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Chaotic Dynamics papers — page 64

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Scaling and Dissipation in the GOY Shell Model
This is a paper about multi-fractal scaling and dissipation in a shell model of turbulence, called the GOY model. This set of equations describes a one dimensional cascade of energy towards higher…
Leo Kadanoff, Detlef Lohse, Jane Wang et al.Sep 8, 1994
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Inclusion of Diffraction Effects in the Gutzwiller Trace Formula
The Gutzwiller trace formula is extended to include diffraction effects. The new trace formula involves periodic rays which have non-geometrical segments as a result of diffraction on the surfaces…
G. Vattay, A. Wirzba, P. E. RosenqvistAug 30, 1994
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Averaged equations for Josephson junction series arrays with LRC load
We derive the averaged equations describing a series array of Josephson junctions shunted by a parallel inductor-resistor-capacitor load. We assume that the junctions have negligable capacitance ($β=…
Kurt Wiesenfeld, James W. SwiftAug 26, 1994
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Temperature spectra in shear flow and thermal convection
We show that the Pu() -7/3 shear velocity power spectrum gives rise to a PΘ( ) -4/3 power spectrum for a passively advected scalar, as measured in experiment…
Detlef LohseAug 25, 1994
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Weakly Chaotic Population Dynamics in Random Ecological Networks
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent…
Shin-ichi Sasa, Tsuyoshi ChawanyaAug 10, 1994
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Non-deterministic chaos
Non-deterministic chaos is a new dynamical paradigm where a non-deterministic system is influenced by random perturbations to produce the appearance of complexity. The non-determinism is envisioned…
D. D. DixonAug 8, 1994
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Conditions on the Existence of Localized Excitations in Nonlinear Discrete Systems
We use recent results that localized excitations in nonlinear Hamiltonian lattices can be viewed and described as multiple-frequency excitations. Their dynamics in phase space takes place on tori of…
S. FlachAug 4, 1994
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Corrections to universal scaling in real maps
I discuss the universal aspects of scaling in period-doubling sequences in families of maps of the real line possessing non-integer degree. I show that the scaling behaviour in both the orbital and…
Keith BriggsAug 4, 1994
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Simple Maps with Fractal Diffusion Coefficients
We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behaviour of an initially nonuniform distribution of points as a function of the slope…
R. Klages, J. R. DorfmanAug 3, 1994
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Stability of Wavelengths and Spatiotemporal Intermittency in Coupled Map Lattices
In relation to spatiotemporal intermittency, as it can be observed in coupled map lattices, we study the stability of different wavelengths in competition. Introducing a two dimensional map, we…
A. Lambert, R. LimaAug 1, 1994
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Anisotropy and scaling corrections in turbulence
Two parametrizations for second order velocity moments, the Batchelor parametrization for the r-space structure function and a common parametrization for the energy spectrum, $E(p)…
Detlef Lohse, Axel Müller-GroelingJul 29, 1994
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A Stochastic Process for the Dynamics of the Turbulent Cascade
Velocity increments over a distance r and turbulent energy dissipation on a box of size r are well described by the multifractal models of fully developed turbulence. These quantities and models…
R. Lima, R. Vilela MendesJul 29, 1994
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A Solvable Nonlinear Reaction-Diffusion Model
We construct a coupled set of nonlinear reaction-diffusion equations which are exactly solvable. The model generalizes both the Burger equation and a Boltzman reaction equation recently introduced by…
Max-Olivier Hongler, Ricardo LimaJul 29, 1994
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Exact Lyapunov Exponent for Infinite Products of Random Matrices
In this work, we give a rigorous explicit formula for the Lyapunov exponent for some binary infinite products of random 2× 2 real matrices. All these products are constructed using only two…
R. Lima, M. RahibeJul 26, 1994
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Texture Segmentation by Local Bi-Orthogonal Decomposition
We investigate the ability of a local bi-orthogonal decomposition to build texture segmentation of images. Using the structures associated to the local decomposition of the image independent row and…
J. A. Dente, R. Vilela Mendes, R. LimaJul 26, 1994
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The Limits of Mathematics---Extended Abstract
We summarize four different versions of our course notes on the limits of mathematics.
G. J. ChaitinJul 25, 1994
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Dynamic Scaling Function at the Quasiperiodic Transition to Chaos
We obtain a five-step approximation to the quasiperiodic dynamic scaling function for experimental Rayleigh-Be'nard convection data. When errors are taken into account in the experiment, the…
Ronnie Mainieri, Robert EckeJul 25, 1994
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The Limits of Mathematics---Fourth Version
This is yet another version of the course notes in chao-dyn/9407003. Here we use m-expressions more aggressively to further reduce the constants in our information-theoretic incompleteness theorems.…
G. J. ChaitinJul 23, 1994
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Rayleigh-Bénard Convection; Patterns, Chaos, Spatiotemporal Chaos and Turbulence
A coupled map lattice for convection is proposed, which consists of Eulerian and Lagrangian procedures. Simulations of the model not only reproduce a wide-range of phenomena in Rayleigh-Bénard…
Tatsuo Yanagita, Kunihiko KanekoJul 22, 1994
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Characterization of the transition from defect- to phase-turbulence
For the complex Ginzburg-Landau equation on a large periodic interval, we show that the transition from defect- to phase-turbulence is more accurately described as a smooth crossover rather than as a…
David A. Egolf, Henry S. GreensideJul 21, 1994
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The Limits of Mathematics---Third Version
This is yet another version of the course notes in chao-dyn/9407003. Here we change the universal Turing machine that is used to measure program-size complexity so that the constants in our…
G. J. ChaitinJul 20, 1994
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The Limits of Mathematics---Alternative Version
This is an alternative version of the course notes in chao-dyn/9407003. The previous version is based on measuring the size of lisp s-expressions. This version is based on measuring the size of what…
G. J. ChaitinJul 17, 1994
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Nonlinear dynamics in one and two dimensional arrays of discrete Josephson elements
Discrete arrays of Josephson junction elements differ from their continuum counterparts in two essential ways: i) localized dynamic states in discrete arrays, which are not present in the…
R. D. ParmentierJul 11, 1994
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The Limits of Mathematics---The Book
This is a revised version of the course notes handed to each participant at the limits of mathematics short course, Orono, Maine, June 1994.
G. J. ChaitinJul 7, 1994
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Remarks on the mean field dynamics of networks of chaotic elements
Fluctuations of the mean field of a globally coupled dynamical systems are discussed. The origin of hidden coherence is related with the instability of the fixed point solution of the self-consistent…
Kunihiko KanekoJul 7, 1994
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