This unique monograph introduces an important new area of control system research and presents some new methods for solving some typical problems in the field of sandwich nonlinear systems. Sandwiched nonsmooth nonlinearities such as dead-zone, hysteresis and backlash between dynamic blocks are presented, as well as continuous-time control designs. A framework for hybrid control is developed that is used to design control schemes for different cases of the control problem with required modifications. Friction compensation is addressed for systems with sandwiched friction along with sandwiched dynamics. An open problem of the control of sandwich nonlinear systems with actuator failures is introduced by a control design for an illustrative case.

This book provides a unified and up-to-date account of techniques for handling circular data, and will interest all who perform data analyses.

Entropy and entropy generation play essential roles in our understanding of many diverse phenomena ranging from cosmology to biology. Their importance is manifest in areas of immediate practical interest such as the provision of global energy as well as in others of a more fundamental flavour such as the source of order and complexity in nature. They also form the basis of most modern formulations of both equilibrium and nonequilibrium thermodynamics. Today much progress is being made in our understanding of entropy and entropy generation in both fundamental aspects and application to concrete problems. The purpose of this volume is to present some of these recent and important results in a manner that not only appeals to the entropy specialist but also makes them accessible to the nonspecialist looking for an overview of the field. This book contains fourteen contributions by leading scientists in their fields. The content covers such topics as quantum thermodynamics, nonlinear processes, gravitational and irreversible thermodynamics, the thermodynamics of Taylor dispersion, higher order transport, the mesoscopic theory of liquid crystals, simulated annealing, information and biological aspects, global energy, photovoltaics, heat and mass transport and nonlinear electrochemical systems. Audience: This work will be of value to physicists, chemists, biologists and engineers interested in the theory and applications of entropy and its generation.

The problem of deriving irreversible thermodynamics from the re versible microscopic dynamics has been on the agenda of theoreti cal physics for a century and has produced more papers than can be digested by any single scientist. Why add to this too long list with yet another work? The goal is definitely not to give a gen eral review of previous work in this field. My ambition is rather to present an approach differing in some key aspects from the stan dard treatments, and to develop it as far as possible using rather simple mathematical tools (mainly inequalities of various kinds). However, in the course of this work I have used a large number of results and ideas from the existing literature, and the reference list contains contributions from many different lines of research. As a consequence the reader may find the arguments a bit difficult to follow without some previous exposure to this set of problems."

Recent years have witnessed a resurgence in the kinetic approach to dynamic many-body problems. Modern kinetic theory offers a unifying theoretical framework within which a great variety of seemingly unrelated systems can be explored in a coherent way. Kinetic methods are currently being applied in such areas as the dynamics of colloidal suspensions, granular material flow, electron transport in mesoscopic systems, the calculation of Lyapunov exponents and other properties of classical many-body systems characterised by chaotic behaviour. The present work focuses on Brownian motion, dynamical systems, granular flows, and quantum kinetic theory.

La meccanica statistica (MS) nell'insegnamente universitario e' spesso confinata in una posizione itermedia tra le tre grandi aree della fisica teorica, la fisica della materia e la fisica matematica. In genere vengono discussi gli aspetti "pratici," di supporto alla fisica della materia, che pur importanti non esauriscono la rilevanza concettule della meccanica statistica. Esistono molti ottimi libri (Huang, Landau-Lifsits, Chandler, Peliti etc) che trattano in modo dettagliato gli aspetti tecnici della meccanica statistica. Lo scopo del nostro libro non e' quello di presentare metodi (esatti ed approssimati) per determinare le proprieta termodinamiche a partire dalle interazioni microscopiche, quanto discutere alcuni aspetti concettuali della meccanica statistica che sono spesso poco trattati. In particolare: 1- Il ruolo dell'ipotesi ergodica 2- L'importanza dei tanti gradi di liberta per le leggi statistiche 3- L'interpretazione degli ensemble in termini di probabilita; 4- L'irreversibilita macroscopica 5- L'utilizzo della meccanica statistica per provare l'ipotesi atomistica e la determinazione delle scale (spaziali ed egernetiche) del mondo microscopico."

The aim of these notes is to link algorithmic problems arising in knot theory with statistical physics and classical combinatorics. Apart from the theory of computational complexity needed to deal with enumeration problems, introductions are given to several of the topics, such as combinatorial knot theory, randomized approximation models, percolation, and random cluster models.

This text is a graduate-level introduction to neural networks, focusing on current theoretical models, examining what these models can reveal about how the brain functions, and discussing the ramifications for psychology, artificial intelligence, and the construction of a new generation of intelligent computers. The book is divided into four parts. The first part gives an account of the anatomy of the central nervous system, followed by a brief introduction to neurophysiology. The second part is devoted to the dynamics of neuronal states, and demonstrates how very simple models may stimulate associative memory. The third part of the book discusses models of learning, including detailed discussions on the limits of memory storage, methods of learning and their associated models, associativity, and error correction. The final section of the book reviews possible applications of neural networks in artificial intelligence, expert systems, optimization problems, and the construction of actual neuronal supercomputers, with the potential for one-hundred fold increase in speed over contemporary serial machines.

This text is a graduate-level introduction to neural networks, focusing on current theoretical models, examining what these models can reveal about how the brain functions, and discussing the ramifications for psychology, artificial intelligence, and the construction of a new generation of intelligent computers. The book is divided into four parts. The first part gives an account of the anatomy of the central nervous system, followed by a brief introduction to neurophysiology. The second part is devoted to the dynamics of neuronal states, and demonstrates how very simple models may stimulate associative memory. The third part of the book discusses models of learning, including detailed discussions on the limits of memory storage, methods of learning and their associated models, associativity, and error correction. The final section of the book reviews possible applications of neural networks in artificial intelligence, expert systems, optimization problems, and the construction of actual neuronal supercomputers, with the potential for one-hundred fold increase in speed over contemporary serial machines.

This book contains six sets of lectures by internationally respected researchers on the statistical physics of crystal growth. The emphasis in the papers is on a description of underlying mechanisms and elaboration of simple models that provide a transparent physical picture. Viewed from a novel vantage point, they cover not only very recent developments in the phenomena of shape and growth, but also reflect on old problems that have not always received the attention they deserve. Contributors include P. Nozières, C. Caroli, B. Caroli, B. Roulet, J.S. Langer, Y. Pomeau, M. Ben Amar, L. Sander, J. Krug and H. Spohn.

It is usually straightforward to calculate the result of a practical experiment in the laboratory. Estimating the accuracy of that result is often regarded by students as an obscure and tedious routine, involving much arithmetic. An estimate of the error is, however, an integral part of the presentation of the results of experiments. This textbook is intended for undergraduates who are carrying out laboratory experiments in the physical sciences for the first time. It is a practical guide on how to analyse data and estimate errors. The necessary formulas for performing calculations are given, and the ideas behind them are explained, although this is not a formal text on statistics. Specific examples are worked through step by step in the text. Emphasis is placed on the need to think about whether a calculated error is sensible. At first students should take this book with them to the laboratory, and the format is intended to make this convenient. The book will provide the necessary understanding of what is involved, should inspire confidence in the method of estimating errors, and enable numerical calculations without too much effort. The author's aim is to make practical classes more enjoyable. Students who use this book will be able to complete their calculations quickly and confidently, leaving time to appreciate the basic physical ideas involved in the experiments.

This book fills the need for an intermediate undergraduate textbook on statistical physics. The subject is introduced from a phenomenalogical stance and presented in terms of thermodynamics, stressing the power and practicality of this approach. The atomic view is then discussed and formal stistical mechanics is brought in. Finally the reader is brought back to phenomenology, in the treatment of noise and random processes.
Examples are drawn from topics of strong current interest, such as quantum optics, superconductivity and Bose-Einstein condensation. The book contains a large number of examples and a solutions manual and teachers guide will accompany the text.
* distiguished and renowned author
* topical presentation of core subject

Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces which illustrates the relations between string theory and statistical physics. The two volumes that make up this work will be useful to theoretical physicists and applied mathematicians who are interested in the exciting developments which have resulted from the synthesis of field theory and statistical physics.

The second volume covers diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces, which illustrates the relations between string theory and statistical physics.

The NATO Advanced Study Institute on Diffuse Waves in Complex Media was held at the "Centre de Physique des Houches" in France from March 17 to 27, 1998. The Schools' scientific content, wave propagation in heterogeneous me dia, has covered many areas of fundamental and applied research. On the one hand, the understanding of wave propagation has considerably improved during the last thirty years. New developments and concepts such as, speckle correlations, weak and strong localization, time reversal, near-field propagation are under active research. On the other hand, wave propagation in random media is now being investigated in many different fields such as applied mathematics, acoustics, optics, atomic physics, geo physics or medical sciences. Each community often uses its own langage to describe the same phenomena. The aim of the School was to gather worldwide specialists to illuminate various aspects of wave propagation in random media. This volume presents fourteen expository articles corresponding to courses and seminars given during the School. They are arranged as follows. The first three articles deal with the phenomena of localization of waves: B. van Tiggelen (p. 1) gives a critical review of the physics of localization, J. Lacroix (p. 61) presents the mathematical theory and A. Klein (p. 73) describes recent results for randomized periodic media."

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.

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.

At the time of its original publication this reissued 'classic' text, co-written by the Nobel Laureate of 1954, Max Born, represented the final account of the subject and in many ways it still does. The book is divided into four sections. The first of these is very general in nature and deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second part deals with the properties of long lattice waves; the third with thermal properties and the fourth with optical properties.

The thermodynamic limit is a mathematical technique for modeling crystals or other macroscopic objects by considering them as infinite periodic arrays of molecules. The technique allows models in solid state physics to be derived directly from models in quantum chemistry. This book presents new results, many previously unpublished, for a large class of models and provides a survey of the mathematics of thermodynamic limit problems. The authors both work closely with Fields Medal-winner Pierre-Louis Lion, and the book will be a valuable tool for applied mathematicians and mathematical physicists studying nonlinear partial differential equations.

Statistical Physics II introduces nonequilibrium theories of statistical mechanics from the viewpoint of the fluctuation-disipation theorem. Emphasis is placed on the relaxation from nonequilibrium to equilibrium states, the response of a system to an external disturbance, and general problems involved in deriving a macroscopic physical process from more basic underlying processes. Fundamental concepts and methods are stressed, rather than the numerous individual applications.

This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular particles, or cells, or of processes that depend on such motion or are markedly affected by it. Readers do not need to understand thermodynamics in order to acquire a knowledge of the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility--subjects that become lively and immediate when the author discusses them in terms of random walks of individual particles.

Disordered systems are statistical mechanics models in random environments. This lecture notes volume concerns the equilibrium properties of a few carefully chosen examples of disordered Ising models. The approach is that of probability theory and mathematical physics, but the subject matter is of interest also to condensed matter physicists, material scientists, applied mathematicians and theoretical computer scientists. (The two main types of systems considered are disordered ferromagnets and spin glasses. The emphasis is on questions concerning the number of ground states (at zero temperature) or the number of pure Gibbs states (at nonzero temperature). A recurring theme is that these questions are connected to interesting issues concerning percolation and related models of geometric/combinatorial probability. One question treated at length concerns the low temperature behavior of short-range spin glasses: whether and in what sense Parisi's analysis of the meanfield (or "infinite-range") model is relevant. Closely related is the more general conceptual issue of how to approach the thermodynamic (i.e., infinite volume) limit in systems which may have many complex competing states. This issue has been addressed in recent joint work by the author and Dan Stein and the book provides a mathematically coherent presentation of their approach.)

Scale Invariance and Beyond B. Dubrulle, F. Graner* and D. Somette**.*** CNRS, CEAIDSMIDAPNWservice d'Astrophysique, L 'Orme des Merisiers, 709, 91191 Gif-sur-Yvette, France * Laboratoire de Spectrometrie Physique, B.P. 87, 38402 Saint-Martin-d'Heres cedex, France ** Laboratoire de Physique de Ia Matiere Condensee, CNRS and Universite de Nice -Sophia Antipolis, Pare Valrose, 06108 Nice, France ***Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095-1567, U.S.A. 1. INTRODUCTION In physics, any symmetry is a bargain. It provides tools to analyze the solutions of a problem without need to explicitly solve the problem, or it can also suggest methods to simplify the problem. In real life, boundary conditions or even physical processes themselves break the initial beautiful symmetry. One has to deal with "approximate symmetry" and means to obtain useful informations from this broken symmetry have to be built. The topic of the school held in Les Houches in March 1997 is the illustration of these general ideas in the case of scale symmetry. Part of the school involved descriptions of tools or concepts used in scale invariant systems, and examples pertaining to them ("Scale Invariance ... "); the second half was devoted to recent attempts to go beyond the invariance or symmetry breaking, discuss causes and consequences, and extract useful informations about the system (" ... and beyond")."

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.

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author's previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time. The text begins with both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models such as: * inverted controlled pendulum; * Nicholson's blowflies equation; * predator-prey relationships; * epidemic development; and * mathematical models that describe human behaviours related to addictions and obesity. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations is primarily addressed to experts in stability theory but will also be of interest to professionals and students in pure and computational mathematics, physics, engineering, medicine, and biology.