This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of "optimal auxiliary functions" which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made. The book contains a large amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more. The book is a continuation of our previous books "Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches", Springer-2011 and "The Optimal Homotopy Asymptotic Method. Engineering Applications", Springer-2015.

This thesis presents the application of non-perturbative, or functional, renormalization group to study the physics of critical stationary states in systems out-of-equilibrium. Two different systems are thereby studied. The first system is the diffusive epidemic process, a stochastic process which models the propagation of an epidemic within a population. This model exhibits a phase transition peculiar to out-of-equilibrium, between a stationary state where the epidemic is extinct and one where it survives. The present study helps to clarify subtle issues about the underlying symmetries of this process and the possible universality classes of its phase transition. The second system is fully developed homogeneous isotropic and incompressible turbulence. The stationary state of this driven-dissipative system shows an energy cascade whose phenomenology is complex, with partial scale-invariance, intertwined with what is called intermittency. In this work, analytical expressions for the space-time dependence of multi-point correlation functions of the turbulent state in 2- and 3-D are derived. This result is noteworthy in that it does not rely on phenomenological input except from the Navier-Stokes equation and that it becomes exact in the physically relevant limit of large wave-numbers. The obtained correlation functions show how scale invariance is broken in a subtle way, related to intermittency corrections.

This volume contains papers based on presentations at the "Nagoya Winter Workshop 2015: Reality and Measurement in Algebraic Quantum Theory (NWW 2015)", held in Nagoya, Japan, in March 2015. The foundations of quantum theory have been a source of mysteries, puzzles, and confusions, and have encouraged innovations in mathematical languages to describe, analyze, and delineate this wonderland. Both ontological and epistemological questions about quantum reality and measurement have been placed in the center of the mysteries explored originally by Bohr, Heisenberg, Einstein, and Schroedinger. This volume describes how those traditional problems are nowadays explored from the most advanced perspectives. It includes new research results in quantum information theory, quantum measurement theory, information thermodynamics, operator algebraic and category theoretical foundations of quantum theory, and the interplay between experimental and theoretical investigations on the uncertainty principle. This book is suitable for a broad audience of mathematicians, theoretical and experimental physicists, and philosophers of science.

This book offers a comprehensive overview of thermodynamics. It is divided into four parts, the first of which equips readers with a deeper understanding of the fundamental principles of thermodynamics of equilibrium states and of their evolution. The second part applies these principles to a series of generalized situations, presenting applications that are of interest both in their own right and in terms of demonstrating how thermodynamics, as a theory of principle, relates to different fields. In turn, the third part focuses on non-equilibrium configurations and the dynamics of natural processes. It discusses both discontinuous and continuous systems, highlighting the interference among non-equilibrium processes, and the nature of stationary states and of fluctuations in isolated systems. Lastly, part four introduces the relation between physics and information theory, which constitutes a new frontier in fundamental research. The book includes step-by-step exercises, with solutions, to help readers to gain a fuller understanding of the subjects, and also features a series of appendices providing useful mathematical formulae. Reflecting the content of modern university courses on thermodynamics, it is a valuable resource for students and young scientists in the fields of physics, chemistry, and engineering.

This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author's extensive teaching and research experience and consulting work, the book offers a valuable guide for researchers, graduate students and professionals alike.

This book presents the Proceedings of the 54th Winter School of Theoretical Physics on Simplicity of Complexity in Economic and Social Systems, held in Ladek Zdroj, Poland, from 18 to 24 February 2018. The purpose of the book is to introduce the new interdisciplinary research that links statistical physics, and particular attention is given to link physics of complex systems, with financial analysis and sociology. The main tools used in these areas are numerical simulation of agents behavior and the interpretation of results with the help of complexity methods, therefore a background in statistical physics and in physics of phase transition is necessary to take the first steps towards these research fields called econophysics and sociophysics. In this perspective, the book is intended to graduated students and young researchers who want to begin the study of this established new area, which connects physicists, economists, sociologists and IT professionals, to better understand complexity phenomena existing not only in physics but also in complex systems being seemingly far from traditional view at physics.

This thesis investigates the combustion chemistry of cyclohexane, methylcyclohexane, and ethylcyclohexane on the basis of state-of-the-art synchrotron radiation photoionization mass spectrometry experiments, quantum chemistry calculations, and extensive kinetic modeling. It explores the initial decomposition mechanism and distribution of the intermediates, proposes a novel formation mechanism of aromatics, and develops a detailed kinetic model to predict the three cycloalkanes' combustion properties under a wide range of conditions. Accordingly, the thesis provides an essential basis for studying much more complex cycloalkanes in transport fuels and has applications in engine and fuel design, as well as emission control.

This classic text provides an excellent introduction to a new and rapidly developing field of research. Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.

Natural phenomena consist of simultaneously occurring transport processes and chemical reactions. These processes may interact with each other and may lead to self-organized structures, fluctuations, instabilities, and evolutionary systems. "Nonequilibrium Thermodynamics, 3rd edition" emphasizes the unifying role of thermodynamics in analyzing the natural phenomena.

This third edition updates and expands on the first and second editions by focusing on the general balance equations for coupled processes of physical, chemical, and biological systems. The new edition contains a new chapter on stochastic approaches to include the statistical thermodynamics, mesoscopic nonequilibrium thermodynamics, fluctuation theory, information theory, and modeling the coupled biochemical systems in thermodynamic analysis. This new addition also comes with more examples and practice problems.

A useful text for seniors and graduate students from diverse engineering and science programs to analyze some nonequilibrium, coupled, evolutionary, stochastic, and dissipative processesHighlights fundamentals of equilibrium thermodynamics, transport processes and chemical reactionsExpands the theory of nonequilibrium thermodynamics and its use in coupled transport processes and chemical reactions in physical, chemical, and biological systemsPresents a unified analysis for transport and rate processes in various time and space scalesDiscusses stochastic approaches in thermodynamic analysis including fluctuation and information theoriesHas 198 fully solved examples and 287 practice problemsAn Instructor Resource containing the Solution Manual can be obtained from the author: ydemirel2@unl.edu

Here is an accurate and readable translation of a seminal article by Henri Poincare that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincare applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations' solutions, such as orbital resonances and horseshoe orbits. Poincare wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.

This book discusses the elementary ideas and tools needed for open quantum systems in a comprehensive manner. The emphasis is given to both the traditional master equation as well as the functional (path) integral approaches. It discusses the basic paradigm of open systems, the harmonic oscillator and the two-level system in detail. The traditional topics of dissipation and tunneling, as well as the modern field of quantum information, find a prominent place in the book. Assuming a basic background of quantum and statistical mechanics, this book will help readers familiarize with the basic tools of open quantum systems. Open quantum systems is the study of quantum dynamics of the system of interest, taking into account the effects of the ambient environment. It is ubiquitous in the sense that any system could be envisaged to be surrounded by its environment which could naturally exert its influence on it. Open quantum systems allows for a systematic understanding of irreversible processes such as decoherence and dissipation, of the essence in order to have a correct understanding of realistic quantum dynamics and also for possible implementations. This would be essential for a possible development of quantum technologies.

This book presents the statistical theory of complex wave scattering and quantum transport in physical systems which have chaotic classical dynamics, as in the case of microwave cavities and quantum dots, or which possess quenched randomness, as in the case of disordered conductors - with an emphasis on mesoscopic fluctuations. The statistical regularity of the phenomena is revealed in a natural way by adopting a novel maximum-entropy approach. Shannon's information entropy is maximised, subject to the symmetries and constraints which are physically relevant, within the powerful and non-perturbative theory of random matrices; this is a most distinctive feature of the book. Aiming for a self-contained presentation, the quantum theory of scattering, set in the context of quasi-one-dimensional, multichannel systems, and related directly to scattering problems in mesoscopic physics, is introduced in chapters two and three. The linear-response theory of quantum electronic transport, adapted to the context of mesoscopic systems, is discussed in chapter four. These chapters, together with chapter five on the maximum-entropy approach and chapter eight on weak localization, have been written in a most pedagogical style, suitable for use on graduate courses. In chapters six and seven, the problem of electronic transport through classically chaotic cavities and quasi-one-dimensional disordered systems is discussed. Many exercises are included, most of which are worked through in detail, aiding graduate students, teachers, and research scholars interested in the subject of quantum transport through disordered and chaotic systems.

This book offers a didactic and a self-contained treatment of the physics of liquid and flowing matter with a statistical mechanics approach. Experimental and theoretical methods that were developed to study fluids are now frequently applied to a number of more complex systems generically referred to as soft matter. As for simple liquids, also for complex fluids it is important to understand how their macroscopic behavior is determined by the interactions between the component units. Moreover, in recent years new and relevant insights have emerged from the study of anomalous phases and metastable states of matter. In addition to the traditional topics concerning fluids in normal conditions, the authors of this book discuss recent developments in the field of disordered systems in condensed and soft matter. In particular they emphasize computer simulation techniques that are used in the study of soft matter and the theories and study of slow glassy dynamics. For these reasons the book includes a specific chapter about metastability, supercooled liquids and glass transition. The book is written for graduate students and active researchers in the field.

Philosophy in Reality offers a new vision of the relation between science and philosophy in the framework of a non-propositional logic of real processes, grounded in the physics of the real world. This logical system is based on the work of the Franco-Romanian thinker Stephane Lupasco (1900-1988), previously presented by Joseph Brenner in the book Logic in Reality (Springer, 2008). The present book was inspired in part by the ancient Chinese Book of Changes (I Ching) and its scientific-philosophical discussion of change. The emphasis in Philosophy in Reality is on the recovery of dialectics and semantics from reductionist applications and their incorporation into a new synthetic paradigm for knowledge. Through an original re-interpretation of both classical and modern Western thought, this book addresses philosophical issues in scientific fields as well as long-standing conceptual problems such as the origin, nature and role of meaning, the unity of knowledge and the origin of morality. In a rigorous transdisciplinary manner, it discusses foundational and current issues in the physical sciences - mathematics, information, communication and systems theory and their implications for philosophy. The same framework is applied to problems of the origins of society, the transformation of reality by human subjects, and the emergence of a global, sustainable information society. In summary, Philosophy in Reality provides a wealth of new perspectives and references, supporting research by both philosophers and physical and social scientists concerned with the many facets of reality.

This textbook presents a concise yet detailed introduction to quantum physics. Concise, because it condenses the essentials to a few principles. Detailed, because these few principles - necessarily rather abstract - are illustrated by several telling examples. A fairly complete overview of the conventional quantum mechanics curriculum is the primary focus, but the huge field of statistical thermodynamics is covered as well. The text explains why a few key discoveries shattered the prevailing broadly accepted classical view of physics. First, matter appears to consist of particles which, when propagating, resemble waves. Consequently, some observable properties cannot be measured simultaneously with arbitrary precision. Second, events with single particles are not determined, but are more or less probable. The essence of this is that the observable properties of a physical system are to be represented by non-commuting mathematical objects instead of real numbers. Chapters on exceptionally simple, but highly instructive examples illustrate this abstract formulation of quantum physics. The simplest atoms, ions, and molecules are explained, describing their interaction with electromagnetic radiation as well as the scattering of particles. A short introduction to many particle physics with an outlook on quantum fields follows. There is a chapter on maximally mixed states of very large systems, that is statistical thermodynamics. The following chapter on the linear response to perturbations provides a link to the material equations of continuum physics. Mathematical details which would hinder the flow of the main text have been deferred to an appendix. The book addresses university students of physics and related fields. It will attract graduate students and professionals in particular who wish to systematize or refresh their knowledge of quantum physics when studying specialized texts on solid state and materials physics, advanced optics, and other modern fields.

This thesis reveals how the feedback trap technique, developed to trap small objects for biophysical measurement, could be adapted for the quantitative study of the thermodynamic properties of small systems. The experiments in this thesis are related to Maxwell's demon, a hypothetical intelligent, "neat fingered" being that uses information to extract work from heat, apparently creating a perpetual-motion machine. The second law of thermodynamics should make that impossible, but how? That question has stymied physicists and provoked debate for a century and a half. The experiments in this thesis confirm a hypothesis proposed by Rolf Landauer over fifty years ago: that Maxwell's demon would need to erase information, and that erasing information-resetting the measuring device to a standard starting state-requires dissipating as much energy as is gained. For his thesis work, the author used a "feedback trap" to study the motion of colloidal particles in "v irtual potentials" that may be manipulated arbitrarily. The feedback trap confines a freely diffusing particle in liquid by periodically measuring its position and applying an electric field to move it back to the origin.

In this book, the authors give an up-to-date account of thermoluminescence (TL) and other thermally stimulated phenomena. Although most recent experimental results of TL in different materials are described in some detail, the main emphasis in the present book is on general processes, and the approach is more theoretical. Thus the details of the possible processes which can take place during the excitation of the sample, and during its heating, are carefully analysed. The methods for analysing TL glow curves are critically discussed, and recommendations as to their application are made. Also discussed is the expected behavior of these phenomena as functions of the experimental parameters, for example, dose of excitation. The consequences of the main applications of TL (for example, radiation dosimetry) are also discussed in detail as are the similarities and dissimilarities of other thermally stimulated phenomena, and the simultaneous measurements of the latter and TL.

Features twenty-five chapter contributions from an international array of distinguished academics based in Asia, Eastern and Western Europe, Russia, and the USA. This multi-author contributed volume provides an up-to-date and authoritative overview of cutting-edge themes involving the thermal analysis, applied solid-state physics, micro- and nano-crystallinity of selected solids and their macro- and microscopic thermal properties. Distinctive chapters featured in the book include, among others, calorimetry time scales from days to microseconds, glass transition phenomena, kinetics of non-isothermal processes, thermal inertia and temperature gradients, thermodynamics of nanomaterials, self-organization, significance of temperature and entropy. Advanced undergraduates, postgraduates and researchers working in the field of thermal analysis, thermophysical measurements and calorimetry will find this contributed volume invaluable. This is the third volume of the triptych volumes on thermal behaviour of materials; the previous two receiving thousand of downloads guaranteeing their worldwide impact.

Starting from a broad overview of heat transport based on the Boltzmann Transport Equation, this book presents a comprehensive analysis of heat transport in bulk and nanomaterials based on a kinetic-collective model (KCM). This has become key to understanding the field of thermal transport in semiconductors, and represents an important stride. The book describes how heat transport becomes hydrodynamic at the nanoscale, propagating very much like a viscous fluid and manifesting vorticity and friction-like behavior. It introduces a generalization of Fourier's law including a hydrodynamic term based on collective behavior in the phonon ensemble. This approach makes it possible to describe in a unifying way recent experiments that had to resort to unphysical assumptions in order to uphold the validity of Fourier's law, demonstrating that hydrodynamic heat transport is a pervasive type of behavior in semiconductors at reduced scales.

This book continues the process of systematization of knowledge about convection. It is important to put the current knowledge on weakly and strongly stratified convection in order, and provide a comprehensive description of the marginal, weakly nonlinear and fully developed stages of convective flow in both cases. The book provides a short compendium of knowledge on the linear and weakly nonlinear limits of the Boussinesq convection, and a review of the theory on fully developed Boussinesq convection. The third chapter is devoted to a detailed derivation and a study of the three aforementioned stages of stratified (anelastic) convection, with a full solution in the marginal stage provided for the first time. Detailed and systematic explanations are given. The book is intended mainly as a textbook for courses on hydrodynamics and convective flows, for the use of lecturers and students; however, it also serves for the entire scientific community as a practical reference.

This volume looks afresh at the life and works of Lord Kelvin including his standing and relationships with Charles Darwin, T. S Huxley and the X-club, thereby throwing new light on the nineteenth-century conflict between the British energy and biology specialists. It focuses on two principal issues. Firstly, there is the contribution made by Kelvin to the formulation of the Laws of Thermodynamics, both personal and in the content of the scientific communications exchanged with other workers, such as Joule and Clausius. Secondly, there is Kelvin's impact on the wider field of science such as thermoelectricity and geology (determination of the age of the earth). Of late a number of studies and initiatives, including the Centenary celebrations of Kelvin's death and exhibits such as that of the 'Revolutionary Scientist' in the Hunterian Museum, Glasgow, have been undertaken aiding the redefinition of Kelvin's greatness and achievements. The book also raises awareness to 'improve our approach to the teaching of elementary thermodynamics by attempting to empathise with Kelvin's perspective'.It is completed by a full biography, overviews of various monuments to his memory, and short 'Stories in Pictures' on the Atlantic cable, Maxwell's Demon, the universities associated with the development of thermodynamics and the Royal Society of Edinburgh. Scientists and engineers with an interest in thermodynamics and anyone interested in the work of Lord Kelvin will find benefit in Kelvin, Thermodynamics and the Natural World.

This book provides deep insight into the physical quantity known as chemical activity. The author probes deep into classical thermodynamics in Part I, and then into statistical thermodynamics in Part II, to provide the necessary background. The treatment has been streamlined by placing some background material in appendices. Chemical Activity is of interest not only to those in chemical thermodynamics, but also to chemical engineers working with mass transfer and its applications - for example, separation methods.

Maximum Dissipation: Non-Equilibrium Thermodynamics and its Geometric Structure explores the thermodynamics of non-equilibrium processes in materials. The book develops a general technique created in order to construct nonlinear evolution equations describing non-equilibrium processes, while also developing a geometric context for non-equilibrium thermodynamics. Solid materials are the main focus in this volume, but the construction is shown to also apply to fluids. This volume also: * Explains the theory behind thermodynamically-consistent construction of non-linear evolution equations for non-equilibrium processes * Provides a geometric setting for non-equilibrium thermodynamics through several standard models, which are defined as maximum dissipation processes * Emphasizes applications to the time-dependent modeling of soft biological tissue Maximum Dissipation: Non-Equilibrium Thermodynamics and its Geometric Structure will be valuable for researchers, engineers and graduate students in non-equilibrium thermodynamics and the mathematical modeling of material behavior.

This volume constitutes the proceedings of NetSci-X 2020: the Sixth International School and Conference on Network Science, which was held in Tokyo, Japan, in January 2020. NetSci-X is the Network Science Society's winter conference series that covers a wide variety of interdisciplinary topics on networks. Participants come from various fields, including (but not limited to): mathematics, physics, computer science, social sciences, management and marketing sciences, organization science, communication science, systems science, biology, ecology, neuroscience, medicine, as well as business. This volume consists of contributed papers that have been accepted to NetSc-X 2020 through a rigorous peer review process. Researchers, students, and professionals will gain first-hand information about today's cutting-edge research frontier of network science.