Barry M McCoy
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199556632
- eISBN:
- 9780191723278
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
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 ...
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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.Less
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.
Akira Namatame and Shu-Heng Chen
- Published in print:
- 2016
- Published Online:
- March 2016
- ISBN:
- 9780198708285
- eISBN:
- 9780191779404
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198708285.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
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 ...
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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.Less
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.
Reinhold A. Bertlmann
- Published in print:
- 2000
- Published Online:
- January 2010
- ISBN:
- 9780198507628
- eISBN:
- 9780191706400
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507628.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
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 ...
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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.Less
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.
Joseph F. Boudreau and Eric. S. Swanson
- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198708636
- eISBN:
- 9780191858598
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198708636.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
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 ...
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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.Less
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.
Michael Silberstein, W.M. Stuckey, and Timothy McDevitt
- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198807087
- eISBN:
- 9780191844850
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198807087.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, History of Physics
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 ...
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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.Less
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.
David P. Feldman
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199566433
- eISBN:
- 9780191774966
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199566433.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
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 ...
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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.Less
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.
Robert C. Hilborn
- Published in print:
- 2000
- Published Online:
- January 2010
- ISBN:
- 9780198507239
- eISBN:
- 9780191709340
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507239.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
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 ...
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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.Less
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.
Michael P. Allen and Dominic J. Tildesley
- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780198803195
- eISBN:
- 9780191841439
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198803195.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Soft Matter / Biological Physics
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 ...
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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.Less
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.
Anthony Duncan
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199573264
- eISBN:
- 9780191743313
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573264.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
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 ...
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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.Less
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.
Vladimir Dobrosavljevic, Nandini Trivedi, and James M. Valles, Jr. (eds)
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199592593
- eISBN:
- 9780191741050
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199592593.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
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. ...
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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.Less
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.
