Juan Luis Vázquez
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199202973
- eISBN:
- 9780191707919
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199202973.001.0001
- Subject:
- Mathematics, Applied Mathematics
This book is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as ...
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This book is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of physics, chemistry, biology, and engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis. Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity (equations of porous medium type), the aim of this book is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular problems. These estimates are the building blocks in understanding the qualitative theory, and the decay rates pave the way to the fine study of asymptotics. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including time decay, smoothing, extinction in finite time, and delayed regularity.Less
This book is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of physics, chemistry, biology, and engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis. Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity (equations of porous medium type), the aim of this book is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular problems. These estimates are the building blocks in understanding the qualitative theory, and the decay rates pave the way to the fine study of asymptotics. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including time decay, smoothing, extinction in finite time, and delayed regularity.
J. N. Reddy
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198525295
- eISBN:
- 9780191711671
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525295.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of ...
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This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of incompressible fluids), and solid mechanics (elasticity, beams and plates). Both geometric as well as material nonlinearities are considered, and static and transient (that is, time-dependent) responses are studied. Although there exist a number of books on nonlinear finite elements that serve as good references for engineers who are familiar with the subject and wish to learn advanced topics or the latest developments, there is currently no book that is suitable as a textbook for a first course on nonlinear finite element analysis. This book fills the void in the market, providing a clear understanding of the concepts of nonlinear finite element analyses through detailed theoretical formulations and computer implementation steps, examples and exercises, in a tutorial, user-oriented style. In addition, the book is a useful reference for industrial engineers and scientists, and serves as a prelude to more advanced books on the subject.Less
This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of incompressible fluids), and solid mechanics (elasticity, beams and plates). Both geometric as well as material nonlinearities are considered, and static and transient (that is, time-dependent) responses are studied. Although there exist a number of books on nonlinear finite elements that serve as good references for engineers who are familiar with the subject and wish to learn advanced topics or the latest developments, there is currently no book that is suitable as a textbook for a first course on nonlinear finite element analysis. This book fills the void in the market, providing a clear understanding of the concepts of nonlinear finite element analyses through detailed theoretical formulations and computer implementation steps, examples and exercises, in a tutorial, user-oriented style. In addition, the book is a useful reference for industrial engineers and scientists, and serves as a prelude to more advanced books on the subject.
Russell L. De Valois and Karen K. De Valois
- Published in print:
- 1991
- Published Online:
- January 2008
- ISBN:
- 9780195066579
- eISBN:
- 9780199872220
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195066579.003.0011
- Subject:
- Psychology, Cognitive Neuroscience
This chapter discusses the nonlinear responses of the visual system. Topics covered include threshold nonlinearity, phase nonlinearity, amplitude nonlinearity, half-wave rectification, and ...
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This chapter discusses the nonlinear responses of the visual system. Topics covered include threshold nonlinearity, phase nonlinearity, amplitude nonlinearity, half-wave rectification, and interactions between different spatial frequencies.Less
This chapter discusses the nonlinear responses of the visual system. Topics covered include threshold nonlinearity, phase nonlinearity, amplitude nonlinearity, half-wave rectification, and interactions between different spatial frequencies.
Mauro Fabrizio and Morro Angelo
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198527008
- eISBN:
- 9780191713316
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527008.003.0010
- Subject:
- Mathematics, Applied Mathematics
This chapter presents some nonlinear constitutive models and develops wave propagation problems in nonlinear electromagnetism. Nonlinear models arise from nonlinear functions or functionals, which ...
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This chapter presents some nonlinear constitutive models and develops wave propagation problems in nonlinear electromagnetism. Nonlinear models arise from nonlinear functions or functionals, which describe the polarization and the magnetization. Various perturbation approaches to the generation of harmonics are outlined. Exact results are provided in connection with wavefronts associated with hyperbolic systems of equations, and the classical Bernoulli equation for the amplitude is obtained. Shock wave solutions in nonlinear dielectrics are investigated.Less
This chapter presents some nonlinear constitutive models and develops wave propagation problems in nonlinear electromagnetism. Nonlinear models arise from nonlinear functions or functionals, which describe the polarization and the magnetization. Various perturbation approaches to the generation of harmonics are outlined. Exact results are provided in connection with wavefronts associated with hyperbolic systems of equations, and the classical Bernoulli equation for the amplitude is obtained. Shock wave solutions in nonlinear dielectrics are investigated.
Brian C. J. Moore
- Published in print:
- 1995
- Published Online:
- January 2008
- ISBN:
- 9780198523307
- eISBN:
- 9780191712456
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198523307.003.0001
- Subject:
- Psychology, Health Psychology
This chapter describes the anatomy and physiology of the cochlea, and the changes associated with cochlear pathology. Evidence is presented supporting the idea that there is an active nonlinear ...
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This chapter describes the anatomy and physiology of the cochlea, and the changes associated with cochlear pathology. Evidence is presented supporting the idea that there is an active nonlinear mechanism in the normal cochlea, and a loss of this mechanism in impaired hearing. The effects of cochlear pathology on cochlear tuning, nonlinearity, and input-output functions are described.Less
This chapter describes the anatomy and physiology of the cochlea, and the changes associated with cochlear pathology. Evidence is presented supporting the idea that there is an active nonlinear mechanism in the normal cochlea, and a loss of this mechanism in impaired hearing. The effects of cochlear pathology on cochlear tuning, nonlinearity, and input-output functions are described.
Michael Wolf-Branigin
- Published in print:
- 2013
- Published Online:
- January 2013
- ISBN:
- 9780199829460
- eISBN:
- 9780199315895
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199829460.001.0001
- Subject:
- Social Work, Research and Evaluation
Complexity theory provides a promising framework for organizing and conducting social work research and evaluation. This book explores the history and roots of complexity and related concepts by ...
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Complexity theory provides a promising framework for organizing and conducting social work research and evaluation. This book explores the history and roots of complexity and related concepts by garnering an understanding of the components that comprise complex systems. These components include being agent-based, being sensitive to initial conditions, having attraction, being heterogeneous, operating as an iterative process, having boundaries, using feedback, and creating a self-organizing emergent behavior. Readers will learn to frame their research using the components found in complex systems by using their existing knowledge of research methods and applying basic mathematical concepts. Several concepts related to complexity theory are introduced and applied to social work research studies, including bordering between chaos and equilibrium, diverse perspectives, diverse heuristics, robustness, and the wisdom of crowds. Many of the theoretical and mathematical concepts underlying complexity are introduced, such as game theory, graph theory, Boolean logic, decision theory, and network science. Using this background, the reader will gain an understanding of the interconnectedness and networking that this approach provides. Statistical methods familiar to many readers are reviewed and applied to complexity. Readers will gain an understanding of agent-based modeling as a new and evolving computational approach for creating simulations to represent and forecast complex systems. To advance this line of inquiry, a complexity research agenda for social work is developed.Less
Complexity theory provides a promising framework for organizing and conducting social work research and evaluation. This book explores the history and roots of complexity and related concepts by garnering an understanding of the components that comprise complex systems. These components include being agent-based, being sensitive to initial conditions, having attraction, being heterogeneous, operating as an iterative process, having boundaries, using feedback, and creating a self-organizing emergent behavior. Readers will learn to frame their research using the components found in complex systems by using their existing knowledge of research methods and applying basic mathematical concepts. Several concepts related to complexity theory are introduced and applied to social work research studies, including bordering between chaos and equilibrium, diverse perspectives, diverse heuristics, robustness, and the wisdom of crowds. Many of the theoretical and mathematical concepts underlying complexity are introduced, such as game theory, graph theory, Boolean logic, decision theory, and network science. Using this background, the reader will gain an understanding of the interconnectedness and networking that this approach provides. Statistical methods familiar to many readers are reviewed and applied to complexity. Readers will gain an understanding of agent-based modeling as a new and evolving computational approach for creating simulations to represent and forecast complex systems. To advance this line of inquiry, a complexity research agenda for social work is developed.
Sylvie Benzoni-Gavage and Denis Serre
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199211234
- eISBN:
- 9780191705700
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211234.003.0011
- Subject:
- Mathematics, Applied Mathematics
The local existence result for smooth solutions follows the guidelines of Chapters 10 (because of the nonlinearity) and 9 (since there is a boundary). Compatibility conditions are needed between the ...
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The local existence result for smooth solutions follows the guidelines of Chapters 10 (because of the nonlinearity) and 9 (since there is a boundary). Compatibility conditions are needed between the initial and boundary data.Less
The local existence result for smooth solutions follows the guidelines of Chapters 10 (because of the nonlinearity) and 9 (since there is a boundary). Compatibility conditions are needed between the initial and boundary data.
Oran R. Young
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199656202
- eISBN:
- 9780191742149
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656202.003.0004
- Subject:
- Economics and Finance, Development, Growth, and Environmental
The thesis of this chapter is that reliance on management tools that assume change will be linear and gradual in the effort to manage complex and dynamic socioecological systems is a liability that ...
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The thesis of this chapter is that reliance on management tools that assume change will be linear and gradual in the effort to manage complex and dynamic socioecological systems is a liability that is already costly and that is likely to produce profoundly undesirable consequences in the future. In developing this thesis, the chapter starts with a brief account of the nature of change in socioecological systems, explores management tools suitable for use in settings characterized by nonlinear, rapid, and irreversible change, and considers the implications of the fact that environmental regimes are complex and dynamic systems themselves. The concluding section formulates a set of principles that will help to (re)form environmental regimes that can produce sustainable outcomes in a world in which change is often nonlinear, abrupt, and irreversible.Less
The thesis of this chapter is that reliance on management tools that assume change will be linear and gradual in the effort to manage complex and dynamic socioecological systems is a liability that is already costly and that is likely to produce profoundly undesirable consequences in the future. In developing this thesis, the chapter starts with a brief account of the nature of change in socioecological systems, explores management tools suitable for use in settings characterized by nonlinear, rapid, and irreversible change, and considers the implications of the fact that environmental regimes are complex and dynamic systems themselves. The concluding section formulates a set of principles that will help to (re)form environmental regimes that can produce sustainable outcomes in a world in which change is often nonlinear, abrupt, and irreversible.
Buzsáki György
- Published in print:
- 2006
- Published Online:
- May 2009
- ISBN:
- 9780195301069
- eISBN:
- 9780199863716
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195301069.003.0003
- Subject:
- Neuroscience, Neuroendocrine and Autonomic, Techniques
In addition to principal cells, the cerebral cortex contains diverse classes of interneurons that selectively and discriminately innervate various parts of principal cells and each other. The ...
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In addition to principal cells, the cerebral cortex contains diverse classes of interneurons that selectively and discriminately innervate various parts of principal cells and each other. The hypothesized “goal” of the daunting connectionist schemes of interneurons is to provide maximum functional complexity. Without inhibition and dedicated interneurons, excitatory circuits cannot accomplish anything useful. Interneurons provide autonomy and independence to neighboring principal cells but at the same time also offer useful temporal coordination. The functional diversity of principal cells is enhanced by the domain-specific actions of GABAergic interneurons, which can dynamically alter the qualities of the principal cells. The balance between excitation and inhibition is often accomplished by oscillations. Connections among interneurons, including electrical gap junctions, are especially suitable for maintaining clocking actions. Thus, the cerebral cortex is not only a complex system with complicated interactions among identical constituents but also has developed a diverse system of components.Less
In addition to principal cells, the cerebral cortex contains diverse classes of interneurons that selectively and discriminately innervate various parts of principal cells and each other. The hypothesized “goal” of the daunting connectionist schemes of interneurons is to provide maximum functional complexity. Without inhibition and dedicated interneurons, excitatory circuits cannot accomplish anything useful. Interneurons provide autonomy and independence to neighboring principal cells but at the same time also offer useful temporal coordination. The functional diversity of principal cells is enhanced by the domain-specific actions of GABAergic interneurons, which can dynamically alter the qualities of the principal cells. The balance between excitation and inhibition is often accomplished by oscillations. Connections among interneurons, including electrical gap junctions, are especially suitable for maintaining clocking actions. Thus, the cerebral cortex is not only a complex system with complicated interactions among identical constituents but also has developed a diverse system of components.
Vladimir M. Agranovich
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199234417
- eISBN:
- 9780191715426
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199234417.003.0007
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter presents the calculation of dielectric tensor based on the application of polariton theory and the theory developed by Dzyaloshinsky and Pitaevsky, as well as the calculation of ...
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This chapter presents the calculation of dielectric tensor based on the application of polariton theory and the theory developed by Dzyaloshinsky and Pitaevsky, as well as the calculation of transverse dielectric tensor for the region of Frenkel exciton resonances. It is shown that the effect of long wavelength absorption in the vicinity and below of the exciton resonances and the absorption corresponding to contribution of high order terms of exciton-photon interaction are automatically taken into account in these theories. The macroscopic and microscopic theories of the optical nonlinearity are also discussed.Less
This chapter presents the calculation of dielectric tensor based on the application of polariton theory and the theory developed by Dzyaloshinsky and Pitaevsky, as well as the calculation of transverse dielectric tensor for the region of Frenkel exciton resonances. It is shown that the effect of long wavelength absorption in the vicinity and below of the exciton resonances and the absorption corresponding to contribution of high order terms of exciton-photon interaction are automatically taken into account in these theories. The macroscopic and microscopic theories of the optical nonlinearity are also discussed.
Vladimir M. Agranovich
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199234417
- eISBN:
- 9780191715426
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199234417.003.0008
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter presents calculations of dielectric tensor of superlattices. In consideration of superlattices having large periods compared to lattice constants, equations of macroscopical ...
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This chapter presents calculations of dielectric tensor of superlattices. In consideration of superlattices having large periods compared to lattice constants, equations of macroscopical electrodynamics are used. For superlattices with anisotropic layers, the spatial dispersion in the vicinity of exciton resonances, magneto-optical as well as electro-optical effects and optical nonlinearities are considered.Less
This chapter presents calculations of dielectric tensor of superlattices. In consideration of superlattices having large periods compared to lattice constants, equations of macroscopical electrodynamics are used. For superlattices with anisotropic layers, the spatial dispersion in the vicinity of exciton resonances, magneto-optical as well as electro-optical effects and optical nonlinearities are considered.
Torben Grodal
- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780195371314
- eISBN:
- 9780199870585
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195371314.003.0008
- Subject:
- Literature, Film, Media, and Cultural Studies
The chapter discusses how storytelling represents an innate mental capacity to synthesize an agency’s perceptual input, its emotions, and its output in terms of action. Insight into the architecture ...
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The chapter discusses how storytelling represents an innate mental capacity to synthesize an agency’s perceptual input, its emotions, and its output in terms of action. Insight into the architecture of the embodied brain and the PECMA flow clarifies how to understand the psychological function of stories and storytelling. The chapter further describes the way that different media—language and oral storytelling, drama, written stories, film, and video games—use different aspects of the mental “storytelling” that characterizes our ordinary experience of daily life and its actions, and it describes the historical development in narrative techniques of representation in different media. It uses this narrative theory to redefine the story-discourse dichotomy, and to argue that film narratives are typically experienced as taking place in a kind of presence, and also discusses the relation between narratives and playing games vital for interactive media. Finally, it discusses the relationship between storytelling interactivity and linearity and shows that there are a number of psychological and motivational reasons that nonlinear storytelling is difficult, and that many so-called nonlinear formats consist in fact of sets of linear stories.</ABS>Less
The chapter discusses how storytelling represents an innate mental capacity to synthesize an agency’s perceptual input, its emotions, and its output in terms of action. Insight into the architecture of the embodied brain and the PECMA flow clarifies how to understand the psychological function of stories and storytelling. The chapter further describes the way that different media—language and oral storytelling, drama, written stories, film, and video games—use different aspects of the mental “storytelling” that characterizes our ordinary experience of daily life and its actions, and it describes the historical development in narrative techniques of representation in different media. It uses this narrative theory to redefine the story-discourse dichotomy, and to argue that film narratives are typically experienced as taking place in a kind of presence, and also discusses the relation between narratives and playing games vital for interactive media. Finally, it discusses the relationship between storytelling interactivity and linearity and shows that there are a number of psychological and motivational reasons that nonlinear storytelling is difficult, and that many so-called nonlinear formats consist in fact of sets of linear stories.</ABS>
Oran R. Young
- Published in print:
- 2017
- Published Online:
- September 2017
- ISBN:
- 9780262035934
- eISBN:
- 9780262338899
- Item type:
- book
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262035934.001.0001
- Subject:
- Political Science, Public Policy
Governing for sustainability in a world of complex systems will require new social capital in the form of innovative steering mechanisms that differ in important respects from those familiar to us ...
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Governing for sustainability in a world of complex systems will require new social capital in the form of innovative steering mechanisms that differ in important respects from those familiar to us from past experience. Complex systems feature high levels of connectivity, nonlinear dynamics, directional change, and emergent properties. Creating effective governance arrangements in such settings calls for an ability to combine the durability required to guide behavior with the agility needed to adjust or reform institutional arrangements to cope with rapidly changing circumstances. Success in such endeavors will depend on a capacity to supplement mainstream regulatory approaches to governance with new governance strategies. Promising examples include governance through goal-setting and principled governance. But additional innovations in this realm will be necessary to address needs for governance arising in the Anthropocene. The way forward in this effort will be to build cooperative relations between analysts and practitioners rather than treating them as separate communities that respond to different incentives and operate in different worlds.Less
Governing for sustainability in a world of complex systems will require new social capital in the form of innovative steering mechanisms that differ in important respects from those familiar to us from past experience. Complex systems feature high levels of connectivity, nonlinear dynamics, directional change, and emergent properties. Creating effective governance arrangements in such settings calls for an ability to combine the durability required to guide behavior with the agility needed to adjust or reform institutional arrangements to cope with rapidly changing circumstances. Success in such endeavors will depend on a capacity to supplement mainstream regulatory approaches to governance with new governance strategies. Promising examples include governance through goal-setting and principled governance. But additional innovations in this realm will be necessary to address needs for governance arising in the Anthropocene. The way forward in this effort will be to build cooperative relations between analysts and practitioners rather than treating them as separate communities that respond to different incentives and operate in different worlds.
Andreas Savvides and Thanasis Stengos
- Published in print:
- 2008
- Published Online:
- June 2013
- ISBN:
- 9780804755405
- eISBN:
- 9780804769761
- Item type:
- book
- Publisher:
- Stanford University Press
- DOI:
- 10.11126/stanford/9780804755405.001.0001
- Subject:
- Economics and Finance, Econometrics
This book provides an in-depth investigation of the link between human capital and economic growth. The book examines the determinants of economic growth through a historical overview of the concept ...
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This book provides an in-depth investigation of the link between human capital and economic growth. The book examines the determinants of economic growth through a historical overview of the concept of human capital. The text fosters an understanding of the connection between human capital and economic growth through the exploration of different theoretical approaches, a review of the literature, and the application of nonlinear estimation techniques to a comprehensive data set. The book discusses nonparametric econometric techniques and their application to estimating nonlinearities—which has emerged as one of the most salient features of empirical work in modeling the human capital–growth relationship, and the process of economic growth in general.Less
This book provides an in-depth investigation of the link between human capital and economic growth. The book examines the determinants of economic growth through a historical overview of the concept of human capital. The text fosters an understanding of the connection between human capital and economic growth through the exploration of different theoretical approaches, a review of the literature, and the application of nonlinear estimation techniques to a comprehensive data set. The book discusses nonparametric econometric techniques and their application to estimating nonlinearities—which has emerged as one of the most salient features of empirical work in modeling the human capital–growth relationship, and the process of economic growth in general.
J. N. REDDY
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198525295
- eISBN:
- 9780191711671
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525295.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
One of the most important thing engineers and scientists do is to model natural phenomena. They develop conceptual and mathematical models to simulate physical events, whether they are aerospace, ...
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One of the most important thing engineers and scientists do is to model natural phenomena. They develop conceptual and mathematical models to simulate physical events, whether they are aerospace, biological, chemical, geological, or mechanical. The mathematical models are developed using laws of physics and they are often described in terms of algebraic, differential, and/or integral equations relating various quantities of interest. A mathematical model of the motion of the pendulum can be constructed using the principle of conservation of linear momentum, that is, Newton's second law of motion. This chapter also discusses the traditional finite element method, nonlinear analysis, and classification of nonlinearities. The finite element method is a powerful method that can be used to perform numerical simulations of engineering problems.Less
One of the most important thing engineers and scientists do is to model natural phenomena. They develop conceptual and mathematical models to simulate physical events, whether they are aerospace, biological, chemical, geological, or mechanical. The mathematical models are developed using laws of physics and they are often described in terms of algebraic, differential, and/or integral equations relating various quantities of interest. A mathematical model of the motion of the pendulum can be constructed using the principle of conservation of linear momentum, that is, Newton's second law of motion. This chapter also discusses the traditional finite element method, nonlinear analysis, and classification of nonlinearities. The finite element method is a powerful method that can be used to perform numerical simulations of engineering problems.
Melvin Lax, Wei Cai, and Min Xu
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198567769
- eISBN:
- 9780191718359
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567769.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter explains why a laser line is so narrow (it can be as low as one cycle per second, even when the laser frequency is of the order of 10 per second) and shows that autonomous oscillators ...
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This chapter explains why a laser line is so narrow (it can be as low as one cycle per second, even when the laser frequency is of the order of 10 per second) and shows that autonomous oscillators (those with no absolute time origin) all behave like the rotating wave van der Pol (RWVP) oscillator, have narrow line-widths, and have a behavior near threshold that is calculated exactly. An oscillator with purely resistive nonlinearities is considered, and the diffusion coefficient is discussed along with a RWVP oscillator scaled to canonical form, phase fluctuations in a resistive oscillator, amplitude fluctuations, Fokker–Planck equation for RWVP oscillators, and eigenfunctions of the Fokker–Planck operator.Less
This chapter explains why a laser line is so narrow (it can be as low as one cycle per second, even when the laser frequency is of the order of 10 per second) and shows that autonomous oscillators (those with no absolute time origin) all behave like the rotating wave van der Pol (RWVP) oscillator, have narrow line-widths, and have a behavior near threshold that is calculated exactly. An oscillator with purely resistive nonlinearities is considered, and the diffusion coefficient is discussed along with a RWVP oscillator scaled to canonical form, phase fluctuations in a resistive oscillator, amplitude fluctuations, Fokker–Planck equation for RWVP oscillators, and eigenfunctions of the Fokker–Planck operator.
Timo Teräsvirta, Dag Tjøstheim, and W. J. Granger
- Published in print:
- 2010
- Published Online:
- May 2011
- ISBN:
- 9780199587148
- eISBN:
- 9780191595387
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199587148.003.0001
- Subject:
- Economics and Finance, Econometrics
This chapter gives a brief overview of the basic concepts and topics used in the book. There exists a large literature on linear stationary models. The purpose of the present book is to look at ...
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This chapter gives a brief overview of the basic concepts and topics used in the book. There exists a large literature on linear stationary models. The purpose of the present book is to look at nonlinear models in both a stationary and nonstationary framework. Linear techniques are contrasted with typical tools used to analyse nonlinearity, such as the conditional mean and the conditional variance, and Markov chain theory. Nonlinear parametric models are mentioned as well as nonparametric ones.Less
This chapter gives a brief overview of the basic concepts and topics used in the book. There exists a large literature on linear stationary models. The purpose of the present book is to look at nonlinear models in both a stationary and nonstationary framework. Linear techniques are contrasted with typical tools used to analyse nonlinearity, such as the conditional mean and the conditional variance, and Markov chain theory. Nonlinear parametric models are mentioned as well as nonparametric ones.
J. N. REDDY
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198525295
- eISBN:
- 9780191711671
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525295.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Nonlinearities arise from two independent sources: nonlinearity due to changes in the geometry or position of the material particles of a continuum, which is called the geometric nonlinearity, and ...
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Nonlinearities arise from two independent sources: nonlinearity due to changes in the geometry or position of the material particles of a continuum, which is called the geometric nonlinearity, and nonlinearity due to the nonlinear material behavior, which is called material nonlinearity. In fluid mechanics and coupled fluid flow and heat transfer, geometric nonlinearity arises as a result of the spatial (or Eulerian) description of motion, and they enter the equations of motion through material time derivative term. This chapter considers material nonlinear formulations and discusses nonlinear elastic and elastic plastic material models for solids and power-law model for viscous incompressible fluids. Nonlinear elastic problems are discussed, along with the small deformation theory of plasticity, ideal plasticity, strain hardening plasticity, elastic plastic analysis of a bar, non-Newtonian fluids, governing equations in cylindrical coordinates, power-law fluids, White-Metzner fluids, and finite element models.Less
Nonlinearities arise from two independent sources: nonlinearity due to changes in the geometry or position of the material particles of a continuum, which is called the geometric nonlinearity, and nonlinearity due to the nonlinear material behavior, which is called material nonlinearity. In fluid mechanics and coupled fluid flow and heat transfer, geometric nonlinearity arises as a result of the spatial (or Eulerian) description of motion, and they enter the equations of motion through material time derivative term. This chapter considers material nonlinear formulations and discusses nonlinear elastic and elastic plastic material models for solids and power-law model for viscous incompressible fluids. Nonlinear elastic problems are discussed, along with the small deformation theory of plasticity, ideal plasticity, strain hardening plasticity, elastic plastic analysis of a bar, non-Newtonian fluids, governing equations in cylindrical coordinates, power-law fluids, White-Metzner fluids, and finite element models.
Elbio Dagotto, Shuai Dong, Rong Yu, Cengiz Sen, Gonzalo Alvarez, and Adriana Moreo
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199592593
- eISBN:
- 9780191741050
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199592593.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
A new paradigm in the study of complex materials is gaining considerable experimental and theoretical support. It is based on the notion that many unusual properties of these materials arise from the ...
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A new paradigm in the study of complex materials is gaining considerable experimental and theoretical support. It is based on the notion that many unusual properties of these materials arise from the competition of phases, often involving a metal and an insulator. A family of materials these effects are very clear are the manganites, that exhibit the colossal magnetoresistance effect. Recent theoretical work has shown that this effect is caused by phase competition between a double-exchange metal and a charge-ordered insulator. But this competition is certainly not restricted to manganites but arises in many other contexts such as underdoped high-Tc cuprates, where the pseudogap phase could also be a mixture of superconducting and antiferromagnetic regions. In this chapter, a generic description of these effects is presented and the typical consequences of phase competition are outlined.Less
A new paradigm in the study of complex materials is gaining considerable experimental and theoretical support. It is based on the notion that many unusual properties of these materials arise from the competition of phases, often involving a metal and an insulator. A family of materials these effects are very clear are the manganites, that exhibit the colossal magnetoresistance effect. Recent theoretical work has shown that this effect is caused by phase competition between a double-exchange metal and a charge-ordered insulator. But this competition is certainly not restricted to manganites but arises in many other contexts such as underdoped high-Tc cuprates, where the pseudogap phase could also be a mixture of superconducting and antiferromagnetic regions. In this chapter, a generic description of these effects is presented and the typical consequences of phase competition are outlined.
H. B. Meerwaldt, G. A. Steele, and H. S. J. van der Zant
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199691388
- eISBN:
- 9780191742255
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691388.003.0012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Carbon nanotubes (CNTs) are nonlinear high-Q resonators with strong coupling to single-electron tunneling. This chapter begins by describing several methods to detect the flexural motion of a CNT ...
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Carbon nanotubes (CNTs) are nonlinear high-Q resonators with strong coupling to single-electron tunneling. This chapter begins by describing several methods to detect the flexural motion of a CNT resonator. Next, it illustrates how single-electron tunneling in quantum dot CNT resonators leads to sharp dips in the mechanical resonance frequency and significant damping. It discusses four different contributions to the nonlinear oscillation of a CNT resonator: beam-like mechanical nonlinearity, nonlinearity due to gate-induced mechanical tension, electrostatic nonlinearity, and nonlinearity due to single-electron tunneling, and provide quantitative estimates of their strengths. Finally, it shows how the large response of the resonance frequency of a CNT resonator to a change in gate voltage or tension makes CNT resonators ideally suited for parametric excitation and for studying the coupling between different mechanical modes.Less
Carbon nanotubes (CNTs) are nonlinear high-Q resonators with strong coupling to single-electron tunneling. This chapter begins by describing several methods to detect the flexural motion of a CNT resonator. Next, it illustrates how single-electron tunneling in quantum dot CNT resonators leads to sharp dips in the mechanical resonance frequency and significant damping. It discusses four different contributions to the nonlinear oscillation of a CNT resonator: beam-like mechanical nonlinearity, nonlinearity due to gate-induced mechanical tension, electrostatic nonlinearity, and nonlinearity due to single-electron tunneling, and provide quantitative estimates of their strengths. Finally, it shows how the large response of the resonance frequency of a CNT resonator to a change in gate voltage or tension makes CNT resonators ideally suited for parametric excitation and for studying the coupling between different mechanical modes.
