Reinhard B. Neder and Thomas Proffen
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199233694
- eISBN:
- 9780191715563
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233694.003.0003
- Subject:
- Physics, Crystallography: Physics
Although it might sound simple, creating a model of a cluster of atoms or an extended crystal has its difficulties. The examples range from creating simple assemblies of atoms to creating the ...
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Although it might sound simple, creating a model of a cluster of atoms or an extended crystal has its difficulties. The examples range from creating simple assemblies of atoms to creating the contents of a unit cell from an asymmetric unit to the building of extended model crystals. This chapter discusses unit cell transformations and general symmetry operations. A disordered perovskite structure is created as an example.Less
Although it might sound simple, creating a model of a cluster of atoms or an extended crystal has its difficulties. The examples range from creating simple assemblies of atoms to creating the contents of a unit cell from an asymmetric unit to the building of extended model crystals. This chapter discusses unit cell transformations and general symmetry operations. A disordered perovskite structure is created as an example.
Paul Bartha
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195325539
- eISBN:
- 9780199776313
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195325539.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This book proposes a theory of analogical arguments, with special focus on analogies in mathematics and science. The core principle of the theory is that a good analogical argument must articulate a ...
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This book proposes a theory of analogical arguments, with special focus on analogies in mathematics and science. The core principle of the theory is that a good analogical argument must articulate a clear relationship capable of generalization. This idea leads to a set of distinct models for the critical analysis of prominent forms of analogical argument, corresponding to different logical, causal and probabilistic relationships that occur in scientific reasoning. The same principle allows us to relate analogical reasoning to broad norms and values of scientific practice, such as symmetry and unification. Elaborating this principle, the book raises questions and proposes answers regarding (1) criteria for evaluating analogical arguments, (2) the philosophical justification for analogical reasoning, and (3) the place of scientific analogies in the context of theoretical confirmation.Less
This book proposes a theory of analogical arguments, with special focus on analogies in mathematics and science. The core principle of the theory is that a good analogical argument must articulate a clear relationship capable of generalization. This idea leads to a set of distinct models for the critical analysis of prominent forms of analogical argument, corresponding to different logical, causal and probabilistic relationships that occur in scientific reasoning. The same principle allows us to relate analogical reasoning to broad norms and values of scientific practice, such as symmetry and unification. Elaborating this principle, the book raises questions and proposes answers regarding (1) criteria for evaluating analogical arguments, (2) the philosophical justification for analogical reasoning, and (3) the place of scientific analogies in the context of theoretical confirmation.
Marco Sozzi
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199296668
- eISBN:
- 9780191712074
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296668.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
The investigation of discrete symmetries is a fascinating subject which has been central to the agenda of physics research for fifty years, and has been the target of many experiments, ongoing and in ...
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The investigation of discrete symmetries is a fascinating subject which has been central to the agenda of physics research for fifty years, and has been the target of many experiments, ongoing and in preparation, all over the world. This book approaches the subject from a somewhat less traditional angle: it puts more emphasis on the experimental aspects of the field, trying to provide a wider picture than usual and to convey the intellectual challenge of experimental physics. The book includes the related connection to phenomenology, a purpose for which the precision experiments in this field — often rather elegant and requiring a good amount of ingenuity — are very well suited. The book discusses discrete symmetries (parity, charge conjugation, time reversal, and of course CP symmetry) in microscopic (atomic, nuclear, and particle) physics, and includes a detailed description of some key or representative experiments. The book discusses their principles and challenges more than the historical development. The main past achievements and the most recent developments are both included.Less
The investigation of discrete symmetries is a fascinating subject which has been central to the agenda of physics research for fifty years, and has been the target of many experiments, ongoing and in preparation, all over the world. This book approaches the subject from a somewhat less traditional angle: it puts more emphasis on the experimental aspects of the field, trying to provide a wider picture than usual and to convey the intellectual challenge of experimental physics. The book includes the related connection to phenomenology, a purpose for which the precision experiments in this field — often rather elegant and requiring a good amount of ingenuity — are very well suited. The book discusses discrete symmetries (parity, charge conjugation, time reversal, and of course CP symmetry) in microscopic (atomic, nuclear, and particle) physics, and includes a detailed description of some key or representative experiments. The book discusses their principles and challenges more than the historical development. The main past achievements and the most recent developments are both included.
Roger E. Raab and Owen L. de Lange
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198567271
- eISBN:
- 9780191717970
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567271.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the ...
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The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the Maxwell fields D and H. Chapter 2 presents a semi-classical account of multipole theory, in which the Barron-Gray gauge is used to derive multipole polarizabilities describing the induction of molecular moments by a harmonic plane wave. Aspects of symmetry are treated in Chapter 3 — space-time behaviour of tensors and physical properties of molecules and crystals. In Chapter 4, D(E,B) and H(E,B) are obtained for linear anisotropic media, yielding expressions for the material constants which are required to satisfy origin independence, the Post constraint, and certain symmetries but fail the first two. Despite these difficulties, the standard theory is used in Chapter 5 to derive a wave propagation equation; this is applied to explain various physical effects in transmission, two of which are also described in a scattering theory. Chapter 6 deals with the reflection of electromagnetic waves from an anisotropic medium. The reflected intensities violate origin independence, showing again the unphysical nature of existing multipole theory. In Chapter 7, the fields are transformed while leaving Maxwell's equations unchanged, from which new material constants are derived in Chapter 8 that meet the three requirements in Chapter 4. Chapter 9 applies the transformed expressions to transmission and reflection phenomena, confirming the results of Chapter 5, while yielding reflected intensities that satisfy space and time invariances.Less
The book opens with a chapter on the classical theory of multipoles in electromagnetism, in which static and dynamic multipole expansions of various physical quantities are derived, including of the Maxwell fields D and H. Chapter 2 presents a semi-classical account of multipole theory, in which the Barron-Gray gauge is used to derive multipole polarizabilities describing the induction of molecular moments by a harmonic plane wave. Aspects of symmetry are treated in Chapter 3 — space-time behaviour of tensors and physical properties of molecules and crystals. In Chapter 4, D(E,B) and H(E,B) are obtained for linear anisotropic media, yielding expressions for the material constants which are required to satisfy origin independence, the Post constraint, and certain symmetries but fail the first two. Despite these difficulties, the standard theory is used in Chapter 5 to derive a wave propagation equation; this is applied to explain various physical effects in transmission, two of which are also described in a scattering theory. Chapter 6 deals with the reflection of electromagnetic waves from an anisotropic medium. The reflected intensities violate origin independence, showing again the unphysical nature of existing multipole theory. In Chapter 7, the fields are transformed while leaving Maxwell's equations unchanged, from which new material constants are derived in Chapter 8 that meet the three requirements in Chapter 4. Chapter 9 applies the transformed expressions to transmission and reflection phenomena, confirming the results of Chapter 5, while yielding reflected intensities that satisfy space and time invariances.
Kazuo Fujikawa and Hiroshi Suzuki
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198529132
- eISBN:
- 9780191712821
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529132.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book provides an introduction to the path integral formulation of quantum field theory and its applications to the analyses of symmetry breaking by the quantization procedure. This symmetry ...
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This book provides an introduction to the path integral formulation of quantum field theory and its applications to the analyses of symmetry breaking by the quantization procedure. This symmetry breaking is commonly called the ‘quantum anomaly’ or simply the ‘anomaly’, and this naming shows that the effect first appeared as an exceptional phenomenon in field theory. However, it is shown that this effect has turned out to be very fundamental in modern field theory. In the path integral formulation, it has been recognized that this effect arises from a non-trivial Jacobian in the change of path integral variables, namely, the path integral measure breaks certain symmetries. The study of the quantum anomaly attempts to bring about a better understanding of the basis of quantum theory and, consequently, it is a basic notion which could influence the entire quantum theory beyond field theory. The quantum anomaly is located at the border of divergence and convergence, though the quantum anomaly itself is perfectly finite, and thus closely related to the presence of an infinite number of degrees of freedom.Less
This book provides an introduction to the path integral formulation of quantum field theory and its applications to the analyses of symmetry breaking by the quantization procedure. This symmetry breaking is commonly called the ‘quantum anomaly’ or simply the ‘anomaly’, and this naming shows that the effect first appeared as an exceptional phenomenon in field theory. However, it is shown that this effect has turned out to be very fundamental in modern field theory. In the path integral formulation, it has been recognized that this effect arises from a non-trivial Jacobian in the change of path integral variables, namely, the path integral measure breaks certain symmetries. The study of the quantum anomaly attempts to bring about a better understanding of the basis of quantum theory and, consequently, it is a basic notion which could influence the entire quantum theory beyond field theory. The quantum anomaly is located at the border of divergence and convergence, though the quantum anomaly itself is perfectly finite, and thus closely related to the presence of an infinite number of degrees of freedom.
Sander Van Smaalen
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570820
- eISBN:
- 9780191718762
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570820.003.0009
- Subject:
- Physics, Crystallography: Physics
This chapter presents the steps that are required to determine the superspace group of an aperiodic crystal from its diffraction pattern. This includes the analysis of the metric of the reciprocal ...
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This chapter presents the steps that are required to determine the superspace group of an aperiodic crystal from its diffraction pattern. This includes the analysis of the metric of the reciprocal lattice in superspace, the point symmetry of the diffraction pattern, and the reflection conditions.Less
This chapter presents the steps that are required to determine the superspace group of an aperiodic crystal from its diffraction pattern. This includes the analysis of the metric of the reciprocal lattice in superspace, the point symmetry of the diffraction pattern, and the reflection conditions.
Dennis Sherwood and Jon Cooper
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199559046
- eISBN:
- 9780191595028
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559046.001.0001
- Subject:
- Physics, Crystallography: Physics
This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book ...
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This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book develops from first principles all relevant mathematics, diffraction, and wave theory. The practical aspects of sample preparation and X-ray data collection using both laboratory and synchrotron sources are covered along with data analysis at both the theoretical and practical levels. The important role played by the Patterson function in structure analysis by both molecular replacement and experimental phasing approaches is covered, as are methods for improving the resulting electron density map. The theoretical basis of methods used in refinement of protein crystal structures are then covered in depth along with the crucial task of defining the binding sites of ligands and drug molecules. The complementary roles of other diffraction methods which reveal further detail of great functional importance in a crystal structure are outlined.Less
This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book develops from first principles all relevant mathematics, diffraction, and wave theory. The practical aspects of sample preparation and X-ray data collection using both laboratory and synchrotron sources are covered along with data analysis at both the theoretical and practical levels. The important role played by the Patterson function in structure analysis by both molecular replacement and experimental phasing approaches is covered, as are methods for improving the resulting electron density map. The theoretical basis of methods used in refinement of protein crystal structures are then covered in depth along with the crucial task of defining the binding sites of ligands and drug molecules. The complementary roles of other diffraction methods which reveal further detail of great functional importance in a crystal structure are outlined.
Peter Müller, Regine Herbst-Irmer, Anthony L. Spek, Thomas R. Schneider, and Michael R. Sawaya
- Published in print:
- 2006
- Published Online:
- September 2010
- ISBN:
- 9780198570769
- eISBN:
- 9780191718809
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570769.001.0001
- Subject:
- Physics, Crystallography: Physics
This book covers advanced aspects of practical crystal structure refinement, focusing on practical problems in the everyday life of a crystallographer. After an introduction to SHELXL in the first ...
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This book covers advanced aspects of practical crystal structure refinement, focusing on practical problems in the everyday life of a crystallographer. After an introduction to SHELXL in the first chapter, the second chapter provides a brief survey of crystal structure refinement. The next few chapters address the various aspects of structure refinement, from the treatment of hydrogen atoms to the assignment of atom types, to disorder, to non-crystallographic symmetry and twinning. One chapter is dedicated to the refinement of macromolecular structures and two shorter chapters deal with structure validation. In most chapters, the book gives refinement examples, based on the program SHELXL, describing every problem in detail.Less
This book covers advanced aspects of practical crystal structure refinement, focusing on practical problems in the everyday life of a crystallographer. After an introduction to SHELXL in the first chapter, the second chapter provides a brief survey of crystal structure refinement. The next few chapters address the various aspects of structure refinement, from the treatment of hydrogen atoms to the assignment of atom types, to disorder, to non-crystallographic symmetry and twinning. One chapter is dedicated to the refinement of macromolecular structures and two shorter chapters deal with structure validation. In most chapters, the book gives refinement examples, based on the program SHELXL, describing every problem in detail.
D. Huybrechts
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199296866
- eISBN:
- 9780191711329
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296866.003.0013
- Subject:
- Mathematics, Geometry / Topology
This chapter gives pointers for more advanced topics, which require prerequisites that are beyond standard introductions to algebraic geometry. The Mckay correspondence relates the ...
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This chapter gives pointers for more advanced topics, which require prerequisites that are beyond standard introductions to algebraic geometry. The Mckay correspondence relates the equivariant-derived category of a variety endowed with the action of a finite group and the derived category of a crepant resolution of the quotient. This chapter gives the results from Bridgeland, King, and Reid for a special crepant resolution provided by Hilbert schemes and of Bezrukavnikov and Kaledin for symplectic vector spaces. A brief discussion of Kontsevich's homological mirror symmetry is included, as well as a discussion of stability conditions on triangulated categories. Twisted sheaves and their derived categories can be dealt with in a similar way, and some of the results in particular for K3 surfaces are presented.Less
This chapter gives pointers for more advanced topics, which require prerequisites that are beyond standard introductions to algebraic geometry. The Mckay correspondence relates the equivariant-derived category of a variety endowed with the action of a finite group and the derived category of a crepant resolution of the quotient. This chapter gives the results from Bridgeland, King, and Reid for a special crepant resolution provided by Hilbert schemes and of Bezrukavnikov and Kaledin for symplectic vector spaces. A brief discussion of Kontsevich's homological mirror symmetry is included, as well as a discussion of stability conditions on triangulated categories. Twisted sheaves and their derived categories can be dealt with in a similar way, and some of the results in particular for K3 surfaces are presented.
Lieven De Winter and Patrick Dumont
- Published in print:
- 2003
- Published Online:
- January 2005
- ISBN:
- 9780198297840
- eISBN:
- 9780191602016
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019829784X.003.0006
- Subject:
- Political Science, Comparative Politics
Reviews the mechanisms of delegation and accountability in post-war Belgium prior to the major reforms of the 1990s and the subsequent reforms. Discusses how political parties dominate these ...
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Reviews the mechanisms of delegation and accountability in post-war Belgium prior to the major reforms of the 1990s and the subsequent reforms. Discusses how political parties dominate these processes and reduce many actors in the parliamentary chain of delegation (MPs, ministers, civil servants) to mere party agents. Partitocracy is unavoidable and even functional for political system stability in Belgium, but it does come at the cost of undermining political legitimacy and governability.Less
Reviews the mechanisms of delegation and accountability in post-war Belgium prior to the major reforms of the 1990s and the subsequent reforms. Discusses how political parties dominate these processes and reduce many actors in the parliamentary chain of delegation (MPs, ministers, civil servants) to mere party agents. Partitocracy is unavoidable and even functional for political system stability in Belgium, but it does come at the cost of undermining political legitimacy and governability.
Daniel L. Stein and Charles M. Newman
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691147338
- eISBN:
- 9781400845637
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147338.001.0001
- Subject:
- Sociology, Science, Technology and Environment
Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. This book ...
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Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. This book offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity. This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into and modify this framework. The book then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling. Providing an essential overview of the history, science, and growing significance of this exciting field, the book also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a useful book for students and practitioners in the natural and social sciences, with new material even for the experts.Less
Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. This book offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity. This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into and modify this framework. The book then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling. Providing an essential overview of the history, science, and growing significance of this exciting field, the book also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a useful book for students and practitioners in the natural and social sciences, with new material even for the experts.
Laurent Lellouch, Rainer Sommer, Benjamin Svetitsky, Anastassios Vladikas, and Leticia F. Cugliandolo (eds)
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199691609
- eISBN:
- 9780191731792
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691609.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
The book is based on the lectures delivered at the XCIII Session of the ´Ecole de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of Ph.D. ...
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The book is based on the lectures delivered at the XCIII Session of the ´Ecole de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of Ph.D. students and postdoctoral Fellows with the principles and methods of modern lattice field theory, which Is set to resolve fundamental, non-perturbative questions about QCD without uncontrolled approximations. The emphasis of the book is on the theoretical developments that have shaped the field in the last two decades and that have turned lattice gauge theory into a robust approach to the determination of low energy hadronic quantities and of fundamental parameters of the Standard Model. By way of introduction, the courses of the school began by covering lattice theory basics (P. Hernández), lattice renormalization and improvement (P. Weisz and A. Vladikas) and the many faces of chirality (D.B. Kaplan). A later course introduced QCD at finite temperature and density (O. Philipsen). A broad view of lattice computation from the basics to recent developments was offered in the corresponding course (M. Lüscher). The students learned the basics of lattice computation in a hands-on tutorial (S. Schaefer)---a first at Les Houches, Extrapolations to physical quark masses and a framework for the parameterization of the low-energy physics by means of effective coupling constants has been covered in the course on chiral perturbation theory (M. Golterman). A course in heavy-quark effective theories (R. Sommer), an essential tool for performing the relevant lattice calculations, covered HQET from its basics to recent advances. A number of shorter courses rounded out the school and broadened its purview. These included recent applications to flavour physics (L. Lellouch) the nucleon--nucleon interation (S. Aoki) and a course on physics beyond the Standard Model (T. Appelquist and E.T. Neil).Less
The book is based on the lectures delivered at the XCIII Session of the ´Ecole de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of Ph.D. students and postdoctoral Fellows with the principles and methods of modern lattice field theory, which Is set to resolve fundamental, non-perturbative questions about QCD without uncontrolled approximations. The emphasis of the book is on the theoretical developments that have shaped the field in the last two decades and that have turned lattice gauge theory into a robust approach to the determination of low energy hadronic quantities and of fundamental parameters of the Standard Model. By way of introduction, the courses of the school began by covering lattice theory basics (P. Hernández), lattice renormalization and improvement (P. Weisz and A. Vladikas) and the many faces of chirality (D.B. Kaplan). A later course introduced QCD at finite temperature and density (O. Philipsen). A broad view of lattice computation from the basics to recent developments was offered in the corresponding course (M. Lüscher). The students learned the basics of lattice computation in a hands-on tutorial (S. Schaefer)---a first at Les Houches, Extrapolations to physical quark masses and a framework for the parameterization of the low-energy physics by means of effective coupling constants has been covered in the course on chiral perturbation theory (M. Golterman). A course in heavy-quark effective theories (R. Sommer), an essential tool for performing the relevant lattice calculations, covered HQET from its basics to recent advances. A number of shorter courses rounded out the school and broadened its purview. These included recent applications to flavour physics (L. Lellouch) the nucleon--nucleon interation (S. Aoki) and a course on physics beyond the Standard Model (T. Appelquist and E.T. Neil).
Barry M. McCoy
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199556632
- eISBN:
- 9780191723278
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.003.0016
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter presents philosophic discussion of the difference between reductionism and complexity, which focuses on the dependence of phenomena on past history, on the size of the system, and on the ...
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This chapter presents philosophic discussion of the difference between reductionism and complexity, which focuses on the dependence of phenomena on past history, on the size of the system, and on the very curious question of why intuition is derived that is applied to real systems from very specialized models that have strong and unrealistic symmetry properties.Less
This chapter presents philosophic discussion of the difference between reductionism and complexity, which focuses on the dependence of phenomena on past history, on the size of the system, and on the very curious question of why intuition is derived that is applied to real systems from very specialized models that have strong and unrealistic symmetry properties.
Reinhold A. Bertlmann
- Published in print:
- 2000
- Published Online:
- February 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.
Valeri P. Frolov and Andrei Zelnikov
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199692293
- eISBN:
- 9780191731860
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199692293.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This book is a thorough and up‐to‐date introduction to black hole physics. It provides a modern and unified overview of all their aspects, physical, mathematical, astrophysical, classical, and ...
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This book is a thorough and up‐to‐date introduction to black hole physics. It provides a modern and unified overview of all their aspects, physical, mathematical, astrophysical, classical, and quantum. Black holes are the most intriguing objects in the Universe. For many years they have been considered just as interesting solutions of the General Relativity with a number of amusing mathematical properties. But now, after discovery of astrophysical black holes, the Einstein gravity has become a practical tool for their study. In this book we present the theory of black holes in the form which might be useful for students and young scientists. This is a self‐contained textbook. It includes pedagogically presented `standard' material on black holes and also quite new subjects such as black holes in spacetimes with large extra dimensions and a role of hidden symmetries in black hole physics.Less
This book is a thorough and up‐to‐date introduction to black hole physics. It provides a modern and unified overview of all their aspects, physical, mathematical, astrophysical, classical, and quantum. Black holes are the most intriguing objects in the Universe. For many years they have been considered just as interesting solutions of the General Relativity with a number of amusing mathematical properties. But now, after discovery of astrophysical black holes, the Einstein gravity has become a practical tool for their study. In this book we present the theory of black holes in the form which might be useful for students and young scientists. This is a self‐contained textbook. It includes pedagogically presented `standard' material on black holes and also quite new subjects such as black holes in spacetimes with large extra dimensions and a role of hidden symmetries in black hole physics.
Beverley J. Glover
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198565970
- eISBN:
- 9780191714009
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198565970.003.0014
- Subject:
- Biology, Plant Sciences and Forestry
This book has previously discussed the ABC model of flower development and the molecular changes that occur to generate the correct numbers and arrangements of the four whorls of floral organs. This ...
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This book has previously discussed the ABC model of flower development and the molecular changes that occur to generate the correct numbers and arrangements of the four whorls of floral organs. This chapter starts with a basic flower, such as the flower of Arabidopsis, and considers the ways in which its form can be altered by known developmental programmes. The chapter then focusses on the petals or corolla, as the whorl of organs of primary importance in attracting potential pollinators, and considers changes to its size, its symmetry (zygomorphy versus actinomorphy), the shape of its component petals, and its position within an inflorescence. The chapter also looks at the development of specialized features such as nectar spurs and landing platforms.Less
This book has previously discussed the ABC model of flower development and the molecular changes that occur to generate the correct numbers and arrangements of the four whorls of floral organs. This chapter starts with a basic flower, such as the flower of Arabidopsis, and considers the ways in which its form can be altered by known developmental programmes. The chapter then focusses on the petals or corolla, as the whorl of organs of primary importance in attracting potential pollinators, and considers changes to its size, its symmetry (zygomorphy versus actinomorphy), the shape of its component petals, and its position within an inflorescence. The chapter also looks at the development of specialized features such as nectar spurs and landing platforms.
Alessandro Minelli
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780198566205
- eISBN:
- 9780191713866
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566205.003.0008
- Subject:
- Biology, Animal Biology, Evolutionary Biology / Genetics
This chapter discusses the evolution of the anteroposterior and dorsoventral patterning of the main body axis and its symmetry properties, then compares it to the ‘internal’ axis represented by the ...
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This chapter discusses the evolution of the anteroposterior and dorsoventral patterning of the main body axis and its symmetry properties, then compares it to the ‘internal’ axis represented by the gut, thus describing metazoans as ‘double animals’ with two components, external and internal, largely independent in their morphogenesis and patterning, and to the secondary axes represented by the appendages. The origin of the latter is presented in light of the notion of paramorphism, according to which the appendages, rather than originating de novo, would derive from a redeployment of the same basic growth and patterning systems already involved in producing the main body axis. Nature and origin of the segmental organization present in several animal groups are discussed. The second half of the chapter surveys the evolution of the main organ systems, following a criticism of the current concept of organogenesis.Less
This chapter discusses the evolution of the anteroposterior and dorsoventral patterning of the main body axis and its symmetry properties, then compares it to the ‘internal’ axis represented by the gut, thus describing metazoans as ‘double animals’ with two components, external and internal, largely independent in their morphogenesis and patterning, and to the secondary axes represented by the appendages. The origin of the latter is presented in light of the notion of paramorphism, according to which the appendages, rather than originating de novo, would derive from a redeployment of the same basic growth and patterning systems already involved in producing the main body axis. Nature and origin of the segmental organization present in several animal groups are discussed. The second half of the chapter surveys the evolution of the main organ systems, following a criticism of the current concept of organogenesis.
Daniel L. Stein and Charles M. Newman
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691147338
- eISBN:
- 9781400845637
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147338.003.0002
- Subject:
- Sociology, Science, Technology and Environment
This chapter introduces the basic concepts and language that will be needed later on: order, symmetry, invariance, broken symmetry, Hamiltonian, condensed matter, order parameter, ground state, and ...
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This chapter introduces the basic concepts and language that will be needed later on: order, symmetry, invariance, broken symmetry, Hamiltonian, condensed matter, order parameter, ground state, and several thermodynamic terms. It also presents the necessary concepts from thermodynamics and statistical mechanics that will be needed later. It boils down the latter to its most elemental and essential ingredient: that of temperature as controlling the relative probabilities of configurations of different energies. For much of statistical mechanics, all else is commentary. This is sufficient to present an intuitive understanding of why and how matter organizes itself into different phases as temperature varies, and leads to the all-important concept of a phase transition.Less
This chapter introduces the basic concepts and language that will be needed later on: order, symmetry, invariance, broken symmetry, Hamiltonian, condensed matter, order parameter, ground state, and several thermodynamic terms. It also presents the necessary concepts from thermodynamics and statistical mechanics that will be needed later. It boils down the latter to its most elemental and essential ingredient: that of temperature as controlling the relative probabilities of configurations of different energies. For much of statistical mechanics, all else is commentary. This is sufficient to present an intuitive understanding of why and how matter organizes itself into different phases as temperature varies, and leads to the all-important concept of a phase transition.
Richard Healey
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199287963
- eISBN:
- 9780191713453
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199287963.003.0006
- Subject:
- Philosophy, Philosophy of Science
This chapter argues that gauge symmetry is a purely formal feature of our theoretical representations with no empirical consequences. It distinguishes theoretical symmetries of a theory from ...
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This chapter argues that gauge symmetry is a purely formal feature of our theoretical representations with no empirical consequences. It distinguishes theoretical symmetries of a theory from empirical symmetries of situations to which a theory may be applied. A theoretical symmetry is purely formal if it implies no corresponding empirical symmetry. The chapter responds to several objections based on phenomena whose explanation apparently requires that gauge symmetry have empirical consequences. It argues that gauge symmetry is not observable and criticizes ‘the gauge argument’ from gauge symmetry to the existence of fundamental interactions. ‘Ghost’ fields are not real fields: despite its name, ‘spontaneous symmetry breaking’ does not involve any breaking of ‘local’ gauge symmetry; the theta-vacuum is not a superposition of distinct states inter-related by ‘large’ gauge transformations; anomalies in empirically successful theories do not involve breaking of any empirical gauge symmetry.Less
This chapter argues that gauge symmetry is a purely formal feature of our theoretical representations with no empirical consequences. It distinguishes theoretical symmetries of a theory from empirical symmetries of situations to which a theory may be applied. A theoretical symmetry is purely formal if it implies no corresponding empirical symmetry. The chapter responds to several objections based on phenomena whose explanation apparently requires that gauge symmetry have empirical consequences. It argues that gauge symmetry is not observable and criticizes ‘the gauge argument’ from gauge symmetry to the existence of fundamental interactions. ‘Ghost’ fields are not real fields: despite its name, ‘spontaneous symmetry breaking’ does not involve any breaking of ‘local’ gauge symmetry; the theta-vacuum is not a superposition of distinct states inter-related by ‘large’ gauge transformations; anomalies in empirically successful theories do not involve breaking of any empirical gauge symmetry.
Mark Casson
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199213979
- eISBN:
- 9780191707469
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213979.003.0003
- Subject:
- Business and Management, Business History, Organization Studies
The counterfactual railway system was constructed using nine heuristic principles. The most important was the Steiner Principle, which asserts that under certain conditions an optimal railway network ...
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The counterfactual railway system was constructed using nine heuristic principles. The most important was the Steiner Principle, which asserts that under certain conditions an optimal railway network is linked up by a set of spatially symmetric three-way hubs. The counterfactual network equals or exceeds the performance of the actual network according to various metrics. The counterfactual network achieves this performance with 13,000 route miles as compared to the 20,000 route miles of the actual system.Less
The counterfactual railway system was constructed using nine heuristic principles. The most important was the Steiner Principle, which asserts that under certain conditions an optimal railway network is linked up by a set of spatially symmetric three-way hubs. The counterfactual network equals or exceeds the performance of the actual network according to various metrics. The counterfactual network achieves this performance with 13,000 route miles as compared to the 20,000 route miles of the actual system.
