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  1. H. D. I. Abarbanel (1992). Local Lyapunov Exponents Computed From Observed Data. Journal of Nonlinear Science 2 (3):343-365.
    We develop methods for determining local Lyapunov exponents from observations of a scalar data set. Using average mutual information and the method of false neighbors, we reconstruct a multivariate time series, and then use local polynomial neighborhood-to-neighborhood maps to determine the phase space partial derivatives required to compute Lyapunov exponents. In several examples we demonstrate that the methods allow one to accurately reproduce results determined when the dynamics is known beforehand. We present a new recursive QR decomposition method for finding (...)
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  2. Michael Agar (2004). We Have Met the Other and We 'Re All Nonlinear: Ethnography as a Nonlinear Dynamic System'. Complexity 10 (2):16-24.
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  3. David Aubin (2008). 'The Memory of Life Itself': Bénard's Cells and the Cinematography of Self-Organization. Studies in History and Philosophy of Science Part A 39 (3):359-369.
    In 1900, the physicist Henri Bénard exhibited the spontaneous formation of cells in a layer of liquid heated from below. Six or seven decades later, drastic reinterpretations of this experiment formed an important component of ‘chaos theory’. This paper therefore is an attempt at writing the history of this experiment, its long neglect and its rediscovery. It examines Bénard’s experiments from three different perspectives. First, his results are viewed in the light of the relation between experimental and mathematical approaches in (...)
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  4. David Aubin (1998). A Cultural History of Catastrophes and Chaos: Around the Institut des Hautes Études Scientifiques. Princeton.
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  5. David Aubin & Amy Dalmedico (2002). Writing the History of Dynamics Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures. Historia Mathematica 29:1–67.
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  6. Sunny Auyang, How Science Comprehends Chaos.
    Behaviors of chaotic systems are unpredictable. Chaotic systems are deterministic, their evolutions being governed by dynamical equations. Are the two statements contradictory? They are not, because the theory of chaos encompasses two levels of description. On a higher level, unpredictability appears as an emergent property of systems that are predictable on a lower level. In this talk, we examine the structure of dynamical theories to see how they employ multiple descriptive levels to explain chaos, bifurcation, and other complexities of nonlinear (...)
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  7. Sunny Auyang, Nonlinear Dynamics: How Science Comprehends Chaos.
    Behaviors of chaotic systems are unpredictable. Chaotic systems are deterministic, their evolutions being governed by dynamical equations. Are the two statements contradictory? They are not, because the theory of chaos encompasses two levels of description. On a higher level, unpredictability appears as an emergent property of systems that are predictable on a lower level. In this talk, we examine the structure of dynamical theories to see how they employ multiple descriptive levels to explain chaos, bifurcation, and other complexities of nonlinear (...)
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  8. Christopher Belanger (2013). On Two Mathematical Definitions of Observational Equivalence: Manifest Isomorphism and Epsilon-Congruence Reconsidered. Studies in History and Philosophy of Science Part B 44 (2):69-76.
    In this article I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss’s ε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence (...)
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  9. P. Berge, Y. Pomeau & C. Vidal (1987). Order Within Chaos. Wiley.
  10. Robert Bishop, Chaos. Stanford Encyclopedia of Philosophy.
    The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system's behavior. The so-called butterfly effect has become one of the most popular images of chaos. The idea is that the flapping of a butterfly's wings in Argentina could cause a tornado in Texas three weeks later. By contrast, in an identical copy of the world sans the Argentinian butterfly, no such storm would have arisen (...)
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  11. Noah Moss Brender (2013). Sense-Making and Symmetry-Breaking. Symposium: The Canadian Journal of Continental Philosophy 17 (2):246-270.
    From his earliest work forward, Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own endogenous sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up Merleau-Ponty’s ontology (...)
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  12. G. Caglioti, H. Haken & L. Lugiato (eds.) (1988). Synergetics and Dynamical Instabilities. North Holland.
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  13. Carlos Castro (2010). On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy. Foundations of Physics 40 (11):1712-1730.
    A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of (...)
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  14. A. Combs & W. Sulis (1996). Nonlinear Dynamics in Human Behavior.
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  15. A. Das & P. Das (2002). Characterization of Chaos Evident in EEG by Nonlinear Data Analysis. Complexity 7 (3).
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  16. Mohammed H. I. Dore & J. Barkley Rosser, Do Nonlinear Dynamics in Economics Amount to a Kuhnian Paradigm Shift?
    Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity can (...)
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  17. Andrew A. Fingelkurts & Alexander A. Fingelkurts (2013). Dissipative Many-Body Model and a Nested Operational Architectonics of the Brain. Physics of Life Reviews 10:103-105.
    This paper briefly review a current trend in neuroscience aiming to combine neurophysiological and physical concepts in order to understand the emergence of spatio-temporal patterns within brain activity by which brain constructs knowledge from multiple streams of information. The authors further suggest that the meanings, which subjectively are experienced as thoughts or perceptions can best be described objectively as created and carried by large fields of neural activity within the operational architectonics of brain functioning.
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  18. Walter J. Freeman Iii (2009). Nonlinear Dynamics and Intention According to Aquinas. Mind and Matter 6 (2).
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  19. Axel Gelfert (2015). Between Rigor and Reality: Many-Body Models in Condensed Matter Physics. In Brigitte Falkenburg & Margaret Morrison (eds.), Why More Is Different: Philosophical Issues in Condensed Matter Physics and Complex Systems. Springer 201-226.
    The present paper focuses on a particular class of models intended to describe and explain the physical behaviour of systems that consist of a large number of interacting particles. Such many-body models are characterized by a specific Hamiltonian (energy operator) and are frequently employed in condensed matter physics in order to account for such phenomena as magnetism, superconductivity, and other phase transitions. Because of the dual role of many-body models as models of physical sys-tems (with specific physical phenomena as their (...)
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  20. GianCarlo Ghirardi (2002). Making Quantum Theory Compatible with Realism. Foundations of Science 7 (1-2):11-47.
    After a brief account of theway quantum theory deals with naturalprocesses, the crucial problem that such atheory meets, the measurement or, better, themacro-objectification problem is discussed.The embarrassing aspects of the occurrence ofentangled states involving macroscopic systemsare analyzed in details. The famous example ofSchroedinger's cat is presented and it ispointed out how the combined interplay of thesuperposition principle and the ensuingentanglement raises some serious difficultiesin working out a satisfactory quantum worldview, agreeing with our definiteperceptions. The orthodox solution to themacro-objectification problem, i.e. (...)
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  21. Giancarlo Ghirardi (1996). Quantum Dynamical Reduction and Reality: Replacing Probability Densities with Densities in Real Space. [REVIEW] Erkenntnis 45 (2-3):349 - 365.
    Consideration is given to recent attempts to solve the objectification problem of quantum mechanics by considering nonlinear and stochastic modifications of Schrödinger's evolution equation. Such theories agree with all predictions of standard quantum mechanics concerning microsystems but forbid the occurrence of superpositions of macroscopically different states. It is shown that the appropriate interpretation for such theories is obtained by replacing the probability densities of standard quantum mechanics with mass densities in real space. Criteria allowing a precise characterization of the idea (...)
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  22. Alfred Gierer (1981). Generation of Biological Patterns and Form: Some Physical, Mathematical and Logical Aspects. Progress in Biophysics and Molecular Biology 37 (1):1-48.
    While many different mechanisms contribute to the generation of spatial order in biological development, the formation of morphogenetic fields which in turn direct cell responses giving rise to pattern and form are of major importance and essential for embryogenesis and regeneration. Most likely the fields represent concentration patterns of substances produced by molecular kinetics. Short range autocatalytic activation in conjunction with longer range “lateral” inhibition or depletion effects is capable of generating such patterns (Gierer and Meinhardt, 1972). Non-linear reactions are (...)
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  23. Alfred Gierer & Hans Meinhardt (1972). A Theory of Biological Pattern Formation. Kybernetik, Continued as Biological Cybernetics 12 (1):30 - 39.
    The paper addresses the formation of striking patterns within originally near-homogenous tissue, the process prototypical for embryology, and represented in particularly purist form by cut sections of hydra regenerating, by internal reorganisation of the pre-existing tissue, a complete animal with head and foot. The essential requirements are autocatalytic, self-enhancing activation, combined with inhibitory or depletion effects of wider range – “lateral inhibition”. Not only de-novo-pattern formation, but also well known, striking features of developmental regulation such as induction, inhibition, and proportion (...)
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  24. N. Gisin (1983). Dissipative Quantum Dynamics for Systems Periodic in Time. Foundations of Physics 13 (7):643-654.
    A model of dissipative quantum dynamics (with a nonlinear friction term) is applied to systems periodic in time. The model is compared with the standard approaches based on the Floquet theorem. It is shown that for weak frictions the asymptotic states of the dynamics we propose are the periodic steady states which are usually postulated to be the states relevant for the statistical mechanics of time-periodic systems. A solution to the problem of nonuniqueness of the “quasienergies” is proposed. The implication (...)
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  25. Leon Glass (1995). Dynamical Disease-The Impact of Nonlinear Dynamics and Chaos on Cardiology and Medicine. In R. J. Russell, N. Murphy & A. R. Peacocke (eds.), Chaos and Complexity. Vatican Observatory Publications 79.
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  26. Gordon G. Globus (2005). Nonlinear Dynamics at the Cutting Edge of Modernity: A Postmodern View. Philosophy, Psychiatry, and Psychology 12 (3):229-234.
  27. Keying Guan, Important Notes on Lyapunov Exponents.
    It is shown that the famous Lyapunov exponents cannot be used as the numerical characteristic for distinguishing different kinds of attractors, such as the equilibrium point, the limit closed curve, the stable torus and the strange attractor.
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  28. Michal Heller (1984). Nonlinear Evolution of Science. Roczniki Filozoficzne 32 (3):124.
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  29. Alfred Hubler & Andrew Friedl (2013). Nonlinear Response of Chemical Reaction Dynamics. Complexity 19 (1):6-8.
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  30. Stephen H. Kellert (2001). Extrascientific Uses of Physics: The Case of Nonlinear Dynamics and Legal Theory. Proceedings of the Philosophy of Science Association 2001 (3):S455-.
    This essay explores the metaphorical use of the area of nonlinear dynamics popularly known as "chaos theory," surveying its use in one particular field: legal theory. After sketching some of the mistakes encountered in these efforts, I outline the possibility of the fruitful use of nonlinear dynamics for thinking about our legal system. I then offer some general lessons to be drawn from these examples-both cautionary maxims and a limited defense of cross-disciplinary borrowing. I conclude with some reflections on the (...)
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  31. Julian Kiverstein & Michael Wheeler (eds.) (2012). Heidegger and Cognitive Science. Palgrave Macmillan.
  32. Helena Knyazeva (1999). Synergetics and the Images of Future. Futures 31 (3):281-290.
    The hope of finding new methods of predicting the course of historical processes could be connected with the recent developments of the theory of self-organisation, also called synergetics. It provides us with knowledge of constructive principles of co-evolution of complex social systems, co-evolution of countries and geopolitical regions being at different stages of development, integration of the East and the West, the North and the South. Due to the growth of population on the Earth in blow-up regime, the general and (...)
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  33. Teresa Kwiatkowska (2001). Beyond Uncertainties: Some Open Questions About Chaos and Ethics. Ethics and the Environment 6 (1):96-115.
    : Lately, a new language for the understanding of the complexity of life (organism, ecosystem, and social system) has been developed. Chaos, fractals, dissipative structures, self-organization, and complex adaptive systems are some of its key concepts. On this view, reality is not the deterministic structure that Newton envisaged, but rather, a partially unknown or at least unpredictable world of multiple possibilities. As the horizon of our knowledge of natural realities expands, the emergent comprehensive perspective requires a radical reconstruction of both (...)
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  34. Jon Lawhead (forthcoming). Structural Modeling Error and the System Individuation Problem. British Journal for the Philosophy of Science.
    Recent work by Frigg et. al. and Mayo-Wilson have called attention to a particular sort of error associated with attempts to model certain complex systems: structural modeling error. The assessment of the degree of SME in a model presupposes agreement between modelers about the best way to individuate natural systems, an agreement which can be more problematic than it appears. This problem, which we dub “the system individuation problem” arises in many of the same contexts as SME, and the two (...)
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  35. Jon Lawhead (2014). Lightning in a Bottle: Complexity, Chaos, and Computation in Climate Science. Dissertation, Columbia University
    Climatology is a paradigmatic complex systems science. Understanding the global climate involves tackling problems in physics, chemistry, economics, and many other disciplines. I argue that complex systems like the global climate are characterized by certain dynamical features that explain how those systems change over time. A complex system's dynamics are shaped by the interaction of many different components operating at many different temporal and spatial scales. Examining the multidisciplinary and holistic methods of climatology can help us better understand the nature (...)
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  36. Steve B. Lazarre (2003). Theory and Application of Chaos Theory and Family Systems Therapy: A Critical Review of the Literature. Dissertation, Alliant International University, San Diego
    This paper is an examination of change as an evolving concept progressing from early philosophies to systems theory. The purpose of the paper was to clarify the dimensions of change in the integration of family systems theory and chaos and complexity theory. The key concept in the material change is articulated from selected interdisciplinary sources in the history of ideas, from Parmenides through deep ecology, related to a current integration of family systems and chaos theory. This study examines whether modern (...)
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  37. Edward Lorenz (1963). Deterministic Nonperiodic Flow. Journal of Atmospheric Sciences 20 (2):130-148.
    Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.A simple system representing cellular convection is solved numerically. All (...)
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  38. Conor Mayo-Wilson (2015). Structural Chaos. Philosophy of Science 82 (5):1236-1247.
    A dynamical system is called chaotic if small changes to its initial conditions can create large changes in its behavior. By analogy, we call a dynamical system structurally chaotic if small changes to the equations describing the evolution of the system produce large changes in its behavior. Although there are many definitions of “chaos,” there are few mathematically precise candidate definitions of “structural chaos.” I propose a definition, and I explain two new theorems that show that a set of models (...)
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  39. Ma Metzger (1988). Predicting Periodic and Chaotic Phenomena of Dynamical-Systems-Insensitivity to Sample-Size. Bulletin of the Psychonomic Society 26 (6):527-527.
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  40. Matthew W. Parker (2009). Computing the Uncomputable; or, the Discrete Charm of Second-Order Simulacra. Synthese 169 (3):447 - 463.
    We examine a case in which non-computable behavior in a model is revealed by computer simulation. This is possible due to differing notions of computability for sets in a continuous space. The argument originally given for the validity of the simulation involves a simpler simulation of the simulation , still further simulations thereof, and a universality conjecture. There are difficulties with that argument, but there are other, heuristic arguments supporting the qualitative results. It is urged, using this example, that absolute (...)
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  41. Matthew W. Parker (2003). Undecidability in Rn: Riddled Basins, the KAM Tori, and the Stability of the Solar System. Philosophy of Science 70 (2):359-382.
    Some have suggested that certain classical physical systems have undecidable long-term behavior, without specifying an appropriate notion of decidability over the reals. We introduce such a notion, decidability in (or d- ) for any measure , which is particularly appropriate for physics and in some ways more intuitive than Ko's (1991) recursive approximability (r.a.). For Lebesgue measure , d- implies r.a. Sets with positive -measure that are sufficiently "riddled" with holes are never d- but are often r.a. This explicates Sommerer (...)
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  42. Matthew W. Parker (1998). Did Poincare Really Discover Chaos? [REVIEW] Studies in the History and Philosophy of Modern Physics 29 (4):575-588.
  43. Paweł Polak (2005). Czas nauki. Zagadnienia Filozoficzne W Nauce 36:151--154.
    Recenzja książki: Andrzej Pelczar, Czas i dynamika. O czasie w równaniach różniczkowych i układach dynamicznych, OBI--Kraków, Biblos-Tarnów 2003, ss. 117.
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  44. Bernard Pullman & Pontificia Accademia Delle Scienze (1996). The Emergence of Complexity in Mathematics, Physics, Chemistry and Biology Proceedings, Plenary Session of the Pontifical Academy of Sciences, 27-31 October 1992. [REVIEW]
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  45. Erik Rietveld (2012). Context-Switching and Responsiveness to Real Relevance. In Julian Kiverstein & Michael Wheeler (eds.), Heidegger and Cognitive Science. Palgrave Macmillan
  46. Erik Rietveld (2008). The Skillful Body as a Concernful System of Possible Actions: Phenomena and Neurodynamics. Theory & Psychology 18 (3):341-361.
    For Merleau-Ponty,consciousness in skillful coping is a matter of prereflective ‘I can’ and not explicit ‘I think that.’ The body unifies many domain-specific capacities. There exists a direct link between the perceived possibilities for action in the situation (‘affordances’) and the organism’s capacities. From Merleau-Ponty’s descriptions it is clear that in a flow of skillful actions, the leading ‘I can’ may change from moment to moment without explicit deliberation. How these transitions occur, however, is less clear. Given that Merleau-Ponty suggested (...)
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  47. Barkley Rosser, Aspects of Dialectics and Nonlinear Dynamics.
    Three principles of dialectical analysis are examined in terms of nonlinear dynamics models. The three principles are the transformation of quantity into quality, the interpenetration of opposites, and the negation of the negation. The first two of these especially are interpreted within the frameworks of catastrophe, chaos, and emergent dynamics complexity theoretic models, with the concept of bifurcation playing a central role. Problems with this viewpoint are also discussed.
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  48. Barkley Rosser, Do Nonlinear Dynamics in Economics Amount to a Kuhnian Paradigm Shift?
    Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity can (...)
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  49. Alexander Rueger & W. David Sharp (1996). Simple Theories of a Messy World: Truth and Explanatory Power in Nonlinear Dynamics. British Journal for the Philosophy of Science 47 (1):93-112.
    Philosophers like Duhem and Cartwright have argued that there is a tension between laws' abilities to explain and to represent. Abstract laws exemplify the first quality, phenomenological laws the second. This view has both metaphysical and methodological aspects: the world is too complex to be represented by simple theories; supplementing simple theories to make them represent reality blocks their confirmation. We argue that both aspects are incompatible with recent developments in nonlinear dynamics. Confirmation procedures and modelling strategies in nonlinear dynamics (...)
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  50. Barry Saltzman (1962). Finite Amplitude Free Convection as an Initial Value Problem. Journal of the Atmospheric Sciences 19 (329).
    The Oberbeck-Boussinesq equations are reduced to a two-dimensional form governing “roll” convection between two free surfaces maintained at a constant temperature difference. These equations are then transformed to a set of ordinary differential equations governing the time variations of the double-Fourier coefficients for the motion and temperature fields. Non-linear transfer processes are retained and appear as quadratic interactions between the Fourier coefficients. Energy and heat transfer relations appropriate to this Fourier resolution, and a numerical method for solution from arbitrary initial (...)
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