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.

Robot and Multibody Dynamics: Analysis and Algorithms provides a comprehensive and detailed exposition of a new mathematical approach, referred to as the Spatial Operator Algebra (SOA), for studying the dynamics of articulated multibody systems. The approach is useful in a wide range of applications including robotics, aerospace systems, articulated mechanisms, bio-mechanics and molecular dynamics simulation. The book also: treats algorithms for simulation, including an analysis of complexity of the algorithms, describes one universal, robust, and analytically sound approach to formulating the equations that govern the motion of complex multi-body systems, covers a range of more advanced topics including under-actuated systems, flexible systems, linearization, diagonalized dynamics and space manipulators. Robot and Multibody Dynamics: Analysis and Algorithms will be a valuable resource for researchers and engineers looking for new mathematical approaches to finding engineering solutions in robotics and dynamics.

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.

This textbook provides a comprehensive and instructive coverage of vehicular traffic flow dynamics and modeling. It makes this fascinating interdisciplinary topic, which to date was only documented in parts by specialized monographs, accessible to a broad readership. Numerous figures and problems with solutions help the reader to quickly understand and practice the presented concepts. This book is targeted at students of physics and traffic engineering and, more generally, also at students and professionals in computer science, mathematics, and interdisciplinary topics. It also offers material for project work in programming and simulation at college and university level. The main part, after presenting different categories of traffic data, is devoted to a mathematical description of the dynamics of traffic flow, covering macroscopic models which describe traffic in terms of density, as well as microscopic many-particle models in which each particle corresponds to a vehicle and its driver. Focus chapters on traffic instabilities and model calibration/validation present these topics in a novel and systematic way. Finally, the theoretical framework is shown at work in selected applications such as traffic-state and travel-time estimation, intelligent transportation systems, traffic operations management, and a detailed physics-based model for fuel consumption and emissions.

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.

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.

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

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.

This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

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.

Thermal Conductivity: Thermal Conductivity of LooseFill Materials by a RadialHeatFlow Method (D.R. Flynn). The Probe Method for Measurement of Thermal Conductivity (A.E. Wechsler). Electrical Resistivity: Methods for Electrical Resistivity Measurement Applicable to Medium and Good Electrical Conductors (B. Cales, P. Abelard). Thermal Diffusivity: Modulated Electron Beam Thermal Diffusivity Equipment (R. De Conink). The Apparatus for Measurement of Thermophysical Properties of Liquids by AC HotWire Technique (L.P. Phylippov et al.). Specific Heat: Practical Modulation Calorimetry (Y.A. Kraftmakher). The Application of Differential Scanning Calorimetry to the Measurement of Specific Heat (M.J. Richardson). Thermal Expansion: Methods of Measuring Thermal Expansion (R.K. Kirby). The Review of Certified Thermophysical Property SRMs. Fourteen additonal articles. Index.

The aim of this book is the pedagogical exploration of the basic principles of quantum-statistical thermodynamics as applied to various states of matter - ranging from rare gases to astrophysical matter with high-energy density. The reader will learn in this work that thermodynamics and quantum statistics are still the concepts on which even the most advanced research is operating - despite of a flood of modern concepts, classical entities like temperature, pressure, energy and entropy are shown to remain fundamental. The physics of gases, plasmas and high-energy density matter is still a growing field and even though solids and liquids dominate our daily life, more than 99 percent of the visible Universe is in the state of gases and plasmas and the overwhelming part of matter exists at extreme conditions connected with very large energy densities, such as in the interior of stars. This text, combining material from lectures and advanced seminars given by the authors over many decades, is a must-have introduction and reference for both newcomers and seasoned researchers alike.

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.

This book provides the first comprehensive description of time crystals which have a repeating structure in time. It introduces the fundamental concepts behind time crystals and explores the many different branches of this new research area. The book starts with the original idea of the time crystallization in quantum systems as introduced by Wilczek and follows the development of the field up to the present day. Both spontaneous formation of crystalline structures in time and concepts of the condensed matter physics in the time domain, ranging from Anderson localization in time to many-body systems with exotic interactions, are described. The prospect of creation of novel objects by means of time engineering is also presented. The book assumes knowledge of quantum mechanics to the graduate level. It serves as a valuable reference with pointers to future research directions for graduate students and senior scientists alike.

This comprehensive and carefully edited volume presents a variety of experimental methods used in Shock Waves research. In 14 self contained chapters this 9th volume of the "Shock Wave Science and Technology Reference Library" presents the experimental methods used in Shock Tubes, Shock Tunnels and Expansion Tubes facilities. Also described is their set-up and operation. The uses of an arc heated wind tunnel and a gun tunnel are also contained in this volume. Whenever possible, in addition to the technical description some typical scientific results obtained using such facilities are described. Additionally, this authoritative book includes techniques for measuring physical properties of blast waves and laser generated shock waves. Information about active shock wave laboratories at different locations around the world that are not described in the chapters herein is given in the Appendix, making this book useful for every researcher involved in shock/blast wave phenomena.

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 book presents mainly studies on the calculation methods of thermal radiative properties of uniaxial anisotropic materials, unidirectional transmission, ultrabroadband perfect absorption, and near-field radiative heat transfer with uniaxial anisotropic materials. The results obtained in this book can not only deepen our understanding of the thermal radiative properties of anisotropic materials, but also have important theoretical guiding significance in energy conversion, energy-saving technology, and design of novel devices.

Ring polymers are one of the last big mysteries in polymer physics, and this thesis tackles the problem of describing their behaviour when interacting in dense solutions and with complex environments and reports key findings that help shed light on these complex issues. The systems investigated are not restricted to artificial polymer systems, but also cover biologically inspired ensembles, contributing to the broad applicability and interest of the conclusions reached. One of the most remarkable findings is the unambiguous evidence that rings inter-penetrate when in dense solutions; here this behaviour is shown to lead to the emergence of a glassy state solely driven by the topology of the constituents. This novel glassy state is unconventional in its nature and, thanks to its universal properties inherited from polymer physics, will attract the attention of a wide range of physicists in the years to come.

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.

This book presents scientific metrics and its applications for approaching scientific findings in the field of Physics, Economics and Scientometrics. Based on a collection of the author's publications in these fields, the book reveals the profound links between the measures and the findings in the natural laws, from micro-particles to macro-cosmos, in the economic rules of human society, and in the core knowledge among mass information. With this book the readers can gain insights or ideas on addressing the questions of how to measure the physical world, economics process and human knowledge, from the perspective of scientific metrics. The book is also useful to scientists, particularly to specialists in physics, economics and scientometrics, for promoting and stimulating their creative ideas based on scientific metrics.

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.

In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac's problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson's theorem, Ringrose's hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us to investigate the special classes of the entire functions.