This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.

This work tries to provide an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, we will emphasize the role of gaussian distributions and their relations with the mean field approximation and Landau's theory of critical phenomena. We will show that quasi-gaussian or mean-field approximations cannot describe correctly phase transitions in three space dimensions. We will assign this difficulty to the coupling of very different physical length scales, even though the systems we will consider have only local, that is, short range interactions. To analyze the unusual situation, a new concept is required: the renormalization group, whose fixed points allow understanding the universality of physical properties at large distance beyond mean-field theory. In the continuum limit, critical phenomena can be described by quantum field theories. In this framework, the renormalization group is directly related to the renormalization process, that is, the necessity to cancel the infinities that arise in straightforward formulations of the theory. We thus discuss the renormalization group in the context of various relevant field theories. This leads to proofs of universality and to efficient tools for calculating universal quantities in a perturbative framework. Finally, we construct a general functional renormalization group, which can be used when perturbative methods are inadequate.

This thesis presents pioneering experimental and numerical studies on three aspects of the combustion characteristics of lean premixed syngas/air flames, namely the laminar flame speed, extinction limit and flammability limit. It illustrates a new extinction exponent concept, which enriches the combustion theory. Above all, the book provides the following: a) a series of carefully measured data and theoretical analyses to reveal the intrinsic mechanisms of the fuel composition effect on the propagation and extinction of lean syngas/air flames; b) a mixing model and correlation to predict the laminar flame speed of multi-component syngas fuels, intended for engineering computations; c) a new "extinction exponent" concept to describe the critical effects of chemical kinetics on the extinction of lean premixed syngas/air flames; and d) the effects and mechanism of the dilution of incombustible components on lean premixed syngas/air flames and the preferential importance among the thermal, chemical and diffusion effects.

This volume provides a compact presentation of modern statistical physics at an advanced level, from the foundations of statistical mechanics to the main modern applications of statistical physics. Special attention is given to new approaches, such as quantum field theory methods and non-equilibrium problems. This second, revised edition is expanded with biographical notes contextualizing the main results in statistical physics.

This unique book gives a comprehensive account of new mathematical tools used to solve polygon problems.

In the 20th and 21st centuries, many problems in mathematics, theoretical physics and theoretical chemistry - and more recently in molecular biology and bio-informatics - can be expressed as counting problems, in which specified graphs, or shapes, are counted.

One very special class of shapes is that of polygons. These are closed, connected paths in space. We usually sketch them in two-dimensions, but they can exist in any dimension. The typical questions asked include "how many are there of a given perimeter?," "how big is the average polygon of given perimeter?," and corresponding questions about the area or volume enclosed. That is to say "how many enclosing a given area?" and "how large is an average polygon of given area?" Simple though these questions are to pose, they are extraordinarily difficult to answer. They are important questions because of the application of polygon, and the related problems of polyomino and polycube counting, to phenomena occurring in the natural world, and also because the study of these problems has been responsible for the development of powerful new techniques in mathematics and mathematical physics, as well as in computer science. These new techniques then find application more broadly.

The book brings together chapters from many of the major contributors in the field. An introductory chapter giving the history of the problem is followed by fourteen further chapters describing particular aspects of the problem, and applications to biology, to surface phenomena and to computer enumeration methods.

Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.

In the present volume numerous descriptions of Ram accelerators are presented. These descriptions provide good overview on the progress made and the present state of the Ram accelerator technology worldwide. In addition, articles describing light gas gun, ballistic range including a chapter dealing with shock waves in solids are given. Along with the technical description of considered facilities, samples of obtained results are also included. Each chapter is written by an expert in the described topic providing a comprehensive description of the discussed phenomena.

This book explores applications of computational intelligence in key and emerging fields of engineering, especially with regard to condition monitoring and fault diagnosis, inverse problems, decision support systems and optimization. These applications can be beneficial in a broad range of contexts, including: water distribution networks, manufacturing systems, production and storage of electrical energy, heat transfer, acoustic levitation, uncertainty and robustness of infinite-dimensional objects, fatigue failure prediction, autonomous navigation, nanotechnology, and the analysis of technological development indexes. All applications, mathematical and computational tools, and original results are presented using rigorous mathematical procedures. Further, the book gathers contributions by respected experts from 22 different research centers and eight countries: Brazil, Cuba, France, Hungary, India, Japan, Romania and Spain. The book is intended for use in graduate courses on applied computation, applied mathematics, and engineering, where tools like computational intelligence and numerical methods are applied to the solution of real-world problems in emerging areas of engineering.

In this thesis, the author describes the development of a software framework to systematically construct a particular class of weakly coupled free fermionic heterotic string models, dubbed gauge models. In their purest form, these models are maximally supersymmetric (N = 4), and thus only contain superpartners in their matter sector. This feature makes their systematic construction particularly efficient, and they are thus useful in their simplicity. The thesis first provides a brisk introduction to heterotic strings and the spin-structure construction of free fermionic models. Three systematic surveys are then presented, and it is conjectured that these surveys are exhaustive modulo redundancies. Finally, the author presents a collection of metaheuristic algorithms for searching the landscape for models with a user-specified spectrum of phenomenological properties, e.g. gauge group and number of spacetime supersymmetries. Such algorithms provide the groundwork for extended generic free fermionic surveys.

One common characteristics of a complex system is its ability to withstand major disturbances and the capacity to rebuild itself. Understanding how such systems demonstrate resilience by absorbing or recovering from major external perturbations requires both quantitative foundations and a multidisciplinary view on the topic.
This book demonstrates how new methods can be used to identify the actions favouring the recovery from perturbations. Examples discussed include bacterial biofilms resisting detachment, grassland savannahs recovering from fire, the dynamics of language competition and Internet social networking sites overcoming vandalism.
The reader is taken through an introduction to the idea of resilience and viability and shown the mathematical basis of the techniques used to analyse systems. The idea of individual or agent-based modelling of complex systems is introduced and related to analytically tractable approximations of such models. A set of case studies illustrates the use of the techniques in real applications, and the final section describes how one can use new and elaborate software tools for carrying out the necessary calculations.
The book is intended for a general scientific audience of readers from the natural and social sciences, yet requires some mathematics to gain a full understanding of the more theoretical chapters.
It is an essential point of reference for those interested in the practical application of the concepts of resilience and viability

In this volume we continue the logical development of the work begun in Volume I, and the equilibrium theory now becomes a very special case of the exposition presented here. Once a departure is made from equilibrium, however, the problems become deeper and more subtle-and unlike the equilibrium theory, many aspects of nonequilibrium phenomena remain poorly understood. For over a century a great deal of effort has been expended on the attempt to develop a comprehensive and sensible description of nonequilibrium phenomena and irreversible processes. What has emerged is a hodgepodge of ad hoc constructs that do little to provide either a firm foundation, or a systematic means for proceeding to higher levels of understanding with respect to ever more complicated examples of nonequilibria. Although one should rightfully consider this situation shameful, the amount of effort invested testifies to the degree of difficulty of the problems. In Volume I it was emphasized strongly that the traditional exposition of equilibrium theory lacked a certain cogency which tended to impede progress with extending those considerations to more complex nonequilibrium problems. The reasons for this were adduced to be an unfortunate reliance on ergodicity and the notions of kinetic theory, but in the long run little harm was done regarding the treatment of equilibrium problems. On the nonequilibrium level the potential for disaster increases enormously, as becomes evident already in Chapter 1.

"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)

This two-volume work provides a comprehensive study of the statistical mechanics of lattice models. It introduces readers to the main topics and the theory of phase transitions, building on a firm mathematical and physical basis. Volume 1 contains an account of mean-field and cluster variation methods successfully used in many applications in solid-state physics and theoretical chemistry, as well as an account of exact results for the Ising and six-vertex models and those derivable by transformation methods.

This book studies the collision, coalescence and deposition of nanoparticles in stagnation flames. With the help of synthesis experiments, in-situ laser diagnostics and molecular dynamics simulations, it investigates the growth of nanoparticles in flames and their deposition in boundary layers at a macroscopic flow field scale, as well as particle and molecular scale issues such as the interaction force between particles, how the collision rate is enhanced by attractive forces, and how the nano-scale coalescence process is influenced by the high surface curvature - all of which are crucial to understanding nanoparticle transport phenomena at high temperatures. The book also reports on a novel in-situ laser diagnostics phenomenon called phase-selective laser-induced breakdown spectroscopy and related applications for tracing gas-to-particle transitions and measuring local particle volume fractions in nano-aerosols.

Most of the interesting and difficult problems in statistical mechanics arise when the constituent particles of the system interact with each other with pair or multipartiele energies. The types of behaviour which occur in systems because of these interactions are referred to as cooperative phenomena giving rise in many cases to phase transitions. This book and its companion volume (Lavis and Bell 1999, referred to in the text simply as Volume 1) are princi pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this subject has developed very rapidly over the last thirty years. ' In our choice of topics we have tried to present a good range of fundamental theory and of applications, some of which reflect our own interests. A broad division of material can be made between exact results and ap proximation methods. We have found it appropriate to inelude some of our discussion of exact results in this volume and some in Volume 1. Apart from this much of the discussion in Volume 1 is concerned with mean-field theory. Although this is known not to give reliable results elose to a critical region, it often provides a good qualitative picture for phase diagrams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available. In this volume our main concern is with scaling theory, algebraic methods and the renormalization group."

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology-and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a 'recipe book' full of tried and tested, successful engineering applications

Deployment of Carbon Capture and Storage: Insights, Case Studies and Best Practices presents the latest research and technologies on Carbon Capture and Storage (CCS), building on the topics to provide case studies and lesson learned from early stage projects. The book highlights CCS storage technologies deployed at scale to offer readers insights and guidance that will ensure they make sound decisions when developing CCS programs. Cost and risk minimization techniques are included to minimize cost and risk for wide-scale commercial deployment required by 2050. Global case studies on CCS technology and high TLR provide readers with unique insight into worldwide activity. Readers will gain a thorough understanding of the full CCS chain as applied across multiple settings including energy, chemical, geological and environmental industries, as well as an authoritative understanding of international policy and regulation factors.

Observation, Prediction and Simulation of Phase Transitions in Complex Fluids presents an overview of the phase transitions that occur in a variety of soft-matter systems: colloidal suspensions of spherical or rod-like particles and their mixtures, directed polymers and polymer blends, colloid--polymer mixtures, and liquid-forming mesogens. This modern and fascinating branch of condensed matter physics is presented from three complementary viewpoints. The first section, written by experimentalists, emphasises the observation of basic phenomena (by light scattering, for example). The second section, written by theoreticians, focuses on the necessary theoretical tools (density functional theory, path integrals, free energy expansions). The third section is devoted to the results of modern simulation techniques (Gibbs ensemble, free energy calculations, configurational bias Monte Carlo). The interplay between the disciplines is clearly illustrated. For all those interested in modern research in equilibrium statistical mechanics.

This book presents the theory of periodic conjugate heat transfer in a detailed way. The effects of thermophysical properties and geometry of a solid body on the commonly used and experimentally determined heat transfer coefficient are analytically presented from a general point of view. The main objective of the book is a simplified description of the interaction between a solid body and a fluid as a boundary value problem of the heat conduction equation for the solid body. At the body surface, the true heat transfer coefficient is composed of two parts: the true mean value resulting from the solution of the steady state heat transfer problem and a periodically variable part, the periodic time and length to describe the oscillatory hydrodynamic effects. The second edition is extended by (i) the analysis of stability boundaries in helium flow at supercritical conditions in a heated channel with respect to the interaction between a solid body and a fluid; (ii) a periodic model and a method of heat transfer simulation in a fluid at supercritical pressure and (iii) a periodic quantum-mechanical model for homogeneous vapor nucleation in a fluid with respect to nanoscale effects.

This work introduces a new method for analysing measured signals: nonlinear mode decomposition, or NMD. It justifies NMD mathematically, demonstrates it in several applications and explains in detail how to use it in practice. Scientists often need to be able to analyse time series data that include a complex combination of oscillatory modes of differing origin, usually contaminated by random fluctuations or noise. Furthermore, the basic oscillation frequencies of the modes may vary in time; for example, human blood flow manifests at least six characteristic frequencies, all of which wander in time. NMD allows us to separate these components from each other and from the noise, with immediate potential applications in diagnosis and prognosis. Mat Lab codes for rapid implementation are available from the author. NMD will most likely come to be used in a broad range of applications.

This book consists of peer-reviewed articles and reviews presented as lectures at the Sixth International Symposium on Thermal Engineering and Sciences for Cold Regions in Darmstadt, Germany. It addresses all relevant aspects of thermal physics and engineering in cold regions, such as the Arctic regions. These environments present many unique freezing and melting phenomena and the relevant heat and mass transfer processes are of basic importance with respect to both the technological applications and the natural context in which they occur. Intended for physicists, engineers, geoscientists, climatologists and cryologists alike, these proceedings cover topics such as: ice formation and decay, heat conduction with phase change, convection with freezing and melting, thermal properties at low temperature, frost heave and permafrost, climate impact in cold regions, thermal design of structures, bio-engineering in cold regions, and many more.

Thermodiffusion describes the coupling between a temperature gradient and a resulting mass flux. Traditionally, the focus has been on simple fluids, and it is now extending to more complex systems such as electrolytes, polymers, colloidal dispersions and magnetic fluids. This book widens the scope even further by including applications in ionic solids. Written as a set of tutorial reviews, it will be useful to experts, nonspecialist researchers and postgraduate students alike.

This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike.

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.

This textbook concerns thermal properties of bulk matter and is aimed at advanced undergraduate or first-year graduate students in a range of programs in science or engineering. It provides an intermediate level presentation of statistical thermodynamics for students in the physical sciences (chemistry, nanosciences, physics) or related areas of applied science/engineering (chemical engineering, materials science, nanotechnology engineering), as they are areas in which statistical mechanical concepts play important roles. The book enables students to utilize microscopic concepts to achieve a better understanding of macroscopic phenomena and to be able to apply these concepts to the types of sub-macroscopic systems encountered in areas of nanoscience and nanotechnology.