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Non-equilibrium Statistical Physics with Application to Disordered Systems
by Manuel Osvaldo CáceresThis textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text. It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluctuations around metastable and unstable points are given. It also describes relaxation theory of non-stationary Markov periodic in time systems. The theory of finite and infinite transport in disordered networks, with a discussion of the issue of anomalous diffusion is introduced. Further, it provides the basis for establishing the relationship between quantum aspects of the theory of linear response and the calculation of diffusion coefficients in amorphous systems.
Non-equilibrium Thermodynamics (Lecture Notes in Physics #1007)
by Andrea Di VitaThe importance of thermodynamics, particularly its Second Principle, to all branches of science in which systems with very large numbers of particles are involved cannot be overstated. This book offers a panoramic view of non-equilibrium thermodynamics. Perhaps the two most attractive aspects of thermodynamic equilibrium are its stability and its independence from the specifics of the particular system involved. Does an equivalent exist for non-equilibrium thermodynamics? Many researchers have tried to describe such stability in the same way that the Second Principle describes the stability of thermodynamic equilibrium - and failed. Most of them invoked either entropy, or its production rate, or some modified version of it. In their efforts, however, those researchers have found a lot of useful stability criteria for far-from-equilibrium states. These criteria usually take the form of variational principles, in terms of the minimization or maximization of some quantity. The aim of this book is to discuss these variational principles by highlighting the role of macroscopic quantities. This book is aimed at a wider audience than those most often exposed to the criteria described, i.e., undergraduates in STEM, as well as the usual interested and invested professionals.
Non-equilibrium Transport of Non-uniform Suspended Load (Hydroscience and Engineering)
by Qiwei Han Mingmin HeThe book is based on stochastic theory of sediment motion, particularly the theory of transition intensities. It provides a complete theory and equation system of non-equilibrium transport of non-uniform suspended load. The content proposed theory reports, for the first time in literature, the general boundary condition of diffusion equations of non-equilibrium transport with transition intensities. The book also introduces the theoretical expressions of size distribution of the carrying sediment capacity, efficient bed material grade, and saturation recovery coefficient This book describes the application of non-equilibrium transport theory and provides solutions to some long-standing unsolved controversial problems related to sediment transport. It establishes a generic mathematic model of reservoir sedimentation and river channel evolution; illustrates the same transport regulars of wash load and bed material load; demonstrates the multi-valued nature of carrying-sediment capacity and its single-valued consideration; and describes the mechanism of bed material coarsening. This book is of interest to a wide audience including students, technicians, and academics, primarily working in the field of river hydra-dynamics. In addition, this book receives attention from the research community working in fields, such as hydrogeology, hydraulic engineering, river navigation, wastewater treatment, and environmental protection
Non-fickian Solute Transport in Porous Media
by Don KulasiriThe advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick's law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.
Non-fickian Solute Transport in Porous Media: A Mechanistic and Stochastic Theory (Advances in Geophysical and Environmental Mechanics and Mathematics)
by Don KulasiriThe advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick’s law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.
Non-invertible Symmetry in 4-Dimensional Z2 Lattice Gauge Theory (Springer Theses)
by Masataka KoideThis book provides a method for concretely constructing defects that represent non-invertible symmetries in four-dimensional lattice gauge theory. In terms of generalized symmetry, a symmetry is considered to be equivalent to a topological operator whose value does not change even if the shape is topologically transformed. Even for models that lack symmetry in the traditional sense and are difficult to analyze, it is possible to analyze them as long as a generalized symmetry exists. Therefore, generalized symmetry is important for the non-perturbative analysis of quantum field theory. Some topological operators have no group structure, and the corresponding symmetries are called non-invertible symmetries. Concrete examples of non-invertible symmetries in higher-dimensional theories were discovered around 2020, and they have been actively studied as a field of generalized symmetries since then. This book explains the non-invertible symmetry represented by the Kramers-Wannier-Wegner duality, which was found firstly in a four-dimensional theory, represented by three-dimensional defects. This book is intended for those with preliminary knowledge of quantum field theory and statistical mechanics.
Non-linear Data Analysis on the Sphere
by Gregor RossmanithThis work deals with the search for signatures of non-Gaussianities in the cosmic microwave background (CMB). Probing Gaussianity in the CMB addresses one of the key questions in modern cosmology because it allows us to discriminate between different models of inflation, and thus concerns a fundamental part of the standard cosmological model. The basic goal here is to adapt complementary methods stemming from the field of complexity science to CMB data analysis. Two key concepts, namely the method of surrogates and estimators for local scaling properties, are applied to CMB data analysis. All results show strong non-Gaussianities and pronounced asymmetries. The consistency of the full sky and cut sky results shows convincingly for the first time that the influence of the Galactic plane is not responsible for these deviations from Gaussianity and isotropy. The findings seriously call into question predictions of isotropic cosmologies based on the widely accepted single field slow roll inflation model.
Non-perturbative Renormalization Group Approach to Some Out-of-Equilibrium Systems: Diffusive Epidemic Process and Fully Developed Turbulence (Springer Theses)
by Malo TarpinThis 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.
Non-representational Theory (Key Ideas in Geography)
by Paul SimpsonNon-representational Theory explores a range of ideas which have recently engaged geographers and have led to the development of an alternative approach to the conception, practice, and production of geographic knowledge. Non-representational Theory refers to a key body of work that has emerged in geography over the past two and a half decades that emphasizes the importance of practice, embodiment, materiality, and process to the ongoing formation of social life. This title offers the first sole-authored, accessible introduction to this work and its impact on geography. Without being prescriptive the text provides a general explanation of what Non-representational Theory is. This includes discussion of the disciplinary context it emerged from, the key ideas and themes that characterise work associated with Non-representational Theory, and the theoretical points of reference that inspires it. The book then explores a series of conjunctions of ‘Non-representational Theory and...’, taking an area of geographic enquiry and exploring the impact Non-representational Theory has had on how it is researched and understood. This includes the relationships between Non-representational Theory and Practice, Affect, Materiality, Landscape, Performance, and Methods. Critiques of Non-representational Theory are also broached, including reflections on issues on identity, power, and difference. The text draws together the work of a range of established and emerging scholars working on the development of non-representational theories, allowing scholars from geography and other disciplines to access and assess the animating potential of such work. This volume is essential reading for undergraduates and post-graduate students interested in the social, cultural, and political geographies of everyday living.
Non-self-adjoint Schrödinger Operator with a Periodic Potential
by Oktay VelievThis book gives a complete spectral analysis of the non-self-adjoint Schrödinger operator with a periodic complex-valued potential. Building from the investigation of the spectrum and spectral singularities and construction of the spectral expansion for the non-self-adjoint Schrödinger operator, the book features a complete spectral analysis of the Mathieu-Schrödinger operator and the Schrödinger operator with a parity-time (PT)-symmetric periodic optical potential. There currently exists no general spectral theorem for non-self-adjoint operators; the approaches in this book thus open up new possibilities for spectral analysis of some of the most important operators used in non-Hermitian quantum mechanics and optics. Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is ideally suited for graduate students at the intersection of physics and mathematics.
Non-standard Problems in Basin Modelling
by Yurii GalushkinThis book details how the GALO system of basin modelling may be used in the analysis of actual, non-standard problems of geology. It begins by addressing the tectonic subsidence of sedimentary basins, and goes on to consider the problems of maturation of organic matter and hydrocarbon generation in the vicinity of intrusions and subtrappean sedimentary complexes. Lastly, the book discusses the formation of temperature and heat flow distributions with depth due to the sharp climate variations in the Quaternary, which was marked by repeated formation and degradation of permafrost. The book studies the application of the GALO basin modelling system to the three problems mentioned above. Employing the GALO system provides a unique opportunity to assess the amplitude and duration of the stretching and thermal activation of the basin lithosphere, and to study in detail the formation of a maturity aureole of organic matter in the basin's subtrappean sedimentary cover. This book offers a valuable resource for all graduate students and professionals interested in numerical modelling of the thermal evolution of sedimentary basins. It will also be of great interest to petroleum geologists engaged in oil and gas exploration in the trap provinces of the world. Lastly, it will benefit those students and geologists dealing with the thermal field of sedimentary blankets in actual and degraded permafrost areas.
Non-standard Spatial Statistics and Spatial Econometrics
by Daniel A. Griffith Jean H. PaelinckDespite spatial statistics and spatial econometrics both being recent sprouts of the general tree "spatial analysis with measurement"--some may remember the debate after WWII about "theory without measurement" versus "measurement without theory"--several general themes have emerged in the pertaining literature. But exploring selected other fields of possible interest is tantalizing, and this is what the authors intend to report here, hoping that they will suscitate interest in the methodologies exposed and possible further applications of these methodologies. The authors hope that reactions about their publication will ensue, and they would be grateful to reader(s) motivated by some of the research efforts exposed hereafter letting them know about these experiences.
Non-state Actors in the Arctic Region (Springer Polar Sciences)
by Nikolas Sellheim Dwayne Ryan MenezesThis book comprehensively discusses the role that non-state actors play in the Arctic and assesses the normative role of these actors. Beyond any organised forum, there are actors that have a significant impact on the way the Arctic is developed, adjudicated, managed, perceived, presented and represented. This book complements the literature on non-state actors in international law and international security, world politics and international relations and provides a geographical account of their role for the Arctic. The book content is not limited to a specific discipline, but takes into account different approaches to the topic. This means that it contains three types of contributions: research articles, shorter research notes and commentaries. While the research articles constitute the main body of the work, it is also the research notes which provide an insight into issues related to the topic of the book.
Non-technological Innovations for Sustainable Transport
by Alexandra HyardExamining non-technological innovations for environmentally and socially-friendly transport, this book provides the reader with a better understanding of this often overlooked topic. It features four illustrative case studies, and presents a concise review of the core transport modes (road, rail and marine transport). Transport companies are compelled to innovate due to economic and environmental pressures, and the aim of these innovations is to improve fuel efficiency and ultimately to transform energy use in the transport sector. Whilst many of these innovations are technological, they can conversely be non-technological in nature. This book is intended for students and researchers interested in economics, environmental economics and economics of innovation. It also offers a useful resource to industry professionals interested in ecology and transport.
Noncommutative Geometry and Cayley-smooth Orders
by Lieven Le BruynNoncommutative Geometry and Cayley-smooth Orders explains the theory of Cayley-smooth orders in central simple algebras over function fields of varieties. In particular, the book describes the etale local structure of such orders as well as their central singularities and finite dimensional representations.After an introduction to partial d
Noncommutative Geometry and Particle Physics (Mathematical Physics Studies)
by Walter D. van SuijlekomThis book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model. The second edition of the book contains numerous additional sections and updates. More examples of noncommutative manifolds have been added to the first part to better illustrate the concept of a noncommutative spin manifold and to showcase some of the key results in the field, such as the local index formula. The second part now includes the complete noncommutative geometric description of particle physics models beyond the Standard Model. This addition is particularly significant given the developments and discoveries at the Large Hadron Collider at CERN over the last few years. Additionally, a chapter on the recent progress in formulating noncommutative quantum theory has been included. The book is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry.
Nondestructive Evaluation and Monitoring Technologies, Documentation, Diagnosis and Preservation of Cultural Heritage (Springer Proceedings in Materials)
by Antonia Moropoulou Ahmad OsmanThis book highlights the benefits of Non-Destructive Testing (NDT) methods and their applications on several cultural heritage sites including the Holy Selphuchre Monitoring System in Jerusalem. This book demonstrates Nondestructive sensing technologies and inspection modules as main tools for documentation, diagnosis, characterization, preservation planning, monitoring and quality of restoration, assessment and evaluation of material and preservation work.
Nondestructive Testing for Archaeology and Cultural Heritage: A Practical Guide And New Perspectives
by Giovanni LeucciThis textbook provides a general introduction to the most important nondestructive testing (NDT) exploration methods for cultural heritage sites. It and highlights the application of NDT exploration methods to archaeology and monumental property. The ability to gauge the extent of an archaeological deposit or the state of preservation of artefacts without resorting to destructive actions is extremely useful in identifying unknown or potential artefacts, and can help to understand and approach a given site in a more targeted manner, both for excavation and restoration operations. This book describes the main physical principles, campaign procedures, and processing and interpretation techniques of NDT, while also introducing a new technique and algorithm for data acquisition and processing. A large section of the book is devoted to actual on-site applications, and focuses on significant historical-archaeological sites in Italy and Turkey. The book offers an essential reference guide for students and scientists in archaeology, geophysics, architecture, and the engineering disciplines, as well as specialists.
Nonequilibrium Green's Functions Approach to Inhomogeneous Systems
by Karsten Balzer Michael BonitzThis book offers a self-contained introduction to non-equilibrium quantum particle dynamics for inhomogeneous systems, including a survey of recent breakthroughs pioneered by the authors and others. The approach is based on real-time Green's functions.
Nonequilibrium Magnons: Theory, Experiment and Applications
by Vladimir L. SafonovThis much-needed book addresses the concepts, models, experiments and applications of magnons and spin wave in magnetic devices. It fills the gap in the current literature by providing the theoretical and technological framework needed to develop innovative magnetic devices, such as recording devices and sensors. Starting with a historical review of developments in the magnon concept, and including original experimental results, the author presents methods of magnon excitation, and several basic models to describe magnon gas. He includes experiments on Bose-Einstein condensation of non-equilibrium magnons, as well as various applications of a magnon approach.
Nonequilibrium Phase Transitions in Driven Vortex Matter: The Reversible-Irreversible Transition, Dynamical Ordering, and Kibble-Zurek Mechanism (Springer Theses)
by Shun MaegochiThis book presents experimental studies of nonequilibrium phase transitions induced by ac and dc forces in collectively interacting systems—a superconducting vortex system with random pinning. It first shows that a phase transition from reversible to irreversible flow occurs by increasing vortex density as well as amplitude of ac shear, which is indicative of the universality of the reversible-irreversible transition. Two distinct flow regimes are also found in the reversible phase. Next, the book presents new methods for dc driven experiments—transverse mode-locking and transverse current-voltage measurements—and provides convincing evidence of the second-order dynamical transition from disordered plastic to anisotropically ordered smectic flow. Lastly it reports on the first experimental demonstration of the Kibble-Zurek mechanism for the nonequilibrium phase transition.The experimental results indicate that both the reversible-irreversible transition and the dynamical ordering transition belong to the directed percolation universality class which is one of the fundamental classes of nonequilibrium phase transitions. Hence, the findings will be generalized to other nonequilibrium systems and stimulate research on nonequilibrium physics.
Nonequilibrium Statistical Physics
by Gerd RöpkeAuthored by a well-known expert in the field of nonequilibrium statistical physics, this book is a coherent presentation of the subject suitable for masters and PhD students, as well as postdocs in physics and related disciplines. Starting from a general discussion of irreversibility and entropy, the method of nonequilibrium statistical operator is presented as a general concept. Stochastic processes are introduced as a necessary prerequisite to describe the evolution of a nonequilibrium state. Different standard approaches such as master equations, kinetic equations and linear response theory, are derived after special assumptions. This allows for an insight into the problems of nonequilibrium physics, a discussion of the limits of the approaches, and suggestions for improvements. The method of thermodynamic Green's function is outlined that allows for the systematic quantum statistical treatment of many-body systems. Applications and typical examples are given, as well as fully worked problems.
Nonequilibrium Statistical Physics of Small Systems
by Heinz Georg Schuster Christopher Jarzynski Rainer Klages Wolfram JustThis book offers a comprehensive picture of nonequilibrium phenomena in nanoscale systems. Written by internationally recognized experts in the field, this book strikes a balance between theory and experiment, and includes in-depth introductions to nonequilibrium fluctuation relations, nonlinear dynamics and transport, single molecule experiments, and molecular diffusion in nanopores.The authors explore the application of these concepts to nano- and biosystems by cross-linking key methods and ideas from nonequilibrium statistical physics, thermodynamics, stochastic theory, and dynamical systems. By providing an up-to-date survey of small systems physics, the text serves as both a valuable reference for experienced researchers and as an ideal starting point for graduate-level students entering this newly emerging research field.
Nonequilibrium Statistical Thermodynamics (Dover Books on Physics)
by Bernard H. LavendaThis book develops in detail the statistical foundations of nonequilibrium thermodynamics, based on the mathematical theory of Brownian motion. Author Bernard H. Lavenda demonstrates that thermodynamic criteria emerge in the limit of small thermal fluctuations and in the Gaussian limit where means and modes of the distribution coincide. His treatment assumes the theory of Brownian motion to be a general and practical model of irreversible processes that are inevitably influenced by random thermal fluctuations. This unifying approach permits the extraction of widely applicable principles from the analysis of specific models.Arranged by argument rather than theory, the text is based on the premises that random thermal fluctuations play a decisive role in governing the evolution of nonequilibrium thermodynamic processes and that they can be viewed as a dynamic superposition of many random events. Intended for nonmathematicians working in the areas of nonequilibrium thermodynamics and statistical mechanics, this book will also be of interest to chemical physicists, condensed matter physicists, and readers in the area of nonlinear optics.
Nonequilibrium and Irreversibility
by Giovanni GallavottiThis book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached. The stationary states of particles or of fluids (understood as probability distributions on microscopic configurations or on the fields describing continua) have received important new ideas and data from numerical simulations and reviews are needed. The starting point is to find out which time invariant distributions come into play in physics. A special feature of this book is the historical approach. To identify the problems the author analyzes the papers of the founding fathers Boltzmann, Clausius and Maxwell including translations of the relevant (parts of) historical documents. He also establishes a close link between treatment of irreversible phenomena in statistical mechanics and the theory of chaotic systems at and beyond the onset of turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the author gives arguments intending to support strongly the viewpoint that stationary states in or out of equilibrium can be described in a unified way. In this book it is the "chaotic hypothesis", which can be seen as an extension of the classical ergodic hypothesis to non equilibrium phenomena, that plays the central role. It is shown that SRB - often considered as a kind of mathematical playground with no impact on physical reality - has indeed a sound physical interpretation; an observation which to many might be new and a very welcome insight. Following this, many consequences of the chaotic hypothesis are analyzed in chapter 3 - 4 and in chapter 5 a few applications are proposed. Chapter 6 is historical: carefully analyzing the old literature on the subject, especially ergodic theory and its relevance for statistical mechanics; an approach which gives the book a very personal touch. The book contains an extensive coverage of current research (partly from the authors and his coauthors publications) presented in enough detail so that advanced students may get the flavor of a direction of research in a field which is still very much alive and progressing. Proofs of theorems are usually limited to heuristic sketches privileging the presentation of the ideas and providing references that the reader can follow, so that in this way an overload of this text with technical details could be avoided.