The fourth Nishinomiya-Yukawa Memorial Symposium, devoted to the topic of dynamics and patterns in complex fluids, was held on October 26 and 27, 1989, in Nishinomiya City, Japan, where ten invited speakers gave their lectures. A one-day meeting, comprising short talks and poster sessions, was then held on the same topic on October 28 at the Research Institute for Fundamental Physics, Kyoto University. The present volume contains the 10 invited papers and 38 contributed papers presented at these two meetings. The symposium was sponsored by Nishinomiya City, where Prof. Hideki Yukawa once lived and where he wrote the celebrated paper describing the work that was later honored by a Nobel prize. The topic of the fourth symposium was chosen from one of the most vigorously evolving and highly interdisciplinary fields in condensed matter physics. The field of complex fluids is very diverse and still in its infancy and, as a result, the definition of a complex fluid varies greatly from one researcher to the next. One of the objectives of the symposium was to clarify its definition by explicitly posing a number of potentially rich problems waiting to be explored. Indeed, experimentalists are disclosing a variety of intriguing dynamical phenomena in complex systems such as polymers, liquid crystals, gels, colloids, and surfactant systems. We, the organizers, hope that the symposium will contribute to the increasing importance of the field in the coming years.

Bifurcation and Chaos presents a collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in physics and engineering. Each chapter is self-contained and includes an elementary introduction, an exposition of the present state of the art, and details of recent theoretical, computational and experimental results. Included among the practical systems analysed are: hysteretic circuits, Josephson circuits, magnetic systems, railway dynamics, rotor dynamics and nonlinear dynamics of speech. This book contains important information and ideas for all mathematicians, physicists and engineers whose work in R & D or academia involves the practical consequences of chaotic dynamics.

Research in the past thirty years on the foundations of thermodynamics has led not only to a better understanding of the early developments of the subject but also to formulations of the First and Second Laws that permit both a rigorous analysis of the consequences of these laws and a substantial broadening of the class of systems to which the laws can fruitfully be applied. Moreover, modem formulations of the laws of thermodynamics have now achieved logically parallel forms at a level accessible to under graduate students in science and engineering who have completed the standard calculus sequence and who wish to understand the role which mathematics can play in scientific inquiry. My goal in writing this book is to make some of the modem develop ments in thermodyamics available to readers with the background and orientation just mentioned and to present this material in the form of a text suitable for a one-semester junior-level course. Most of this presentation is taken from notes that I assembled while teaching such a course on two occasions. I found that, aside from a brief review of line integrals and exact differentials in two dimensions and a short discussion of infima and suprema of sets of real numbers, juniors (and even some mature sophomores) had sufficient mathematical background to handle the subject matter. Many of the students whom I taught had very limited experience with formal and rigorous mathematical exposition."

Correlation Effects in Low-Dimensional Electron Systems describes recent developments in theoretical condensed-matter physics, emphasizing exact solutions in one dimension including conformal-field theoretical approaches, the application of quantum groups, and numerical diagonalization techniques. Various key properties are presented for two-dimensional, highly correlated electron systems.

A good deal of the material presented in this book has been prepared by top experts in the field lecturing in January 1987 at the Winter School on Solitons in Tiruchirapalli, India. The lectures begin at an elementary level but go on to include even the most recent developments in the field. The book makes a handy introduction to the various facets of the soliton concept, and will be useful both to newcomers to the field and to researchers who are interested in developments in new branches of physics and mathematics

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.

This volume is the proceedings of the Hiroshima Symposium on Elementary Excitations in Quantum Fluids, which was held on August 17 and 18, 1987, in Hiroshima, Japan, and was attended by thirty-two scientists from seven countries. Quantum fluids have been the subject of intense study as a consequence of their superfluid properties at very low temperatures. Elementary excitations in them are an important concept about which many important discoveries have been made in recent years. This symposium was arranged by a group of physicists from Hiroshima University to provide an opportunity to discuss these recent developments. It was conceived as a satellite conference of the 18th International Conference on Low Temperature Physics (LT 18), which was held in Kyoto, August 20-26, 1987. Emphasis was placed on the dynamic structures and correlations of ele mentary excitations, which resulted in invited speakers being selected from this field. However, enthusiastic contributors reported notable new results on various other aspects of the elementary excitations, which made the sympo sium lively and successful. It is our great satisfaction to present this volume, which includes papers of good quality and originality. We thank all the parti cipants for their cooperation throughout this symposium, and for preparing their manuscripts within a reasonable time."

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.

Professor Sluzalec is a well-known and respected authority in the field of Computational Mechanics, and his personal experience forms the basis of the book. Introduction to Nonlinear Thermomechanics provides both an elementary and advanced exposition of nonlinear thermomechanics. The scope includes theoretical aspects and their rational application in thermal problems, thermo-elastoplasticity, finite strain thermoplasticity and coupled thermoplasticity. The use of numerical techniques for the solution of problems and implementation of basic theory is included. Engineers, technicians, researchers, and advanced students will find the book an extremely useful compendium of solutions to problems. The scope is such that it would also be an effective teaching aid.

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.

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."

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.

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.

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.

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."

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."

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.

Oaxaca, Mexico, was the place chosen by a large international group of scientists to meet and discuss on the recent advances on the understanding of the physical prop- ties of low dimensional systems; one of the most active fields of research in condensed matter in the last years. The International Symposium on the Physics of Low Dim- sions took place in January 16-20, 2000. The group of scientists converging into the historical city of Oaxaca, in the state of the same name, had come from Argentina, Chile, Venezuela, several places in Mexico, Canada, U. S. A. , England, France, Italy, Germany, Russia, and Switzerland. The presentations at the workshop provided sta- of-art reviews of many of the most important problems, currently under study. Equally important to all the participants in the workshop was the fact that we had come to honor a friend, Hans Christoph Siegmann, on his sixty-fifth birthday. This Festschrift recognizes the intellectual leadership of Professor Siegmann in the field and as a sincere homage to his qualities as an exceptional friend, college and mentor. Those who have had the privilege to work closely with Hans Christoph have been deeply impressed by his remarkable analytic mind as well as by his out of range kindness and generosity. Hans Christoph has contributed to the understanding of the difficult and very important problem of the magnetic properties of finite systems: surfaces, thin films, heterostructures.

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."

Quantum trajectory theory is largely employed in theoretical quantum optics and quantum open system theory and is closely related to the conceptual formalism of quantum mechanics (quantum measurement theory). However, even research articles show that not all the features of the theory are well known or completely exploited. We wrote this monograph mainly for researchers in theoretical quantum optics and related ?elds with the aim of giving a self-contained and solid p- sentation of a part of quantum trajectory theory (the diffusive case) together with some signi?cant applications (mainly with purposes of illustration of the theory, but which in part have been recently developed). Another aim of the monograph is to introduce to this subject post-graduate or PhD students. To help them, in the most mathematical and conceptual chapters, summaries are given to ?x ideas. Moreover, as stochastic calculus is usually not in the background of the studies in physics, we added Appendix A to introduce these concepts. The book is written also for ma- ematicians with interests in quantum theories. Quantum trajectory theory is a piece of modern theoretical physics which needs an interplay of various mathematical subjects, such as functional analysis and probability theory (stochastic calculus), and offers to mathematicians a beautiful ?eld for applications, giving suggestions for new mathematical developments.