This book contains the courses given at the Fifth School on Complex Systems held at Santiago, Chile, from 9th .to 13th December 1996. At this school met researchers working on areas related with recent trends in Complex Systems, which include dynamical systems, cellular automata, symbolic dynamics, spatial systems, statistical physics and thermodynamics. Scientists working in these subjects come from several areas: pure and applied mathematics, physics, biology, computer science and electrical engineering. Each contribution is devoted to one of the above subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The paper of Bruno Durand presents the state of the art on the relationships between the notions of surjectivity, injectivity and reversibility in cellular automata when finite, infinite or periodic configurations are considered, also he discusses decidability problems related with the classification of cellular automata as well as global properties mentioned above. The paper of Eric Goles and Martin Matamala gives a uniform presentation of simulations of Turing machines by cellular automata. The main ingredient is the encoding function which must be fixed for all Turing machine. In this context known results are revised and new results are presented.

In the decades the of the formation of structures past subject spontaneous in far from has into a branch of - systems equilibrium major physics grown search with ties to It has become evident that strong neighboring disciplines. a diverse of can be understood within a common mat- phenomena range matical framework which has been called nonlinear of continuous dynamics This name the close to the field of nonlinear systems. emphasizes relationship of with few of freedom which has evolved into a dynamics systems degrees mature in the recent features mathematically subject past. Many dynamical of continuous be described reduction few can a to a systems actually through of freedom and of the latter of continue to degrees properties type systems of continuous the inspire study systems. The of this book is to demonstrate the numerous goal through examples that exist for the of nonlinear the opportunities study phenomena through tools of mathematical and use of common analyses dynamical interpretations. Instead of overview of the a providing comprehensive rapidly evolving field, the contributors to this book are to communicate to a wide scientific trying audience the of what have learnt about the formation of essence they spon- neous structures in continuous and about the dissipative systems competition between order and chaos that characterizes these It is that systems. hoped the book will be even to those scientists whose not helpful are disciplines the authors.

This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

In this monograph, nonequilibrium statistical mechanics is developed by means of ensemble methods on the basis of the Boltzmann equation, the generic Boltzmann equations for classical and quantum dilute gases, and a generalised Boltzmann equation for dense simple fluids. The theories are developed in forms parallel with the equilibrium Gibbs ensemble theory in a way fully consistent with the laws of thermodynamics. The generalised hydrodynamics equations are the integral part of the theory and describe the evolution of macroscopic processes in accordance with the laws of thermodynamics of systems far removed from equilibrium. Audience: This book will be of interest to researchers in the fields of statistical mechanics, condensed matter physics, gas dynamics, fluid dynamics, rheology, irreversible thermodynamics and nonequilibrium phenomena.

This book contributes to the mathematical theory of systems of differential equations consisting of the partial differential equations resulting from conservation of mass and momentum, and of constitutive equations with internal variables. The investigations are guided by the objective of proving existence and uniqueness, and are based on the idea of transforming the internal variables and the constitutive equations. A larger number of constitutive equations from the engineering sciences are presented. The book is therefore suitable not only for specialists, but also for mathematicians seeking for an introduction in the field, and for engineers with a sound mathematical background.

Statistical mechanics deals with systems in which chaos and randomness reign supreme. The current theory is therefore firmly based on the equations of classical mechanics and the postulates of probability theory. This volume seeks to present a unified account of classical mechanical statistics, rather than a collection of unconnected reviews on recent results. To help achieve this, one element is emphasised which integrates various parts of the prevailing theory into a coherent whole. This is the hierarchy of the BBGKY equations, which enables a relationship to be established between the Gibbs theory, the liquid theory, and the theory of nonequilibrium phenomena. As the main focus is on the complex theoretical subject matter, attention to applications is kept to a minimum. The book is divided into three parts. The first part describes the fundamentals of the theory, embracing chaos in dynamic systems and distribution functions of dynamic systems. Thermodynamic equilibrium, dealing with Gibbs statistical mechanics and the statistical mechanics of liquids, forms the second part. Lastly, the third part concentrates on kinetics, and the theory of nonequilibrium gases and liquids in particular. Audience: This book will be of interest to graduate students and researchers whose work involves thermophysics, theory of surface phenomena, theory of chemical reactions, physical chemistry and biophysics.

Provides unified coverage of computational heat transfer and fluid dynamics. Covers basic concepts and then applies computational methods for problem analysis and solution. Contains new chapters on mesh generation and computer modeling of turbulent flow. Includes ANSYS, STAR CCM+, and COMSOL CFD code and tutorials in the appendix. Includes a Solutions Manual for instructor use.

This book will help readers understand thermodynamic properties caused by magnetic fields. Providing a concise review of time independent magnetic fields, it goes on to discuss the thermodynamic properties of magnetizing materials of different shapes, and finally, the equilibrium properties of superconductors of different shapes and also of different sizes. Chapters are accompanied by problems illustrating the applications of the principles to optimize and enhance understanding. This book will be of interest to advanced undergraduates, graduate students, and researchers specializing in thermodynamics, solid state physics, magnetism, and superconductivity. Features: The first book to provide comprehensive coverage of thermodynamics in magnetic fields, only previously available, in part, in journal articles Chapters include problems and worked solutions demonstrating real questions in contemporary superconductivity, such as properties of vortex matter

One of the main goals of optimal control theory is to provide a theoretical basis for choosing an appropriate controller for whatever system is under consideration by the researcher or engineer. Two popular norms that have proved useful are known as H-2 and H - infinity control. The first has been particularly applicable to problems arising in the aerospace industry. However, most industrial problems are badly modeled and the second norm proved to be more appropriate when the actual conditions of the problem did not conform to the stipulated conditions of the theory. This book takes the topic of H-infinity control as a point of departure and pursues an improved controller design which has been suggested in the mainstream of robust control. Its main theme, minimum entropy control, provides a means of trading off some of the features of other control problems. The book is aimed at research workers in networking systems as well as those in operator theory and linear multivariable control. The use of stochastic methods makes the book also of importance to the circuits and systems community. CONTENTS: Preface Introduction Preliminaries Induced Operator Norms Discrete-Time Entropy Connections With Related Optimal Control Problems Minimum Entropy Control Continuous-Time Entropy A. Proof of Theorem B. Proof of Theorem Bibliography Notation Index"

This book aims to present an information-theoretical approach to thermodynamics and its generalisations. On the one hand, it generalises the concept of information thermodynamics' to that of information dynamics' in order to stress applications outside thermal phenomena. On the other hand, it is a synthesis of the dynamics of state change and the theory of complexity, which provide a common framework to treat both physical and nonphysical systems together. Both classical and quantum systems are discussed, and two appendices are included to explain principal definitions and some important aspects of the theory of Hilbert spaces and operator algebras. The concept of higher-order temperatures is explained and applied to biological and linguistic systems. The theory of open systems is presented in a new, much more general form. Audience: This volume is intended mainly for theoretical and mathematical physicists, but also for mathematicians, experimental physicists, physical chemists, theoretical biologists, communication engineers, and all those interested in entropy and open systems. It can also be recommended as a supplementary text.

From the reviews: "The book is excellent, and covers a very broad area (usually treated as separate topics) from a unified perspective. [ ] It will be very useful for both mathematicians and physicists." EMS Newsletter

This manual contains detailed solutions of slightly more than half of the end of chapter problems in The Dynamics of Heat. The numbers of the problems includ ed here are listed on the following page. A friend who knows me well noticed that I have included only those problems which I could actually solve myself. Also, to make things more interesting, I have built random errors into the solutions. If you find any of them, please let me know. Also, if you have different ways of solving a problem, I would be happy to hear from you. Any feedback, also on the book in general, would be greatly appreciated. There is an Errata sheet for the first printing of The Dynamics of Heat. By the time you read this, it should be available on the Internet for you to download. A reference to the URL of the sheet can be found in the announcement of my book on Springer's WWWpages (www.springer-ny.com). Winterthur, 1996 Hans Fuchs vi Numbers of Problems Solved Prologue 1,2,4,5,6,8, 12, 13, 17, 19,23,25,27,30,32,33,34,38,39,40,42,44,47, 49,50,53,55,60,61,62 Chapter 1 2,4,5,8,9,11,13,15, 16, 17, 18,20,21,24,26,27,29,31,33,34,37,39,41, 42,44,45,47,49,51,53,55,57,58,60,62 Chapter 2 1,3,5,6,7,9,10,12,14,15,16,17,19,20,22,23,24,26,27, 29, 30, 32, 33, 36,37,38,41,42,46,47,49 Interlude 2,3,4,5,6,8,10,11,12,13, 18, 19,20,21,23,24,28 Chapter 3 2,4,6,8,10,12,15,16,17,18,22,24,25,28,30,31,35,36 Chapter 4 1,2,4,6,8,9, 11, 12, 13, 15, 18,20,21,22,25,27,28,29,30,31,33,34,35, 39,40,43,44,46 Epilogue 1, 2, 11 PROLOGUE Solutions of Selected Problems 2 PROLOGUE: Problem 1 Calculate the hydraulic capacitance of a glass tube used in a mercury pressure gauge. The inner diameter of the tube is 8.0 mm.

This book contains the courses given at the Fourth School on Statistical Physics and Cooperative Systems held at Santiago, Chile, from 12th to 16th December 1994. This School brings together scientists working on subjects related to recent trends in complex systems. Some of these subjects deal with dynamical systems, ergodic theory, cellular automata, symbolic and arithmetic dynamics, spatial systems, large deviation theory and neural networks. Scientists working in these subjects come from several aeras: pure and applied mathematics, non linear physics, biology, computer science, electrical engineering and artificial intelligence. Each contribution is devoted to one or more of the previous subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The expository text of Roberto Livi concerns the study of coupled map lattices (CML) as models of spatially extended dynamical systems. CML is one of the most used tools for the investigation of spatially extended systems. The paper emphasizes rigorous results about the dynamical behavior of one dimensional CML; i.e. a uniform real local function defined in the interval [0,1], interacting with its nearest neighbors in a one dimensional lattice.

This is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.

This volume records papers given at the fourteenth international maximum entropy conference, held at St John's College Cambridge, England. It seems hard to believe that just thirteen years have passed since the first in the series, held at the University of Wyoming in 1981, and six years have passed since the meeting last took place here in Cambridge. So much has happened. There are two major themes at these meetings, inference and physics. The inference work uses the confluence of Bayesian and maximum entropy ideas to develop and explore a wide range of scientific applications, mostly concerning data analysis in one form or another. The physics work uses maximum entropy ideas to explore the thermodynamic world of macroscopic phenomena. Of the two, physics has the deeper historical roots, and much of the inspiration behind the inference work derives from physics. Yet it is no accident that most of the papers at these meetings are on the inference side. To develop new physics, one must use one's brains alone. To develop inference, computers are used as well, so that the stunning advances in computational power render the field open to rapid advance. Indeed, we have seen a revolution. In the larger world of statistics beyond the maximum entropy movement as such, there is now an explosion of work in Bayesian methods, as the inherent superiority of a defensible and consistent logical structure becomes increasingly apparent in practice.

This book provides a comprehensive framework for workers in materials science, physics, chemistry, metrology and non-destructive testing, entering the field of photothermal and thermal wave techniques and can be used by those making use of these methods for a wide range of applications. The essential physics is covered from basic principles, using thermal wave analysis to gain physical insight. Each of the commonly used measurement systems is described and assessed, and the major application areas: spectroscopy; non-destructive evaluation; thermal properties measurement and semiconductor material evaluation are each reviewed.

Concise yet thorough, accessible, authoritative, and affordable. These are the hallmarks of books in the remarkable Physics and its Applications series. Thermodynamics is an essential part of any physical sciences education, but it is so full of pitfalls and subtleties, that many students fail to appreciate its elegance and power. In Thermal Physics, the author emphasizes understanding the basic ideas and shows how the important thermodynamics results can be simply obtained from the fundamental relations without getting lost in a maze of partial differentials. In this second edition, the author incorporated new sections on scales of temperature, availability, the degradation of energy, and lattice defects. The text contains ample illustrations and examples of applications of thermodynamics in physics, engineering, and chemistry.

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

During the last decades a considerable effort has been made on the computation of the isothermal flow of viscoelastic fluids. In fact the activities related to this particular field of non-Newtonian fluid mechanics have focused on the following questions: which type of constitutive equation describes non-Newtonian fluid behaviour; how to measure fluid parameters; and what type of computational scheme leads to reliable, stable and cost-effective computer programs. During the same period, typical non-Newtonian fluid phenomena have been experimentally examined, such as the flow through a four-to-one' contraction, the flow around a sphere or separation flow, providing fresh challenges for numerical modellers. Apart from momentum transport, however, fluid flow is strongly influenced by heat treansport in most real industrial operations in which non-Newtonian fluids are processed. The IUTAM Symposium on Numerical Simulation of Nonisothermal Flow of Viscoelastic Liquids' held at Rolduc Abbey in Kerkrade, the Netherlands, November 1--3, 1993, was organised to monitor the state of affairs in regard to the influence of nonisothermal effects on the flow of a viscoelastic liquid. The present collection of papers gives an overview of what has been achieved so far. It is a milestone in the rapidly emerging and exciting new field in non-Newtonian fluid mechanics.

This monograph gives a systematic presentation of ideas, methods and results of the modern statistical theory of open systems -- systems capable of exchanging matter, energy and information with the surrounding world. The resulting self-organization can lead to more sophisticated and advanced structures. Central to this work are the statistical criteria of self-organization. The feasibility of a unified description of kinetic, hydrodynamic and diffusion processes in passive and active macroscopic systems without resorting to the methods of perturbation theory is demonstrated. On this basis, a general definition of thermal flux is given in terms of the entropy gradient. Moreover, a consistent method for calculating both kinetic and hydrodynamic fluctuations is proposed. This approach is then used to construct a theory of classical and anomalous Brownian motion in nonlinear media. This theory makes it possible to treat in an original way the phenomenon of turbulence, and to propose a unified kinetic description of laminar and turbulent motion. The proposed methods are also applied to the statistical description of quantum macroscopic open systems. This provides answers as to whether or not the quantum mechanical description is complete, and whether or not there are hidden parameters in quantum mechanics. The book has no analogy in the existing literature. It is both a monograph and a textbook, and is based largely on the author's original research. The book will be useful to postgraduate students and researchers in chemistry, physics, mathematics, economics, sociology, and engineering.

"Great progress has been made in electrical science, chiefly in Germany, by cultivators of the theory of action at a distance. The valuable electrical measurements of W. Weber are interpreted by him according to this theory, and the electromagnetic speculation which was originated by Gauss, and carried on by Weber, Riemann, F. and C. Neumann, Lorenz, etc. , is founded on the theory of action at a distance, but depending either directly on the relative velocity of the particles, or on the gradual propagation of something, whether potential or force, from the one particle to the other. The great success which these eminent men have attained in the application of mathematics to electrical phenomena, gives, as is natural, additional weight to their theoretical speculations, so that those who, as students of electricity, turn to them as the greatest authorities in mathematical electricity, would probably imbibe, along with their mathematical methods, their physical hypothesis. These physical hypotheses, however, are entirely alien from the way of looking at things which I adopt, and one object which I have in view is that some of those who wish to study electricity may, by reading this treatise, come to see that there is another way of treating the subject, which is no less fitted to explain the phenomena, and which, though in some parts it may appear less definite, corresponds, as I think, more faithfuHy with our actual knowledge, both in what it affirms and in what it leaves undecided.

This monograph is devoted to an entirely new branch of nonlinear physics - solitary intrinsic states, or autosolitons, which form in a broad class of physical, chemical and biological dissipative systems. Autosolitons are often observed as highly nonequilibrium regions in slightly nonequilibrium systems, in many ways resembling ball lightning which occurs in the atmosphere. We develop a new approach to problems of self-organization and turbulence, treating these phenomena as a result of spontaneous formation and subsequent evolution of autosolitons. Scenarios of self-organization involve sophisticated interactions between autosolitons, whereas turbulence is regarded as a pattern of autosolitons which appear and disappear at random in different parts of the system. This monograph is the first attempt to provide a comprehensive summary of the theory of autosolitons as developed by the authors over the years of research. The monograph is comprised of three more or less autonomous parts. Part I deals with the physical nature and experimental studies of autosolitons and self organization in various physical systems: semiconductor and gas plasma, heated gas mixture, semiconductor structures, composite superconductors, optical and magnetic media, systems with uniformly generated combustion matter, distributed gas-discharge and electronic systems. We discuss feasibility of autosolitons in the form of highly nonequilibrium regions in slightly nonequilibrium gases and semiconductors, "hot" and "cold" regions in semiconductor and gas plasmas, static, pulsating and traveling combustion fronts."

This study is one of the first attempts to bridge the theoretical models of variational dynamics of perfect fluids and some practical approaches worked out in chemical and mechanical engineering in the field newly called thermo-hydrodynamics. In recent years, applied mathematicians and theoretical physicists have made significant progress in formulating analytical tools to describe fluid dynamics through variational methods. These tools are much loved by theoretists, and rightly so, because they are quite powerful and beautiful theoretical tools. Chemists, physicists and engineers, however, are limited in their ability to use these tools, because presently they are applicable only to "perfect fluids" (i. e. those fluids without viscosity, heat transfer, diffusion and chemical reactions). To be useful, a model must take into account important transport and rate phenomena, which are inherent to real fluid behavior and which cannot be ignored. This monograph serves to provide the beginnings of a means by which to extend the mathematical analyses to include the basic effects of thermo-hydrodynamics. In large part a research report, this study uses variational calculus as a basic theoretical tool, without undo compromise to the integrity of the mathematical analyses, while emphasizing the conservation laws of real fluids in the context of underlying thermodynamics --reversible or irreversible. The approach of this monograph is a new generalizing approach, based on Nother's theorem and variational calculus, which leads to the energy-momentum tensor and the related conservation or balance equations in fluids.

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

This book contains the courses given at the Third School on Statistical Physics and Cooperative Systems held at Santiago, Chile, from 14th to 18th December 1992. The main idea of this periodic school was to bring together scientists work with recent trends in Statistical Physics. More precisely ing on subjects related related with non linear phenomena, dynamical systems, ergodic theory, cellular au tomata, symbolic dynamics, large deviation theory and neural networks. Scientists working in these subjects come from several areas: mathematics, biology, physics, computer science, electrical engineering and artificial intelligence. Recently, a very important cross-fertilization has taken place with regard to the aforesaid scientific and technological disciplines, so as to give a new approach to the research whose common core remains in statistical physics. Each contribution is devoted to one or more of the previous subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The expository text of Fran"