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.

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.

The book deals with the development of continual models of turbulent natural media. Such models serve as a ground for the statement and numerical evaluation of the key problems of the structure and evolution of the numerous astrophysical and geophysical objects. The processes of ordering (self-organization) in an originally chaotic turbulent medium are addressed and treated in detail with the use of irreversible thermodynamics and stochastic dynamics approaches which underlie the respective models. Different examples of ordering set up in the natural environment and outer space are brought and thoroughly discussed, the main focus being given to the protoplanetary discs formation and evolution.

Bridging the gap between statistical theory and physical experiment, this is a thorough introduction to the statistical methods used in the experimental physical sciences and to the numerical methods used to implement them. An accompanying CD-ROM provides detailed code for implementing many of these algorithms. The treatment emphasises concise but rigorous mathematics but always retains its focus on applications. Readers are assumed to have a sound basic knowledge of differential and integral calculus and some knowledge of vectors and matrices. After an introduction to probability, random variables, computer generation of random numbers and important distributions, the book turns to statistical samples, the maximum likelihood method, and the testing of statistical hypotheses. The discussion concludes with several important statistical methods: least squares, analysis of variance, polynomial regression, and analysis of time series. Appendices provide the necessary methods of matrix algebra, combinatorics, and many sets of useful algorithms and formulae.

This textbook covers a broad spectrum of developments in QFT, emphasizing those aspects that are now well consolidated and for which satisfactory theoretical descriptions have been provided. The book is unique in that it offers a new approach to the subject and explores many topics merely touched upon, if covered at all, in standard reference works. A detailed and largely non-technical introductory chapter traces the development of QFT from its inception in 1926. The elegant functional differential approach put forward by Schwinger, referred to as the quantum dynamical (action) principle, and its underlying theory are used systematically in order to generate the so-called vacuum-to-vacuum transition amplitude of both abelian and non-abelian gauge theories, in addition to Feynman's well-known functional integral approach, referred to as the path-integral approach. Given the wealth of information also to be found in the abelian case, equal importance is put on both abelian and non-abelian gauge theories. Particular emphasis is placed on the concept of a quantum field and its particle content to provide an appropriate description of physical processes at high energies, where relativity becomes indispensable. Moreover, quantum mechanics implies that a wave function renormalization arises in the QFT field independent of any perturbation theory - a point not sufficiently emphasized in the literature. The book provides an overview of all the fields encountered in present high-energy physics, together with the details of the underlying derivations. Further, it presents "deep inelastic" experiments as a fundamental application of quantum chromodynamics. Though the author makes a point of deriving points in detail, the book still requires good background knowledge of quantum mechanics, including the Dirac Theory, as well as elements of the Klein-Gordon equation. The present volume sets the language, the notation and provides additional background for reading Quantum Field Theory II - Introduction to Quantum Gravity, Supersymmetry and String Theory, by the same author. Students in this field might benefit from first reading the book Quantum Theory: A Wide Spectrum (Springer, 2006), by the same author.

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.

This set of lecture notes gives a first coherent account on a novel aspect of the living world that can be called biological information. The book presents both a pedagogical and state-of-the art roadmap of this rapidly evolving field and covers the whole range from information which is encoded in the molecular genetic code to the description of large-scale evolution of complex species networks. The book will prove useful for all those who work at the interface of biology, physics and information science.

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.

This book provides a unique insight into the latest breakthroughs in a consistent manner, at a level accessible to undergraduates, yet with enough attention to the theory and computation to satisfy the professional researcher Statistical physics addresses the study and understanding of systems with many degrees of freedom. As such it has a rich and varied history, with applications to thermodynamics, magnetic phase transitions, and order/disorder transformations, to name just a few. However, the tools of statistical physics can be profitably used to investigate any system with a large number of components. Thus, recent years have seen these methods applied in many unexpected directions, three of which are the main focus of this volume. These applications have been remarkably successful and have enriched the financial, biological, and engineering literature. Although reported in the physics literature, the results tend to be scattered and the underlying unity of the field overlooked.

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.

The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker--Planck equations. Particular attention is given to the theory of optical bistability formulated in terms of the positive P-representation, and the theory of small bistable systems. This is a textbook at an advanced graduate level. It is intended as a bridge between an introductory discussion of the master equation method and problems of current research.

Complexity science has been a source of new insight in physical and social systems and has demonstrated that unpredictability and surprise are fundamental aspects of the world around us. This book is the outcome of a discussion meeting of leading scholars and critical thinkers with expertise in complex systems sciences and leaders from a variety of organizations, sponsored by the Prigogine Center at The University of Texas at Austin and the Plexus Institute, to explore strategies for understanding uncertainty and surprise. Besides contributions to the conference, it includes a key digest by the editors as well as a commentary by the late nobel laureate Ilya Prigogine, "Surprises in half of a century." The book is intended for researchers and scientists in complexity science, as well as for a broad interdisciplinary audience of both practitioners and scholars. It will well serve those interested in the research issues and in the application of complexity science to physical and social systems.

Computer science and physics have been closely linked since the birth of modern computing. In recent years, an interdisciplinary area has blossomed at the junction of these fields, connecting insights from statistical physics with basic computational challenges. Researchers have successfully applied techniques from the study of phase transitions to analyze NP-complete problems such as satisfiability and graph coloring. This is leading to a new understanding of the structure of these problems, and of how algorithms perform on them.
Computational Complexity and Statistical Physics will serve as a standard reference and pedagogical aid to statistical physics methods in computer science, with a particular focus on phase transitions in combinatorial problems. Addressed to a broad range of readers, the book includes substantial background material along with current research by leading computer scientists, mathematicians, and physicists. It will prepare students and researchers from all of these fields to contribute to this exciting area.

The primary goal of the book is to present the ideas and research findings of active researchers such as physicists, economists, mathematicians and financial engineers working in the field of "Econophysics," who have undertaken the task of modeling and analyzing systemic risk, network dynamics and other topics.

Of primary interest in these studies is the aspect of systemic risk, which has long been identified as a potential scenario in which financial institutions trigger a dangerous contagion mechanism, spreading from the financial economy to the real economy.

This type of risk, long confined to the monetary market, has spread considerably in the recent past, culminating in the subprime crisis of 2008. As such, understanding and controlling systemic risk has become an extremely important societal and economic challenge. The Econophys-Kolkata VI conference proceedings are dedicated to addressing a number of key issues involved. Several leading researchers in these fields report on their recent work and also review contemporary literature on the subject.

Within the framework of Jaynes' "Predictive Statistical Mechanics," this book presents a detailed derivation of an ensemble formalism for open systems arbitrarily away from equilibrium. This involves a large systematization and extension of the fundamental works and ideas of the outstanding pioneers Gibbs and Boltzmann, and of Bogoliubov, Kirkwood, Green, Mori, Zwanzig, Prigogine and Zubarev, among others.
Chapters 1 to 5 include a description of the philosophy, foundations, and construction (methodology) of the formalism, including the derivation of a nonequilibrium grand-canonical ensemble for far-from-equilibrium systems as well as the derivation of a quantum nonlinear kinetic theory and a response function theory together with a theory of scattering. In chapter 6 applications of the theory are cataloged, making comparisons with experimental data (a basic step for the validation of any theory). Chapter 7 is devoted to the description of irreversible thermodynamics, providing a far-reaching generalization of Informational-Statistical Thermodynamics. The last chapter gives an overall picture of the formalism, and questions and criticisms related to it are discussed.
Audience: This book is directed at an audience of researchers in the field of Statistical Mechanics and Thermodynamics of open nonequilibrium systems. In addition, it is relevant for the study of far-from-equilibrium processes in condensed matter, particularly semiconductor physics, as well as molecular Hydrodynamics, Rheology, many-body systems with complex behavior and areas of engineering, etc. The book can also be used as a complement to advanced graduate courses in Statistical Mechanics.

Kinetic Theory of granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics as it has been developed mainly during the past decade. The book is aimed at readers from the advanced undergraduate level onwards and leads up to the present state of research. The text is self-contained, in the sense that no mathematical or physical knowledge is required that goes beyond standard undergraduate physics courses. The material is adequate for a one-semester course and contains chapter summaries as well as exercises with detailed solutions. Special emphasis is put on a microscopically consistent description of pairwise particle collisions which leads to an impact-velocity dependent coefficient of restitution. The description of the many-particle system, based on the Boltzmann equation, starts with the derivation of the velocity distribution function, followed by the investigation of self-diffusion and Brownian motion. Using hydrodynamical methods, transport processes and self-organized structure formulation are studies. An appendix gives a brief introduction to event-driven molecular dynamics. A second appendix describes a novel mathematical technique for the derivation of the kinetic properties which allows for the application of computer algebra. The book is accompanied by a web page where the molecular dynamics program as well as the computer-algebra programs are provided.

This book draws on the latest research to discuss the history and development of high-entropy alloys and ceramics in bulk, film, and fiber form. High-entropy materials have recently been developed using the entropy of mixing and entropy of configuration of materials, and have proven to exhibit unique properties superior to those of conventional materials. The field of high-entropy alloys was born in 2004, and has since been developed for both scientific and engineering applications. Although there is extensive literature, this field is rapidly transforming. This book highlights the cutting edge of high-entropy materials, including their fundamentals and applications. Above all, it reflects two major milestones in their development: the equi-atomic ratio single-phase high-entropy alloys; and the non-equi-atomic ratio dual-phase high-entropy alloys.

This book presents the latest advances in ultrafast science, including both ultrafast optical technology and the study of ultrafast phenomena. It covers picosecond, femtosecond, and attosecond processes relevant to applications in physics, chemistry, biology, and engineering. Ultrafast technology has a profound impact in a wide range of applications, amongst them biomedical imaging, chemical dynamics, frequency standards, material processing, and ultrahigh-speed communications. This book summarizes the results presented at the 19th International Conference on Ultrafast Phenomena and provides an up-to-date view of this important and rapidly advancing field.

What do combustion engines, fusion reactors, weather forecast, ocean ?ows, our sun, and stellar explosions in outer space have in common? Of course, the physics and the length and time scales are vastly di?erent in all cases, but it is alsowellknownthatinallofthem,onsomerelevantlengthscales,thematerial ?ows that govern the dynamical and/or secular evolution of the systems are chaotic and often unpredictable: they are said to be turbulent. In fact, the term "turbulence" is used for an enormous variety of p- nomena in very di?erent ?elds, including geophysics, astrophysics, and - gineering. Unfortunately, these communities do not talk to each other too often. Therefore, back in 2005, we organized a workshop on "Interdis- plinary Aspects of Turbulence" at the Ringberg Castle in the Bavarian Alps, to discuss topics such as the basic concepts of turbulence, the di?- ent approaches of modelling and simulations used in the various areas, and also possible tests. This workshop was a great success and the proceedings can be found on the Internet (www.mpa-garching.mpg.de/mpa/publications/ proceedings/proceedings-en.html) as well as pdf-?les of several of the talks presented (www.mpa-garching. mpg.de/hydro/Turbulence/).

This is a graduate level monographic textbook in the field of Computational Intelligence. It presents a modern dynamical theory of the computational mind, combining cognitive psychology, artificial and computational intelligence, and chaos theory with quantum consciousness and computation. The book introduces to human and computational mind, comparing and contrasting main themes of cognitive psychology, artificial and computational intelligence.

This thesis discusses in detail the measurement of the polarizations of all S-wave vector quarkonium states in LHC proton-proton collisions with the CMS detector. Heavy quarkonium states constitute an ideal laboratory to study non-perturbative effects of quantum chromodynamics and to understand how quarks bind into hadrons. The experimental results are interpreted through an original phenomenological approach, which leads to a coherent picture of quarkonium production cross sections and polarizations within a simple model, dominated by one single color-octet production mechanism. These findings provide new insights into the dynamics of heavy quarkonium production at the LHC, an important step towards a satisfactory understanding of hadron formation within the standard model of particle physics.

Evolution is a critical challenge for many areas of science, technology and development of society. The book reviews general evolutionary facts such as origin of life and evolution of the genome and clues to evolution through simple systems. Emerging areas of science such as "systems biology" and "bio-complexity" are founded on the idea that phenomena need to be understood in the context of highly interactive processes operating at different levels and on different scales. This is where physics meets complexity in nature, and where we must begin to learn about complexity if we are to understand it. Similarly, there is an increasingly urgent need to understand and predict the evolutionary behavior of highly interacting man-made systems, in areas such as communications and transport, which permeate the modern world. The same applies to the evolution of human networks such as social, political and financial systems, where technology has tended to vastly increase both the complexity and speed of interaction, which is sometimes effectively instantaneous. The book contains reviews on such diverse areas as evolution experiments with microorganisms, the origin and evolution of viruses, evolutionary dynamics of genes and environment in cancer development, aging as an evolution-facilitating program, evolution of vision and evolution of financial markets.

Metaphors, generalizations and unifications are natural and desirable ingredients of the evolution of scientific theories and concepts. Physics, in particular, obviously walks along these paths since its very beginning. This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics, one of the greatest monuments of contemporary physics. Conceived more than 130 years ago by Maxwell, Boltzmann and Gibbs, the BG theory exhibits uncountable - some of them impressive - successes in physics, chemistry, mathematics, and computational sciences, to name a few. Presently, more than two thousand publications, by over 1800 scientists around the world, have been dedicated to the nonextensive generalization. Remarkable applications have emerged, and its mathematical grounding is by now relatively well established. A pedagogical introduction to its concepts - nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT's, among others - is presented in this book as well as a selection of paradigmatic applications in various sciences together with diversified experimental verifications of some of its predictions.

• This is the first pedagogical book on the subject, written by the proponent of the theory
• Presents many applications to interdisciplinary complex phenomena in virtually all sciences, ranging from physics to medicine, from economics to biology, through signal and image processing and others
• Offers a detailed derivation of results, illustrations and for the first time detailed presentation of Nonextensive Statistical Mechanics

The domain of non-extensive thermostatistics has been subject to intensive research over the past twenty years and has matured significantly. Generalised Thermostatistics cuts through the traditionalism of many statistical physics texts by offering a fresh perspective and seeking to remove elements of doubt and confusion surrounding the area. The book is divided into two parts - the first covering topics from conventional statistical physics, whilst adopting the perspective that statistical physics is statistics applied to physics. The second developing the formalism of non-extensive thermostatistics, of which the central role is played by the notion of a deformed exponential family of probability distributions. Presented in a clear, consistent, and deductive manner, the book focuses on theory, part of which is developed by the author himself, but also provides a number of references towards application-based texts. Written by a leading contributor in the field, this book will provide a useful tool for learning about recent developments in generalized versions of statistical mechanics and thermodynamics, especially with respect to self-study. Written for researchers in theoretical physics, mathematics and statistical mechanics, as well as graduates of physics, mathematics or engineering. A prerequisite knowledge of elementary notions of statistical physics and a substantial mathematical background are required.

This book is a result of teaching stochastic processes to junior and senior undergr- uates and beginning graduate students over many years. In teaching such a course, we have realized a need to furnish students with material that gives a mathematical presentation while at the same time providing proper foundations to allow students to build an intuitive feel for probabilistic reasoning. We have tried to maintain a b- ance in presenting advanced but understandable material that sparks an interest and challenges students, without the discouragement that often comes as a consequence of not understanding the material. Our intent in this text is to develop stochastic p- cesses in an elementary but mathematically precise style and to provide suf?cient examples and homework exercises that will permit students to understand the range of application areas for stochastic processes. We also practice active learning in the classroom. In other words, we believe that the traditional practice of lecturing continuously for 50 to 75 minutes is not a very effective method for teaching. Students should somehow engage in the subject m- ter during the teaching session. One effective method for active learning is, after at most 20 minutes of lecture, to assign a small example problem for the students to work and one important tool that the instructor can utilize is the computer. So- times we are fortunate to lecture students in a classroom containing computers with a spreadsheet program, usually Microsoft's Excel.