This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

The fast progress in many areas of research related to non-equilibrium ther- dynamics has prompted us to write a fourth edition of this book. Like in the previous editions, our main concern is to open the subject to the widest au- ence, including students, teachers, and researchers in physics, chemistry, engine- ing, biology, and materials sciences. Our objective is to present a general view on several open problems arising in non-equilibrium situations, and to afford a wide perspective of applications illustrating their practical outcomes and con- quences. A better comprehension of the foundations is generally correlated to an increase of the range of applications, implying mutual feedback and cross fert- ization. Truly, thermodynamic methods are widely used in many areas of science but, surprisingly, the active dynamism of thermodynamics as a ?eld on its own is not suf?ciently perceived outside a relatively reduced number of specialized researchers. Extended irreversible thermodynamics (EIT) goes beyond the classical f- malisms based on the local equilibrium hypothesis; it was also referred to in an earlier publication by the authors (Lebon et al. 1992) as a thermodynamics of the third type, as it provides a bridge between classical irreversible thermodynamics and rational thermodynamics, enlarging at the same time their respective range of application. The salient feature of the theory is that the ?uxes are incorporated into the set of basic variables.

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.

Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged.

Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself.

This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The following chapters gradually guide the student towards the current "state of the art" and provide a comprehensive overview of the field. Every chapter is accompanied by exercises to deepen the reader's understanding of important topics, with detailed solutions at the end of the book.

Overthe nearly 20 years of Kelvin probe force microscopy, an increasing interest in the technique and its applications has developed. This book gives a concise introduction into the method and describes various experimental techniques. Surface potential studies on semiconductor materials, nanostructures and devices are described, as well as application to molecular and organic materials. The current state of surface potential at the atomic scale is also considered. This book presents an excellent introduction for the newcomer to this field, as much as a valuable resource for the expert."

Thermodynamicsandstatisticalphysicsstudythephysicalproperties(mec- nical, thermal, magnetic, optical, electrical, etc.) of the macroscopic system. The tasks and objects of study in thermodynamics and statistical physics are identical. However, the methods of investigationinto macroscopicsystems are di?erent. Thermodynamics is a phenomenological theory. It studies the properties of bodies, without going into the mechanism of phenomena, i.e., not taking into consideration the relation between the internal structure of substance and phenomena, it generalizes experimental results. As a result of such a g- eralization, postulates and laws of thermodynamics made their appearance. These laws make it possible to ?nd general relations between the di?erent properties of macroscopic systems and the physical events occurring in them. Statisticalphysicsisa microscopic theory.Onthebasisoftheknowledgeof the type of particles a system consists of, the nature of their interaction, and thelawsofmotionoftheseparticlesissuingfromtheconstructionofsubstance, it explains the properties being observedon experiment, and predicts the new properties of systems. Using the laws of classical or quantum mechanics, and alsothe theoryofprobability, itestablishesqualitativelynewstatistical app- priatenesses of the physical properties of macroscopic systems, substantiates the laws of thermodynamics, determines the limits of their applicability, gives the statistical interpretation of thermodynamic parameters, and also works out methods of calculations of their means. The Gibbs method is based on statisticalphysics.Thismethodis themostcanonical.Therefore, inthis book, the exposition of the Gibbs method takes an important pla

The term transport phenomena is used to describe processes in which mass, momentum, energy and entropy move about in matter. Advances in Transport Phenomena provide state-of-the-art expositions of major advances by theoretical, numerical and experimental studies from a molecular, microscopic, mesoscopic, macroscopic or megascopic point of view across the spectrum of transport phenomena, from scientific enquiries to practical applications. The annual review series intends to fill the information gap between regularly published journals and university-level textbooks by providing in-depth review articles over a broader scope than in journals. The authoritative articles, contributed by internationally-leading scientists and practitioners, establish the state of the art, disseminate the latest research discoveries, serve as a central source of reference for fundamentals and applications of transport phenomena, and provide potential textbooks to senior undergraduate and graduate students. This review book provides state-of-the-art expositions of major advances by theoretical, numerical and experimental studies from a molecular, microscopic, mesoscopic, macroscopic or megascopic point of view across the spectrum of transport phenomena, from scientific enquiries to practical applications. This new volume of the annual review "Advances in Transport Phenomena" series provides in-depth review articles covering the fields of mass transfer, fluid mechanics, heat transfer and thermodynamics. This review book provides state-of-the-art expositions of major advances by theoretical, numerical and experimental studies from a molecular, microscopic, mesoscopic, macroscopic or megascopic point of view across the spectrum of transport phenomena, from scientific enquiries to practical applications. This new volume of the annual review "Advances in Transport Phenomena" series provides in-depth review articles covering the fields of mass transfer, fluid mechanics, heat transfer and thermodynamics.

This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respect to macroscopic fluxes or thermodynamic forces. Both irreversible Boltzmann and generalized Boltzmann equations are used for deriving theories of irreversible transport equations and generalized hydrodynamic equations, which rigorously conform to the tenet. All observables described by the so-formulated theories therefore also strictly obey the tenet.

Calorimetry is one of the oldest areas of physical chemistry. The date on which calorimetry came into being may be taken as 13 June 1783, the day on which Lavoisier and Laplace presented a contribution entitled, Memoire de la Chaleur" at a session of the Academie Francaise. Throughout the existence of calorimetry, many new methods have been developed and the measuring techniques have been improved. At p- sent, numerous laboratories worldwide continue to focus attention on the development and applications of calorimetry, and a number of com- nies specialize in the production of calorimeters. The calorimeter is an instrument that allows heat effects in it to be determined by directly measurement of temperature. Accordingly, to determine a heat effect, it is necessary to establish the relationship - tween the heat effect generated and the quantity measured in the ca- rimeter. It is this relationship that unambiguously determines the mathematical model of the calorimeter. Depending on the type of ca- rimeter applied, the accuracy required, and the conditions of heat and mass transfer that prevail in the device, the relationship between the measured and generated quantities can assume different mathematical forms."

This book presents an up-to-date formalism of non-equilibrium Green's functions covering different applications ranging from solid state physics, plasma physics, cold atoms in optical lattices up to relativistic transport and heavy ion collisions. Within the Green's function formalism, the basic sets of equations for these diverse systems are similar, and approximations developed in one field can be adapted to another field. The central object is the self-energy which includes all non-trivial aspects of the system dynamics. The focus is therefore on microscopic processes starting from elementary principles for classical gases and the complementary picture of a single quantum particle in a random potential. This provides an intuitive picture of the interaction of a particle with the medium formed by other particles, on which the Green's function is built on.

Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schr dinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.

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.

The emphasis of this book is on engineering aspects of fluid turbulence. The book explains for example how to tackle turbulence in industrial applications. It is useful to several disciplines, such as, mechanical, civil, chemical, aerospace engineers and also to professors, researchers, beginners, under graduates and post graduates. The following issues are emphasized in the book: - Modeling and computations of engineering flows: The author discusses in detail the quantities of interest for engineering turbulent flows and how to select an appropriate turbulence model; Also, a treatment of the selection of appropriate boundary conditions for the CFD simulations is given. - Modeling of turbulent convective heat transfer: This is encountered in several practical situations. It basically needs discussion on issues of treatment of walls and turbulent heat fluxes. - Modeling of buoyancy driven flows, for example, smoke issuing from chimney, pollutant discharge into water bodies, etc

This monograph is devoted to construction of novel theoretical approaches of m- eling non-homogeneous structural members as well as to development of new and economically ef?cient (simultaneously keeping the required high engineering ac- racy)computationalalgorithmsofnonlineardynamics(statics)ofstronglynonlinear behavior of either purely continuous mechanical objects (beams, plates, shells) or hybrid continuous/lumped interacting mechanical systems. In general, the results presented in this monograph cannot be found in the - isting literature even with the published papers of the authors and their coauthors. We take a challenging and originally developed approach based on the integrated mathematical-numerical treatment of various continuous and lumped/continuous mechanical structural members, putting emphasis on mathematical and physical modeling as well as on the carefully prepared and applied novel numerical - gorithms used to solve the derived nonlinear partial differential equations (PDEs) mainly via Bubnov-Galerkin type approaches. The presented material draws on the ?elds of bifurcation, chaos, control, and s- bility of the objects governed by strongly nonlinear PDEs and ordinary differential equations (ODEs),and may have a positive impact on interdisciplinary ? elds of n- linear mechanics, physics, and applied mathematics. We show, for the ?rst time in a book, the complexity and fascinating nonlinear behavior of continual mechanical objects, which cannot be found in widely reported bifurcational and chaotic dyn- ics of lumped mechanical systems, i. e. , those governed by nonlinear ODEs.

Chaos is a fascinating phenomenon that has been observed in nature, laboratory, and has been applied in various real-world applications. Chaotic systems are deterministic with no random elements involved yet their behavior appears to be random. Obser- tions of chaotic behavior in nature include weather and climate, the dynamics of sat- lites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, to mention only a few examples. Chaos has been observed in the laboratory in a number of systems such as electrical circuits, lasers, chemical reactions, fluid dynamics, mechanical systems, and magneto-mechanical devices. Chaotic behavior has also found numerous applications in electrical and communication engineering, information and communication technologies, biology and medicine. To the best of our knowledge, this is the first book edited on chaos applications in intelligent computing. To access the latest research related to chaos applications in intelligent computing, we launched the book project where researchers from all over the world provide the necessary coverage of the mentioned field. The primary obj- tive of this project was to assemble as much research coverage as possible related to the field by defining the latest innovative technologies and providing the most c- prehensive list of research references.

In May 2002 a number of about 20 scientists from various disciplines were invited by the Berlin-Brandenburg Academy of Sciences and Humanities to participate in an interdisciplinary workshop on structures and structure generating processes. The site was the beautiful little castle of Blankensee, south of Berlin. The disciplines represented ranged from mathematics and information theory, over various ?elds of engineering, biochemistry and biology, to the economic and social sciences. All participants presented talks explaining the nature of structures considered in their ?elds and the associated procedures of analysis. It soon became evident that the study of structures is indeed a common c- cern of virtually all disciplines. The motivation as well as the methods of analysis, however, differ considerably. In engineering, the generation of artifacts, such as infrastructures or technological processes, are of primary interest. Frequently, the analysis aims there at de?ning a simpli?ed mathematical model for the optimization of the structures and the structure generating processes. Mathematical or heuristic methods are applied, the latter preferably of the type of biology based evolutionary algorithms. On the other hand, setting up complex technical structures is not pos- ble by such simpli?ed model calculations but requires a different and less model but rather knowledge-based type of approach, using empirical rules rather than formal equations. In biochemistry, interest is frequently focussed on the structures of molecules, such as proteins or ribonucleic acids. Again, optimal structures can usually be de?ned.

Jiji's extensive understanding of how students think and learn, what they find difficult, and which elements need to be stressed is integrated in this work. He employs an organization and methodology derived from his experience and presents the material in an easy to follow form, using graphical illustrations and examples for maximum effect. The second, enlarged edition provides the reader with a thorough introduction to external turbulent flows, written by Glen Thorncraft. Additional highlights of note: Illustrative examples are used to demonstrate the application of principles and the construction of solutions, solutions follow an orderly approach used in all examples, systematic problem-solving methodology emphasizes logical thinking, assumptions, approximations, application of principles and verification of results. Chapter summaries help students review the material. Guidelines for solving each problem can be selectively given to students.

The primary goal of the book is to present the ideas and research findings of active researchers from various communities (physicists, economists, mathematicians, financial engineers) working in the field of "Econophysics," who have undertaken the task of modelling and analyzing order-driven markets. Of primary interest in these studies are the mechanisms leading to the statistical regularities ("stylized facts") of price statistics. Results pertaining to other important issues such as market impact, the profitability of trading strategies, or mathematical models for microstructure effects, are also presented. Several leading researchers in these fields report on their recent work and also review the contemporary literature. Some historical perspectives, comments and debates on recent issues in Econophysics research are also included.

Dynamics of an open system interacting with theenvironment considered as a thermostate may be formulatedin terms of a master equation with an integral operator allowing for the relaxation process, [Zwanzig 1960]. In some part- ular cases this operator hasashort-lastingkernel that enables one to consider therelaxation as a Markovian process and to obtainthe master equation inthe Lindblad form, [Lindblad 1976 (a)]. In some situations the memory effects become, however, important and the dynamics of thesystem gets much more involved, [Barnett 2001]. A similar situation arises inthe case where a set of consecutive or continuous measurements is performed. The purpose of this article is to consider a situation where some simplification of the generalform of the master equation with memory isstill possibleand the result isasimpler master equation. In particular, we consider the case of a dynamic system c- pled to a measured ancilla via a nondemolition interaction, [Caves 1980]. This simplifies the consideration essentiallywhereas providing an important special case inwhich the energy of the dynamic part is conserved. We consider a composite quantum system consisting of a dynamic part - teracting with an ancillary part, the latter being subject to repeated projective measurements. The entire quantum system is assumed to evolve unitarily d- ing time ? t between the measurements. As a specific example, we analyze a harmonic oscillator coupledtoatwo-level ancillathat issubject to measu- ments.

This monograph presents, from the viewpoint of continuum mechanics, a newly emerging field of irreversible thermodynamics, in which linear irreversible thermodynamics are extended to the nonlinear regime and macroscopic phenomena far removed from equilibrium are studied in a manner consistent with the laws of thermodynamics. The tool to develop this thermodynamic theory of irreversible processes are the generalized thermodynamics, which also extends the classical hydrodynamics of Navier, Stokes and Fourier to nonlinear irreversible processes. On the basis of mathematically rigorous representations of the first and the second law of thermodynamics, phenomenological theory (continuum mechanics) deductions are made from the thermodynamic laws of R. Clausius and Lord Kelvin and by this continuum mechanics theories are formulated for macroscopic irreversible processes occurring far removed from equilibrium. Non-equilibrium thermodynamics are developed for thermodynamic functions.

The macroscopic irreversible processes studied include global irreversible processes as well as local hydrodynamic processes at an arbitrary degree of removal from equilibrium. Applications of the theories cover global irreversible processes, simple flows of non-Newtonian and non-Fourier fluids, shock waves of monatomic and diatomic gases, rarefied gas dynamics, ultrasonic wave absorption and dispersion of monatomic and diatomic gases, electrochemical processes, neural networks of chemical reactors, microflows, etc. Variational principles in irreversible thermodynamics and contact manifolds in thermodynamics are also discussed.'

This monograph, will be of interest to condensed matter physicists, chemicalphysicists, biophysicists, mechanical and aerospace engineers, and specialists and graduate students in the fields of irreversible thermodynamics and non-equilibrium statistical mechanics.

This book is devoted to applications of complex nonlinear dynamic phenomena to real systems and device applications. In recent decades there has been significant progress in the theory of nonlinear phenomena, but there are comparatively few devices that actually take this rich behavior into account. The text applies and exploits this knowledge to propose devices which operate more efficiently and cheaply, while affording the promise of much better performance.