Kevin S. McCann
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691134178
- eISBN:
- 9781400840687
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691134178.003.0002
- Subject:
- Biology, Ecology
This chapter introduces the reader to some of the main conceptual ideas behind dynamical systems theory from the perspective of an experimentalist. It first considers the qualitative approaches used ...
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This chapter introduces the reader to some of the main conceptual ideas behind dynamical systems theory from the perspective of an experimentalist. It first considers the qualitative approaches used to study complex problems before discussing dynamical systems and bifurcations. In particular, it examines the use of time series to represent solutions and dynamics in the phase space, phase space respresentations of equilibrium and nonequilibrium steady states, the qualitative analysis of steady states, and some of the mechanics of local stability analysis for an equilibrium using the Lotka–Volterra model for an equilibrium steady state. It also explores the relationship between the type of model dynamics and the geometry of the underlying mathematical functions. Finally, it presents an empirical example from ecology, Hopf bifurcation in an aquatic microcosm, to illustrate the main concepts of dynamical systems theory and shows that the mathematics of dynamical systems underlies the dynamics of real ecological systems.Less
This chapter introduces the reader to some of the main conceptual ideas behind dynamical systems theory from the perspective of an experimentalist. It first considers the qualitative approaches used to study complex problems before discussing dynamical systems and bifurcations. In particular, it examines the use of time series to represent solutions and dynamics in the phase space, phase space respresentations of equilibrium and nonequilibrium steady states, the qualitative analysis of steady states, and some of the mechanics of local stability analysis for an equilibrium using the Lotka–Volterra model for an equilibrium steady state. It also explores the relationship between the type of model dynamics and the geometry of the underlying mathematical functions. Finally, it presents an empirical example from ecology, Hopf bifurcation in an aquatic microcosm, to illustrate the main concepts of dynamical systems theory and shows that the mathematics of dynamical systems underlies the dynamics of real ecological systems.
Gregor Schöner
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195300598
- eISBN:
- 9780199867165
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195300598.003.0002
- Subject:
- Psychology, Cognitive Psychology, Developmental Psychology
Dynamical systems thinking can provide metaphors that help ask new questions, generate new experimental paradigms and measures, and lead to new kinds of explanations. This chapter reviews dynamical ...
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Dynamical systems thinking can provide metaphors that help ask new questions, generate new experimental paradigms and measures, and lead to new kinds of explanations. This chapter reviews dynamical systems theory (DST) as a set of concepts that formalizes such metaphors and thus becomes a scientific theory of considerable rigor. It considers five concepts: (1) Behavioral patterns resist change; that is, they are stable. This may be mathematically characterized by considering behavioral patterns as the attractor states of a dynamical system. (2) Behavioral change is brought about by a loss of stability. (3) Representations possess stability properties, as well, and can be understood as the attractor states of dynamic fields, that is, of continuous distributions of neuronal activation. (4) Cognitive processes emerge from instabilities of dynamic fields. (5) Learning occurs as changes in behavioral or field dynamics that shift the behavioral and environmental context in which these instabilities occur.Less
Dynamical systems thinking can provide metaphors that help ask new questions, generate new experimental paradigms and measures, and lead to new kinds of explanations. This chapter reviews dynamical systems theory (DST) as a set of concepts that formalizes such metaphors and thus becomes a scientific theory of considerable rigor. It considers five concepts: (1) Behavioral patterns resist change; that is, they are stable. This may be mathematically characterized by considering behavioral patterns as the attractor states of a dynamical system. (2) Behavioral change is brought about by a loss of stability. (3) Representations possess stability properties, as well, and can be understood as the attractor states of dynamic fields, that is, of continuous distributions of neuronal activation. (4) Cognitive processes emerge from instabilities of dynamic fields. (5) Learning occurs as changes in behavioral or field dynamics that shift the behavioral and environmental context in which these instabilities occur.
Han L. J. van der Maas and Maartje E. J. Raijmakers
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195300598
- eISBN:
- 9780199867165
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195300598.003.0015
- Subject:
- Psychology, Cognitive Psychology, Developmental Psychology
This chapter discusses old-fashioned cognitive development from the point of view of two modern approaches, connectionism and nonlinear dynamical systems theory. The main assertion in both ...
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This chapter discusses old-fashioned cognitive development from the point of view of two modern approaches, connectionism and nonlinear dynamical systems theory. The main assertion in both connectionist and dynamic systems approaches is that higher cognitive functioning is largely based on nonsymbolic, graded, and dynamic properties, of which these same approaches provide the best account. The chapter argues that the claim concerning nonsymbolic higher order cognition is overstated and explains its position by focusing on sudden transitions in cognitive development.Less
This chapter discusses old-fashioned cognitive development from the point of view of two modern approaches, connectionism and nonlinear dynamical systems theory. The main assertion in both connectionist and dynamic systems approaches is that higher cognitive functioning is largely based on nonsymbolic, graded, and dynamic properties, of which these same approaches provide the best account. The chapter argues that the claim concerning nonsymbolic higher order cognition is overstated and explains its position by focusing on sudden transitions in cognitive development.
John Spencer (ed.)
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195300598
- eISBN:
- 9780199867165
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195300598.001.0001
- Subject:
- Psychology, Cognitive Psychology, Developmental Psychology
From William James to Sigmund Freud to Jean Piaget to B. F. Skinner, scholars (and parents) have wondered how children move from the blooming, buzzing confusion of infancy, through the tumult of ...
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From William James to Sigmund Freud to Jean Piaget to B. F. Skinner, scholars (and parents) have wondered how children move from the blooming, buzzing confusion of infancy, through the tumult of childhood and adolescence, into adulthood. Does development occur continuously over time or in a series of dramatic stages? Is development driven by learning or by biological maturational processes? What is the nature of experience, and how does it generate change? The study of development has always been organized around these big questions. Answers to these questions have a profound influence on daily life, forming a framework for how parents think about their own children, and influencing both national policy and educational curricula. This book defines and refines two major theoretical approaches within developmental science that address the central issues of development-connectionism and dynamical systems theory. The chapters in this book provide an introduction, overview, and critical evaluation of each approach, including three sets of case studies that illustrate how these approaches have been used to study topics ranging from early motor development to the acquisition of grammar. It also presents a collection of commentaries by leading scholars, which offer a critical view from both an “outsiders” and an “insiders” perspective.Less
From William James to Sigmund Freud to Jean Piaget to B. F. Skinner, scholars (and parents) have wondered how children move from the blooming, buzzing confusion of infancy, through the tumult of childhood and adolescence, into adulthood. Does development occur continuously over time or in a series of dramatic stages? Is development driven by learning or by biological maturational processes? What is the nature of experience, and how does it generate change? The study of development has always been organized around these big questions. Answers to these questions have a profound influence on daily life, forming a framework for how parents think about their own children, and influencing both national policy and educational curricula. This book defines and refines two major theoretical approaches within developmental science that address the central issues of development-connectionism and dynamical systems theory. The chapters in this book provide an introduction, overview, and critical evaluation of each approach, including three sets of case studies that illustrate how these approaches have been used to study topics ranging from early motor development to the acquisition of grammar. It also presents a collection of commentaries by leading scholars, which offer a critical view from both an “outsiders” and an “insiders” perspective.
ANDRÉ AUTHIER
- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528920
- eISBN:
- 9780191713125
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528920.003.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter provides a historical introduction to X-ray dynamical diffraction. It starts with an account of Ewald's thesis on the dispersion of light and of the famous experiment of the diffraction ...
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This chapter provides a historical introduction to X-ray dynamical diffraction. It starts with an account of Ewald's thesis on the dispersion of light and of the famous experiment of the diffraction of X-rays by crystals by M. Laue, W. Friedrich, and P. Knipping. The successive steps in the development of the theory of X-ray diffraction are then summarized: Laue's and Darwin's geometrical theories; Darwin's, Ewald's, and Laue's dynamical theories; early experimental proofs, the notion of extinction and the mosaic crystal model, observation in the fifties and sixties of the fundamental properties of the X-ray wavefields in crystals (anomalous absorption and the Borrmann effect, double refraction, Pendellösung, bent trajectories in deformed crystals), extension of the dynamical theory to the case of deformed crystals, modern applications for the characterization of crystal defects and X-ray optics for synchrotron radiation.Less
This chapter provides a historical introduction to X-ray dynamical diffraction. It starts with an account of Ewald's thesis on the dispersion of light and of the famous experiment of the diffraction of X-rays by crystals by M. Laue, W. Friedrich, and P. Knipping. The successive steps in the development of the theory of X-ray diffraction are then summarized: Laue's and Darwin's geometrical theories; Darwin's, Ewald's, and Laue's dynamical theories; early experimental proofs, the notion of extinction and the mosaic crystal model, observation in the fifties and sixties of the fundamental properties of the X-ray wavefields in crystals (anomalous absorption and the Borrmann effect, double refraction, Pendellösung, bent trajectories in deformed crystals), extension of the dynamical theory to the case of deformed crystals, modern applications for the characterization of crystal defects and X-ray optics for synchrotron radiation.
André Authier
- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528920
- eISBN:
- 9780191713125
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528920.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
X-ray diffraction is a major tool for the study of crystal structures and the characterization of crystal perfection. Since the discovery of X-ray diffraction by von Laue, Friedrich, and Knipping in ...
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X-ray diffraction is a major tool for the study of crystal structures and the characterization of crystal perfection. Since the discovery of X-ray diffraction by von Laue, Friedrich, and Knipping in 1912 two basic theories have been used to describe this diffraction. One is the approximate geometrical, or kinematical theory, applicable to small or highly imperfect crystals; it is used for the determination of crystal structures and the study of powders and polycrystalline materials. The other one is the rigorous dynamical theory, applicable to perfect or nearly perfect crystals and, for that reason, is the one used for the assessment of the structural properties of high technology materials. It has witnessed exciting developments since the advent of synchrotron radiation. This book provides an account of the dynamical theory of diffraction and of its applications. The first part serves as an introduction to the subject, presenting early developments, Ewald's theory of dispersion and the basic results of Laue's dynamical theory. This is followed in the second part by a detailed development of the diffraction and propagation properties of X-rays in perfect crystals, including the study of anomalous absorption, Pendellösung, grazing incidence diffraction (GID) and n-beam or multiple-beam diffraction. The third part constitutes an extension of the theory to the case of slightly and highly deformed crystals. The last part gives three applications of the theory: X-ray optics for synchrotron radiation, location of atoms at surfaces and interfaces and X-ray diffraction topography.Less
X-ray diffraction is a major tool for the study of crystal structures and the characterization of crystal perfection. Since the discovery of X-ray diffraction by von Laue, Friedrich, and Knipping in 1912 two basic theories have been used to describe this diffraction. One is the approximate geometrical, or kinematical theory, applicable to small or highly imperfect crystals; it is used for the determination of crystal structures and the study of powders and polycrystalline materials. The other one is the rigorous dynamical theory, applicable to perfect or nearly perfect crystals and, for that reason, is the one used for the assessment of the structural properties of high technology materials. It has witnessed exciting developments since the advent of synchrotron radiation. This book provides an account of the dynamical theory of diffraction and of its applications. The first part serves as an introduction to the subject, presenting early developments, Ewald's theory of dispersion and the basic results of Laue's dynamical theory. This is followed in the second part by a detailed development of the diffraction and propagation properties of X-rays in perfect crystals, including the study of anomalous absorption, Pendellösung, grazing incidence diffraction (GID) and n-beam or multiple-beam diffraction. The third part constitutes an extension of the theory to the case of slightly and highly deformed crystals. The last part gives three applications of the theory: X-ray optics for synchrotron radiation, location of atoms at surfaces and interfaces and X-ray diffraction topography.
Domitilla Del Vecchio and Richard M. Murray
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161532
- eISBN:
- 9781400850501
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161532.003.0001
- Subject:
- Biology, Biochemistry / Molecular Biology
This chapter provides a brief introduction to concepts from systems biology; tools from differential equations and control theory; and approaches to the modeling, analysis, and design of biomolecular ...
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This chapter provides a brief introduction to concepts from systems biology; tools from differential equations and control theory; and approaches to the modeling, analysis, and design of biomolecular feedback systems. It begins with a discussion of the role of modeling, analysis, and feedback in biological systems. This is followed by a short review of key concepts and tools from control and dynamical systems theory, which is intended to provide insight into the main methodology described in this volume. Finally, this chapter gives another brief introduction—this time to the field of synthetic biology, which is the primary topic of the latter portion of this book.Less
This chapter provides a brief introduction to concepts from systems biology; tools from differential equations and control theory; and approaches to the modeling, analysis, and design of biomolecular feedback systems. It begins with a discussion of the role of modeling, analysis, and feedback in biological systems. This is followed by a short review of key concepts and tools from control and dynamical systems theory, which is intended to provide insight into the main methodology described in this volume. Finally, this chapter gives another brief introduction—this time to the field of synthetic biology, which is the primary topic of the latter portion of this book.
Robert D. Rupert
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195379457
- eISBN:
- 9780199869114
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195379457.003.0009
- Subject:
- Philosophy, Philosophy of Mind
This chapter spells out the embedded view and the principles of modeling normally associated with it. The embedded approach aims to minimize the amount of computation and representation included in ...
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This chapter spells out the embedded view and the principles of modeling normally associated with it. The embedded approach aims to minimize the amount of computation and representation included in cognitive models, thereby explaining how the cognitive system carries out its cognitive tasks in a timely fashion; the general strategy for doing so employs locally valid heuristics. The chapter then focuses on the role of computation in the embedded view, advancing the following contentions: that the embedded view has been most successful when set within a computational framework, that simplifying computation does not amount to eliminating computation—even where explicit rules are eliminated—and that dynamical systems theory does not model the subtle timing of the organism's interaction with the environment in a way inherently superior to computationalist strategies.Less
This chapter spells out the embedded view and the principles of modeling normally associated with it. The embedded approach aims to minimize the amount of computation and representation included in cognitive models, thereby explaining how the cognitive system carries out its cognitive tasks in a timely fashion; the general strategy for doing so employs locally valid heuristics. The chapter then focuses on the role of computation in the embedded view, advancing the following contentions: that the embedded view has been most successful when set within a computational framework, that simplifying computation does not amount to eliminating computation—even where explicit rules are eliminated—and that dynamical systems theory does not model the subtle timing of the organism's interaction with the environment in a way inherently superior to computationalist strategies.
E. Miranda and V. Dobrosavljević
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199592593
- eISBN:
- 9780191741050
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199592593.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter provides a review of recently-developed Dynamical Mean-Field Theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. The chapter first ...
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This chapter provides a review of recently-developed Dynamical Mean-Field Theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. The chapter first describes the standard DMFT approach, which is exact in the limit of large coordination, and explain why in its simplest form it cannot capture either Anderson localization or the glassy behavior of electrons. Various extensions of DMFT are then described, including statistical DMFT, typical medium theory, and extended DMFT, methods specifically designed to overcome the limitations of the original formulation. The chapter provides an overview of the results obtained using these approaches, including the formation of electronic Griffiths phases, the self-organized criticality of the Coulomb glass, and the two-fluid behavior near Mott-Anderson transitions. Finally, the chapter outlines research directions that may provide a route to bridge the gap between the DMFT-based theories and the complementary diffusion-mode approaches to the metal-insulatorLess
This chapter provides a review of recently-developed Dynamical Mean-Field Theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. The chapter first describes the standard DMFT approach, which is exact in the limit of large coordination, and explain why in its simplest form it cannot capture either Anderson localization or the glassy behavior of electrons. Various extensions of DMFT are then described, including statistical DMFT, typical medium theory, and extended DMFT, methods specifically designed to overcome the limitations of the original formulation. The chapter provides an overview of the results obtained using these approaches, including the formation of electronic Griffiths phases, the self-organized criticality of the Coulomb glass, and the two-fluid behavior near Mott-Anderson transitions. Finally, the chapter outlines research directions that may provide a route to bridge the gap between the DMFT-based theories and the complementary diffusion-mode approaches to the metal-insulator
Roman Frigg and Charlotte Werndl
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199577439
- eISBN:
- 9780191730603
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577439.003.0005
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology
This chapter explains the most important notions of entropy and clarifies their interrelations. It furthermore explores what notions of probabilities are at work when entropy is defined in terms of ...
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This chapter explains the most important notions of entropy and clarifies their interrelations. It furthermore explores what notions of probabilities are at work when entropy is defined in terms of probability. Entropies from thermodynamics, information theory, statistical mechanics, dynamical systems theory, and fractal geometry are surveyed. Notions of entropy from statistical mechanics such as varieties of the Boltzmann and Gibbs entropies can be traced back to information-theoretic entropy. As the chapter points out, an analytic connection between fine-grained Boltzmann entropy and thermodynamic entropy can be established for ideal gases. No easy results about probabilities follow, since several interpretations are compatible with each definition of entropy.Less
This chapter explains the most important notions of entropy and clarifies their interrelations. It furthermore explores what notions of probabilities are at work when entropy is defined in terms of probability. Entropies from thermodynamics, information theory, statistical mechanics, dynamical systems theory, and fractal geometry are surveyed. Notions of entropy from statistical mechanics such as varieties of the Boltzmann and Gibbs entropies can be traced back to information-theoretic entropy. As the chapter points out, an analytic connection between fine-grained Boltzmann entropy and thermodynamic entropy can be established for ideal gases. No easy results about probabilities follow, since several interpretations are compatible with each definition of entropy.
ANDRÉ AUTHIER
- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528920
- eISBN:
- 9780191713125
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528920.003.0014
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are ...
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This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are extended so as to apply to highly deformed crystals. Their resolution is the discussed and the principle of their numerical integration in an inverted Borrmann triangle given. The ray concept is generalized to the case of strong deformations by noting that new wavefields are generated in the highly strained regions; this is known as the interbranch scattering effect. The last part of the chapter is devoted to an account of the statistical dynamical theories for highly imperfect crystals, with emphasis on Kato's statistical theories. Examples of experimental test of the dynamical theory are also given.Less
This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are extended so as to apply to highly deformed crystals. Their resolution is the discussed and the principle of their numerical integration in an inverted Borrmann triangle given. The ray concept is generalized to the case of strong deformations by noting that new wavefields are generated in the highly strained regions; this is known as the interbranch scattering effect. The last part of the chapter is devoted to an account of the statistical dynamical theories for highly imperfect crystals, with emphasis on Kato's statistical theories. Examples of experimental test of the dynamical theory are also given.
Giovanna Colombetti
- Published in print:
- 2014
- Published Online:
- May 2014
- ISBN:
- 9780262019958
- eISBN:
- 9780262318419
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262019958.003.0003
- Subject:
- Philosophy, Philosophy of Mind
In this chapter I draw on the conceptual tools of dynamical systems theory to conceptualize emotional episodes as self-organizing patterns of the entire organism. I first overview how dynamical ...
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In this chapter I draw on the conceptual tools of dynamical systems theory to conceptualize emotional episodes as self-organizing patterns of the entire organism. I first overview how dynamical systems concepts have been used in “dynamical affective science” to model emotions. Although existing proposals apply at very different levels of description, they all characterize the organism as complex, self-organizing, open, and plastic, realizing emotional episodes that are softly assembled, context dependent, and highly variable, yet patterned and recurrent. I then elaborate on the implications of this dynamical conceptualization for the debate on the nature of the emotions discussed in the previous chapter. This dynamical conceptualization notably posits neither internal causes of emotional episodes and of their different aspects, nor a distinction between alleged basic and nonbasic emotions; rather, it treats all emotions as complex organismic patterns subject to both evolutionary and developmental pressures. I conclude with a discussion of how dynamical systems concepts also help characterize the relationship between emotions and moods.Less
In this chapter I draw on the conceptual tools of dynamical systems theory to conceptualize emotional episodes as self-organizing patterns of the entire organism. I first overview how dynamical systems concepts have been used in “dynamical affective science” to model emotions. Although existing proposals apply at very different levels of description, they all characterize the organism as complex, self-organizing, open, and plastic, realizing emotional episodes that are softly assembled, context dependent, and highly variable, yet patterned and recurrent. I then elaborate on the implications of this dynamical conceptualization for the debate on the nature of the emotions discussed in the previous chapter. This dynamical conceptualization notably posits neither internal causes of emotional episodes and of their different aspects, nor a distinction between alleged basic and nonbasic emotions; rather, it treats all emotions as complex organismic patterns subject to both evolutionary and developmental pressures. I conclude with a discussion of how dynamical systems concepts also help characterize the relationship between emotions and moods.
Niels E. Henriksen and Flemming Y. Hansen
- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199203864
- eISBN:
- 9780191708251
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199203864.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter considers unimolecular reactions; photo-induced reactions, i.e. true unimolecular reactions; and reactions initiated by collisional activation, i.e. apparent unimolecular reactions where ...
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This chapter considers unimolecular reactions; photo-induced reactions, i.e. true unimolecular reactions; and reactions initiated by collisional activation, i.e. apparent unimolecular reactions where it is assumed that the time scales for activation and subsequent reaction are well separated. Elements of classical and quantum dynamical descriptions are discussed, including Slater theory and the quantum mechanical description of photo-induced reactions. Statistical theories aiming at the calculation of micro-canonical as well as canonical rate constants are discussed, including a detailed discussion of RRKM theory. It concludes with a discussion of femtochemistry, i.e. the observation and control of chemical dynamics using femtosecond pulses of electromagnetic radiation, focusing on the control of unimolecular reactions via the interaction with coherent light, that is, laser control.Less
This chapter considers unimolecular reactions; photo-induced reactions, i.e. true unimolecular reactions; and reactions initiated by collisional activation, i.e. apparent unimolecular reactions where it is assumed that the time scales for activation and subsequent reaction are well separated. Elements of classical and quantum dynamical descriptions are discussed, including Slater theory and the quantum mechanical description of photo-induced reactions. Statistical theories aiming at the calculation of micro-canonical as well as canonical rate constants are discussed, including a detailed discussion of RRKM theory. It concludes with a discussion of femtochemistry, i.e. the observation and control of chemical dynamics using femtosecond pulses of electromagnetic radiation, focusing on the control of unimolecular reactions via the interaction with coherent light, that is, laser control.
Johannes Jaeger and James Sharpe
- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199671427
- eISBN:
- 9780191781117
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199671427.003.0004
- Subject:
- Biology, Developmental Biology
Due to the finite number of dynamic behaviours that can be implemented by regulatory systems, it should be possible to enumerate and classify different developmental mechanisms that can achieve the ...
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Due to the finite number of dynamic behaviours that can be implemented by regulatory systems, it should be possible to enumerate and classify different developmental mechanisms that can achieve the same biological function. For example, there are only a small number of ways by which small regulatory networks can create a stripe of gene expression in a static or growing tissue. By comparing these different mechanisms, we can discover the design principles of stripe-producing regulatory networks. Such a rigorous and mechanistic classification scheme would constitute the basis for a theory of development that characterizes and explains the regularities and recurring motifs observed in organismal morphology. This tackles a central question in biology, which has fascinated numerous researchers since the rational taxonomists first raised it in the 19th century. This chapter introduces and defines a concept of developmental mechanism suitable for this endeavour, based on the conceptual framework of dynamical systems theory, which characterizes the dynamical repertoire of regulatory networks. Equivalent mechanisms are defined as sharing the same topology of their phase portraits: they have the same number and geometrical arrangement of attracting states, saddle points, and basins of attraction, and undergo structurally stable bifurcations as systems parameters change over time. These abstract concepts and their application are illustrated using specific examples such as simulated stripe-forming networks, vertebrate limb development, and the segmentation gene network in insects. This constitutes a first, tentative step towards a more general geometrical theory of developmental mechanisms and the complex map from genotype to phenotype.Less
Due to the finite number of dynamic behaviours that can be implemented by regulatory systems, it should be possible to enumerate and classify different developmental mechanisms that can achieve the same biological function. For example, there are only a small number of ways by which small regulatory networks can create a stripe of gene expression in a static or growing tissue. By comparing these different mechanisms, we can discover the design principles of stripe-producing regulatory networks. Such a rigorous and mechanistic classification scheme would constitute the basis for a theory of development that characterizes and explains the regularities and recurring motifs observed in organismal morphology. This tackles a central question in biology, which has fascinated numerous researchers since the rational taxonomists first raised it in the 19th century. This chapter introduces and defines a concept of developmental mechanism suitable for this endeavour, based on the conceptual framework of dynamical systems theory, which characterizes the dynamical repertoire of regulatory networks. Equivalent mechanisms are defined as sharing the same topology of their phase portraits: they have the same number and geometrical arrangement of attracting states, saddle points, and basins of attraction, and undergo structurally stable bifurcations as systems parameters change over time. These abstract concepts and their application are illustrated using specific examples such as simulated stripe-forming networks, vertebrate limb development, and the segmentation gene network in insects. This constitutes a first, tentative step towards a more general geometrical theory of developmental mechanisms and the complex map from genotype to phenotype.
Wassim M. Haddad and Sergey G. Nersesov
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691153469
- eISBN:
- 9781400842667
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153469.003.0004
- Subject:
- Mathematics, Applied Mathematics
This chapter describes the thermodynamic modeling of large-scale interconnected dynamical systems. Using compartmental dynamical system theory, it develops energy flow models possessing energy ...
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This chapter describes the thermodynamic modeling of large-scale interconnected dynamical systems. Using compartmental dynamical system theory, it develops energy flow models possessing energy conservation and energy equipartition principles for large-scale dynamical systems. It then gives a deterministic definition of entropy for a large-scale dynamical system that is consistent with the classical definition of entropy and shows that it satisfies a Clausius-type inequality leading to the law of nonconservation of entropy. It also introduces the notion of ectropy as a measure of the tendency of a dynamical system to do useful work and grow more organized. It demonstrates how conservation of energy in an isolated thermodynamic large-scale system leads to nonconservation of ectropy and entropy. Finally, the chapter uses the system ectropy as a Lyapunov function candidate to show that the large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.Less
This chapter describes the thermodynamic modeling of large-scale interconnected dynamical systems. Using compartmental dynamical system theory, it develops energy flow models possessing energy conservation and energy equipartition principles for large-scale dynamical systems. It then gives a deterministic definition of entropy for a large-scale dynamical system that is consistent with the classical definition of entropy and shows that it satisfies a Clausius-type inequality leading to the law of nonconservation of entropy. It also introduces the notion of ectropy as a measure of the tendency of a dynamical system to do useful work and grow more organized. It demonstrates how conservation of energy in an isolated thermodynamic large-scale system leads to nonconservation of ectropy and entropy. Finally, the chapter uses the system ectropy as a Lyapunov function candidate to show that the large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.
Dorothea Olkowski
- Published in print:
- 2007
- Published Online:
- March 2012
- ISBN:
- 9780748625567
- eISBN:
- 9780748652402
- Item type:
- chapter
- Publisher:
- Edinburgh University Press
- DOI:
- 10.3366/edinburgh/9780748625567.003.0007
- Subject:
- Philosophy, General
This chapter is a final attempt to think about an epistemology and an aesthetics outside of the constraints of dynamical systems theory. It investigates the photographic image and what has been ...
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This chapter is a final attempt to think about an epistemology and an aesthetics outside of the constraints of dynamical systems theory. It investigates the photographic image and what has been called cinematographic knowledge, explaining that for cinematographic knowledge, time is an independent variable, a parameter of the spatial manifold. The chapter proposes the concept of the discrete photograph and a new image of philosophy.Less
This chapter is a final attempt to think about an epistemology and an aesthetics outside of the constraints of dynamical systems theory. It investigates the photographic image and what has been called cinematographic knowledge, explaining that for cinematographic knowledge, time is an independent variable, a parameter of the spatial manifold. The chapter proposes the concept of the discrete photograph and a new image of philosophy.
Michael Silberstein
- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780262027236
- eISBN:
- 9780262322461
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262027236.003.0017
- Subject:
- Philosophy, Philosophy of Mind
Psychopathology might be one domain where we can get some empirical perch on the Systematicity debate. In patients with schizophrenia transformational systematicity and other types of systematicity ...
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Psychopathology might be one domain where we can get some empirical perch on the Systematicity debate. In patients with schizophrenia transformational systematicity and other types of systematicity often break down. Systems neuroscience has provided some reason to believe that the best explanation for this break down is in terms of the degradation of key brain subsymbolic network properties such as small-world graphical structures. It is argued that if such systems neuroscience explanations for failures of systematicity in schizophrenia are robust then this is a victory for network approaches over symbol-and-rule approaches that themselves provide little insight into said failures. Finally, there is speculation that the relevant dynamical and graphical relations in such cases extend beyond the brain to include body and environment.Less
Psychopathology might be one domain where we can get some empirical perch on the Systematicity debate. In patients with schizophrenia transformational systematicity and other types of systematicity often break down. Systems neuroscience has provided some reason to believe that the best explanation for this break down is in terms of the degradation of key brain subsymbolic network properties such as small-world graphical structures. It is argued that if such systems neuroscience explanations for failures of systematicity in schizophrenia are robust then this is a victory for network approaches over symbol-and-rule approaches that themselves provide little insight into said failures. Finally, there is speculation that the relevant dynamical and graphical relations in such cases extend beyond the brain to include body and environment.
André Authier
- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199659845
- eISBN:
- 9780191748219
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199659845.003.0009
- Subject:
- Physics, Crystallography
This chapter is devoted to optical properties of X-rays. In the first section the early measurements of optical properties of X-rays are discussed briefly (specular reflection, refraction, ...
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This chapter is devoted to optical properties of X-rays. In the first section the early measurements of optical properties of X-rays are discussed briefly (specular reflection, refraction, diffraction by a slit). In the ensuing sections the principle of the Ewald and Laue dynamical theories of X-ray diffraction is presented. The special optical properties of X-ray wavefields are described, such as their direction of propagation inside the crystal, anomalous absorption, and standing waves, as well as their application to the Kossel effect and the location of impurities at crystal surfaces. It is shown how the deviation from Bragg’s law, which is due to the effect of refraction, was measured experimentally, and the principle of the double-crystal spectrometer is given. The discovery of the Compton effect is also related, and its consequences as to the nature of X-rays are discussed.Less
This chapter is devoted to optical properties of X-rays. In the first section the early measurements of optical properties of X-rays are discussed briefly (specular reflection, refraction, diffraction by a slit). In the ensuing sections the principle of the Ewald and Laue dynamical theories of X-ray diffraction is presented. The special optical properties of X-ray wavefields are described, such as their direction of propagation inside the crystal, anomalous absorption, and standing waves, as well as their application to the Kossel effect and the location of impurities at crystal surfaces. It is shown how the deviation from Bragg’s law, which is due to the effect of refraction, was measured experimentally, and the principle of the double-crystal spectrometer is given. The discovery of the Compton effect is also related, and its consequences as to the nature of X-rays are discussed.
Dan C. Christensen
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199669264
- eISBN:
- 9780191748745
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199669264.003.0008
- Subject:
- Physics, History of Physics
Ch 8 is an analysis of Ørsted's doctoral thesis, which is a revised version (in Latin) of his review of Hauch's textbook. The ‘architecture’ of the thesis follows Kant's Metaphysical Foundations of ...
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Ch 8 is an analysis of Ørsted's doctoral thesis, which is a revised version (in Latin) of his review of Hauch's textbook. The ‘architecture’ of the thesis follows Kant's Metaphysical Foundations of Natural Science, which is basically a critical survey of Newton's Philosophiae Naturalis Principia Mathematica. Ørsted, however, adheres even more meticulously to Kant's epistemological scheme, which he calls ‘Ariadne's Clew’, than Kant himself. In conclusion he agrees with Kant that Newton's mechanical concepts, although they are conducive to mathematical treatment if subsumed under the quantitative category as matter, forces per se defy mathematization, because they are immeasurable and uncountable. Consequently, we are left with the paradox that corpuscular theory makes sense in mathematical terms, but is epistemologically flawed, while Kant's (and Ørsted's) alternative, dynamical theory, does make sense epistemologically, but lacks the quantifiable concepts necessary for constituting equations and thus the precondition of becoming scientific.Less
Ch 8 is an analysis of Ørsted's doctoral thesis, which is a revised version (in Latin) of his review of Hauch's textbook. The ‘architecture’ of the thesis follows Kant's Metaphysical Foundations of Natural Science, which is basically a critical survey of Newton's Philosophiae Naturalis Principia Mathematica. Ørsted, however, adheres even more meticulously to Kant's epistemological scheme, which he calls ‘Ariadne's Clew’, than Kant himself. In conclusion he agrees with Kant that Newton's mechanical concepts, although they are conducive to mathematical treatment if subsumed under the quantitative category as matter, forces per se defy mathematization, because they are immeasurable and uncountable. Consequently, we are left with the paradox that corpuscular theory makes sense in mathematical terms, but is epistemologically flawed, while Kant's (and Ørsted's) alternative, dynamical theory, does make sense epistemologically, but lacks the quantifiable concepts necessary for constituting equations and thus the precondition of becoming scientific.
Dorothea Olkowski
- Published in print:
- 2007
- Published Online:
- March 2012
- ISBN:
- 9780748625567
- eISBN:
- 9780748652402
- Item type:
- chapter
- Publisher:
- Edinburgh University Press
- DOI:
- 10.3366/edinburgh/9780748625567.003.0001
- Subject:
- Philosophy, General
This introductory chapter explains the theme of this book, which is about universal philosophy. The book proposes a critique of the limits of the particular formalist, mathematical structure used by ...
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This introductory chapter explains the theme of this book, which is about universal philosophy. The book proposes a critique of the limits of the particular formalist, mathematical structure used by Gilles Deleuze and the manifold of continuous space–time of dynamical systems theory. It proposes a methodology and an ontology oriented in relation to formal, mathematical structures, but able to be coherently and consistently asserted apart from them in terms of what is called sensibility. The book also recommends a rethink of the concept of time–space relations espoused by several philosophers, including Luce Irigaray, Henri Bergson, and Maurice Merleau-Ponty.Less
This introductory chapter explains the theme of this book, which is about universal philosophy. The book proposes a critique of the limits of the particular formalist, mathematical structure used by Gilles Deleuze and the manifold of continuous space–time of dynamical systems theory. It proposes a methodology and an ontology oriented in relation to formal, mathematical structures, but able to be coherently and consistently asserted apart from them in terms of what is called sensibility. The book also recommends a rethink of the concept of time–space relations espoused by several philosophers, including Luce Irigaray, Henri Bergson, and Maurice Merleau-Ponty.
