics .. .'; 'One service logic has rendered computer science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series."

Markov processes play an important role in the study of probability theory. Homogeneous denumerable Markov processes are among the main topics in the theory and have a wide range of application in various fields of science and technology (for example, in physics, cybernetics, queuing theory and dynamical programming). This book is a detailed presentation and summary of the research results obtained by the authors in recent years. Most of the results are published for the first time. Two new methods are given: one is the minimal nonnegative solution, the second the limit transition method. With the help of these two methods, the authors solve many important problems in the framework of denumerable Markov processes.

Cellular automata are fully discrete dynamical systems with dynamical variables defined at the nodes of a lattice and taking values in a finite set. Application of a local transition rule at each lattice site generates the dynamics. The interpretation of systems with a large number of degrees of freedom in terms of lattice gases has received considerable attention recently due to the many applications of this approach, e.g. for simulating fluid flows under nearly realistic conditions, for modeling complex microscopic natural phenomena such as diffusion-reaction or catalysis, and for analysis of pattern-forming systems. The discussion in this book covers aspects of cellular automata theory related to general problems of information theory and statistical physics, lattice gas theory, direct applications, problems arising in the modeling of microscopic physical processes, complex macroscopic behavior (mostly in connection with turbulence), and the design of special-purpose computers.

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

Our aim in this book is to present and enlarge upon those aspects of parallel computing that are needed by practitioners of computational science. Today al most all classical sciences, such as mathematics, physics, chemistry and biology, employ numerical methods to help gain insight into nature. In addition to the traditional numerical methods, such as matrix inversions and the like, a whole new field of computational techniques has come to assume central importance, namely the numerical simulation methods. These methods are much less fully developed than those which are usually taught in a standard numerical math ematics course. However, they form a whole new set of tools for research in the physical sciences and are applicable to a very wide range of problems. At the same time there have been not only enormous strides forward in the speed and capability of computers but also dramatic new developments in computer architecture, and particularly in parallel computers. These improvements offer exciting prospects for computer studies of physical systems, and it is the new techniques and methods connected with such computer simulations that we seek to present in this book, particularly in the light of the possibilities opened up by parallel computers. It is clearly not possible at this early stage to write a definitive book on simulation methods and parallel computing."

by W. J. Freeman These two volumes on "Brain Oscillations" appear at a most opportune time. As the "Decade of the Brain" draws to its close, brain science is coming to terms with its ultimate problem: understanding the mechanisms by which the immense number of neurons in the human brain interact to produce the higher cognitive functions. The ideas, concepts, methods, interpretations and examples, which are presented here in voluminous detail by a world-class authority in electrophysiology, summarize the intellectual equipment that will be required to construct satisfactory solutions to the problem. Neuroscience is ripe for change. The last revolution of ideas took place in the middle of the century now ending, when the field took a sharp turn into a novel direction. During the preceding five decades the prevailing view, carried forward from the 19th century, was that neurons are the carriers of nerve energy, either in chemical or electrical forms (Freeman, 1995). That point of view was enormously productive in terms of coming to understand the chemical basis for synaptic transmission, the electrochemistry of the ac tion potential, the ionic mechanisms of membrane currents and gates, the functional neuroanatomy that underlies the hierarchy of reflexes, and the neural fields and'their resonances that support Gestalt phenomena. No bet ter testimony can be given of the power of the applications of this approach than to point out that it provides the scientific basis for contemporary neu rology, neuropsychiatry, and brain imaging."

For four decades, information theory has been viewed almost exclusively as a theory based upon the Shannon measure of uncertainty and information, usually referred to as Shannon entropy. Since the publication of Shannon's seminal paper in 1948, the theory has grown extremely rapidly and has been applied with varied success in almost all areas of human endeavor. At this time, the Shannon information theory is a well established and developed body of knowledge. Among its most significant recent contributions have been the use of the complementary principles of minimum and maximum entropy in dealing with a variety of fundamental systems problems such as predic tive systems modelling, pattern recognition, image reconstruction, and the like. Since its inception in 1948, the Shannon theory has been viewed as a restricted information theory. It has often been argued that the theory is capable of dealing only with syntactic aspects of information, but not with its semantic and pragmatic aspects. This restriction was considered a v~rtue by some experts and a vice by others. More recently, however, various arguments have been made that the theory can be appropriately modified to account for semantic aspects of in formation as well. Some of the most convincing arguments in this regard are in cluded in Fred Dretske's Know/edge & Flow of Information (The M.LT. Press, Cambridge, Mass., 1981) and in this book by Guy lumarie.

Lectures on Non-linear Plasma Kinetics is an introduction to modern non-linear plasma physics showing how many of the techniques of modern non-linear physics find applications in plasma physics and how, in turn, the results of this research find applications in astrophysics. Emphasis is given to explaining the physics of nonlinear processes and the radical change of cross-sections by collective effects. The author discusses new nonlinear phenomena involving the excitation of coherent nonlinear structures and the dynamics of their random motions in relation to new self-organization processes. He also gives a detailed description of applications of the general theory to various research fields, including the interaction of powerful radiation with matter, controlled thermonuclear research, etc.

Mon but n'a jamais be de m'occuper des ces matieres comme physicien, mais seulement comme /ogicien ... F. REECH, 1856 I do not think it possible to write the history of a science until that science itself shall have been understood, thanks to a clear, explicit, and decent logical structure. The exuberance of dim, involute, and undisciplined his torical essays upon classical thermodynamics reflects the confusion of the theory itself. Thermodynamics, despite its long history, has never had the benefit of a magisterial synthesis like that which EULER gave to hydro dynamics in 1757 or that which MAXWELL gave to electromagnetism in 1873; the expositions in the works of discovery in thermodynamics stand a pole apart from the pellucid directness of the notes in which CAUCHY presented his creation and development of the theory of elasticity from 1822 to 1845. Thermodynamics was born in obscurity and disorder, not to say confusion, and there the common presentations of it have remained. With this tractate I aim to provide a simple logical structure for the classical thermodynamics of homogeneous fluid bodies. Like any logical structure, it is only one of many possible ones. I think it is as simple and pretty as can be."

analyzing the experimental data and constructing math.ematical models of the processes under study, one has to rely rather on the physical intuition than on the strict calculations. Now let us go one step higher and explain the main title of the book. The concepts of "laminary" and "turbulent" motions were first introduced in hydrodynamics. Since the old days these concepts have considerably broadened; now the laminar and the turbulent motions have been discovered and investigated at all levels of description of nonequilibrium processes in the open systems, from kinetics to reaction diffusion. In any case, one of the principal characteristics of the turbulent motion is the existence of a large number of well-developed macroscopic degrees of freedom. For this reason the turbulent motion is extremely complicated and to a large extent unpredictable. As the laminar and the turbulent flows play an important role in the processes of evolution in the open systems, and in particular, in the processes of self-organization, the need arises for assessing the relative degree of order of laminar and turbulent motions, and also for comparing the degree of order of various turbulent motions. Without being able to make such estimates it will be impossible to determine whether the evolution is going towards higher or towards lower organization when one turbulent state is replaced by another.

Vision-based mobile robot guidance has proved difficult for classical machine vision methods because of the diversity and real-time constraints inherent in the task. This book describes a connectionist system called ALVINN (Autonomous Land Vehicle In a Neural Network) that overcomes these difficulties. ALVINN learns to guide mobile robots using the back-propagation training algorithm. Because of its ability to learn from example, ALVINN can adapt to new situations and therefore cope with the diversity of the autonomous navigation task. But real world problems like vision-based mobile robot guidance present a different set of challenges for the connectionist paradigm. Among them are: * how to develop a general representation from a limited amount of real training data; * how to understand the internal representations developed by artificial neural networks; * how to estimate the reliability of individual networks; * how to combine multiple networks trained for different situations into a single system; * how to combine connectionist perception with symbolic reasoning.Neural Network Perception for Mobile Robot Guidance presents novel solutions to each of these problems. Using these techniques, the ALVINN system can learn to control an autonomous van in under 5 minutes by watching a person drive. Once trained, individual ALVINN networks can drive in a variety of circumstances, including single-lane paved and unpaved roads, and multi-lane lined and unlined roads, at speeds of up to 55 miles per hour. The techniques also are shown to generalize to the task of controlling the precise foot placement of a walking robot.

The last decades have demonstrated that quantum mechanics is an inexhaustible source of inspiration for contemporary mathematical physics. Of course, it seems to be hardly surprising if one casts a glance toward the history of the subject; recall the pioneering works of von Neumann, Weyl, Kato and their followers which pushed forward some of the classical mathematical disciplines: functional analysis, differential equations, group theory, etc. On the other hand, the evident powerful feedback changed the face of the "naive" quantum physics. It created a contem porary quantum mechanics, the mathematical problems of which now constitute the backbone of mathematical physics. The mathematical and physical aspects of these problems cannot be separated, even if one may not share the opinion of Hilbert who rigorously denied differences between pure and applied mathemat ics, and the fruitful oscilllation between the two creates a powerful stimulus for development of mathematical physics. The International Conference on Mathematical Results in Quantum Mechan ics, held in Blossin (near Berlin), May 17-21, 1993, was the fifth in the series of meetings started in Dubna (in the former USSR) in 1987, which were dedicated to mathematical problems of quantum mechanics. A primary motivation of any meeting is certainly to facilitate an exchange of ideas, but there also other goals. The first meeting and those that followed (Dubna, 1988; Dubna, 1989; Liblice (in the Czech Republic), 1990) were aimed, in particular, at paving ways to East-West contacts."

Multilayer networks is a rising topic in Network Science which characterizes the structure and the function of complex systems formed by several interacting networks. Multilayer networks research has been propelled forward by the wide realm of applications in social, biological and infrastructure networks and the large availability of network data, as well as by the significance of recent results, which have produced important advances in this rapidly growing field. This book presents a comprehensive account of this emerging field. It provides a theoretical introduction to the main results of multilayer network science.

Fuzzy technology has emerged as one of the most exciting new concepts available. Fuzzy Logic and its Applications... covers a wide range of the theory and applications of fuzzy logic and related systems, including industrial applications of fuzzy technology, implementing human intelligence in machines and systems. There are four main themes: intelligent systems, engineering, mathematical foundations, and information sciences. Both academics and the technical community will learn how and why fuzzy logic is appreciated in the conceptual, design and manufacturing stages of intelligent systems, gaining an improved understanding of the basic science and the foundations of human reasoning.

Physicists firmly believe that the differential equations of nature should be hyperbolic so as to exclude action at a distance; yet the equations of irreversible thermodynamics - those of Navier-Stokes and Fourier - are parabolic. This incompatibility between the expectation of physicists and the classical laws of thermodynamics has prompted the formulation of extended thermodynamics. After describing the motifs and early evolution of this new branch of irreversible thermodynamics, the authors apply the theory to mon-atomic gases, mixtures of gases, relativistic gases, and "gases" of phonons and photons. The discussion brings into perspective the various phenomena called second sound, such as heat propagation, propagation of shear stress and concentration, and the second sound in liquid helium. The formal mathematical structure of extended thermodynamics is exposed and the theory is shown to be fully compatible with the kinetic theory of gases. The study closes with the testing of extended thermodynamics through the exploitation of its predictions for measurements of light scattering and sound propagation.

The motion of a particle in a random potential in two or more dimensions is chaotic, and the trajectories in deterministically chaotic systems are effectively random. It is therefore no surprise that there are links between the quantum properties of disordered systems and those of simple chaotic systems. The question is, how deep do the connec tions go? And to what extent do the mathematical techniques designed to understand one problem lead to new insights into the other? The canonical problem in the theory of disordered mesoscopic systems is that of a particle moving in a random array of scatterers. The aim is to calculate the statistical properties of, for example, the quantum energy levels, wavefunctions, and conductance fluctuations by averaging over different arrays; that is, by averaging over an ensemble of different realizations of the random potential. In some regimes, corresponding to energy scales that are large compared to the mean level spacing, this can be done using diagrammatic perturbation theory. In others, where the discreteness of the quantum spectrum becomes important, such an approach fails. A more powerful method, devel oped by Efetov, involves representing correlation functions in terms of a supersymmetric nonlinear sigma-model. This applies over a wider range of energy scales, covering both the perturbative and non-perturbative regimes. It was proved using this method that energy level correlations in disordered systems coincide with those of random matrix theory when the dimensionless conductance tends to infinity.