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80 records · Page 5

All sources NASA NTRS DOE OSTI

NASA NTRS1995

The Dripping Handrail Model: Transient Chaos in Accretion Systems

We define and study a simple dynamical model for accretion systems, the "dripping handrail" (DHR). The time evolution of this spatially extended system is a mixture of periodic and apparently random (but actually deterministic) behavior. The nature of this mixture depends on the values of its physical parameters - the accretion rate, diffusion coefficient, and density threshold. The aperiodic component is a special kind of deterministic chaos called transient chaos. The model can simultaneously exhibit both the quasiperiodic oscillations (QPO) and very low frequency noise (VLFN) that characterize the power spectra of fluctuations of several classes of accretion systems in astronomy. For this reason, our model may be relevant to many such astrophysical systems, including binary stars with accretion onto a compact object - white dwarf, neutron star, or black hole - as well as active galactic nuclei. We describe the systematics of the DHR's temporal behavior, by exploring its physical parameter space using several diagnostics: power spectra, wavelet "scalegrams," and Lyapunov exponents. In addition, we note that for large accretion rates the DHR has periodic modes; the effective pulse shapes for these modes - evaluated by folding the time series at the known period - bear a resemblance to the similarly- determined shapes for some x-ray pulsars. The pulsing observed in some of these systems may be such periodic-mode accretion, and not due to pure rotation as in the standard pulsar model.

Young, Karl↗

NASA NTRS2009

Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation

The growing demand for air travel is increasing the need for mitigation of air traffic congestion and complexity problems, which are already at high levels. At the same time new information and automation technologies are enabling the distribution of tasks and decisions from the service providers to the users of the air traffic system, with potential capacity and cost benefits. This distribution of tasks and decisions raises the concern that independent user actions will decrease the predictability and increase the complexity of the traffic system, hence inhibiting and possibly reversing any potential benefits. In answer to this concern, the authors propose the introduction of decision-making metrics for preserving user trajectory flexibility. The hypothesis is that such metrics will make user actions naturally mitigate traffic complexity. In this paper, the impact of using these metrics on traffic complexity is investigated. The scenarios analyzed include aircraft in en route airspace with each aircraft meeting a required time of arrival in a one-hour time horizon while mitigating the risk of loss of separation with the other aircraft, thus preserving its trajectory flexibility. The experiments showed promising results in that the individual trajectory flexibility preservation induced self-separation and self-organization effects in the overall traffic situation. The effects were quantified using traffic complexity metrics based on Lyapunov exponents and traffic proximity.

Idris, Husni↗

NASA NTRS2006

Stochastic Representation of Chaos Using Terminal Attractors

A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Zak, Michail↗

DOE OSTI2021

How Hall electric fields intrinsically chaotize and heat ions during collisionless magnetic reconnection

The origin of extreme and anomalous ion heating during magnetic reconnection has been a longstanding mystery. It is shown in this paper that, at the core of the process, the stochastic heating mechanism is responsible for this energization. The in-plane Hall electric fields that intrinsically develop during collisionless reconnection not only accelerate ions, but also thermalize them by inducing chaotic motion. The mechanism explains various observed features of ion heating, e.g., its relation to the guide field strength and the ion mass-to-charge ratio.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

The rapid destruction of toroidal magnetic surfaces

The operation of ITER will require reliable simulations in order to avoid major damage to the device from disruptions. Disruptions are the sudden breakup of magnetic surfaces across the plasma volume—a fast magnetic reconnection. This reconnection can be caused by the growth of perturbations outside of the plasma core causing an ideal perturbation to the core. This causes an increasing ratio of the maximum to the minimum separation, Δmax/Δmin, between neighboring magnetic surfaces. Magnetic reconnection becomes a dominant process when magnetic field lines can quickly interchange connections over a spatial scale ar. This occurs when Δmax/Δmin≳ar/Δd, where Δd is the scale over which non-ideal effects make magnetic field lines indistinguishable. Traditional reconnection theory is fundamentally different. It is a study of the steady-state cancelation of oppositely directed magnetic field components across a thin layer. During more than sixty years, mathematical implications of Faraday's law have been derived that clarify and constrain the physics of fast magnetic reconnection. These are reviewed because they are not commonly known but are needed to understand and to place in context how an ideal magnetic evolution can cause reconnection to quickly become a dominant process no matter how small Δd/ar may be.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Out of time order correlation of the Hubbard model with random local disorder

The out-of-time-order correlator (OTOC) serves as a powerful tool for investigating quantum information spreading and chaos in complex systems. We present a method employing non-equilibrium dynamical mean-field theory and coherent potential approximation combined with diagrammatic perturbation on the Schwinger–Keldysh contour to calculate the OTOC for correlated fermionic systems subjected to both random disorder and electron interaction. Furthermore, our key finding is that random disorder enhances the OTOC decay in the Hubbard model for the metallic phase in the weakly interacting limit. However, the current limitation of our perturbative solver restricts the applicability to weak interaction regimes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1982

The applicability of Lyapunov characteristic numbers in the study of the stability of satellite orbits

It is pointed out that the Lyapunov Characteristic Numbers constitute a new tool for determining stability of trajectories of dynamical systems, or, even more generally, of solutions of systems of ordinary differential equations. In contrast with the characteristic exponents, which apply only to periodic solutions, the Lyapunov Characteristic Numbers apply to arbitrary nonperiodic solutions as well. A description is presented of the numerical experiments which have been made in order to investigate the practical value of the Lyapunov Characteristic Number and the Kolmogorov Entropy for the purpose of estimating the stability of trajectories and/or numerical integration methods in celestial mechanics. It is found that the Lyapunov Characteristic Numbers are extremely useful for the classification of the solutions of nonintegrable dynamical systems, especially in order to distinguish between quasi-periodic and chaotic solutions. However, the Lyapunov Characteristics Numbers do not appear to be useful for the purpose of evaluating numerical integration methods.

Broucke, R.↗

NASA NTRS1991

Computing the Lyapunov spectrum of a dynamical system from an observed time series

The paper examines the problem of accurately determining, from an observed time series, the Liapunov exponents for the dynamical system generating the data. It is shown that, even with very large data sets, it is clearly advantageous to utilize local neighborhood-to-neighborhood mappings with higher-order Taylor series rather than just local linear maps. This procedure is demonstrated on the Henon and Ikeda maps of the plane itself, the Lorenz system of three ordinary differential equations, and the Mackey-Glass delay differential equation.

Brown, Reggie↗