The aim of this book is to present a statistical theory of wave scattering by complex systems -systems which have a chaotic classical dynamics, as in the case of microwave cavities and quantum dots, or possess quenched randomness, as in the case of disordered conductors- with emphasis on mesoscopic fluctuations. The universal character of the statistical behavior of these phenomena is incorporated in a natural way by approaching the problem from a Maximum-Entropy viewpoint -Shannon's information entropy is maximized, subject to the symmetries and constraints that are physically relevant- within the powerful, non-perturbative Theory of Random Matrices. This is a distinctive feature of the present book that greatly motivated our writing it. Another reason is that it collects in one place the material and notions -derived from the published work of the authors in collaboration with several co-workers, as well as from the work of others- which are scattered through research journals and textbooks on the subject. To make the book self-contained, we present in Chapters 2 and 3 the quantum theory of scattering, set in the context of quasi-one-dimensional, multichannel systems, thus related directly to scattering problems in mesoscopic physics. Chapter 4 discusses the linear-response theory of quantum electronic transport, adapted to the context of mesoscopic systems. These chapters, together with Chapter 5 on the Maximum-Entropy Approach and Chapter 8 on weak localization, have been written in a pedagogical style, and can be used as part of a graduate course. Chapters 6 and 7 discuss the problem of electronic transport through classically chaotic cavities and quasi-one-dimensional disordered systems. There are many exercises, most of them worked out in detail, distributed throughout the book. This should help graduate students, their teachers and the research scholars interested generally in the subject of quantum transport through disordered and chaotic systems in their preparation for it, and beyond.

This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincare inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere.

Statistical Mechanics is the study of systems where the number of interacting particles becomes infinite. In the last fifty years tremendous advances have been made which have required the invention of entirely new fields of mathematics such as quantum groups and affine Lie algebras. They have engendered remarkable discoveries concerning non-linear differential equations and algebraic geometry, and have produced profound insights in both condensed matter physics and quantum field theory. Unfortunately, none of these advances are taught in graduate courses in statistical mechanics.
This book is an attempt to correct this problem. It begins with theorems on the existence (and lack) of order for crystals and magnets and with the theory of critical phenomena, and continues by presenting the methods and results of fifty years of analytic and computer computations of phase transitions. It concludes with an extensive presentation of four of the most important of exactly solved problems: the Ising, 8 vertex, hard hexagon and chiral Potts models.

Functionality, Advancements and Industrial Applications of Heat Pipes introduces heat pipe technologies and highlights a variety of applications for passive thermal control. The book begins with a thorough analysis of heat pipe infrastructure, including principles of operation, temperature limits, reliability and lessons learned from worked examples and case studies. It also presents a concise design guideline for the assembly of heat pipes. The second part moves on to consider a variety of modern day applications for the heat pipe principles discussed, covering nuclear and solar thermal energy engineering facilities as well as applications in space, in the sea and in the air. A final section works through manufacturing elements of different types of heat pipe to ensure they are well maintained and remain fully operational. This section includes the cleaning of parts, the assembly of the heat pipe, an analysis of gas blockages and how to deal with them, as well as performance versification.

This book contains the courses given at the Fifth School on Complex Systems held at Santiago, Chile, from 9th .to 13th December 1996. At this school met researchers working on areas related with recent trends in Complex Systems, which include dynamical systems, cellular automata, symbolic dynamics, spatial systems, statistical physics and thermodynamics. Scientists working in these subjects come from several areas: pure and applied mathematics, physics, biology, computer science and electrical engineering. Each contribution is devoted to one of the above subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The paper of Bruno Durand presents the state of the art on the relationships between the notions of surjectivity, injectivity and reversibility in cellular automata when finite, infinite or periodic configurations are considered, also he discusses decidability problems related with the classification of cellular automata as well as global properties mentioned above. The paper of Eric Goles and Martin Matamala gives a uniform presentation of simulations of Turing machines by cellular automata. The main ingredient is the encoding function which must be fixed for all Turing machine. In this context known results are revised and new results are presented.

Quantum information- the subject- is a new and exciting area of science, which brings together physics, information theory, computer science and mathematics. Quantum Information- the book- is based on two successful lecture courses given to advanced undergraduate and beginning postgraduate students in physics. The intention is to introduce readers at this level to the fundamental, but offer rather simple, ideas behind ground-breaking developments including quantum cryptography, teleportation and quantum computing. The text is necessarily rather mathematical in style, but the mathematics nowhere allowed priority over the key physical ideas. My aim throughout was to be as complete and self- contained but to avoid, as far as possible, lengthy and formal mathematical proofs. Each of the eight chapters is followed by about forty exercise problems with which the reader can test their understanding and hone their skills. These will also provide a valuable resource to tutors and lectures.
To request a copy of the Solutions Manual, visit: http: //global.oup.com/uk/academic/physics/admin/solutions

This thesis demonstrates the potential of two platforms to explore experimentally the emerging field of quantum thermodynamics that has remained mostly theoretical so far. It proposes methods to define and measure work in the quantum regime. The most important part of the thesis focuses on hybrid optomechanical devices, evidencing that they are proper candidates to measure directly the fluctuations of work and the corresponding fluctuation theorem. Such devices could also give rise to the observation of mechanical lasing and cooling, based on mechanisms similar to a heat engine. The final part of the thesis studies how quantum coherence can improve work extraction in superconducting circuits. All the proposals greatly clarify the concept of work since they are based on measurable quantities in state of the art devices.

Since 1950, the Highway Capacity Manual has been a standard used in the planning, design, analysis, and operation of virtually any highway traffic facility in the United States. It has also been widely used around the globe and has inspired the development of similar manuals in other countries. This book is Volume II of a series on the conceptual and research origins of the methodologies found in the Highway Capacity Manual. It focuses on the most complex points in a traffic system: signalized and unsignalized intersections, and the concepts and methodologies developed over the years to model their operations. It also includes an overview of the fundamental concepts of capacity and level of service, particularly as applied to intersections. The historical roots of the manual and its contents are important to understanding current methodologies, and improving them in the future. As such, this book is a valuable resource for current and future users of the Highway Capacity Manual, as well as researchers and developers involved in advancing the state-of-the-art in the field.

This book studies the fundamental aspects of many-body physics in quantum systems open to an external world. Recent remarkable developments in the observation and manipulation of quantum matter at the single-quantum level point to a new research area of open many-body systems, where interactions with an external observer and the environment play a major role. The first part of the book elucidates the influence of measurement backaction from an external observer, revealing new types of quantum critical phenomena and out-of-equilibrium dynamics beyond the conventional paradigm of closed systems. In turn, the second part develops a powerful theoretical approach to study the in- and out-of-equilibrium physics of an open quantum system strongly correlated with an external environment, where the entanglement between the system and the environment plays an essential role. The results obtained here offer essential theoretical results for understanding the many-body physics of quantum systems open to an external world, and can be applied to experimental systems in atomic, molecular and optical physics, quantum information science and condensed matter physics.

This book discusses non-equilibrium quantum many-body dynamics, recently explored in an analog quantum simulator of strongly correlated ultracold atoms. The first part presents a field-theoretical analysis of the experimental observability of the Higgs amplitude mode that emerges as a relativistic collective excitation near a quantum phase transition of superfluid Bose gases in an optical lattice potential. The author presents the dynamical susceptibilities to external driving of the microscopic parameters, taking into account a leading-order perturbative correction from quantum and thermal fluctuations and shows clear signatures of the Higgs mode in these observables. This is the first result that strongly supports the stability of the Higgs mode in three-dimensional optical lattices even in the presence of a spatially inhomogeneous confinement potential and paves the way for desktop observations of the Higgs mode. In the second part, the author applies the semi-classical truncated-Wigner approximation (TWA) to far-from-equilibrium quantum dynamics. Specifically, he considers the recent experiments on quantum-quench dynamics in a Bose-Hubbard quantum simulator. A direct comparison shows remarkable agreement between the numerical results from TWA and the experimental data. This result clearly indicates the potential of such a semi-classical approach in reliably simulating many-body systems using classical computers. The book also includes several chapters providing comprehensive reviews of the recent studies on cold-atomic quantum simulation and various theoretical methods, including the Schwinger-boson approach in strongly correlated systems and the phase-space semi-classical method for far-from-equilibrium quantum dynamics. These chapters are highly recommended to students and young researchers who are interested in semi-classical approaches in non-equilibrium quantum dynamics.

In the high energy gas flows, associating high velocities and high temperatures, physical and chemical processes such as molecular vibrational excitation, dissociation, ionisation or various reactions take palce and deeply influence the structure of the flows. The characteristic times of these processes have the same order of magnitude as aerodynamic characteristic times so that these reactive media are generally in thermodynamic and chemical non-equilibrium. This book presents a general introductory study of these media. In the first part their fundamental statistical aspects are described, starting from their discrete structure and taking into account the interactions between elementary particles: the transport phenomena, relaxation and kinetics as well as their coupling are thus analysed and illustrated by many examples. The second part deals with the macroscopic re-entry bodies. Finally the experimental aspects of these flows, their simulations in shock tube and shock tunnel are described as well as their application, particularly in the aero- spatial domain.
This book is intended for researchers and students that have acquired basic knowledge in thermodynamics, statistical physics and fluid mechanics. It must also interest the engineers engaged in research and industry related to the applications of the reactive flows, in particular in the aerospace field and, more generally, all the researchers trying to simulate and calculate complex reactive flows.

The principal objective of this book is to provide information needed to define human thermal behavior quantitatively. Human thermal physiology is defined using mathematical methods routinely employed by physicists and engineers, but seldom used by physiologists. Major sections of the book are devoted to blood flow, sweating, shivering, heat transfer within the body, and heat and mass transfer from skin and clothing to the environment. Simple algebraic models based on experimental data from a century of physiological investigation are developed for bodily processes. The book offers an invaluable source of information for physiologists and physical scientists interested in quantitative approaches to the fascinating field of human thermoregulation.

The accurate measurement of temperature is a vital parameter in many fields of engineering and scientific practice. Responding to emerging trends, this classic reference has been fully revised to include coverage of the latest instrumentation and measurement methods.

Featuring:

• Brand new chapters on computerised temperature measuring systems and temperature measurement in medicine.

• Sections on noise thermometers, the development of photoelectric and two-wave pyrometers and the latest IEC (International Electrotechnical Commission) standards

• Coverage of fibre optic thermometers, imaging of temperature fields and measurement in hazardous areas.

• Examination of virtual instruments, fuzzy logic in temperature measurement and new methods for thermometer calibration.

This book takes the notions of adaptivity and learning from the realm of engineering into the realm of biology and natural processes. It introduces a Hebbian-LMS algorithm, an integration of unsupervised Hebbian learning and supervised LMS learning in neural networks, as a mathematical representation of a general theory for synaptic learning in the brain, and adaptation and functional control of homeostasis in living systems. Written in a language that is able to address students and scientists with different backgrounds, this book accompanies readers on a unique journey through various homeostatic processes in living organisms, such as body temperature control and synaptic plasticity, explaining how the Hebbian-LMS algorithm can help understand them, and suggesting some open questions for future research. It also analyses cell signalling pathways from an unusual perspective, where hormones and hormone receptors are shown to be regulated via the principles of the Hebbian-LMS algorithm. It further discusses addiction and pain, and various kinds of mood disorders alike, showing how they can be modelled with the Hebbian-LMS algorithm. For the first time, the Hebbian-LMS algorithm, which has been derived from a combination of Hebbian theory from the neuroscience field and the LMS algorithm from the engineering field of adaptive signal processing, becomes a potent model for understanding how biological regulation works. Thus, this book is breaking new ground in neuroscience by providing scientists with a general theory for how nature does control synaptic learning. It then goes beyond that, showing that the same principles apply to hormone-mediated regulation of physiological processes. In turn, the book tackles in more depth the concept of learning. It covers computer simulations and strategies for training neural networks with the Hebbian-LMS algorithm, demonstrating that the resulting algorithms are able to identify relationships between unknown input patterns. It shows how this can translate in useful ideas to understand human memory and design cognitive structures. All in all, this book offers an absolutely, unique, inspiring reading for biologists, physiologists, and engineers, paving the way for future studies on what we could call the nature's secret learning algorithm.

Complexity and Complex Thermoeconomic Systems describes the properties of complexity and complex thermo-economic systems as the consequence of formulations, definitions, tools, solutions and results consistent with the best performance of a system. Applying to complex systems contemporary advanced techniques, such as static optimization, optimal control, and neural networks, this book treats the systems theory as a science of general laws for functional integrities. It also provides a platform for the discussion of various definitions of complexity, complex hierarchical structures, self-organization examples, special references, and historical issues. This book is a valuable reference for scientists, engineers and graduated students in chemical, mechanical, and environmental engineering, as well as those in physics, ecology and biology, helping them better understand the complex thermodynamic systems and enhance their technical skills in research.

This book provides a theoretical, step-by-step comprehensive explanation of superconductivity for undergraduate and graduate students who have completed elementary courses on thermodynamics and quantum mechanics. To this end, it adopts the unique approach of starting with the statistical mechanics of quantum ideal gases and successively adding and clarifying elements and techniques indispensible for understanding it. They include the spin-statistics theorem, second quantization, density matrices, the Bloch-De Dominicis theorem, the variational principle in statistical mechanics, attractive interaction and bound states. Ample examples of their usage are also provided in terms of topics from advanced statistical mechanics such as two-particle correlations of quantum ideal gases, derivation of the Hartree-Fock equations, and Landau's Fermi-liquid theory, among others. With these preliminaries, the fundamental mean-field equations of superconductivity are derived with maximum mathematical clarity based on a coherent state in terms of the Cooper-pair creation operator, a quasiparticle field for describing the excitation and the variational principle in statistical mechanics. They have the advantage that the phase coherence due to the Cooper-pair condensation can be clearly seen making the superfluidity comprehensible naturally. Subsequently, they are applied to homogeneous cases to describe the BCS theory for classic s-wave superconductors and its extension to the p-wave superfluidity of 3He. Later, the mean-field equations are simplified to the Eilenberger and Ginzburg-Landau equations so as to describe inhomogeneous superconductivity such as Abrikosov's flux-line lattice concisely and transparently. Chapters provide the latest studies on the quasiclassical theory of superconductivity and a discovery of p-wave superfluidity in liquid 3He. The book serves as a standard reference for advanced courses of statistical mechanics with exercises along with detailed answers.

This book is placed at the interface between string theory and elementary particle physics and shows novel results in the search for a heterotic string vacuum that reproduces those matter particles and interactions observed in our universe. The author provides a systematic classification of potentially realistic heterotic covariant lattice vacua, which possess a lower number of moduli fields when compared to conventional compactification methods, by means of number theoretical methods. These methods, while well known to the mathematics community, have not yet found many applications to physics. They are introduced to the degree necessary to understand the computations carried out throughout this work. Furthermore, explicit covariant lattice models with particularly interesting properties are analyzed in detail. Finally, new light is shed on the relation between covariant lattice models and asymmetric orbifold compactifications, the result being a concrete correspondence between certain types of asymmetric orbifolds and those classified covariant lattices.

This thesis presents several related advances in the field of nonequilibrium quantum thermodynamics. The central result is an ingenious proof that the local temperature and voltage measurement in a nonequilibrium system of fermions exists and is unique, placing the concept of local temperature on a rigorous mathematical footing for the first time. As an intermediate step, a proof of the positivity of the Onsager matrix of linear response theory is given -- a statement of the second law of thermodynamics that had lacked an independent proof for 85 years. A new experimental method to measure the local temperature of an electron system using purely electrical techniques is also proposed, which could enable improvements to the spatial resolution of thermometry by several orders of magnitude. Finally, a new mathematically-exact definition for the local entropy of a quantum system in a nonequilibrium steady state is derived. Several different measures of the local entropy are discussed, relating to the thermodynamics of processes that a local observer with varying degrees of information about the microstates of the system could carry out, and it is shown that they satisfy a hierarchy of inequalities. Proofs of the third law of thermodynamics for generic open quantum systems are presented, taking into account the entropic contribution due to localized states. Appropriately normalized (per-state) local entropies are defined and are used to quantify the departure from local equilibrium.

This book is dedicated to Professor Leonid V Keldysh. His brilliant contributions to condensed matter physics include the Franz-Keldysh effect, an electron-hole liquid, the nonequilibrium (Keldysh) diagram technique, Bose-Einstein condensation (of excitons) and a metal-dielectric'' transition, acoustically-induced superlattices, multi-photon transitions and impact ionization in solids. In many respects, his work influenced and formed the paradigm of modern condensed matter physics. As a result, many famous researchers in the field have enthusiastically provided unique contributions to the book.

Illustrating the development of Brownian ratchets, from their foundations, to their role in the description of life at the molecular scale and in the design of artificial nano-machinery, this text will appeal to both advanced graduates and researchers entering the field. Providing a self-contained introduction to Brownian ratchets, devices which rectify microscopic fluctuations, Part I avoids technicalities and sets out the broad range of physical systems where the concept of ratchets is relevant. Part II supplies a single source for a complete and modern theoretical analysis of ratchets in regimes such as classical vs quantum and stochastic vs deterministic, and in Part III readers are guided through experimental developments in different physical systems, each highlighting a specific unique feature of ratchets. The thorough and systematic approach to the topic ensures that this book provides a complete guide to Brownian ratchets for newcomers and established researchers in physics, biology and biochemistry.

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 book offers a comprehensive survey of basic elements of nuclear dynamics at low energies and discusses similarities to mesoscopic systems. It addresses systems with finite excitations of their internal degrees of freedom, so that their collective motion exhibits features typical for transport processes in small and isolated systems. The importance of quantum aspects is examined with respect to both the microscopic damping mechanism and the nature of the transport equations. The latter must account for the fact that the collective motion is self-sustained. This implies highly nonlinear couplings between internal and collective degrees of freedom --- different to assumptions made in treatments known in the literature. A critical discussion of the use of thermal concepts is presented. The book can be considered self-contained. It presents existing models, theories and theoretical tools, both from nuclear physics and other fields, which are relevant to an understanding of the observed physical phenomena.

This book contains contributions presented at the 12th International Conference on Complex Networks (CompleNet), 24-26 May 2021. CompleNet is an international conference on complex networks that brings together researchers and practitioners from diverse disciplines-from sociology, biology, physics, and computer science-who share a passion to better understand the interdependencies within and across systems. CompleNet is a venue to discuss ideas and findings about all types networks, from biological, to technological, to informational and social. It is this interdisciplinary nature of complex networks that CompleNet aims to explore and celebrate.

This book explores recent developments in theoretical research and data analysis of real-world complex systems, organized in three parts, namely Entropy, information, and complexity functions Multistability, oscillations, and rhythmic synchronization Diffusions, rotation, and convection in fluids The collection of works devoted to the memory of Professor Valentin Afraimovich provides a deep insight into the recent developments in complexity science by introducing new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to economics, genetics, engineering vibrations, as well as classic problems in physics, fluid and climate dynamics, and urban dynamics. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, and urban planners.

This edited volume provides an essential resource for urban morphology, the study of urban forms and structures, offering a much-needed mathematical perspective. Experts on a variety of mathematical modeling techniques provide new insights into specific aspects of the field, such as street networks, sustainability, and urban growth. The chapters collected here make a clear case for the importance of tools and methods to understand, model, and simulate the formation and evolution of cities. The chapters cover a wide variety of topics in urban morphology, and are conveniently organized by their mathematical principles. The first part covers fractals and focuses on how self-similar structures sort themselves out through competition. This is followed by a section on cellular automata, and includes chapters exploring how they generate fractal forms. Networks are the focus of the third part, which includes street networks and other forms as well. Chapters that examine complexity and its relation to urban structures are in part four.The fifth part introduces a variety of other quantitative models that can be used to study urban morphology. In the book's final section, a series of multidisciplinary commentaries offers readers new ways of looking at the relationship between mathematics and urban forms. Being the first book on this topic, Mathematics of Urban Morphology will be an invaluable resource for applied mathematicians and anyone studying urban morphology. Additionally, anyone who is interested in cities from the angle of economics, sociology, architecture, or geography will also find it useful. "This book provides a useful perspective on the state of the art with respect to urban morphology in general and mathematics as tools and frames to disentangle the ideas that pervade arguments about form and function in particular. There is much to absorb in the pages that follow and there are many pointers to ways in which these ideas can be linked to related theories of cities, urban design and urban policy analysis as well as new movements such as the role of computation in cities and the idea of the smart city. Much food for thought. Read on, digest, enjoy." From the foreword by Michael Batty