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This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on general theory which includes a summary of the basic principles of statistical mechanics; a presentation of the physical phenomena covered and the models used to discuss them; theorems on the existence and uniqueness of partition functions; theorems on order; and critical phenomena and scaling theory. The second part is on series and numerical methods which includes derivations of the Mayer and Ree–Hoover expansions of the low density virial equation of state; Groeneveld's theorems; the application to hard spheres and discs; a summary of numerical studies of systems at high density; and the use of high temperature series expansions to estimate critical exponents for magnets. The third part covers exactly solvable models which includes a detailed presentation of the Pfaffian methods of computing the Ising partition function, magnetization, correlation functions, and susceptibility; the star-triangle (Yang–Baxter equation); functional equations and the free energy for the eight-vertex model; and the hard hexagon and chiral Potts models. All needed mathematics is developed in detail and many open questions are discussed. The goal is to guide the reader to the current forefront of research.

The book integrates agent-based modeling and network science. It is divided into three parts, namely, foundations, primary dynamics on and of social networks, and applications. The book begins with the network origin of agent-based models, known as cellular automata, and introduce a number of classic models, such as Schelling’s segregation model and Axelrod’s spatial game. The essence of the foundation part is the network-based agent-based models in which agents follow network-based decision rules. Under the influence of the substantial progress in network science in late 1990s, these models have been extended from using lattices into using small-world networks, scale-free networks, etc. The book also shows that the modern network science mainly driven by game-theorists and sociophysicists has inspired agent-based social scientists to develop alternative formation algorithms, known as agent-based social networks. The book reviews a number of pioneering and representative models in this family. Upon the given foundation, the second part reviews three primary forms of network dynamics, i.e., diffusions, cascades, and influences. These primary dynamics are further extended and enriched by practical networks in goods-and-service markets, labor markets, and international trade. The book ends with two challenging issues using agent-based models of networks, i.e., network risks and economic growth.

This book is the first to examine the history of imaginative thinking about intelligent machines. As real artificial intelligence (AI) begins to touch on all aspects of our lives, this long narrative history shapes how the technology is developed, deployed, and regulated. It is therefore a crucial social and ethical issue. Part I of this book provides a historical overview from ancient Greece to the start of modernity. These chapters explore the revealing prehistory of key concerns of contemporary AI discourse, from the nature of mind and creativity to issues of power and rights, from the tension between fascination and ambivalence to investigations into artificial voices and technophobia. Part II focuses on the twentieth and twenty-first centuries in which a greater density of narratives emerged alongside rapid developments in AI technology. These chapters reveal not only how AI narratives have consistently been entangled with the emergence of real robotics and AI, but also how they offer a rich source of insight into how we might live with these revolutionary machines. Through their close textual engagements, these chapters explore the relationship between imaginative narratives and contemporary debates about AI’s social, ethical, and philosophical consequences, including questions of dehumanization, automation, anthropomorphization, cybernetics, cyberpunk, immortality, slavery, and governance. The contributions, from leading humanities and social science scholars, show that narratives about AI offer a crucial epistemic site for exploring contemporary debates about these powerful new technologies.

The Analytic Element Method provides a foundation to solve boundary value problems commonly encountered in engineering and science. The goals are: to introduce readers to the basic principles of the AEM, to provide a template for those interested in pursuing these methods, and to empower readers to extend the AEM paradigm to an even broader range of problems. A comprehensive paradigm: place an element within its landscape, formulate its interactions with other elements using linear series of influence functions, and then solve for its coefficients to match its boundary and interface conditions with nearly exact precision. Collectively, sets of elements interact to transform their environment, and these synergistic interactions are expanded upon for three common types of problems. The first problem studies a vector field that is directed from high to low values of a function, and applications include: groundwater flow, vadose zone seepage, incompressible fluid flow, thermal conduction and electrostatics. A second type of problem studies the interactions of elements with waves, with applications including water waves and acoustics. A third type of problem studies the interactions of elements with stresses and displacements, with applications in elasticity for structures and geomechanics. The Analytic Element Method paradigm comprehensively employs a background of existing methodology using complex functions, separation of variables and singular integral equations. This text puts forth new methods to solving important problems across engineering and science, and has a tremendous potential to broaden perspective and change the way problems are formulated.

The anomaly, which forms the central part of this book, is the failure of classical symmetry to survive the process of quantization and regularization. The study of anomalies is the key to a deeper understanding of quantum field theory and has played an increasingly important role in the theory over the past twenty years. This book presents all the different aspects of the study of anomalies in an accessible and self-contained way. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. This approach is followed here, and the derivations and calculations are given explicitly. Topics discussed include the relevant ideas from differential geometry and topology and the application of these paths (path integrals, differential forms, homotopy operators, etc.) to the study of anomalies. Chapters are devoted to abelian and nonabelian anomalies, consistent and covariant anomalies, and gravitational anomalies.

Applied Computational Physics describes methods for solving a vast array of classical and quantum mechanical scientific problems while stressing modern computational paradigms for achieving these solutions. The text develops computational techniques, numerical algorithms, and physics applications in parallel. The goal of the book is to provide students of physics with essential and modern computational skills and to increase the confidence with which they write computer programs within their problem domain. Hundreds of original problems reinforce programming skills and increase the ability to solve real-life physics problems at and beyond the graduate level.

Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. This book provides the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. The book follows Mather's strategy but emphasizes a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, the book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

Nonlocality was discovered by John Bell in 1964, in the context of the debates about quantum theory, but is a phenomenon that can be studied in its own right. Its observation proves that measurements are not revealing pre-determined values, falsifying the idea of “local hidden variables” suggested by Einstein and others. One is then forced to make some radical choice: either nature is intrinsically statistical and individual events are unspeakable, or our familiar space-time cannot be the setting for the whole of physics. As phenomena, nonlocality and its consequences will have to be predicted by any future theory, and may possibly play the role of foundational principles in these developments. But nonlocality has found a role in applied physics too: it can be used for “device-independent” certification of the correct functioning of random number generators and other devices. After a self-contained introduction to the topic, this monograph on nonlocality presents the main tools and results following a logical, rather than a chronological, order.

Theoretical physics and foundations of physics have not made much progress in the last few decades. There is no consensus among researchers on how to approach unifying general relativity and quantum field theory (quantum gravity), explaining so-called dark energy and dark matter (cosmology), or the interpretation and implications of quantum mechanics and relativity. In addition, both fields are deeply puzzled about various facets of time including, above all, time as experienced. This book argues that this impasse is the result of the “dynamical universe paradigm,” the idea that reality fundamentally comprises physical entities that evolve in time from some initial state according to dynamical laws. Thus, in the dynamical universe, the initial conditions plus the dynamical laws explain everything else going exclusively forward in time. In cosmology, for example, the initial conditions reside in the Big Bang and the dynamical law is supplied by general relativity. Accordingly, the present state of the universe is explained exclusively by its past. A completely new paradigm (called Relational Blockworld) is offered here whereby the past, present, and future co-determine each other via “adynamical global constraints,” such as the least action principle. Accordingly, the future is just as important for explaining the present as the past is. Most of the book is devoted to showing how Relational Blockworld resolves many of the current conundrums of both theoretical physics and foundations of physics, including the mystery of time as experienced and how that experience relates to the block universe.

At the heart of many fields—physics, chemistry, engineering—lays thermodynamics. While this science plays a critical role in determining the boundary between what is and is not possible in the natural world, it occurs to many as an indecipherable black box, thus making the subject a challenge to learn. Two obstacles contribute to this situation, the first being the disconnect between the fundamental theories and the underlying physics and the second being the confusing concepts and terminologies involved with the theories. While one needn’t confront either of these two obstacles to successfully use thermodynamics to solve real problems, overcoming both provides access to a greater intuitive sense of the problems and more confidence, more strength, and more creativity in solving them. Success in this regard necessarily involves learning both the science and the history that led to the science. The two were intertwined during the evolution of thermodynamics and are thus likewise intertwined in this book.With this book I offer an original perspective on thermodynamic science and history based on standing at the interface between three worlds: practicing engineer, academician, and historian. I synthesize and gather into one accessible volume a strategic range of foundational topics involving the atomic theory, energy, entropy, and the laws of thermodynamics. For each topic I capture both the physical and historical underpinnings together with the human-interest stories as the hundreds of years of thermodynamic history are filled with many such stories. I share them to further engage, educate, and inspire the reader.

This book provides an elementary introduction to chaos and fractals. It introduces the key phenomena of chaos — aperiodicity, sensitive dependence on initial conditions, bifurcations — via simple iterated functions. Fractals are introduced as self-similar geometric objects and analysed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia sets and the Mandelbrot set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations.

This book introduces the full range of activity in the rapidly growing field of nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, this book includes a thorough treatment of both differential equation models and iterated map models (including a detailed derivation of the famous Feigenbaum numbers). It includes the increasingly important field of pattern formation and a survey of the controversial question of quantum chaos. Important tools such as Lyapunov exponents, fractal dimensions, and correlation dimensions are treated in detail. Several appendices provide a detailed derivation of the Lorenz model from the Navier-Stokes equation, a summary of bifurcation theory, and some simple computer programs to study nonlinear dynamics. Each chapter includes an extensive, annotated bibliography.

This book is the first to make chi-squared model testing, one of the data analysis methods used to discover the Higgs boson and gravitational waves, accessible to undergraduate students in introductory physics laboratory courses. By including uncertainties in the curve fitting, chi-squared data analysis improves on the centuries old ordinary least squares and linear regression methods and combines best fit parameter estimation and model testing in one method. A toolkit of essential statistical and experimental concepts is developed from the ground up with novel features to interest even those familiar with the material. The presentation of one- and two-parameter chi-squared model testing, requiring only elementary probability and algebra, is followed by case studies that apply the methods to simple introductory physics lab experiments. More challenging topics, requiring calculus, are addressed in an advanced topics chapter. This self-contained and student-friendly introduction to chi-squared analysis and model testing includes a glossary, end-of-chapter problems with complete solutions, and software scripts written in several popular programming languages, that the reader can use for chi-squared model testing. In addition to introductory physics lab students, this accessible introduction to chi-squared analysis and model testing will be of interest to all who need to learn chi-squared model testing, e.g. beginning researchers in astrophysics and particle physics, beginners in data science, and lab students in other experimental sciences.

After briefly presenting (for the physicist) some notions frequently used in combinatorics (such as graphs or combinatorial maps) and after briefly presenting (for the combinatorialist) the main concepts of quantum field theory (QFT), the book shows how algebraic combinatorics can be used to deal with perturbative renormalisation (both in commutative and non-commutative quantum field theory), how analytic combinatorics can be used for QFT issues (again, for both commutative and non-commutative QFT), how Grassmann integrals (frequently used in QFT) can be used to proCve new combinatorial identities (generalizing the Lindström–Gessel–Viennot formula), how combinatorial QFT can bring a new insight on the celebrated Jacobian conjecture (which concerns global invertibility of polynomial systems) and so on. In the second part of the book, matrix models, and tensor models are presented to the reader as QFT models. Several tensor model results (such as the implementation of the large N limit and of the double-scaling limit for various such tensor models, N being here the size of the tensor) are then exposed. These results are natural generalizations of results extensively used by theoretical physicists in the study of matrix models and they are obtained through intensive use of combinatorial techniques (this time mainly enumerative techniques). The last part of the book is dedicated to the recently discovered relation between tensor models and the holographic Sachdev–Ye–Kitaev model, model which has been extensively studied in the last years by condensed matter and by high-energy physicists.

This book provides a practical guide to molecular dynamics and Monte Carlo simulation techniques used in the modelling of simple and complex liquids. Computer simulation is an essential tool in studying the chemistry and physics of condensed matter, complementing and reinforcing both experiment and theory. Simulations provide detailed information about structure and dynamics, essential to understand the many fluid systems that play a key role in our daily lives: polymers, gels, colloidal suspensions, liquid crystals, biological membranes, and glasses. The second edition of this pioneering book aims to explain how simulation programs work, how to use them, and how to interpret the results, with examples of the latest research in this rapidly evolving field. Accompanying programs in Fortran and Python provide practical, hands-on, illustrations of the ideas in the text.

This is a textbook of elementary particle physics whose goal is to explain the Standard Model of particle interactions. Part I introduces the basic concepts governing high-energy particle physics: elements of relativity and quantum field theory, the quark model of hadrons, methods for detection and measurement of elementary particles, methods for calculating predictions for observable quantitites. Part II builds up our understanding of the strong interaction from the key experiments to the formulation of Quantum Chromodynamics and its application to the description of evetns at the CERN Large Hadron Collider. Part III build up our understanding of the weak interaction from the key experiments to the formulation of spontaneously broken gauge theories. It then describes the tests and extensions of this theory, including the precision study of the W and Z bosons, CP violation, neutrino mass, and the Higgs boson.

This short book describes ten fundamental concepts – big ideas – of materials science. Some of them come from mainstream physics and chemistry, including thermodynamic stability and phase diagrams, symmetry, and quantum behaviour. Others are about restless atomic motion and thermal fluctuations, defects in crystalline materials as the agents of change in materials, nanoscience and nanotechnology, materials design and materials discovery, metamaterials, and biological matter as a material. A cornerstone of materials science is the idea that materials are complex systems that interact with their environments and display the emergence of new science from the collective behaviour of atoms and defects. Great attention is paid to the clarity of explanations using only high school algebra and quoting the occasional useful formula. Exceptionally, elementary calculus is used in the chapter on metamaterials. It is not a text-book, but it offers undergraduates and their teachers a unique overview and insight into materials science. It may also help graduates of other subjects to decide whether to study materials science at postgraduate level.

The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more ‘utilitarian’ treatments of the subject. The book is divided into four parts, which look in turn at origins, dynamics, symmetries, and scales. The emphasis is conceptual — the aim is to build the theory up systematically from some clearly stated foundational concepts — and therefore to a large extent anti-historical, but two historical chapters are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The second section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quantum-mechanical, relativistic and locality constraints. The central role of symmetries in relativistic quantum field theories is explored in the third section of the book, while in the final section the book explores in detail the feature of quantum field theories most critical for their enormous phenomenological success — the scale separation property embodied by the renormalization group properties of a theory defined by an effective local Lagrangian.

Quantum phase transitions describe the violent rearrangement of electrons or atoms as they evolve from well defined excitations in one phase to a completely different set of excitations in another. The book chapters give insights into how a coherent metallic or superconducting state can be driven into an incoherent insulating state by increasing disorder, magnetic field, carrier concentration and inter-electron interactions. They illustrate the primary methods employed to develop a multi-faceted theory of many interacting particle systems. They describe how recent experiments probing the microscopic structure, transport, charge and spin dynamics have yielded guiding insights. What sets this book apart is this strong dialog between experiment and theory, which reveals the recent progress and emergent opportunities to solve some major problems in many body physics. The pedagogical style of the chapters has been set for graduate students starting in this dynamic field.

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.