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

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."

In this book the concept of indistinguishability is defined for identical particles by the symmetry of the state. It applies, therefore, to both the classical and the quantum framework. The author describes symmetric statistical operators and classifies these by means of extreme points. For the description of infinitely extendible interchangeable random variables de Finetti's theorem is derived and generalizations covering the Poisson limit and the central limit are presented. A characterization and interpretation of the integral representations of classical photon states in quantum optics are derived in abelian subalgebras. Unextendible indistinguishable particles are analyzed in the context of nonclassical photon states. The book addresses mathematical physicists and philosophers of science.

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.

With the aim of providing a deeper insight into possible mechanisms of biological self-organization, this thesis presents new approaches to describe the process of self-assembly and the impact of spatial organization on the function of membrane proteins, from a statistical physics point of view. It focuses on three important scenarios: the assembly of membrane proteins, the collective response of mechanosensitive channels and the function of the twin arginine translocation (Tat) system. Using methods from equilibrium and non-equilibrium statistical mechanics, general conclusions were drawn that demonstrate the importance of the protein-protein interactions. Namely, in the first part a general aggregation dynamics model is formulated, and used to show that fragmentation crucially affects the efficiency of the self-assembly process of proteins. In the second part, by mapping the membrane-mediated forces into a simplified many-body system, the dynamic and equilibrium behaviour of interacting mechanosensitive channels is derived, showing that protein agglomeration strongly impacts its desired function. The final part develops a model that incorporates both the agglomeration and transport function of the Tat system, thereby providing a comprehensive description of this self-organizing process.

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."

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology-and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a 'recipe book' full of tried and tested, successful engineering applications

One common characteristics of a complex system is its ability to withstand major disturbances and the capacity to rebuild itself. Understanding how such systems demonstrate resilience by absorbing or recovering from major external perturbations requires both quantitative foundations and a multidisciplinary view on the topic.
This book demonstrates how new methods can be used to identify the actions favouring the recovery from perturbations. Examples discussed include bacterial biofilms resisting detachment, grassland savannahs recovering from fire, the dynamics of language competition and Internet social networking sites overcoming vandalism.
The reader is taken through an introduction to the idea of resilience and viability and shown the mathematical basis of the techniques used to analyse systems. The idea of individual or agent-based modelling of complex systems is introduced and related to analytically tractable approximations of such models. A set of case studies illustrates the use of the techniques in real applications, and the final section describes how one can use new and elaborate software tools for carrying out the necessary calculations.
The book is intended for a general scientific audience of readers from the natural and social sciences, yet requires some mathematics to gain a full understanding of the more theoretical chapters.
It is an essential point of reference for those interested in the practical application of the concepts of resilience and viability

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.

This book deals with the theory and the applications of a new time domain, termed natural time domain, that has been forwarded by the authors almost a decade ago (P.A. Varotsos, N.V. Sarlis and E.S. Skordas, Practica of Athens Academy 76, 294-321, 2001; Physical Review E 66, 011902, 2002). In particular, it has been found that novel dynamical features hidden behind time series in complex systems can emerge upon analyzing them in this new time domain, which conforms to the desire to reduce uncertainty and extract signal information as much as possible. The analysis in natural time enables the study of the dynamical evolution of a complex system and identifies when the system enters a critical stage. Hence, natural time plays a key role in predicting impending catastrophic events in general. Relevant examples of data analysis in this new time domain have been published during the last decade in a large variety of fields, e.g., Earth Sciences, Biology and Physics. The book explains in detail a series of such examples including the identification of the sudden cardiac death risk in Cardiology, the recognition of electric signals that precede earthquakes, the determination of the time of an impending major mainshock in Seismology, and the analysis of the avalanches of the penetration of magnetic flux into thin films of type II superconductors in Condensed Matter Physics. In general, this book is concerned with the time-series analysis of signals emitted from complex systems by means of the new time domain and provides advanced students and research workers in diverse fields with a sound grounding in the fundamentals of current research work on detecting (long-range) correlations in complex time series. Furthermore, the modern techniques of Statistical Physics in time series analysis, for example Hurst analysis, the detrended fluctuation analysis, the wavelet transform etc., are presented along with their advantages when natural time domain is employed.

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.

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.

In this book, a number of the world's leading researchers in quantum, classical and atomic physics cooperate to present an up-to-date account of the recent progress in the field. The first part highlights the latest advances in semiclassical theory, whilst the second one is devoted to applications to atomic systems. The authors present the material in pedagogical form to make it easy reading for non-specialists, too. Among the topics treated, the reader will find a new quasiclassical quantization scheme for Hamiltonian dynamics, an application of the semiclassical formalism to photodissociation of small molecules and to the Lorentz gas and discussions of tunneling corrections. Furthermore, one finds papers on chaotic ionization, on the behaviour of hydrogen atoms in external fields, e.g. magnetic or microwave fields.

- Models of vibro-impact systems are widely used in machine dynamics, vibration engineering, and structural mechanics. - Only monograph on this subject in English language. - Systematically presents the theory of vibro-impact systems by analysis of typical engineering applications. - Experimental data and computer simulations are presented. - Targeted to engineers and researchers in design and investigation of mechanical systems as well as to lecturers and advanced students.

The book contains the notes of the lectures presented by outstanding experts at the 7th EADN School on plasma astrophysics. It is an up-to-date review of a number of basic topics in the physics of cosmic plasmas. The subject is treated both from a theoretical point of view and from that of the observational and diagnostic tools that provide us with the physically relevant data. The reader will have at hands a comprehensive and rather complete presentation of the subject, thanks also to the parallel development of the theoretical and experimental aspects. The book addresses graduate students and researchers in different areas who want to have a rapid and up-to-date introduction to this subject.

Written for researchers and advanced students the book exhibits a combination of various methods and tools required to describe the complexity of the chemical and physical behaviour of fluid surfaces. The common denominator for all the contributions presented here is the simultaneous use of concepts from surface chemistry and physics and from hydrodynamics where external force fields can be introduced. Theoretical and experimental work is equally represented. Most of the basic problems in the area of nonequilibrium multiphase systems have not yet received extensive treatment. This volume should be a reference for physicists, physico-chemists, and chemical engineers and will serve as a jumping-off point for new directions and new points of view.

The book covers the basics and some generalizations of Monte Carlo methods and its applications to discrete and field theoretic models. It covers the study of nonequilibrium models of granular media by computer simulation and pattern formation. Furthermore, the lectures deal with details of phenomena such as chaos, segregation, pattern formation and phase transitions, convection, fluidification, density waves, surface reaction and growth, spread of epidemics, acoustics, deformation, etc. The book addresses students in physics and scientific computation. It should be a valuable reference work for researchers as well.

This is a collection of papers on a variety of topics of current interest in mathematical physics: integrable systems, quantum groups, topological quantum theory, string theory. Some of the contributions are lengthy reviews of lasting value on subjects like symplectic geometry of the Chern-Simons theory or on mirror symmetry. The book addresses graduate students as well as researchers in mathematical physics.

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.

hereafter calledvolume the of In a volume study previous (H6non 1997, I), the restricted initiated. families in problem (We generating three body was recallthat families defined asthe limits offamilies of are periodic generating determinationof orbitsfor Themain wasfoundto lieinthe 4 problem p 0.) bifurcation wheretwo the betweenthebranches ata ormore orbit, junctions A solutionto this was familiesof orbits intersect. partial problem generating and sidesof theuseofinvariants: Manysimple symmetries passage. givenby In the evolution of the bifurcations can be solved in this way. particular, orbits be described almost nine natural families of can completely. periodic become i.e.when thenumber of asthe bifurcations morecomplex, However, fails. the bifurcation orbit themethod families increases, passingthrough of This volume describes another to the a approach problem, consisting in of bifurcation ofthe families the a analysis vicinity detailed, quantitative used in Vol. I. orbit. This moreworkthan the requires qualitativeapproach in at to deter it has the of least, However, advantage allowing us, principle branches Infact it morethanthat: minein allcaseshowthe are joined. gives almost all the first order we will see in asymptotic approxima that, cases, the families in the ofthe bifurcation can be derived. tion of neighbourhood found in with This a comparison numerically allows, particular, quantitative families. and The 11 dealswiththerelevant definitions Chapter generalequations. of describedin 12 16.The ofbifurcations 1 is Chaps. study type quantitative it is described in 17 23. 3 of 2 ismore Chaps. Type analysis type involved; its hadnot been at thetime of isevenmore completed complex; analysis yet writing.

In agent-based modeling the focus is very much on agent-based simulation, as simulation is a very important tool for agent-based modeling. We also use agent-based simulation in this book with a stress on the mathematical foundation of agent-based modeling. We introduce two original mathematical frameworks, a theory of SLD (Social Learning Dynamics) and an axiomatic theory of economic exchange (Exchange Algebra) among agents. Exchange algebra gives bottom-up reconstruction of SNA (System of National Accountings). SLD provides the concept of indirect control of socio-economic systems to manage structural change and its stability. We also compare agent-based simulation with gaming simulation and investigate the epistemological foundation of agent-based modeling.

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The book guides the reader from the foundations of statisti- cal thermodynamics including the theory of intermolecular forces to modern computer-aided applications in chemical en- gineering and physical chemistry. The approach is new. The foundations of quantum and statistical mechanics are presen- ted in a simple way and their applications to the prediction of fluid phase behavior of real systems are demonstrated. A particular effort is made to introduce the reader to expli- cit formulations of intermolecular interaction models and to show how these models influence the properties of fluid sy- stems. The established methods of statistical mechanics - computer simulation, perturbation theory, and numerical in- tegration - are discussed in a style appropriate for newcom- ers and are extensively applied. Numerous worked examples illustrate how practical calculations should be carried out.