This book collects together recent results on large-scale structures in non-linear science. Coherent states, convective and turbulent patterns, inverse cascades, interfaces and cooperative phenomena in fluids and plasmas are discussed, together with the implementation of concepts of statistical mechanics to particle physics and nuclear matter. Special attention is devoted to phenomena, such as mixing, which display macroscopicfeatures, even though generated by small-scale dynamical processes. In this context, homoclinic structure, the KAM theorem, Lyapunov stability, and singularities are addressed. A new perturbative technique for classical and quantum fields and new results concerning the analysis of hierarchially organized objects are presented. The book should be attractive for a large audience including engineers, mathematicians and physicists.

The study of the magnetic fields of the Earth and Sun, as well as those of other planets, stars, and galaxies, has a long history and a rich and varied literature, including in recent years a number of review articles and books dedicated to the dynamo theories of these fields. Against this background of work, some explanation of the scope and purpose of the present monograph, and of the presentation and organization of the material, is therefore needed. Dynamo theory offers an explanation of natural magnetism as a phenomenon of magnetohydrodynamics (MHD), the dynamics governing the evolution and interaction of motions of an electrically conducting fluid and electromagnetic fields. A natural starting point for a dynamo theory assumes the fluid motion to be a given vector field, without regard for the origin of the forces which drive it. The resulting kinematic dynamo theory is, in the non-relativistic case, a linear advection-diffusion problem for the magnetic field. This kinematic theory, while far simpler than its magnetohydrodynamic counterpart, remains a formidable analytical problem since the interesting solutions lack the easiest symmetries. Much ofthe research has focused on the simplest acceptable flows and especially on cases where the smoothing effect of diffusion can be exploited. A close analog is the advection and diffusion of a scalar field by laminar flows, the diffusion being measured by an appropriate Peclet number. This work has succeeded in establishing dynamo action as an attractive candidate for astrophysical magnetism.

Inspired by the general configuration characteristics of automatic production lines, the author discusses the modelisation of important sectors of a factory. Typical topics such as parts feeders, part orienting devices, insertion mechanisms and buffered flows are analysed using random evolution models and non-linear dynamical systems theory.

We consider quantum dynamical systems (in general, these could be either Hamiltonian or dissipative, but in this review we shall be interested only in quantum Hamiltonian systems) that have, at least formally, a classical limit. This means, in particular, that each time-dependent quantum-mechanical expectation value X (t) has as i cl Ii -+ 0 a limit Xi(t) -+ x1 )(t) of the corresponding classical sys- tem. Quantum-mechanical considerations include an additional di- mensionless parameter f = iiiconst. connected with the Planck constant Ii. Even in the quasiclassical region where f~ 1, the dy- namics of the quantum and classicalfunctions Xi(t) and XiCcl)(t) will be different, in general, and quantum dynamics for expectation val- ues may coincide with classical dynamics only for some finite time. This characteristic time-scale, TIi., could depend on several factors which will be discussed below, including: choice of expectation val- ues, initial state, physical parameters and so on. Thus, the problem arises in this connection: How to estimate the characteristic time- scale TIi. of the validity of the quasiclassical approximation and how to measure it in an experiment? For rather simple integrable quan- tum systems in the stable regions of motion of their corresponding classical phase space, this time-scale T" usually is of order (see, for example, [2]) const TIi. = p,li , (1.1) Q where p, is the dimensionless parameter of nonlinearity (discussed below) and a is a constant of the order of unity.

Like relativity and quantum theory chaos research is another prominent concept of 20th century physics that has triggered deep and far-reaching discussions in the philosophy of science. In this volume outstanding scientists discuss the fundamental problems of the concepts of law and of prediction. They present their views in their contributions to this volume, but they also are exposed to criticism in transcriptions of recordings made during discussions and in comments on their views also published in this book. Although all authors assume familiarity with some background in physics they also address the philosophers of science and even a general audience interested in modern science's contribution to a deeper understanding of reality.

In this monograph the recursion method is presented as a method for the analysis of dynamical properties of quantum and classical many-body systems in thermal equilibrium. Such properties are probed by many different experimental techniques used in materials science. Several representations and formulations of the recursion method are described in detail and documented with numerous examples, ranging from elementary illustrations for tutorial purposes to realistic models of interest in current research in the areas of spin dynamics and low-dimensional magnetism. The performance of the recursion method is calibrated by exact results in a number of benchmark tests and compared with the performance of other calculational techniques. The book addresses graduate students and researchers.

The purpose of this book is to gather contributions from scientists in fluid mechanics who use asymptotic methods to cope with difficult problems. The selected topics are as follows: vorticity and turbulence, hydrodynamic instability, non-linear waves, aerodynamics and rarefied gas flows. The last chapter of the book broadens the perspective with an overview of other issues pertaining to asymptotics, presented in a didactic way.

This volume has its origin in the Semigroup Symposium which was organized in connection with the 21st International Colloquium on Group Theoretical Methods in Physics (ICGTMP) at Goslar, Germany, July 16-21, 1996. Just as groups are important tools for the description of reversible physical processes, semigroups are indispensable in the description of irreversible physical processes in which a direction of time is distinguished. There is ample evidence of time asymmetry in the microphysical world. The desire to go beyond the stationary systems has generated much recent effort and discussion regarding the application of semigroups to time-asymmetric processes. The book should be of interest to scientists and graduate students

Published in honour of Marc Feix this book tries to give a thorough overview of mathematical methods, analytical and numerical techniques and simulations applied to a variety of problems from physics and engineering. The book addresses graduate students, researchers and especially engineers. The main emphasis is to apply the generality of methods to form a coherent and stimulating approach to practical investigations.

This book brings new scientific methods to intelligence research that is still under the influence of 19th century single causal theory and method. The author describes a rigorous and exhaustive classification of natural intelligence while demonstrating a more adequate scientific and mathematical approach than current statistical and psychometric approaches construct to shore up the out-dated and misused IQ hypothetical. The author demonstrates the superiority of a highly developed multidisciplinary-theory models view of intelligence.

Beginning with Nobel laureate I. Prigogine's lecture "Entropy Revisited", this book gives a well-balanced survey on capillarity properties at liquid and solid interfaces. It approaches the subject from both the microscopic (statistical mechanics) and the macroscopic (mechanics and thermodynamics) points of view. Experimental aspects and technological applications are also presented. The book addresses researchers and graduate students of physics and physical chemistry.

This book has grown out of eight years of close collaboration among its authors. From the very beginning we decided that its content should come out as the result of a truly common effort. That is, we did not "distribute" parts of the text planned to each one of us. On the contrary, we made a point that each single paragraph be the product of a common reflection. Genuine team-work is not as usual in philosophy as it is in other academic disciplines. We think, however, that this is more due to the idiosyncrasy of philosophers than to the nature of their subject. Close collaboration with positive results is as rewarding as anything can be, but it may also prove to be quite difficult to implement. In our case, part of the difficulties came from purely geographic separation. This caused unsuspected delays in coordinating the work. But more than this, as time passed, the accumulation of particular results and ideas outran our ability to fit them into an organic unity. Different styles of exposition, different ways of formalization, different levels of complexity were simultaneously present in a voluminous manuscript that had become completely unmanageable. In particular, a portion of the text had been conceived in the language of category theory and employed ideas of a rather abstract nature, while another part was expounded in the more conventional set-theoretic style, stressing intui tivity and concreteness.

In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.

This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure the Schrodinger-Virasoro algebra. Just as Poincare invariance or conformal (Virasoro) invariance play a key role in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence.

The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schrodinger operators."

Particles with fractional statistics interpolating between bosons and fermions have attracted considerable interest from mathematical physicists. In recent years it has emerged that these so-called anyons have rather unexpected applications, such as the fractional Hall effect, anyonic excitations in films of liquid helium, and high-temrperature superconductivity. Furthermore, they are discussed also in the context of conformal field theories. This book is a systematic and pedagogical introduction that considers the subject of anyons from many different points of view. In particular, the author presents the relation of anyons to braid groups and Chern-Simons field theory and devotes three chapters to physical applications. The book, while being of interest to researchers, primarily addresses advanced students of mathematics and physics.

This monograph gives a detailed introductory exposition of research results for various models, mostly two-dimensional, of directed walks, interfaces, wetting, surface adsorption (of polymers), stacks, compact clusters (lattice animals), etc. The unifying feature of these models is that in most cases they can be solved analytically. The methods used include transfer matrices, generating functions, recurrence relations, and difference equations, and in some cases involve utilization of less familiar mathematical techniques such as continued fractions and q-series. The authors emphasize an overall view of what can be learned generally of the statistical mechanics of anisotropic systems, including phenomena near surfaces, by studying the solvable models. Thus, the concept of scaling and, where known, finite-size scaling properties are elucidated. Scaling and statistical mechanics of anisoptropic systems in general are active research topics. The volume provides a comprehensive survey of exact model results in this field.

Complexity, Cognition and the City aims at a deeper understanding of urbanism, while invoking, on an equal footing, the contributions both the hard and soft sciences have made, and are still making, when grappling with the many issues and facets of regional planning and dynamics. In this work, the author goes beyond merely seeing the city as a self-organized, emerging pattern of some collective interaction between many stylized urban "agents" - he makes the crucial step of attributing cognition to his agents and thus raises, for the first time, the question on how to deal with a complex system composed of many interacting complex agents in clearly defined settings. Accordingly, the author eventually addresses issues of practical relevance for urban planners and decision makers. The book unfolds its message in a largely nontechnical manner, so as to provide a broad interdisciplinary readership with insights, ideas, and other stimuli to encourage further research - with the twofold aim of further pushing back the boundaries of complexity science and emphasizing the all-important interrelation of hard and soft sciences in recognizing the cognitive sciences as another necessary ingredient for meaningful urban studies.

In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.

Advances in the dynamics of stellar systems have been made recently by applying mathematical methods of ergodic theory and chaotic dynamics, by numerous computer simulations, and by observations with the most powerful telescopes. This has led to a considerable change of our view on stellar systems. These systems appear much more chaotic than was previously thought and subject to various instabilities leading to new paths of evolution than previously thought. The implications are fundamental for our views on the evolution of the galaxies and the universe. Such questions are addressed in this book, especially in the 8 review papers by leading experts on various aspects of the N-body problem, explaining at the graduate/postgraduate level the concepts, methods, techniques and results.

This volume contains the lectures and invited seminars pre sented at the NATO Advanced Study Institute on NON-EQUILIBRIUM COOPERATIVE PHENOMENA IN PHYSICS AND RELATED FIELDS that was held at EL ESCORIAL (MADRID), SPAIN, on August 1-11, 1983. Most nonlinear problems in dissipative systems, i . e . , most mathematical models in SYNERGETICS are highly trans disciplinary in practice and the list of lecturers and participants at the ASI reflects this di versi ty both in background and interest. The presentation of the material fell into two main categories: tutopia~ Zectures on some basic ideas and methods, both experimental and theoretical, intended to lay a common base for all participants, and a series of more specific lectures and seminars, serving the purpose of exemplying selected but typical applications in their current state of development. Topics were chosen for their basic interest as well as for their potential for applications (laser, hydrodynamics, liquid crystals, EHD, combustion, thermoelasticity, etc. ). We had more seminars and some of the oral presentations were supported or complemented with 16 mm films and on occasion with experimental demonstrations including a special seminar, a social one on broken symmetries in Art and Music. There is here no record of these non-standard acti vi ties. We had, indeed, quite a heavy load for which I was fully responsible. However, the reader and, above all, the participants at the ASI ought to be aware of the fact that in Spain, with.

The book aims to give an overview of the previous Sitges Conferences, which have been held during the last 25 years, with special emphasis on topics related to non-equilibrium phenomena. It includes review articles and articles dealing with new trends in the subject, written by scientists who have played an important role in the development of this area. The book is intended as a commemorative edition of the Sitges Conferences. Graduate students of physics and researchers will find this a stimulating account of the development of non-equilibrium statistical mechanics in the last years, covering a wide scope of topics: kinetic theory, hydrodynamics, fluctuation phenomena and stochastic processes, relaxation phenomena, kinetics of phase transitions, growth kinetics, and so on.

Starting from basic principles, the book covers a wide variety of topics, ranging from Heisenberg, Schroedinger, second quantization, density matrix and path integral formulations of quantum mechanics, to applications that are (or will be) corner stones of present and future technologies. The emphasis is on spin waves, quantum information, recent tests of quantum physics and decoherence. The book provides a large amount of information without unbalancing the flow of the main ideas by laborious detail.

P. Levy's work on random walks with infinite moments, developed more than half a century ago, has now been fully appreciated as a foundation of probabilistic aspects of fractals and chaos as well as scale-invariant processes. This is the first book for physicists devoted to Levy processes. It includes thorough review articles on applications in fluid and gas dynamics, in dynamical systems including anomalous diffusion and in statistical mechanics. Various articles approach mathematical problems and finally the volume addresses problems in theoretical biology. The book is introduced by a personal recollection of P. Levy written by B. Mandelbrot."

Written in a pedagogical way, the articles in this book address graduate students as well as researchers and are well suited for seminar work. Subjects at the forefront of nuclear research, bordering other areas of many-particle physics, such as electron scattering at different energy scales, new physics with radioactive beams, multifragmentation, relativistic nuclear physics, high spin nuclear problems, chaos, the role of the continuum in nuclear physics or recent calculations with the shell model are presented. It is felt that the topics treated in this book address the main future lines of development of nuclear physics.

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