It is universally recognized that the end of the current and the beginning of the next century will be characterized by a radical change in the existing trends in the economic development of all countries and a transition to new principles of economic management on the basis of a resource and energy conservation policy. Thus there is an urgent necessity to study methods, technical aids and economic consequences of this change, and particularly, to determine the possible amounts of energy resources which could be conserved (energy "reserves") in different spheres of the national economy. An increased interest towards energy conservation in industry, one of the largest energy consumers, is quite natural and is manifested by the large num ber of publications on this topic. But the majority of publications are devoted to the solution of narrowly defined problems, determination of energy reserves in specific processes and plants, efficiency estimation of individual energy conserva tion measures, etc. However, it is necessary to develop a general methodological approach to the solution of such problems and create a scientific and methodical base for realizing an energy conservation policy. Such an effort is made in this book, which is concerned with methods for studying energy use efficiency in technological processes and estimation of the theoretical and actual energy reserves in a given process, technology, or industrial sector on the basis of their complete energy balances."

In the past three decades there has been enormous progress in identifying the essential role that nonlinearity plays in physical systems, including supporting soliton-like solutions and self-trapped sxcitations such as polarons. during the same period, similarly impressive progress has occurred in understanding the effects of disorder in linear quantum problems, especially regarding Anderson localization arising from impurities, random spatial structures, stochastic applied fields, and so forth. These striking consequences of disorder, noise and nonlinearity frequently occur together in physical systems. Yet there have been only limited attempts to develop systematic techniques which can include all of these ingredients, which may reinforce, complement or frustrate each other. This book contains a range of articles which provide important steps toward the goal of systematic understanding and classification of phenomenology. Experts from Australia, Europe, Japan, USA, and the USSR describe both mathematical and numerical techniques - especially from soliton and statistical physics disciplines - and applicaations to a number of important physical systems and devices, including optical and electronic transmission lines, liquid crystals, biophysics and magnetism.

This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.

In 1979, a historical meeting took place at the Institute for Theoretical Physics in Kiev, USSR, where 48 American Scientists, specialists in nonlinear and turbulent processes, met for two weeks with their soviet counterparts. This meeting pro vided the unique opportunity for USA and USSR participants to directly interact personally and scientifically with each other. This interaction was of great impor not only for the individuals involved but also for the science of nonlinear tance phenomena in general. At the end of the meeting, it was agreed that this exchange should continue, and it was decided to have the next meeting in the USA in 1981. Unfortunately, due to the political situation at that time, the second meeting in the USA never materialized. However, in 1983, the Soviet scientists organized in Kiev a second Workshop. This second meeting was again quite successful. Similar meetings, with growing success were organized at Kiev in 1987, and 1989. It should be noted that 405 participants from 22 countries participated at the fourth Kiev workshop on Nonlinear and Turbulent Processes. The Chainnan of this workshop was V. Zakharov, who has also been a co-chainnan of all the previous workshops."

The methods of statistical physics have become increasingly important in recent years for the treatment of a variety of diverse physical problems. Of principal interest is the microscopic description of the dynamics of dissipative systems. Although a unified theoretical description has at present not yet been achieved, we have assumed the task of writing a textbook which summarizes those of the most important methods which are self-contained and complete in themselves. We cannot, of course, claim to have treated the field exhaustively. A microscopic description of physical phenomena must necessarily be based upon quantum theory, and we have therefore carried out the treatment of dynamic processes strictly within a quantum-theoretical framework. For this reason alone it was necessary to omit a number of extremely important theories which have up to now been formulated only in terms of classical statistics. The goal of this book is, on the one hand, to give an introduction to the general principles of the quantum statistics of dynamical processes, and, on the other, to provide readers who are interested in the treatment of particular phenomena with methods for solving specific problems. The theory is for the most part formulated within the calculational frame work of Liouville space, which, together with projector formalism, has become an expedient mathematical tool in statistical physics."

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.

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

Semiconductor technology has developed considerably during the past several decades. The exponential growth in microelectronic processing power has been achieved by a constant scaling down of integrated cir, cuits. Smaller fea ture sizes result in increased functional density, faster speed, and lower costs. One key ingredient of the LSI technology is the development of the lithog raphy and microfabrication. The current minimum feature size is already as small as 0.2 /tm, beyond the limit imposed by the wavelength of visible light and rapidly approaching fundamental limits. The next generation of devices is highly likely to show unexpected properties due to quantum effects and fluctuations. The device which plays an important role in LSIs is MOSFETs (metal oxide-semiconductor field-effect transistors). In MOSFETs an inversion layer is formed at the interface of silicon and its insulating oxide. The inversion layer provides a unique two-dimensional (2D) system in which the electron concentration is controlled almost freely over a very wide range. Physics of such 2D systems was born in the mid-1960s together with the development of MOSFETs. The integer quantum Hall effect was first discovered in this system."

This text on the statistical theory of nonequilibrium phenomena grew out of lecture notes for courses on advanced statistical mechanics that were held more or less regularly at the Physics Department of the Technical University in Munich. My aim in these lectures was to incorporate various developments of many-body theory made during the last 20-30 years, in particular the correlation function approach, not just as an "extra" alongside the more "classical" results; I tried to use this approach as a unifying concept for the presentation of older as well as more recent results. I think that after so many excellent review articles and advanced treatments, correlation functions and memory kernels are as much a matter of course in nonequilibrium statistical physics as partition functions are in equilibrium theory, and should be used as such in regular courses and textbooks. The relations between correlation functions and earlier vehicles for the formulation of nonequilibrium theory such as kinetic equations, master equations, Onsager's theory, etc. , are discussed in detail in this volume. Since today there is growing interest in nonlinear phenomena I have included several chapters on related problems. There is some nonlinear response theory, some results on phenomenological nonlinear equations and some microscopic applications of the nonlinear response formalism. The main focus, however, is on the linear regime.

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."

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.

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."

This short but complicated book is very demanding of any reader. The scope and style employed preserve the nature of its subject: the turbulence phe nomena in gas and liquid flows which are believed to occur at sufficiently high Reynolds numbers. Since at first glance the field of interest is chaotic, time-dependent and three-dimensional, spread over a wide range of scales, sta tistical treatment is convenient rather than a description of fine details which are not of importance in the first place. When coupled to the basic conserva tion laws of fluid flow, such treatment, however, leads to an unclosed system of equations: a consequence termed, in the scientific community, the closure problem. This is the central and still unresolved issue of turbulence which emphasizes its chief peculiarity: our inability to do reliable predictions even on the global flow behavior. The book attempts to cope with this difficult task by introducing promising mathematical tools which permit an insight into the basic mechanisms involved. The prime objective is to shed enough light, but not necessarily the entire truth, on the turbulence closure problem. For many applications it is sufficient to know the direction in which to go and what to do in order to arrive at a fast and practical solution at minimum cost. The book is not written for easy and attractive reading."

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."