"Stochastic Tools in Mathematics and Science" covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, renormalization, basic statistical mechanics, and generalized Langevin equations and the Mori-Zwanzig formalism. The applications include sampling algorithms, data assimilation, prediction from partial data, spectral analysis, and turbulence. The book is based on lecture notes from a class that has attracted graduate and advanced undergraduate students from mathematics and from many other science departments at the University of California, Berkeley. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications. For this new edition the material has been thoroughly reorganized and updated, and new sections on scaling, sampling, filtering and data assimilation, based on recent research, have been added. There are additional figures and exercises. Review of earlier edition: "This is an excellent concise textbook which can be used for self-study by graduate and advanced undergraduate students and as a recommended textbook for an introductory course on probabilistic tools in science." Mathematical Reviews, 2006

Among resummation techniques for perturbative QCD in the context of collider and flavor physics, soft-collinear effective theory (SCET) has emerged as both a powerful and versatile tool, having been applied to a large variety of processes, from B-meson decays to jet production at the LHC. This book provides a concise, pedagogical introduction to this technique. It discusses the expansion of Feynman diagrams around the high-energy limit, followed by the explicit construction of the effective Lagrangian - first for a scalar theory, then for QCD. The underlying concepts are illustrated with the quark vector form factor at large momentum transfer, and the formalism is applied to compute soft-gluon resummation and to perform transverse-momentum resummation for the Drell-Yan process utilizing renormalization group evolution in SCET. Finally, the infrared structure of n-point gauge-theory amplitudes is analyzed by relating them to effective-theory operators. This text is suitable for graduate students and non-specialist researchers alike as it requires only basic knowledge of perturbative QCD.

The aim of this interdisciplinary study is to reconstruct the evolution of our changing conceptions of time in the light of scientific discoveries. It will adopt a new perspective and organize the material around three central themes, which run through our history of time reckoning: cosmology and regularity; stasis and flux; symmetry and asymmetry. It is the physical criteria that humans choose - relativistic effects and time-symmetric equations or dynamic-kinematic effects and asymmetric conditions - that establish our views on the nature of time. This book will defend a dynamic rather than a static view of time.

This volume contains a contemporary, integrated description of the processes of language. These range from fast scales (fractions of a second) to slow ones (over a million years). The contributors, all experts in their fields, address language in the brain, production of sentences and dialogues, language learning, transmission and evolutionary processes that happen over centuries or millenia, the relation between language and genes, the origins of language, self-organization, and language competition and death. The book as a whole will help to show how processes at different scales affect each other, thus presenting language as a dynamic, complex and profoundly human phenomenon.

Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance of a closed concept and the lack of a comprehensive disquisition. The fascinating part is that field equations can have localized solutions exhibiting the typical characteristics of particles. Regarding the field equations this book focuses on, the field phenomenon of localized solutions can be described in the context of a particle formalism, which leads to a set of ordinary differential equations covering the time evolution of the position and the velocity of each particle. Moreover, starting from these particle dynamics and making the transition to many body systems, one considers typical phenomena of many body systems as shock waves and phase transitions, which themselves can be described as field phenomena. Such transitions between different level of modelling are well known from conservative systems, where localized solutions of quantum field theory lead to the mechanisms of elementary particle interaction and from this to field equations describing the properties of matter. However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. This model allows to understand the existence of localized structures, their mechanisms of movement, and their interaction, at least, on a qualitative level. But this model is also the starting point for developing a data analysis method that enables the detection of movement and interaction mechanisms of the investigated localized solutions. The topic is rounded of by applying the data analysis to real experimental data and comparing the experimental observations to the predictions of the model. A comprehensive publication covering the interesting topic of localized solutions in reaction diffusion systems in its width and its relation to the well known phenomena of spirals and patterns does not yet exist, and this is the third reason for writing this book. Although the book focuses on a specific experimental system the model equations are as simple as possible so that the discussed methods should be adaptable to a large class of systems showing particle-like structures. Therefore, this book should attract not only the experienced scientist, who is interested in self-organization phenomena, but also the student, who would like to understand the investigation of a complex system on the basis of a continuous description.

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.

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.

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 thesis presents a new method for following evolving interactions between coupled oscillatory systems of the kind that abound in nature. Examples range from the subcellular level, to ecosystems, through climate dynamics, to the movements of planets and stars. Such systems mutually interact, adjusting their internal clocks, and may correspondingly move between synchronized and non-synchronized states. The thesis describes a way of using Bayesian inference to exploit the presence of random fluctuations, thus analyzing these processes in unprecedented detail. It first develops the basic theory of interacting oscillators whose frequencies are non-constant, and then applies it to the human heart and lungs as an example. Their coupling function can be used to follow with great precision the transitions into and out of synchronization. The method described has the potential to illuminate the ageing process as well as to improve diagnostics in cardiology, anesthesiology and neuroscience, and yields insights into a wide diversity of natural processes.

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.

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.

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.

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.

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.

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 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.

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 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.

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.

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.

In recent years, as part of the increasing "informationization" of industry and the economy, enterprises have been accumulating vast amounts of detailed data such as high-frequency transaction data in nancial markets and point-of-sale information onindividualitems in theretail sector. Similarly,vast amountsof data arenow ava- able on business networks based on inter rm transactions and shareholdings. In the past, these types of information were studied only by economists and management scholars. More recently, however, researchers from other elds, such as physics, mathematics, and information sciences, have become interested in this kind of data and, based on novel empirical approaches to searching for regularities and "laws" akin to those in the natural sciences, have produced intriguing results. This book is the proceedings of the international conference THICCAPFA7 that was titled "New Approaches to the Analysis of Large-Scale Business and E- nomic Data," held in Tokyo, March 1-5, 2009. The letters THIC denote the Tokyo Tech (Tokyo Institute of Technology)-Hitotsubashi Interdisciplinary Conference. The conference series, titled APFA (Applications of Physics in Financial Analysis), focuses on the analysis of large-scale economic data. It has traditionally brought physicists and economists together to exchange viewpoints and experience (APFA1 in Dublin 1999, APFA2 in Liege ` 2000, APFA3 in London 2001, APFA4 in Warsaw 2003, APFA5 in Torino 2006, and APFA6 in Lisbon 2007). The aim of the conf- ence is to establish fundamental analytical techniques and data collection methods, taking into account the results from a variety of academic disciplines.

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".