POLYNOMIAL CHAOS SURROGATE FOR STOCHASTIC MODELS WITH PARAMETRIC UNCERTAINTY
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Bahr-Mueller, Joy Noel↗
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Polynomial Chaos Expansion for Uncertainty and Sensitivity Analysis of Integral Experiment Benchmark Evaluations
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Lutz, Elijah [Sandia National Laboratories (SNL-NM↗
Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field
The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.
Chen, J.↗
Modeling aerodynamic discontinuities and the onset of chaos in flight dynamical systems
Various representations of the aerodynamic contribution to the aircraft's equation of motion are shown to be compatible within the common assumption of their Frechet differentiability. Three forms of invalidating Frechet differentiality are identified, and the mathematical model is amended to accommodate their occurrence. Some of the ways in which chaotic behavior may emerge are discussed, first at the level of the aerodynamic contribution to the equation of motion, and then at the level of the equations of motion themselves.
Tobak, M.↗
Rheologic properties and kinematics of emplacement of the Chaos Jumbles rockfall avalanche, Lassen Volcanic National Park, California
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Eppler, Dean B.↗
Traveling waves and chaos in thermosolutal convection
Numerical experiments on two-dimensional thermosolutal convection reveal oscillations in the form of traveling, standing, modulated, and chaotic waves. Transitions between these wave forms and steady convection are investigated and compared with theory. Such rich nonlinear behavior is possible in fluid layers of wide horizontal extent, and provides an explanation for waves observed in recent laboratory experiments with binary fluid mixtures.
Deane, A. E.↗
Nonlinear dynamics, chaos and complex cardiac arrhythmias
Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.
Glass, L.↗
Modeling aerodynamic discontinuities and onset of chaos in flight dynamical systems
Various representations of the aerodynamic contribution to the aircraft's equation of motion are shown to be compatible within the common assumption of their Frechet differentiability. Three forms of invalidating Frechet differentiability are identified, and the mathematical model is amended to accommodate their occurrence. Some of the ways in which chaotic behavior may emerge are discussed, first at the level of the aerodynamic contribution to the equations of motion, and then at the level of the equations of motion themselves.
Tobak, M.↗
Deterministic representation of chaos with application to turbulence
Chaotic motions of nonlinear dynamical systems are decomposed into mean components and fluctuations. The approach is based upon the concept that the fluctuations driven by the instability of the original (unperturbed) motion grow until a new stable state is approached. The Reynolds-type equations written for continuous as well as for finite-degrees-of-freedom dynamical systems are closed by using this stabilization principle. The theory is applied to conservative systems, to strange attractors and to turbulent motions.
Zak, M.↗
Chaos motion in robot manipulators
It is shown that a simple two-link planar manipulator exhibits a phenomenon of global instability in a subspace of its configuration space. A numerical example, as well as results of a graphic simulation, is given.
Lokshin, A.↗
Chaos as a part of logical structure in neurodynamics
It is proposed that chaotic attractors incorporated in neural net models can represent classes of patterns in the same way in which a set of static attractors represent unrelated patterns. Therefore, chaotic states of neuron activity are associated with higher level cognitive processes such as generalization and abstraction.
Zak, Michail↗
The evolution from weak to strong geomagnetic activity - An interpretation in terms of deterministic chaos
An analogue of the magnetosphere developed on the basis of Shaw's (1984) dripping faucet model was used to model the mechanisms of the magnetospheric response to energy transfer from the solar wind. It is demonstrated that geomagnetic activity results from nonlinearly coupled physical processes and that the strength and the nature of the coupling changes dramatically as the magnetosphere is driven harder and harder by increasing energy input. Based on initial results obtained from the model, is is suggested that a chaotic transition takes place in the analogue system as the loading rate is increased beyond a critical value. This model is able to explain many of the features in the results of linear prediction filtering techniques.
Baker, D. N.↗
Triplets of galaxies: Their dynamics, evolution, and the origin of chaos in them
Recently Karachentsev's group at The Smithsonian Astrophysical Observatory (SAO) (6-meter Telescope Observatory) published a list of 84 triple systems of galaxies with their distances, radial (line of sight) velocities, and angular sizes (Karachentseva et al., 1988). This gives a new ground for studies of the dark matter problem which fills the gap between the large cosmic scales (White, 1987; Dekel and Rees, 1987, and Einasto et al., 1977) and the scale of individual galaxies (Erickson et al., 1987). The data on the typical velocity dispersions and linear dimension of the triplets indicate that they contain considerable amounts of dark matter (see also earlier work of Karachentseva et al., 1979). Numerical simulations show that the statistical characteristics of the Karachentsev triplets can be imitated by model ensembles of triple systems with dark matter masses M sub d = (1-3 x 10(exp 12) M sub O, which is almost ten times greater than the typical mass of stellar galaxies estimated by the standard mass-to-luminosity ration (Kiseleva and Chernin, 1988). Here, the authors report that important information can be drawn from the data on the visible configurations of these systems. The statistics of configurations provide an independent evidence for dark matter in the triplets; moreover, it enables one to argue that dark matter seems to be distributed over the whole volume of the typical triplet forming its common corona rather than concentrated within individual coronae (or haloes) of the member galaxies.
Chernin, Arthur D.↗
Low-dimensional chaos in magnetospheric activity from AE time series
The magnetospheric response to the solar-wind input, as represented by the time-series measurements of the auroral electrojet (AE) index, has been examined using phase-space reconstruction techniques. The system was found to behave as a low-dimensional chaotic system with a fractal dimension of 3.6 and has Kolmogorov entropy less than 0.2/min. These indicate that the dynamics of the system can be adequately described by four independent variables, and that the corresponding intrinsic time scale is of the order of 5 min. The relevance of the results to magnetospheric modeling is discussed.
Vassiliadis, D. V.↗
Chaos in the sunspot cycle - Analysis and prediction
The variability of solar activity over long time scales, given semiquantitatively by measurements of sunspot numbers, is examined as a nonlinear dynamical system. First, a discussion of the data set used and the techniques utilized to reduce the noise and capture the long-term dynamics inherent in the data is presented. Subsequently, an attractor is reconstructed from the data set using the method of time delays. The reconstructed attractor is then used to determine both the dimension of the underlying system and also the largest Lyapunov exponent, which together indicate that the sunspot cycle is indeed chaotic and also low dimensional. In addition, recent techniques of exploiting chaotic dynamics to provide accurate, short-term predictions are utilized in order to improve upon current forecasting methods and also to place theoretical limits on predictability extent. The results are compared to chaotic solar-dynamo models as a possible physically motivated source of this chaotic behavior.
Mundt, Michael D.↗
Chaos and ion heating in a slow shock
An ion heating mechanism is proposed of slow shocks, which is associated with the chaotic motion of particles in the downstream wave field. For a coherent electromagnetic wave propagating along the downstream magnetic field, corresponding to switch-off shocks, the particle motions are not chaotic. For an oblique wave, the interaction between the particles and the wave field may lead to chaotic particle motions. Such particles may be greatly thermalized within one wavelength after they are incident into the downstream wave field. The results can be used to explain the existence of the critical intermediate Mach number observed in the hybrid simulations.
Lin, Y.↗
Turbulence and deterministic chaos
Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low Reynolds number fully developed turbulence are compared. Several flows are noted: fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, only fully chaotic is classified as turbulent. Besides the sustained flows, a flow which decays as it becomes turbulent is examined. For the finest grid, 128(exp 3) points, the spatial resolution appears to be quite good. As a final note, the variation of the velocity derivatives skewness of a Navier-Stokes flow as the Reynolds number goes to zero is calculated numerically. The value of the skewness is shown to become small at low Reynolds numbers, in agreement with intuitive arguments that nonlinear terms should be negligible.
Deissler, Robert G.↗
Nonlinear vibration and radiation from a panel with transition to chaos
The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling), and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance bifurcation is diffused and difficult to maintain; thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on an aluminum panel and a graphite epoxy panel having the same size and weight. Good agreement is obtained betwen the experimental and numerical results.
Maestrello, Lucio↗