This book presents a careful selection of the most important developments of the \phi^4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead. Over the past four decades, the \phi^4 model has been the basis for a broad array of developments in the physics and mathematics of nonlinear waves. From kinks to breathers, from continuum media to discrete lattices, from collisions of solitary waves to spectral properties, and from deterministic to stochastic models of \phi^4 (and \phi^6, \phi^8, \phi^12 variants more recently), this dynamical model has served as an excellent test bed for formulating and testing the ideas of nonlinear science and solitary waves.

This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular particles, or cells, or of processes that depend on such motion or are markedly affected by it. Readers do not need to understand thermodynamics in order to acquire a knowledge of the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility--subjects that become lively and immediate when the author discusses them in terms of random walks of individual particles.

This book focuses on theoretical thermotics, the theory of transformation thermotics and its extended theories for the active control of macroscopic thermal phenomena of artificial systems, which is in sharp contrast to classical thermodynamics comprising the four thermodynamic laws for the passive description of macroscopic thermal phenomena of natural systems. The book covers the basic concepts and mathematical methods, which are necessary to understand thermal problems extensively investigated in physics, but also in other disciplines of engineering and materials. The analyses rely on models solved by analytical techniques accompanied with computer simulations and laboratory experiments. This book serves both as a reference work for senior researchers and a study text for zero beginners.

Continuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics. Developed over the last two decades, it is based on the mathematical theory of nonlinear thermoelasticity, in which a new viewpoint on material symmetry, motivated by molecular theories, plays a central role.

This is the first organized presentation of a nonlinear elastic approach to twinning and displacive phase transition in crystalline solids. The authors develop geometry, kinematics, and energy invariance in crystals in strong connection and with the purpose of investigating the actual mechanical aspects of the phenomena, particularly in an elastostatics framework based on the minimization of a thermodynamic potential. Interesting for both mechanics and mathematical analysis, the new theory offers the possibility of investigating the formation of microstructures in materials undergoing martensitic phase transitions, such as shape-memory alloys.

Although phenomena such as twinning and phase transitions were once thought to fall outside the range of elastic models, research efforts in these areas have proved quite fruitful. Relevant to a variety of disciplines, including mathematical physics, continuum mechanics, and materials science, Continuum Models for Phase Transitions and Twinning in Crystals is your opportunity to explore these current research methods and topics.

Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle - the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion - first formulated by Langevin in 1908 - so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker-Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject.

Providing a systematic introduction to the techniques which are fundamental to quantum field theory, this book pays special attention to the use of these techniques in a wide variety of areas, including ordinary quantum mechanics, quantum mechanics in the second-quantized formulation, relativistic quantum field theory, Euclidean field theory, quantum statistics at finite temperature, and the classical statistics of nonideal gas and spin systems. The extended chapter on variational methods and functional Legendre transformations contains completely original material.

Presenting in a coherent and accessible fashion current results in nanomagnetism, this book constitutes a comprehensive, rigorous and readable account, from first principles of the classical and quantum theories underlying the dynamics of magnetic nanoparticles subject to thermal fluctuations.Starting with the Larmor-like equation for a giant spin, both the stochastic (Langevin) equation of motion of the magnetization and the associated evolution (Fokker-Planck) equation for the distribution function of the magnetization orientations of ferromagnetic nanoparticles (classical spins) in a heat bath are developed along with their solution (using angular momentum theory) for arbitrary magnetocrystalline-Zeeman energy. Thus, observables such as the magnetization reversal time, relaxation functions, dynamic susceptibilities, etc. are calculated and compared with the predictions of classical escape rate theory including in the most general case spin-torque-transfer. Regarding quantum effects, which are based on the reduced spin density matrix evolution equation in Hilbert space as is described at length, they are comprehensively treated via the Wigner-Stratonovich formulation of the quantum mechanics of spins via their orientational quasi-probability distributions on a classically meaningful representation space. Here, as suggested by the relevant Weyl symbols, the latter is the configuration space of the polar angles. Hence, one is led, by mapping the reduced density matrix equation onto that space, to a master equation for the quasi-probability evolution akin to the Fokker-Planck equation which may be solved in a similar way. Thus, one may study in a classical-like manner the evolution of observables with spin number ranging from an elementary spin to molecular clusters to the classical limit, viz. a nanoparticle. The entire discussion hinges on the one-to-one correspondence between polarization operators in Hilbert space and the spherical harmonics allied to concepts of spin coherent states long familiar in quantum optics.Catering for the reader with only a passing knowledge of statistical and quantum mechanics, the book serves as an introductory text on a complicated subject where the literature is remarkably sparse.

This book deals with certain important problems in Classical and Quantum Information Theory Quantum Information Theory, A Selection of Matrix Inequalities Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings Wigner-distributions in Quantum Mechanics Quantization of Classical Field Theories Statistical Signal Processing Quantum Field Theory, Quantum Statistics, Gravity, Stochastic Fields and Information Problems in Information Theory It will be very helpful for students of Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).

In this resource, acknowledged leaders in the field examine current state-of-the-art and recent developments in technology, of flow boiling systems which are affected by convective flows. This important volume consists of expanded and revised peer-reviewed papers presented at the Engineering Foundations's Convective Flow Boiling: An International Conference held in 1995.

The general non equilibrium statistical approach, due to Zubarev, is presented briefly in Chapter 1. Chapter 2 is devoted to construction of an application of this approach to a statistical mechanical description of transport processes on a dividing surface between two immiscible fluids when singular densities of mass, and/or momentum, and/or energy are presented. In chapter 3 the shock wave in a gas is considered an interphase boundary of the gas-gas type. Chapters 4 and 5 fluctuations of flows of mass or momentum across the surfaces of sufficiently small liquid or solid particles, respectively, are discussed. Finally, chapter 6 discusses a generalization of the one-particle Brownian motion theory to many-particle situations, where the interparticle hydrodynamic ineraction are essential.

Il testo si configura come un' introduzione alla fisica statistica rivolto in primo luogo a quei corsi di studio in ingegneria che piu hanno a che fare con le proprieta fisiche dei materiali, ed ha lo scopo di fornire le basi microscopiche del comportamento termodinamico di cui si fa uso sia in molti corsi tradizionali, quali quelli di termofluidica d'interesse per l'ingegneria chimica e nucleare, che in corsi rivolti ad applicazioni avanzate nella scienza dei materiali e nelle nanotecnologie. Particolare attenzione viene quindi dedicata all'impiego di metodi di fisica statistica nella scienza dei materiali, approfondendo tematiche relative alle vibrazioni nei solidi, ai processi di nucleazione liquido/vapore, alla struttura dello stato fluido e vetroso, ai plasmi, ai materiali magnetici, al gas di Fermi e alla superfluidita. Per il suo carattere generale, e per l'accento posto sui fondamenti della meccanica quantistica, il volume si presta comunque a costituire anche un testo introduttivo alla meccanica statistica per studenti dei corsi di laurea in fisica."

This suberb text is designed to introduce the fundamentals of the subject of statistical mechanics at a level suitable for students who meet the subject for the first time. The treatment given is designed to give the student a feeling for the topic of statistical mechanics without being held back by the need to understand complex mathematics. The text is concise and concentrates on the understanding of fundamental aspects. Numerous questions with worked solutions are given throughout.

Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.

The science of networks represented a substantial change in the way we see natural and technological phenomena. Now we have a better understanding that networks are, in most cases, networks of networks or multi-layered networks. This book provides a summary of the research done during one of the largest and most multidisciplinary projects in network science and complex systems (Multiplex). The science of complex networks originated from the empirical evidence that most of the structures of systems such as the internet, sets of protein interactions, and collaboration between people, share (at least qualitatively) common structural properties. This book examines how properties of networks that interact with other networks can change dramatically. The authors show that, dependent on the properties of links that interconnect two or more networks, we may derive different conclusions about the function and the possible vulnerabilities of the overall system of networks. This book presents a series of novel theoretical results together with their applications, providing a comprehensive overview of the field.

vi The amalgamation of individual approaches and results from various schools into a comprehensive scientific theory, which can be generally appreciated throughout the international scientific com munity, is oftendifficult and time consuming. We believe that one of the best ways to give a complete and clear presentation of a theoryis to include a review of the developmental history of that theory. We are convinced that explaining a theory in a historical perspectiveis essential for a proper understanding ofits present state and for a sound choice of future developments. So we have endeavored to present a complete picture of investi gations performed in both Western and Soviet nations. We understand that Soviet investigations are less familiar to English-speaking readers due to the languagebarrier and the obvious sad circumstances of the interruption of scientific connections before and after World War II, because of this there is an emphasis on Soviet publications in the bibliography. Our attempt to present a comprehensive picture has made our book rather large becauseit has had to include some fundamentals of thermochemistry and kinetics as well as self-ignition and flame propagation invarious conditions. We have also included stability problems in some detail but we have had to leave out the problems of combustion of solid propellants and detonation. We hope that our bookwill be useful to the reader wishing to learn about both the present state of combustion theory and howit originated due to the efforts of many people from different countries. Ya.B.Z."

Statistics lectures have been a source of much bewilderment and frustration for generations of students. This book attempts to remedy the situation by expounding a logical and unified approach to the whole subject of data analysis.
This text is intended as a tutorial guide for senior undergraduates and research students in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image
processing. Other topics covered include reliability analysis, multivariate optimization, least-squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy and experimental design.
The Second Edition of this successful tutorial book contains a new chapter on extensions to the ubiquitous least-squares procedure, allowing for the straightforward handling of outliers and unknown correlated noise, and a cutting-edge contribution from John Skilling on a novel numerical technique
for Bayesian computation called 'nested sampling'.

The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.

Exploiting powerful techniques from physics and mathematics, this book studies animal movement in ecology, with a focus on epidemic spread. Pulmonary syndrome is not only feared in epidemics of recent times, such as COVID-19, but is also characteristic of epidemics studied earlier such as Hantavirus. The Hantavirus is one of the book's central topics. Correlations between epidemic outbreaks and precipitation events like El Nino are analyzed and spatial reservoirs of infection in off-period of the epidemic, known as refugia, are studied. Predicted traveling waves of infection are successfully compared to field observations. Territoriality in scent-marking animals is presented, with parallels drawn with the theory of melting. The flocking and herding of birds and mammals are described in terms of collective excitations. For scientists interested in movement ecology and epidemic spread, this book provides effective solutions to long-standing problems.

This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the world and our everyday empirical experience of it. The trouble is about the direction of time. The situation (very briefly) is that it is a consequence of almost every one of those fundamental scientific pictures--and that it is at the same time radically at odds with our common sense--that whatever can happen can just as naturally happen backwards.

Albert provides an unprecedentedly clear, lively, and systematic new account--in the context of a Newtonian-Mechanical picture of the world--of the ultimate origins of the statistical regularities we see around us, of the temporal irreversibility of the Second Law of Thermodynamics, of the asymmetries in our epistemic access to the past and the future, and of our conviction that by acting now we can affect the future but not the past. Then, in the final section of the book, he generalizes the Newtonian picture to the quantum-mechanical case and (most interestingly) suggests a very deep potential connection between the problem of the direction of time and the quantum-mechanical measurement problem.

The book aims to be both an original contribution to the present scientific and philosophical understanding of these matters at the most advanced level, and something in the nature of an elementary textbook on the subject accessible to interested high-school students.

The Ising model provides a detailed mathematical description of ferromagnetism and is widely used in statistical physics and condensed matter physics. In this Student's Guide, the author demystifies the mathematical framework of the Ising model and provides students with a clear understanding of both its physical significance, and how to apply it successfully in their calculations. Key topics related to the Ising model are covered, including exact solutions of both finite and infinite systems, series expansions about high and low temperatures, mean-field approximation methods, and renormalization-group calculations. The book also incorporates plots, figures, and tables to highlight the significance of the results. Designed as a supplementary resource for undergraduate and graduate students, each chapter includes a selection of exercises intended to reinforce and extend important concepts, and solutions are also available for all exercises.

This book offers a compact tutorial on basic concepts and tools in quantum many-body physics, and focuses on the correlation effects produced by mutual interactions. The content is divided into three parts, the first of which introduces readers to perturbation theory. It begins with the simplest examples-hydrogen and oxygen molecules-based on their effective Hamiltonians, and looks into basic properties of electrons in solids from the perspective of localized and itinerant limits. Readers will also learn about basic theoretical methods such as the linear response theory and Green functions. The second part focuses on mean-field theory for itinerant electrons, e.g. the Fermi liquid theory and superconductivity. Coulomb repulsion among electrons is addressed in the context of high-Tc superconductivity in cuprates and iron pnictides. A recent discovery concerning hydride superconductors is also briefly reviewed. In turn, the third part highlights quantum fluctuation effects beyond the mean-field picture. Discussing the dramatic renormalization effect in the Kondo physics, it provides a clear understanding of nonperturbative interaction effects. Further it introduces readers to fractionally charged quasi-particles in one and two dimensions. The last chapter addresses the dynamical mean field theory (DMFT). The book is based on the author's long years of experience as a lecturer and researcher. It also includes reviews of recent focus topics in condensed matter physics, enabling readers to not only grasp conventional condensed matter theories but also to catch up on the latest developments in the field.

This thesis deals with two main procedures performed with the ATLAS detector at the Large Hadron Collider (LHC). The noise description in the hadronic calorimeter TileCal represents a very valuable technical job. The second part presents a fruitful physics analysis - the cross section measurement of the process p+p Z0 + .

The Monte Carlo simulations of the TileCal are described in the first part of the thesis, including a detailed treatment of the electronic noise and multiple interactions (so-called pile-up). An accurate description of both is crucial for the reconstruction of e.g. jets or hadronic tau-jets.

The second part reports a Standard Model measurement of the Z0 + process with the emphasis on the final state with an electron and a hadronically decaying tau-lepton. The Z0 + channel forms the dominant background in the search for Higgs bosons decaying into tau lepton pairs, and thus the good understanding achieved here can facilitate more sensitive Higgs detection."

This book introduces and discusses the analysis of interacting many-body complex systems exhibiting spontaneous synchronization from the perspective of nonequilibrium statistical physics. While such systems have been mostly studied using dynamical system theory, the book underlines the usefulness of the statistical physics approach to obtain insightful results in a number of representative dynamical settings. Although it is intractable to follow the dynamics of a particular initial condition, statistical physics allows to derive exact analytical results in the limit of an infinite number of interacting units. Chapter one discusses dynamical characterization of individual units of synchronizing systems as well as of their interaction and summarizes the relevant tools of statistical physics. The latter are then used in chapters two and three to discuss respectively synchronizing systems with either a first- or a second-order evolution in time. This book provides a timely introduction to the subject and is meant for the uninitiated as well as for experienced researchers working in areas of nonlinear dynamics and chaos, statistical physics, and complex systems.

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.

Arturo Carsetti According to molecular Biology, true invariance (life) can exist only within the framework of ongoing autonomous morphogenesis and vice versa. With respect to this secret dialectics, life and cognition appear as indissolubly interlinked. In this sense, for instance, the inner articulation of conceptual spaces appears to be linked to an inner functional development based on a continuous activity of selection and "anchorage" realised on semantic grounds. It is the work of "invention" and g- eration (in invariance), linked with the "rooting" of meaning, which determines the evolution, the leaps and punctuated equilibria, the conditions related to the unfo- ing of new modalities of invariance, an invariance which is never simple repetition and which springs on each occasion through deep-level processes of renewal and recovery. The selection perpetrated by meaning reveals its autonomy aboveall in its underpinning, in an objective way, the ongoing choice of these new modalities. As such it is not, then, concerned only with the game of "possibles," offering itself as a simple channel for pure chance, but with providing a channel for the articulation of the " le" in the humus of a semantic (and embodied) net in order to prepare the necessary conditionsfor a continuousrenewal and recoveryof original creativity. In effect, it is this autonomy in inventing new possible modules of incompressibility whichdeterminestheactualemergenceofnew(andtrue)creativity, whichalsotakes place through the "narration" of the effected construction.