Although the study of dynamical systems is mainly concerned with single trans formations and one-parameter flows (i. e. with actions of Z, N, JR, or JR+), er godic theory inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multi-dimensional sym metry groups. However, the wealth of concrete and natural examples, which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. A remarkable exception is provided by a class of geometric actions of (discrete subgroups of) semi-simple Lie groups, which have led to the discovery of one of the most striking new phenomena in multi-dimensional ergodic theory: under suitable circumstances orbit equivalence of such actions implies not only measurable conjugacy, but the conjugating map itself has to be extremely well behaved. Some of these rigidity properties are inherited by certain abelian subgroups of these groups, but the very special nature of the actions involved does not allow any general conjectures about actions of multi-dimensional abelian groups. Beyond commuting group rotations, commuting toral automorphisms and certain other algebraic examples (cf. [39]) it is quite difficult to find non-trivial smooth Zd-actions on finite-dimensional manifolds. In addition to scarcity, these examples give rise to actions with zero entropy, since smooth Zd-actions with positive entropy cannot exist on finite-dimensional, connected manifolds. Cellular automata (i. e.

Combined for researchers and graduate students the articles from the Sitges Summer School together form an excellent survey of the applications of neural-network theory to statistical mechanics and computer-science biophysics. Various mathematical models are presented together with their interpretation, especially those to do with collective behaviour, learning and storage capacity, and dynamical stability.

This book is devoted to the applications of the mathematical theory of solitons to physics, statistical mechanics, and molecular biology. It contains contributions on the signature and spectrum of solitons, nonlinear excitations in prebiological systems, experimental and theoretical studies on chains of hydrogen-bonded molecules, nonlinear phenomena in solid-state physics, including charge density waves, nonlinear wave propagation, defects, gap solitons, and Josephson junctions. The content is interdisciplinary in nature and displays the new trends in nonlinear physics.

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author's previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time. The text begins with both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models such as: * inverted controlled pendulum; * Nicholson's blowflies equation; * predator-prey relationships; * epidemic development; and * mathematical models that describe human behaviours related to addictions and obesity. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations is primarily addressed to experts in stability theory but will also be of interest to professionals and students in pure and computational mathematics, physics, engineering, medicine, and biology.

This book explains the minimum error entropy (MEE) concept applied to data classification machines. Theoretical results on the inner workings of the MEE concept, in its application to solving a variety of classification problems, are presented in the wider realm of risk functionals. Researchers and practitioners also find in the book a detailed presentation of practical data classifiers using MEE. These include multi-layer perceptrons, recurrent neural networks, complexvalued neural networks, modular neural networks, and decision trees. A clustering algorithm using a MEE-like concept is also presented. Examples, tests, evaluation experiments and comparison with similar machines using classic approaches, complement the descriptions.

Materials sciences relate the macroscopic properties of materials to their microscopic structure and postulate the need for holistic multiscale research. The investigation of shape memory alloys is a prime example in this regard. This particular class of materials exhibits strong coupling of temperature, strain and stress, determined by solid state phase transformations of their metallic lattices. The present book presents a collection of simulation studies of this behaviour. Employing conceptually simple but comprehensive models, the fundamental material properties of shape memory alloys are qualitatively explained from first principles. Using contemporary methods of molecular dynamics simulation experiments, it is shown how microscale dynamics may produce characteristic macroscopic material properties. The work is rooted in the materials sciences of shape memory alloys and covers thermodynamical, micro-mechanical and crystallographical aspects. It addresses scientists in these research fields and their students.

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.

As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japenese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the usefil for self-teaching, as well as for classroom learning.

In this comprehensive text a systematic numerical and analytical treatment of the procedures for reducing complicated systems to a simplified reaction mechanism is presented. The results of applying the reduced reaction mechanism to a one-dimensional laminar flame are discussed. A set of premixed and non-premixed methane-air flames with simplified transport and skeletal chemistry are employed as test problems that are used later on to evaluate the results and assumptions in reduced reaction networks. The first four chapters form a short tutorial on the procedures used in formulating the test problems and in reducing reaction mechanisms by applying steady-state and partial-equilibrium approximations. The final six chapters discuss various aspects of the reduced chemistry problem for premixed and nonpremixed combustion.

In this volume the author gives a detailed presentation of his theory of multiphase mixtures with structure. The book also addresses students, and in addition encourages further research. Based on the concept of averaging the field equations, conservation and balance equations are developed. A material deformation postulate leads to structured mixtures. The resulting model is compared with those in use elsewhere. The final chapters are devoted to constitutive theory and constitutive equations. In particular, two-phase mixtures are treated in some detail.

This thesis presents a novel coarse-grained model of DNA, in which bases are represented as rigid nucleotides. The model is shown to quantitatively reproduce many phenomena, including elastic properties of the double-stranded state, hairpin formation in single strands and hybridization of pairs of strands to form duplexes, the first time such a wide range of properties has been captured by a coarse-grained model. The scope and potential of the model is demonstrated by simulating DNA tweezers, an iconic nanodevice, and a two-footed DNA walker - the first time that coarse-grained modelling has been applied to dynamic DNA nanotechnology.

The book is about the key elements required for designing, building and controlling effective artificial swarms comprised of multiple moving physical agents. Therefore this book presents the fundamentals of each of those key elements in the particular frame of dynamic swarming, specifically exposing the profound connections between these elements and establish some general design principles for swarming behaviors. This scientific endeavor requires an inter-disciplinary approach: biomimetic inspiration from ethology and ecology, study of social information flow, analysis of temporal and adaptive signaling network of interaction, considerations of control of networked real-time systems, and lastly, elements of complex adaptive dynamical systems. This book offers a completely new perspective on the scientific understanding of dynamic collective behaviors thanks to its multi-disciplinary approach and its focus on artificial swarm of physical agents. Two of the key problems in understanding the emergence of swarm intelligent behaviors are identifying the social interaction rules a.k.a. the behavioral algorithm and uncovering how information flows between swarming agents. While most books about swarm dynamics have been focusing on the former, this book emphasizes the much-less discussed topic of distributed information flow, always with the aim of establishing general design principles.

There are many examples of cooperation in Nature: cells cooperate to form tissues, organs cooperate to form living organisms, and individuals cooperate to raise their offspring or to hunt. However, why cooperation emerges and survives in hostile environments, when defecting would be a much more profitable short-term strategy, is a question that still remains open. During the past few years, several explanations have been proposed, including kin and group selection, punishment and reputation mechanisms, or network reciprocity. This last one will be the center of the present study. The thesis explores the interface between the underlying structure of a given population and the outcome of the cooperative dynamics taking place on top of it, (namely, the Prisoner's Dilemma Game). The first part of this work analyzes the case of a static system, where the pattern of connections is fixed, so it does not evolve over time. The second part develops two models for growing topologies, where the growth and the dynamics are entangled.

What are the principles that keep our society together? This question is even more difficult to answer than the long-standing question, what are the forces that keep our world together. However, the social challenges of humanity in the 21st century ranging from the financial crises to the impacts of globalization, require us to make fast progress in our understanding of how society works, and how our future can be managed in a resilient and sustainable way. This book can present only a few very first steps towards this ambitious goal. However, based on simple models of social interactions, one can already gain some surprising insights into the social, ``macro-level'' outcomes and dynamics that is implied by individual, ``micro-level'' interactions. Depending on the nature of these interactions, they may imply the spontaneous formation of social conventions or the birth of social cooperation, but also their sudden breakdown. This can end in deadly crowd disasters or tragedies of the commons (such as financial crises or environmental destruction). Furthermore, we demonstrate that classical modeling approaches (such as representative agent models) do not provide a sufficient understanding of the self-organization in social systems resulting from individual interactions. The consideration of randomness, spatial or network interdependencies, and nonlinear feedback effects turns out to be crucial to get fundamental insights into how social patterns and dynamics emerge. Given the explanation of sometimes counter-intuitive phenomena resulting from these features and their combination, our evolutionary modeling approach appears to be powerful and insightful. The chapters of this book range from a discussion of the modeling strategy for socio-economic systems over experimental issues up the right way of doing agent-based modeling. We furthermore discuss applications ranging from pedestrian and crowd dynamics over opinion formation, coordination, and cooperation up to conflict, and also address the response to information, issues of systemic risks in society and economics, and new approaches to manage complexity in socio-economic systems. Selected parts of this book had been previously published in peer reviewed journals.

This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.>

The thesis deals with averaging dynamics in a multiagent networked system, which is a main mechanism for diffusing the information over such networks. It arises in a wide range of applications in engineered physical networks (such as mobile communication and sensor networks), as well as social and economic networks. The thesis provides in depth study of stability and other phenomena characterizing the limiting behavior of both deterministic and random averaging dynamics. By developing new concepts, and using the tools from dynamic system theory and non-negative matrix theory, several novel fundamental results are rigorously developed. These contribute significantly to our understanding of averaging dynamics as well as to non-negative random matrix theory. The exposition, although highly rigorous and technical, is elegant and insightful, and accompanied with numerous illustrative examples, which makes this thesis work easily accessible to those just entering this field and will also be much appreciated by experts in the field.

Local and global spatial coupling mechanisms form the basis of transport processes that are of fundamental importance for the occurrence and the dynamic evolution of patterns on a mesoscopic and macroscopic scale. The present volume deals with these concepts and investigates applications in the fields of biophysics and chemistry.

Neural-network models for event analysis are widely used in experimental high-energy physics, star/galaxy discrimination, control of adaptive optical systems, prediction of nuclear properties, fast interpolation of potential energy surfaces in chemistry, classification of mass spectra of organic compounds, protein-structure prediction, analysis of DNA sequences, and design of pharmaceuticals. This book, devoted to this highly interdisciplinary research area, addresses scientists and graduate students. The pedagogically written review articles range over a variety of fields including astronomy, nuclear physics, experimental particle physics, bioinformatics, linguistics, and information processing.

One of the driving forces behind much of modern science and technology is the desire to foresee and thereby control the future. In recent years, however, it has become clear that, even in a deterministic world, there is alimit to the accuracy with which we can predict the future. This book details, in a largely nontechnical style, the extent to which we can predict the future development of various physical, biological and socio-economic processes.

For the present edition four chapters have been added which form the fourth 1 part at the end of the book . Entitled The triumph of neoliberalism , the new partexplains how theimplementation worldwide oftheneoliberal agenda paved the way for the present crisis. As a matter of fact, the evidence provided in chapter 9 suggests that the present crisis already began to build up in the mid-1970s. It is around 1975 that (real) US wages reached a peak-level they would never regain in f- lowing decades. It was also around 1975 that the number of strikes began to fall sharply. The mid-1970s also marked the beginning of a huge in ow of immigrants (in large part of Hispanic origin) into the United States. The in ated supply of labor depressed wages and this had the consequence that consumption could be increased only by an unprecedented development of credit. Perhaps the reader may think that to blame the prevailing economic system for the unfolding depression is a fairly common and all too easy temptation.

We started our work on theoretical methods in the phys ics of high pressures (in connec tion with geophysical applications) in 1956, and we immediately encountered many problems. Naturally, we searched the published Iiterature for solutions to these problems but whenever we failed to find a solution or when the solution did not satisfy us, we attempted to solve the problern ourselves. We realized that other investigators working in the physics of high pres sures would probably encounter the same problems and doubts. Therefore, we decided to write this book in order to save our colleagues time and effort. Apart from the descriptions of ex perimental methods, the book deals only with those problems which we encountered in our own work. Allproblems in high-pressure physics have, at present, only approximate solutions, which are very rough. Therefore, it is not surprising that different investigators approach the same problems in different ways. Our approach does not prejudge the issue and we are fully aware that there are other points of view. Our aim was always to solve a glven problern on a physical basis. For example, the concept of the Gruneisenparameter needs further develop ment but it is based on reliable physical ideas. On the other hand, Simon's equation for the melting curve has, in our opinion, no clear physical basis and is purely empirical. Equations of this type are useful in systematic presentation of the experimental material but they are un suitable for any major extrapolation.

Mechanics, Motion Control, Sensing and Programming, Synthesis and Design, Legged Locomotion and Biomechanical Aspects of Robots and Manipulators - world view of the state of the art. Characterization: This volume presents the latest contribution to the theory and practice of modern robotics given by the world recognized scientists from Australia, Canada, Europe, Japan, Mexico, Singapore and USA.

The investigation of nonlinear wave phenomena has been one of the main direc tions of research in optics for the last few decades. Soliton concepts applied to the description of intense electromagnetic beams and ultrashort pulse propagation in various media have contributed much to this field. The notion of solitons has proved to be very useful in describing wave processes in hydrodynamics, plasma physics and condensed matter physics. Moreover, it is also of great importance in optics for ultrafast information transmission and storage, radiation propagation in resonant media, etc. In 1973, Hasegawa and Tappert made a significant contribution to optical soliton physics when they predicted the existence of an envelope soliton in the regime of short pulses in optical fibres. In 1980, Mollenauer et al. conducted ex periments to elucidate this phenomenon. Since then the theory of optical solitons as well as their experimental investigation has progressed rapidly. The effects of inhomogeneities of the medium and energy pumping on optical solitons, the interaction between optical solitons and their generation in fibres, etc. have all been investigated and reported. Logical devices using optical solitons have been developed; new types of optical solitons in media with Kerr-type nonlinearity and in resonant media have been described."

For the first time this subject, including many systems of interest in Condensed Matter Physics, is treated in an unified way. Complexity emerges as one of the main ingredients dictating the collective behaviour of many systems. Glassy systems constitute one of the most interesting fields of Condensed Matter Physics for which also a considerable amount of experimental data and industial applications have been collected during the last twenty years. Systems exhibiting glassy behaviour are for example: real glasses, spin glasses, vortex flasses in superconductors, protein folding, etc. In this book the reader can see how the present theoretical understanding of these subjects is based on similar techniques and approaches hopefully allowing to develop a unifying structure that underlies the physical mechanism.

At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge.

These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory.

Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications.

The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.