This eleventh volume in the Poincare Seminar Series presents an interdisciplinary perspective on the concept of Time, which poses some of the most challenging questions in science. Five articles, written by the Fields medalist C. Villani, the two outstanding theoretical physicists T. Damour and C. Jarzynski, the leading experimentalist C. Salomon, and the famous philosopher of science H. Price, describe recent developments related to the mathematical, physical, experimental, and philosophical facets of this fascinating concept. These articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a description of the manifold fundamental physical issues in play with time, in particular with the changes of perspective implied by Special and General Relativity; a mathematically precise discussion of irreversibility and entropy in the context of Boltzmann's and Vlasov's equations; a thorough survey of the recently developed "thermodynamics at the nanoscale," the scale most relevant to biological physics; a description of the new cold atom space clock PHARAO to be installed in 2015 onboard the International Space Station, which will allow a test of Einstein's gravitational shift with a record precision of 2 x 10-6, and enable a test of the stability over time of the fundamental constants of physics, an issue first raised by Dirac in 1937; and last, but not least, a logical and clarifying philosophical discussion of 'Time's arrow', a phrase first coined by Eddington in 1928 in a challenge to physics to resolve the puzzle of the time-asymmetry of our universe, and echoed here in a short poeme en prose by C. de Mitry. This book should be of broad general interest to physicists, mathematicians, and philosophers.

Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications. The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the "4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems," which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysics, and from nonlinear analysis to the history of chaos theory. The corresponding proceedings collected in this volume address a broad spectrum of contemporary topics, including but not limited to networks, circuits, systems, biology, evolution and ecology, nonlinear dynamics and pattern formation, as well as neural, psychological, psycho-social, socio-economic, management complexity and global systems.

Fundamental Aspects of Plasma Chemical Physics: Transport develops basic and advanced concepts of plasma transport to the modern treatment of the Chapman-Enskog method for the solution of the Boltzmann transport equation. The book invites the reader to consider actual problems of the transport of thermal plasmas with particular attention to the derivation of diffusion- and viscosity-type transport cross sections, stressing the role of resonant charge-exchange processes in affecting the diffusion-type collision calculation of viscosity-type collision integrals. A wide range of topics is then discussed including (1) the effect of non-equilibrium vibrational distributions on the transport of vibrational energy, (2) the role of electronically excited states in the transport properties of thermal plasmas, (3) the dependence of transport properties on the multitude of Saha equations for multi-temperature plasmas, and (4) the effect of the magnetic field on transport properties. Throughout the book, worked examples are provided to clarify concepts and mathematical approaches. This book is the second of a series of three published by the Bari group on fundamental aspects of plasma chemical physics. The first book, Fundamental Aspects of Plasma Chemical Physics: Thermodynamics, is dedicated to plasma thermodynamics; and the third, Fundamental Aspects of Plasma Chemical Physics: Kinetics, deals with plasma kinetics.

Design happens everywhere, whether in animate objects (e.g., dendritic lung structures, bacterial colonies, and corals), inanimate patterns (river basins, beach slope, and dendritic crystals), social dynamics (pedestrian traffic flows), or engineered systems (heat dissipation in electronic circuitry). This "design in nature" often takes on remarkably similar patterns, which can be explained under one unifying Constructal Law. This book explores the unifying power of the Constructal Law and its applications in all domains of design generation and evolution, ranging from biology and geophysics to globalization, energy, sustainability, and security. The Constructal Law accounts for the universal tendency of flow systems to morph into evolving configurations that provide greater and easier access over time. The Constructal Law resolves the many and contradictory ad hoc statements of "optimality", end design, and destiny in nature, such as minimum and maximum entropy production and minimum and maximum flow resistance, and also explains the designs that are observed and copied in biomimetics. Constructal Law and the Unifying Principle of Design covers the fundamentals of Constructal Theory and Design, as well as presenting a variety of state-of-the-art applications. Experts from the biological, physical and social sciences demonstrate the unification of all design phenomena in nature, and apply this knowledge to novel designs in modern engineering, such as vascularization for self-healing and self-cooling materials for aircraft, and tree fins and cavities for heat transfer enhancement.

This dissertation contributes to the understanding of fundamental issues in the highly interdisciplinary field of colloidal science. Beyond colloid science, the system also serves as a model for studying interactions in biological matter. This work quantitatively investigated the scaling laws of the characteristic lengths of the structuring of colloidal dispersions and tested the generality of these laws, thereby explaining and resolving some long-standing contradictions in literature. It revealed the effect of confinement on the structuring, independently of specific properties of the confining interfaces. In addition, it resolved the influence of roughness and charge of the confining interfaces on the structuring and as well providing a method to measure the effect of surface deformability on colloidal structuring.

The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematicians, the essential aspects of the Parisi solution were clarified and proved mathematically. The core ideas of the theory that emerged are the subject of this book, including the recent solution of the Parisi ultrametricity conjecture and a conceptually simple proof of the Parisi formula for the free energy. The treatment is self-contained and should be accessible to graduate students with a background in probability theory, with no prior knowledge of spin glasses. The methods involved in the analysis of the Sherrington-Kirkpatrick model also serve as a good illustration of such classical topics in probability as the Gaussian interpolation and concentration of measure, Poisson processes, and representation results for exchangeable arrays.

This is the third edition of a well-received textbook on modern physics theory. This book provides an elementary but rigorous and self-contained presentation of the simplest theoretical framework that will meet the needs of undergraduate students. In addition, a number of examples of relevant applications and an appropriate list of solved problems are provided.Apart from a substantial extension of the proposed problems, the new edition provides more detailed discussion on Lorentz transformations and their group properties, a deeper treatment of quantum mechanics in a central potential, and a closer comparison of statistical mechanics in classical and in quantum physics. The first part of the book is devoted to special relativity, with a particular focus on space-time relativity and relativistic kinematics. The second part deals with Schroedinger's formulation of quantum mechanics. The presentation concerns mainly one-dimensional problems, but some three-dimensional examples are discussed in detail. The third part addresses the application of Gibbs' statistical methods to quantum systems and in particular to Bose and Fermi gases.

Gaining a theoretical understanding of the properties of ultra-relativistic dense matter has been one of the most important and challenging goals in quantum chromodynamics (QCD). In this thesis, the author analyzes dense quark matter in QCD with gauge group SU(2) using low-energy effective theoretical techniques and elucidates a novel connection between statistical properties of the Dirac operator spectrum at high baryon chemical potential and a special class of random matrix theories. This work can be viewed as an extension of a similar correspondence between QCD and matrix models which was previously known only for infinitesimal chemical potentials. In future numerical simulations of dense matter the analytical results reported here are expected to serve as a useful tool to extract physical observables such as the BCS gap from numerical data on the Dirac spectrum.

This book is intended as an introduction to the field of planetary systems at the postgraduate level. It consists of four extensive lectures on Hamiltonian dynamics, celestial mechanics, the structure of extrasolar planetary systems and the formation of planets. As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics.

This book is about the theoretical and practical aspects of the statistics of Extreme Events in Nature. Most importantly, this is the first text in which Copulas are introduced and used in Geophysics. Several topics are fully original, and show how standard models and calculations can be improved by exploiting the opportunities offered by Copulas. In addition, new quantities useful for design and risk assessment are introduced.

"The career structure and funding of the universities [...] currently strongly d- courages academics and faculties from putting any investment into teaching - there are no career or ?nancial rewards in it. This is a great pity, because [...] it is the need toengage indialogue,and to makethings logicaland clear,that istheprimary defence against obscurantism and abstraction. " B. Ward-Perkins, The fall of Rome, Oxford (2005) This is the ?rst volume of a planned two-volume treatise on non-equilibrium phase transitions. While such a topic might sound rather special and a- demic, non-equilibrium critical phenomena occur in much wider contexts than their equilibrium counterparts, and without having to ?ne-tune th- modynamic variables to their 'critical' values in each case. As a matter of fact, most systems in Nature are out of equilibrium. Given that the theme of non-equilibrium phase transitions of second order is wide enough to amount essentially to a treatment of almost all theoretical aspects of non-equilibrium many-body physics, a selection of topics is required to keep such a project within a manageable length. Therefore, Vol. 1 discusses a particular kind of non-equilibrium phase transitions, namely those between an active, ?- tuating state and absorbing states. Volume 2 (to be written by one of us (MH) with M. Pleimling) will be devoted to ageing phenomena.

Throughout the history of economics, a variety of analytical tools have been borrowed from the so-called exact sciences. As Schoe?er (1955) puts it: "They have taken their mathematics and their ded- tive techniques from physics, their statistics from genetics and agr- omy, their systems of classi?cation from taxonomy and chemistry, their model-construction techniques from astronomy and mechanics, and their methods of analysis of the consequences of actions from en- neering". The possibility of similarities of structure in mathematical models of economic and physical systems has been an important f- tor in the development of neoclassical theory. To treat the state of an economy as an equilibrium, analogous to the equilibrium of a mech- ical system has been a key concept in economics ever since it became a mathematically formalized science. Adopting a Newtonian paradigm neoclassical economics often is based on three fundamental concepts. Firstly, the representative agent who is a scale model of the whole society with extraordinary capacities, particularly concerning her - pability of information processing and computation. Of course, this is a problematic reduction as agents are both heterogeneous and bou- edly rational and limited in their cognitive capabilities. Secondly, it often con?ned itself to study systems in a state of equilibrium. But this concept is not adequate to describe and to support phenomena in perpetual motion.

After about a century of success, physicists feel the need to probe the limits of validity of special-relativity base theories. This book is the outcome of a special seminar held on this topic. The authors gather in a single volume an extensive collection of introductions and reviews of the various facets involved, and also includes detailed discussion of philosophical and historical aspects.

The interest of the applied mechanics community in chaotic dynamics of engineering systems has exploded in the last fifteen years, although research activity on nonlinear dynamical problems in mechanics started well before the end of the Eighties. It developed first within the general context of the classical theory of nonlinear oscillations, or nonlinear vibrations, and of the relevant engineering applications. This was an extremely fertile field in terms of formulation of mechanical and mathematical models, of development of powerful analytical techniques, and of understanding of a number of basic nonlinear phenomena. At about the same time, meaningful theoretical results highlighting new solution methods and new or complex phenomena in the dynamics of deterministic systems were obtained within dynamical systems theory by means of sophisticated geometrical and computational techniques. In recent years, careful experimental studies have been made to establish the actual occurrence and observability of the predicted dynamic phenomena, as it is vitally needed in all engineering fields. Complex dynamics have been shown to characterize the behaviour of a great number of nonlinear mechanical systems, ranging from aerospace engineering applications to naval applications, mechanical engineering, structural engineering, robotics and biomechanics, and other areas. The International Union of Theoretical and Applied Mechanics grasped the importance of such complex phenomena in the Eighties, when the first IUTAM Symposium devoted to the general topic of nonlinear and chaotic dynamics in applied mechanics and engineering was held in Stuttgart (1989).

The paper of Admal & Tadmor, "A Uni ed Interpretation of Stress in Molecular S- tems," takes up the various existing microscopic de nitions of the Cauchy stress tensor. Here the ambition is to establish a unifying framework in which all of these molecular surfacial interactions can be derived and the connections between them made evident. Developments in this paper draw upon the non-equilibrium statistical mechanics of Irving & Kirkwood and Noll, together with spatial averaging techniques. Extensions of the early work of Irving & Kirkwood to include multibody potentials and a generalization of the lemmas of Noll to include non-straight bonds are incorporated. Connections to the direct spatial averaging - proach of Murdoch and Hardy are exposed and the troublesome sources of non-uniqueness of the stress tensor are identi ed. Finally, numerical experiments based on molecular - namics and lattice statics are reported. These contrast the various de nitions of stress, - cluding convergence questions related to the size of the domain over which spatial averaging is performed. It is natural to wonder about the connection between works focused on the microscopic foundation of stress and more kinematically-focused works, such as those of Ericksen, P- teri, and Zanzotto, which emphasize the utility of and explore the validity of the Cauchy- Born rule. Podio-Guidugli's paper, "On (Andersen-)Parrinello-Rahman Molecular Dyn- ics, the Related Metadynamics, and the Use of the Cauchy-Born Rule," discusses scale bridging between molecular dynamics and continuum mechanics for Parrinello-Rahman molecular dynamics.

The most important characteristic of the "world filled with nonlinearity" is the existence of scale interference: disparate space-time scales interfere with each other. Thus, the effects of unknowable scales invade the world that we can observe directly. This leads to various peculiar phenomena such as chaos, critical phenomena, and complex biological phenomena, among others. Conceptual analysis and phenomenology are the keys to describe and understand phenomena that are subject to scale interference, because precise description of unfamiliar phenomena requires precise concepts and their phenomenological description. The book starts with an illustration of conceptual analysis in terms of chaos and randomness, and goes on to explain renormalization group philosophy as an approach to phenomenology. Then, abduction is outlined as a way to express what we have understood about the world. The book concludes with discussions on how we can approach genuinely complex phenomena, including biological phenomena. The main target of this volume is young people who have just started to appreciate the world seriously. The author also wishes the book to be helpful to those who have been observing the world, but who wish to appreciate it afresh from a different angle.

The understanding of empirical traf?c congestion occurring on unsignalized mul- lane highways and freeways is a key for effective traf?c management, control, or- nization, and other applications of transportation engineering. However, the traf?c ?ow theories and models that dominate up to now in transportation research journals and teaching programs of most universities cannot explain either traf?c breakdown or most features of the resulting congested patterns. These theories are also the - sis of most dynamic traf?c assignment models and freeway traf?c control methods, which therefore are not consistent with features of real traf?c. For this reason, the author introduced an alternative traf?c ?ow theory called three-phase traf?c theory, which can predict and explain the empirical spatiot- poral features of traf?c breakdown and the resulting traf?c congestion. A previous book "The Physics of Traf?c" (Springer, Berlin, 2004) presented a discussion of the empirical spatiotemporal features of congested traf?c patterns and of three-phase traf?c theory as well as their engineering applications. Rather than a comprehensive analysis of empirical and theoretical results in the ?eld, the present book includes no more empirical and theoretical results than are necessary for the understanding of vehicular traf?c on unsignalized multi-lane roads. The main objectives of the book are to present an "elementary" traf?c ?ow theory and control methods as well as to show links between three-phase traf?c t- ory and earlier traf?c ?ow theories. The need for such a book follows from many commentsofcolleaguesmadeafterpublicationofthebook"ThePhysicsofTraf?c".

Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.

The 1994 GWIC was held June 6th, 7th and 8th, 1994, on the Campus of the UNLV. It was sponsored by UNLV, UNR, and ACM-SIGART. The keynote speakers were Prof. Bonnie Weber of the University of Pennsylvania, Prof Stuart Shapiro, Director of the Center for Cognitive Science at SUNY at Buffalo, and Prof. Nicolas Bourbakis of SUNY at Binghamton. Dr. Bonnie Webber, the first keynote speaker, presented the first talk of the conference Monday morning June 6th, entitled "Instructing Animated Agents: Natural Language and Human Figure Animation". Her one hour lecture and the computer graphics video in which figures emulating realistically humans were able to successfully perform a number of human motions and functions, were very well received by the participants. Dr. Stuart Shapiro, presented his keynote speech, entitled "Formalizing English", Tues day morning, June 7th. His objective was to construct a natural language using an intelli gent agent. His talk was of great interest and drew a great deal of discussion and questions by the participants. "The Role of AI in Multimedia Information Systems", was the topic presented by the third keynote speaker, Dr. N. Bourbakis, Wednesday morning June 8th. He addressed the changes in computing with the introduction of Multimedia and the usage of AI to store and retrieve intelligently massive visual, audio, and other data.

As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japenese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the usefil for self-teaching, as well as for classroom learning.

Systems driven far from thermodynamic equilibrium can create dissipative structures through the spontaneous breaking of symmetries. A particularly fascinating feature of these pattern-forming systems is their tendency to produce spatially confined states. These localized wave packets can exist as propagating entities through space and/or time. Various examples of such systems will be dealt with in this book, including localized states in fluids, chemical reactions on surfaces, neural networks, optical systems, granular systems, population models, and Bose-Einstein condensates. This book should appeal to all physicists, mathematicians and electrical engineers interested in localization in far-from-equilibrium systems. The authors - all recognized experts in their fields - strive to achieve a balance between theoretical and experimental considerations thereby giving an overview of fascinating physical principles, their manifestations in diverse systems, and the novel technical applications on the horizon.

This is the second of two volumes offering the very first comprehensive treatise of self-organization and non-linear dynamics in electrochemical systems. The first volume covers general principles of self-organization as well as temporal instabilities. The content of both volumes is organized so that each description of a particular electrochemical system is preceded by an introduction to basic concepts of nonlinear dynamics, in order to help the reader unfamiliar with this discipline to understand at least fundamental concepts and the methods of stability analysis. The presentation of the systems is not limited to laboratory models but stretches out to real-life objects and processes, including systems of biological importance, such as neurons in living matter. Marek Orlik presents a comprehensive and consistent survey of the field.

Model integration - the process by which different modelling efforts can be brought together to simulate the target system - is a core technology in the field of Systems Biology. In the work presented here model integration was addressed directly taking cancer systems as an example. An in-depth literature review was carried out to survey the model forms and types currently being utilised. This was used to formalise the main challenges that model integration poses, namely that of paradigm (the formalism on which a model is based), focus (the real-world system the model represents) and scale. A two-tier model integration strategy, including a knowledge-driven approach to address model semantics, was developed to tackle these challenges. In the first step a novel description of models at the level of behaviour, rather than the precise mathematical or computational basis of the model, is developed by distilling a set of abstract classes and properties. These can accurately describe model behaviour and hence describe focus in a way that can be integrated with behavioural descriptions of other models. In the second step this behaviour is decomposed into an agent-based system by translating the models into local interaction rules. The book provides a detailed and highly integrated presentation of the method, encompassing both its novel theoretical and practical aspects, which will enable the reader to practically apply it to their model integration needs in academic research and professional settings. The text is self-supporting. It also includes an in-depth current bibliography to relevant research papers and literature. The review of the current state of the art in tumour modelling provides added value.

Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics. The outstanding points of these proceedings are Coherent compendium of the current state of modelling and analysis of non-linear stochastic systems from engineering, applied mathematics and physics point of view. Subject areas include: Multiscale phenomena, stability and bifurcations, control and estimation, computational methods and modelling. For the Engineering and Physics communities, this book will provide first-hand information on recent mathematical developments. The applied mathematics community will benefit from the modelling and information on various possible applications.

Dealing with Uncertainties is an innovative monograph that lays special emphasis on the deductive approach to uncertainties and on the shape of uncertainty distributions. This perspective has the potential for dealing with the uncertainty of a single data point and with sets of data that have different weights. It is shown that the inductive approach that is commonly used to estimate uncertainties is in fact not suitable for these two cases. The approach that is used to understand the nature of uncertainties is novel in that it is completely decoupled from measurements. Uncertainties which are the consequence of modern science provide a measure of confidence both in scientific data and in information in everyday life. Uncorrelated uncertainties and correlated uncertainties are fully covered and the weakness of using statistical weights in regression analysis is discussed. The text is abundantly illustrated with examples and includes more than 150 problems to help the reader master the subject.