Systems driven far from thermodynamic equilibrium can create dissipative structures through the spontaneous breaking of symmetries. A particularlyfascinating feature of these pattern-forming systems is their tendency toproduce spatially confined states. These localized wave packets can exist as propagating entities through space and/or time.

Various examples of suchsystems 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 givingan overview offascinating physical principles, their manifestations in diverse systems, and the noveltechnical applications on the horizon.

The occurrence of fractional statistics has been discovered in more and more quantum field theory models, including some of the most geometrical and canonical ones. In a remarkable case, the fractional quantum statistics of quasiparticles in the fractional quantized Hall effect (FQHE) contributes to the understanding of states found there. Very recent work has indicated that similar possibilities arise for two-dimensional films in certain states of liquid 3He. Perhaps most exciting, although quite speculative at this moment, are recent attempts to apply fractional statistics to spin systems, and specifically to the behaviour of the 2-dimensional copper oxide layers that seem to be critical to the phenomenon of high-temperature superconductivity. It has recently been shown that fractional statistics automatically implies superconductivity of a qualitatively new kind. This collection of reprints with comprehensive commentary will serve as a valuable reference for those interested in the subject but have found it difficult to acquire basic knowledge, or a coherent view of the whole, due to the scattered literature available at present.

This work provides an enormous contribution to the broad effort of modeling heat, mass and momentum transport in multi-physics problems with the development of new solution approaches. It re-visits the time-honored technique of network application using flow network solutions for all transport process components for a coupled modeling task. The book further provides as formulation of the conservation laws for mass, energy and momentum, specifically for the branches and nodes of transport networks using the combination of the Eulerian and Lagrangean modeling methods. With the extension of Bernoulli's original concept, a new solution is given for the flow field of viscous and compressible fluids as driven by the balance of mechanical energy, coupled to the thermodynamics of the transport system. Applicable to simple or large-scale tasks, the new model elements and methods are built on first principles. Throughout the work, the book provides original formulations, their mathematical derivations as well as applications in a numerical solution scheme.

This book is based on the results of our interest in the ?eld of ultrashort laser pulses interaction with matter. The aim of our monograph was to build the balanced description of the thermal transport phenomena generated by laser pulses shorter than the characteristic relaxation time. In the book we explore the matter on the quark, nuclear as well atomic scales. Also on the cosmic scale (Planck Era) the thermal disturbance shorter than the Planck time creates the new picture of the Universe. The mathematics, especially PDE, are the main tool in the description of the ultrashort thermal phenomena. Two types of the PDE: parabolic and hyperbolic partial di?erential equations are of special interest in the study of the thermal processes. We assume a moderate knowledge of basic Fourier and d'Alembert eq- tions. The scope of the book is deliberately limited to the background of the quantum mechanics equations: Schr] odinger and Klein-Gordon. In this book the attosecond laser pulses are the main source of the dist- bance of the thermal state of the matter. Recently, the attosecond laser pulses constitute a novel tool for probing processes taking place on the time scale of electron motion inside atoms. The research presented in this book appears to provide the basic tools and concepts for attosecond thermal dynamics. Nevertheless much research is still needed to make this emerging ?eld routinely applicable for a broad range of processes on atomic and subatomic scales."

"The first volume might be especially useful for specialists in its subject, but it also contains good expositions for nonspecialists." Acta Sci. Math. (Szeged) Contents: Notes on Subfactors and Statistical Mechanics (V F R Jones); Polynomial Invariants in Knot Theory (L H Kauffman); Algebras of Loops on Surfaces, Algebras of Knots, and Quantization (V G Turaev); Quantum Groups (L Faddeev et al.); Introduction to the Yang-Baxter Equation (M Jimbo); Integrable Systems Related to Braid Groups and Yang-Baxter Equation (T Kohno); The Yang-Baxter Relation: A New Tool for Knot Theory (Y Akutsu et al.); Akutsu-Wadati Link Polynomials from Feynman-Kauffman Diagrams (M-L Ge et al.); Quantum Field Theory and the Jones Polynomial (E Witten)

"The first volume might be especially useful for specialists in its subject, but it also contains good expositions for nonspecialists." Acta Sci. Math. (Szeged) Contents: Notes on Subfactors and Statistical Mechanics (V F R Jones); Polynomial Invariants in Knot Theory (L H Kauffman); Algebras of Loops on Surfaces, Algebras of Knots, and Quantization (V G Turaev); Quantum Groups (L Faddeev et al.); Introduction to the Yang-Baxter Equation (M Jimbo); Integrable Systems Related to Braid Groups and Yang-Baxter Equation (T Kohno); The Yang-Baxter Relation: A New Tool for Knot Theory (Y Akutsu et al.); Akutsu-Wadati Link Polynomials from Feynman-Kauffman Diagrams (M-L Ge et al.); Quantum Field Theory and the Jones Polynomial (E Witten)

Studies of surfaces and interactions between dissimilar materials or phases are vital for modern technological applications. Computer simulation methods are indispensable in such studies and this book contains a substantial body of knowledge about simulation methods as well as the theoretical background for performing computer experiments and analyzing the data.

The book is self-contained, covering a range of topics from classical statistical mechanics to a variety of simulation techniques, including molecular dynamics, Langevin dynamics and Monte Carlo methods. A number of physical systems are considered, including fluids, magnets, polymers, granular media, and driven diffusive systems. The computer simulation methods considered include both standard and accelerated versions. The simulation methods are clearly related to the fundamental principles of thermodynamics and statistical mechanics.

From the reviews: "The book is excellent, and covers a very broad area (usually treated as separate topics) from a unified perspective. [ ] It will be very useful for both mathematicians and physicists." EMS Newsletter

This book gives a rigorous yet 'physics-focused' introduction to mathematical logic that is geared towards natural science majors. We present the science major with a robust introduction to logic, focusing on the specific knowledge and skills that will unavoidably be needed in calculus topics and natural science topics in general (rather than taking a philosophical math fundamental oriented approach that is commonly found in mathematical logic textbooks).

The need for tsunami research and analysis has grown dramatically following the devastating tsunami of December 2004, which affected Southern Asia. This book pursues a detailed theoretical and mathematical analysis of the fundamentals of tsunamis, especially the evolution and dynamics of tsunamis and other great waves. Of course, it includes specific measurement results from the 2004 tsunami, but the emphasis is on the nature of the waves themselves and their links to nonlinear phenomena.

Statistical mechanics deals with systems in which chaos and randomness reign supreme. The current theory is therefore firmly based on the equations of classical mechanics and the postulates of probability theory. This volume seeks to present a unified account of classical mechanical statistics, rather than a collection of unconnected reviews on recent results. To help achieve this, one element is emphasised which integrates various parts of the prevailing theory into a coherent whole. This is the hierarchy of the BBGKY equations, which enables a relationship to be established between the Gibbs theory, the liquid theory, and the theory of nonequilibrium phenomena. As the main focus is on the complex theoretical subject matter, attention to applications is kept to a minimum. The book is divided into three parts. The first part describes the fundamentals of the theory, embracing chaos in dynamic systems and distribution functions of dynamic systems. Thermodynamic equilibrium, dealing with Gibbs statistical mechanics and the statistical mechanics of liquids, forms the second part. Lastly, the third part concentrates on kinetics, and the theory of nonequilibrium gases and liquids in particular. Audience: This book will be of interest to graduate students and researchers whose work involves thermophysics, theory of surface phenomena, theory of chemical reactions, physical chemistry and biophysics.

The papers collected in this volume address all aspects related to thermofluidynamic processses in Diesel engines, from basic studies aiming to obtain a better understanding of the physical processes underlying diesel engine operation, to the real day-to-day problems associated with engine development. The topics covered comprise: Air management, injection systems, spray development and air interaction, combustion and pollutant formation, emission control strategies, and new concepts.

The book presents - based on the most recent research and development results worldwide - the perspectives of new propulsion concepts such as electric cars with batteries and fuel cells, and furthermore plug in hybrids with conventional and alternative fuels. The propulsion concepts are evaluated based on specific power, torque characteristic, acceleration behaviour, specific fuel consumption and pollutant emissions. The alternative fuels are discussed in terms of availability, production, technical complexity of the storage on board, costs, safety and infrastructure. The book presents summarized data about vehicles with electric and hybrid propulsion. The propulsion of future cars will be marked by diversity - from compact electric city cars and range extender vehicles for suburban and rural areas up to hybrid or plug in SUVs, Pick ups and luxury class automobiles.

Recent groundbreaking discoveries in physics, including the discovery of the Higgs Boson and gravitational waves, have relied on chi-squared analysis and model testing, a data analysis method. This is the first book to make chi-squared model testing accessible to students in introductory physics lab courses and others who need to learn this method, such as beginning researchers in astrophysics and particle physics, beginners in data science, and lab students in other experimental sciences. For over a decade, Harvard University's introductory physics lab sequence has made chi-squared model testing its central theme. Written by two faculty members, the book is based on years of experience teaching students learn how to think like scientists by testing their models using chi-squared analysis. By including uncertainties in the curve fitting technique, chi-squared data analysis improves on the centuries old ordinary least squares and linear regression methods and combines best fit parameter estimation and model testing in one method. A toolkit of essential statistical and experimental concepts is developed from the ground up with novel features to interest even those familiar with the material. The presentation of one and two parameter chi-squared model testing, requiring only elementary probability and algebra, is followed by case studies that apply the methods to simple introductory physics lab experiments. More challenging topics requiring calculus are addressed in an advanced topic chapter. This self-contained and student-friendly introduction includes a glossary, end of chapter problems with complete solutions, and software scripts available in several popular programming languages that the reader can use for chi-squared model testing.

Discover the many facets of non-equilibrium thermodynamics. The first part of this book describes the current thermodynamic formalism recognized as the classical theory. The second part focuses on different approaches. Throughout the presentation, the emphasis is on problem-solving applications. To help build your understanding, some problems have been analyzed using several formalisms to underscore their differences and their similarities.

This IMA Volume in Mathematics and its Applications DYNAMICAL ISSUES IN COMBUSTION THEORY is based on the proceedings of a workshop which was an integral part of the 1989-90 IMA program on "Dynamical Systems and their Applications." The aim of this workshop was to cross-fertilize research groups working in topics of current interest in combustion dynamics and mathematical methods applicable thereto. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, George R. Sell, Paul Fife, Amable Liiian and Foreman Williams for organizing the meeting. We especially thank Paul Fife, Amable Liiilin and Foreman Williams for editing the proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, the National Science Foundation and the Office of Naval Research. Avner Friedman Willard Miller, Jr. ix PREFACE The world ofcombustion phenomena is rich in problems intriguing to the math ematical scientist. They offer challenges on several fronts: (1) modeling, which involves the elucidation of the essential features of a given phenomenon through physical insight and knowledge of experimental results, (2) devising appropriate asymptotic and computational methods, and (3) developing sound mathematical theories. Papers in the present volume, which are based on talks given at the Workshop on Dynamical Issues in Combustion Theory in November, 1989, describe how all of these challenges have been met for particular examples within a number of common combustion scenarios: reactiveshocks, low Mach number premixed reactive flow, nonpremixed phenomena, and solid propellants."

Thermal processes are ubiquitous and an understanding of thermal phenomena is essential for a complete description of the physics of nanoparticles, both for the purpose of modeling the dynamics of the particles and for the correct interpretation of experimental data.
This book has the twofold aim to present coherently the relevant results coming from the recent scientific literature and to guide the readers through the process of deriving results, enabling them to explore the limits of the mathematical approximations and test the power of the method. The book is focused on the fundamental properties of nanosystems in the gas phase. For this reason there is a strong emphasis on microcanonical physics. Each chapter is enrichedwith exercises and 3 Appendices provide additional useful materials."

Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior.

Thetopics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful referencetext forapplied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems."

Con?gurational mechanics has attracted quite a bit of attention from various - search ?elds over the recent years/decades. Having been regarded in its infancy of the early years as a somewhat obscureand almost mystic ?eld of researchthat could only be understood by a happy few of insiders with a pronounced theoretical inc- nation, con?gurational mechanics has developed by now into a versatile tool that can be applied to a variety of problems. Since the seminal works of Eshelby a general notion of con?gurational - chanics has been developed and has successfully been applied to many pr- lems involving various types of defects in continuous media. The most pro- nent application is certainly the use of con?gurational forces in fracture - chanics. However, as con?gurational mechanics is related to arbitrary mat- ial inhomogeneities it has also very successfully been applied to many ma- rials science and engineering problems such as phase transitions and inelastic deformations. Also the modeling of materials with micro-structure evolution is an important ?eld, in which con?gurational mechanics can provide a better understanding of processes going on within the material. Besides these mechanically, physically, and chemically motivated applications, ideas from con?gurational mechanics are now increasingly applied within computational mechanics.

This book is the Proceedings of the First International Symposium for Science on Form. The Symposium was held on November 26 through 30, 1985 at the University of Tsukuba, Japan. It was organized by The Society for Science on Form, J::.!pan, and sponsored by the Foundation for Advancement of International Science (F AIS). The purpose of the Symposium was to discuss interdisciplinal science aspects of form. "Form", to exhibit its tremendous characters, depends on the material and the changes. But, it is the form that appears evident at once and endures. Form is absorbed from every field as media of information. Thirty years and more ago, interdisciplinal problems between earthethics and science were submitted to a symposium on Form in Nature and Art. The relation between form and function had been emphasized philosophically and psychologically. In this quarter century, information theory had exactly decided figures, electronic computer had easily calculated graphics, and laser hologram had completely contained the objective image and reconstructed it.

Our world is composed of systems within systems-the machines we build, the information we share, the organizations we form, and elements of nature that surround us. Therefore, nearly every field of study and practice embodies behaviors stemming from system dynamics. Yet the study of systems has remained somewhat fragmented based on philosophies, methodologies, and intentions. Many methodologies for analyzing complex systems extend far beyond the traditional framework of deduction evaluation and may, thus, appear mysterious to the uninitiated. This book seeks to dispel the mysteries of systems analysis by holistically explaining the philosophies, methodologies, and intentions in the context of understanding how all types of systems in our world form and how these systems break. This presentation is made at the level of conceptual understanding, with plenty of figures but no mathematical formulas, for the beginning student and interested readers new to studying systems. Through the conceptual understanding provided, students are given a powerful capability to see the hidden behaviors and unexplained consequences in the world around us.

100 years after the first observation of ripening by Ostwald and 40 years after the first publication of a theory describing this process, this monograph presents, in a self-consistent and comprehensive manner, all the bits and pieces of coarsening theories so that the main issues and the underlying mathematics of self-similar coarsening of dispersed systems can be understood. It contains all of the background material necessary to understand growth and coarsening of spherical particles or droplets in a liquid or solid matrix. Some basic knowledge of heat and mass transfer, thermodynamics and differential equations would be helpful, but not necessary, as all the concepts required are introduced. The text is suitable for advanced undergraduate and graduate students as well as for researchers. Rather than giving a complete survey of the field, it presents a careful derivation of the existing results and places them into some perspective.

One of the main goals of optimal control theory is to provide a theoretical basis for choosing an appropriate controller for whatever system is under consideration by the researcher or engineer. Two popular norms that have proved useful are known as H-2 and H - infinity control. The first has been particularly applicable to problems arising in the aerospace industry. However, most industrial problems are badly modeled and the second norm proved to be more appropriate when the actual conditions of the problem did not conform to the stipulated conditions of the theory. This book takes the topic of H-infinity control as a point of departure and pursues an improved controller design which has been suggested in the mainstream of robust control. Its main theme, minimum entropy control, provides a means of trading off some of the features of other control problems. The book is aimed at research workers in networking systems as well as those in operator theory and linear multivariable control. The use of stochastic methods makes the book also of importance to the circuits and systems community. CONTENTS: Preface Introduction Preliminaries Induced Operator Norms Discrete-Time Entropy Connections With Related Optimal Control Problems Minimum Entropy Control Continuous-Time Entropy A. Proof of Theorem B. Proof of Theorem Bibliography Notation Index"

This book aims to present an information-theoretical approach to thermodynamics and its generalisations. On the one hand, it generalises the concept of information thermodynamics' to that of information dynamics' in order to stress applications outside thermal phenomena. On the other hand, it is a synthesis of the dynamics of state change and the theory of complexity, which provide a common framework to treat both physical and nonphysical systems together. Both classical and quantum systems are discussed, and two appendices are included to explain principal definitions and some important aspects of the theory of Hilbert spaces and operator algebras. The concept of higher-order temperatures is explained and applied to biological and linguistic systems. The theory of open systems is presented in a new, much more general form. Audience: This volume is intended mainly for theoretical and mathematical physicists, but also for mathematicians, experimental physicists, physical chemists, theoretical biologists, communication engineers, and all those interested in entropy and open systems. It can also be recommended as a supplementary text.

This book contains the courses given at the Fourth School on Statistical Physics and Cooperative Systems held at Santiago, Chile, from 12th to 16th December 1994. This School brings together scientists working on subjects related to recent trends in complex systems. Some of these subjects deal with dynamical systems, ergodic theory, cellular automata, symbolic and arithmetic dynamics, spatial systems, large deviation theory and neural networks. Scientists working in these subjects come from several aeras: pure and applied mathematics, non linear physics, biology, computer science, electrical engineering and artificial intelligence. Each contribution is devoted to one or more of the previous subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The expository text of Roberto Livi concerns the study of coupled map lattices (CML) as models of spatially extended dynamical systems. CML is one of the most used tools for the investigation of spatially extended systems. The paper emphasizes rigorous results about the dynamical behavior of one dimensional CML; i.e. a uniform real local function defined in the interval [0,1], interacting with its nearest neighbors in a one dimensional lattice.