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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

Presented here is a preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. The authors show that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Ashrafi, S.↗
NASA NTRS1991

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

A preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity is presented. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. It is shown that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Ashrafi, S.↗
NASA NTRS1994

Evolution of the Earth-Moon system

The tidal evolution of the Earth-Moon system is reexamined. Several models of tidal friction are first compared in an averaged Hamiltonian formulation of the dynamics. With one of these models, full integrations of the tidally evolving Earth-Moon system are carried out in the complete, fully interacting, and chaotically evolving planetary system. Classic results on the history of the lunar orbit are confirmed by our more general model. A detailed history of the obliquity of the Earth which takes into account the evolving lunar orbit is presented.

Touma, Jihad↗
DOE OSTI2024

Mixed Delay/Nondelay Embeddings Based Neuromorphic Computing with Patterned Nanomagnet Arrays

Patterned nanomagnet arrays (PNAs) have been shown to exhibit a strong geometrically frustrated dipole interaction. Some PNAs have also shown emergent domain wall dynamics. Previous works have demonstrated methods to physically probe these magnetization dynamics of PNAs to realize neuromorphic reservoir systems that exhibit chaotic dynamical behavior and high-dimensional nonlinearity. These PNA reservoir systems from prior works leverage echo state properties and linear/nonlinear short-term memory of component reservoir nodes to map and preserve the dynamical information of the input time-series data into nondelay spatial embeddings. Such mappings enable these PNA reservoir systems to imitate and predict/forecast the input time series data. However, these prior PNA reservoir systems are based solely on the nondelay spatial embeddings obtained at component reservoir nodes. As a result, they require a massive number of component reservoir nodes, or a very large spatial embedding (i.e., high-dimensional spatial embedding) per reservoir node, or both, to achieve acceptable imitation and prediction accuracy. These requirements reduce the practical feasibility of such PNA reservoir systems. To address this shortcoming, we present a mixed delay/nondelay embeddings-based PNA reservoir system. Our system uses a single PNA reservoir node with the ability to obtain a mixture of delay/nondelay embeddings of the dynamical information of the time-series data applied at the input of a single PNA reservoir node. Our analysis shows that when these mixed delay/nondelay embeddings are used to train a perceptron at the output layer, our reservoir system outperforms existing PNA-based reservoir systems for the imitation of NARMA 2, NARMA 5, NARMA 7, and NARMA 10 time series data, and for the short-term and long-term prediction of the Mackey Glass time series data.

Ti, Changpeng↗
DOE OSTI2023

Chaotic saddles and interior crises in a dissipative nontwist system

Here, we consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be regular or chaotic depending on the control parameters. Chaotic attractors can undergo sudden and qualitative changes as a parameter is varied. These changes are called crises, and at an interior crisis the attractor suddenly expands. Chaotic saddles are nonattracting chaotic sets that play a fundamental role in the dynamics of nonlinear systems; they are responsible for chaotic transients, fractal basin boundaries, and chaotic scattering, and they mediate interior crises. In this work we discuss the creation of chaotic saddles in a dissipative nontwist system and the interior crises they generate. We show how the presence of two saddles increases the transient times and we analyze the phenomenon of crisis induced intermittency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2016

Chaos in Kepler's Multiple Planet Systems and K2s Observations of the Atmospheres of Uranus Neptune

More than one-third of the 4700 planet candidates found by NASA's Kepler spacecraft during its prime mission are associated with target stars that have more than one planet candidate, and such "multis" account for the vast majority of candidates that have been verified as true planets. The large number of multis tells us that flat multiplanet systems like our Solar System are common. Virtually all of the candidate planetary systems are stable, as tested by numerical integrations that assume a physically motivated mass-radius relationship, but some of the systems lie in chaotic regions close to instability. The characteristics of some of the most interesting confirmed Kepler multi-planet systems will be discussed. The Kepler spacecraft's 'second life' in theK2 mission has allowed it to obtain long time-series observations of Solar System targets, including the giant planets Uranus & Neptune. These observations show variability caused by the chaotic weather patterns on Uranus & Neptune.

planet candidates↗
DOE OSTI2025

Confined and deconfined chaos in classical spin systems

Weakly perturbed integrable many-body systems are typically chaotic, and thermal at late times. However, there are distinct relationships between the timescales for thermalization and chaos. The typical relationship is confined chaos: when trajectories are still confined to regions in phase space with constant conserved quantities (actions), the conjugate angle variables are already unstable. Chaotic instabilities thus far precede thermalization. In a different relationship, which we term deconfined chaos, chaotic instabilities and thermalization occur on the same timescale. We investigate these two qualitatively distinct scenarios through numerical and analytical studies of two perturbed integrable classical spin models: the Ishimori spin chain (confined chaos), and the central spin model with XX interactions (deconfined chaos). We analytically establish (super)-integrability in the latter model in a microcanonical shell. Deconfined chaos emerges through the separation of phase space into large quasi-integrable regions and a thin chaotic manifold. The latter leads to chaos and thermalization on the fastest possible timescale, which is proportional to the inverse perturbation strength. This behavior is reminiscent of the quantum SYK models and strange metals.

Chaotic Dynamics (nlin.CD)↗
DOE OSTI2021

Ergodic and nonergodic many-body dynamics in strongly nonlinear lattices

The study of nonlinear oscillator chains in classical many-body dynamics has a storied history going back to the seminal work of Fermi et al. [Los Alamos Scientific Laboratory Report No. LA-1940, 1955 (unpublished)]. Here, we introduce a family of such systems which consist of chains of N harmonically coupled particles with the nonlinearity introduced by confining the motion of each individual particle to a box or stadium with hard walls. The stadia are arranged on a one-dimensional lattice but they individually do not have to be one dimensional, thus permitting the introduction of chaos already at the lattice scale. For the most part we study the case where the motion is entirely one dimensional. We find that the system exhibits a mixed phase space for any finite value of N . Computations of Lyapunov spectra at randomly picked phase space locations and a direct comparison between Hamiltonian evolution and phase space averages indicate that the regular regions of phase space are not significant at large system sizes. While the continuum limit of our model is itself a singular limit of the integrable sinh Gordon theory, we do not see any evidence for the kind of nonergodicity famously seen in the work of Fermi et al. Finally, we examine the chain with particles confined to two-dimensional stadia where the individual stadium is already chaotic and find a much more chaotic phase space at small system sizes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Spectral anomalies and broken symmetries in maximally chaotic quantum maps

Spectral statistics such as the level spacing statistics and spectral form factor (SFF) are widely expected to accurately identify “ergodicity,” including the presence of underlying macroscopic symmetries, in generic quantum systems ranging from quantized chaotic maps to interacting many-body systems. By studying various quantizations of maximally chaotic maps that break a discrete classical symmetry upon quantization, we demonstrate that this approach can be misleading and fail to detect macroscopic symmetries. Notably, the same classical map can exhibit signatures of different random matrix symmetry classes in short-range spectral statistics depending on the quantization. While the long-range spectral statistics encoded in the early time ramp of the SFF are more robust and correctly identify macroscopic symmetries in several common quantizations, we also demonstrate analytically and numerically that the presence of Berry-like phases in the quantization leads to spectral anomalies, which break this correspondence. Finally, we provide numerical evidence that long-range spectral rigidity remains directly correlated with ergodicity in the quantum dynamical sense of visiting a complete orthonormal basis.

Shou, Laura [Univ. of Maryland, College Park, MD (↗
DOE OSTI2024

Respecting causality for training physics-informed neural networks

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. Here we provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto–Sivashinsky equation in the chaotic regime, and the Navier–Stokes equations. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Quantum Ising model on (2+1)-dimensional anti–de Sitter space using tensor networks

We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using matrix product states (MPS) and matrix product operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space with coordination number seven and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with holography. At the critical point, we find the boundary entanglement entropy scales logarithmically with subsystem size but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and/or highly connected systems. We also measure out of time ordered correlators (OTOCs) to explore the scrambling behavior of the theory.

Quantum spin models↗
NASA NTRS2008

Jet Propulsion Laboratory: Annual Report 2007

Many milestones are celebrated in the business of space exploration, but one of them that arrived this year has particular meaning for us. Half a century ago, on January 31, 1958, the Jet Propulsion Laboratory was responsible for creating America's first satellite, Explorer 1, and joined with the Army to launch it into orbit. That makes 2007 the 50th year we have been sending robotic craft from Earth to explore space. No other event before or since has had such a profound effect on JPL's basic identity, setting it on the path to become the world's leader in robotic solar system exploration. It is not lost on historians that Explorer 1, besides being America's first satellite, was also the first spacecraft from any country to deliver scientific results in its case, the discovery of the Van Allen Radiation Belts that surround Earth. Science, of course, has been the prime motivator for all the dozens of missions that we have lofted into space in the half-century since then. JPL has sent spacecraft to every planet in the solar system from Mercury to Neptune, some of them very sophisticated machines. But in one way or another, they all owe their heritage to the 31-pound bullet-shaped probe JPL shot into space in 1958. Although we have ranged far and wide across the solar system, we have a very strong contingent of satellites and instruments dedicated, like Explorer, to the environment of our home planet. JPL missions have been providing much of the data to establish the facts of global warming - most especially, the melting of ice sheets in Greenland and Antarctica. During the past year, JPL and our parent organization, the California Institute of Technology, have created a task force to focus the special capabilities of the Laboratory and campus on ways to better understand the physics of global change. While Earth is a chaotic and dynamic system capable of large natural variations, evidence is mounting that human activities are playing an increasingly important role. A central piece of this effort is a search for novel energy sources to replace fossil fuels, the combustion of which adds carbon dioxide to our atmosphere. All of this is supported by our worldwide Deep Space Network, which provides the communication link between spacecraft and the ground. In addition, missions are infused with technologies developed by researchers working on projects for non-NASA sponsors as well as on pure research.

Jet Propulsion Laboratory (JPL)↗
DOE OSTI2022

Spectral form factor of a quantum spin glass

It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infinite-range quantum spin glass, the quantum p-spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations — the exponential of the spin glass “complexity” as obtained from the quantum Thouless-Anderson-Palmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicity-breaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semi-classical limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Moisture-induced autonomous surface potential oscillations for energy harvesting

A variety of autonomous oscillations in nature such as heartbeats and some biochemical reactions have been widely studied and utilized for applications in the fields of bioscience and engineering. Here, we report a unique phenomenon of moisture-induced electrical potential oscillations on polymers, poly([2-(methacryloyloxy)ethyl] dimethyl-(3-sulfopropyl) ammonium hydroxide-co-acrylic acid), during the diffusion of water molecules. Chemical reactions are modeled by kinetic simulations while system dynamic equations and the stability matrix are analyzed to show the chaotic nature of the system which oscillates with hidden attractors to induce the autonomous surface potential oscillation. Using moisture in the ambient environment as the activation source, this self-excited chemoelectrical reaction could have broad influences and usages in surface-reaction based devices and systems. As a proof-of-concept demonstration, an energy harvester is constructed and achieved the continuous energy production for more than 15,000 seconds with an energy density of 16.8 mJ/cm 2 . A 2-Volts output voltage has been produced to power a liquid crystal display toward practical applications with five energy harvesters connected in series.

42 ENGINEERING↗
NASA NTRS1985

Volcano/ground ice interactions in Elysium Planitia, Mars

The occurrence within Elysium Planitia of meltwater deposits, possible pseudocraters, collapse features within troughs, and outflow channels indicates that a layer of subsurface volatiles existed at the time of volcanic activity within this area. The pseudocraters are interpreted to be indicators of near-surface volatiles, while meltwater deposits and the degree of preservation of trough walls and floors are thought to signify greater volatile depths. A latitudinal variation in the distribution of these features indicates either that the depth to the volatile layer increased from less than about 50 m at 35 deg N to greater than 600 m at 24 deg N, or that an ice wedge that existed at 35 deg N thinned to nonexistence at 24 deg N. Braided distributary channel systems within the chaotic terrain north of Elysium Planitia show that ephemeral lakes were repeatedly created and drained at this locality. The existence of volatiles contemporaneous with volcanic activity permits a search to be made for explosively generated landforms predicted to exist by previous theoretical models. Morphological evidence for strombolian, vulcanian and plinian eruptions is lacking within western Elysium Planitia; there are no identifiable cinder cones, pyroclastic flow deposits, or mantled areas indicative of large airfall deposits at an image resolution of 50-150 m/pixel. However, the pseudocraters indicate that small-scale phreatomagmatic activity may have taken place.

Mouginis-Mark, P. J.↗
NASA NTRS1991

Plasma transport in the Io torus - The importance of microscopic diffusion

This paper considers the question of whether the distribution of mass in the Io plasma torus is consistent with the concept of interchange eddy transport. Specifically, the flux tube content exhibits a gradual decrease with increasing radial distance from the source near Io without any evidence for substantial density irregularity associated with the plasma source or loss. Using a simple one-dimensional numerical model to simulate macroscopic interchange eddy transport, it is demonstrated that this smooth equilibrium distribution of mass can occur but only with the inclusion of a minimal level of small scale microscopic mixing at a rate approaching Bohm diffusion. Otherwise, the system exhibits a chaotic appearance which never approaches an equilibrium distribution. Various physical mechanisms for the microscopic diffusion process which is required to provide a sufficiently rapid mixing of material between the macroscopic eddies are discussed.

Mei, YI↗
NASA NTRS1996

Intraseasonal and Interannual Variability of Mars Present Climate

This is a Final Report for a Joint Research Interchange (JRI) between NASA Ames Research Center and San Jose State University, Department of Meteorology. The focus of this JRI has been to investigate the nature of intraseasonal and interannual variability of Mars'present climate. We have applied a three-dimensional climate model based on the full hydrostatic primitive equations to determine the spatial, but primarily, the temporal structures of the planet's large-scale circulation as it evolves during a given seasonal advance, and, over multi-annual cycles. The particular climate model applies simplified physical parameterizations and is computationally efficient. It could thus easily be integrated in a perpetual season or advancing season configuration, as well as over many Mars years. We have assessed both high and low-frequency components of the circulation (i.e., motions having periods of Omicron(2-10 days) or greater than Omicron(10 days), respectively). Results from this investigation have explored the basic issue whether Mars' climate system is naturally 'chaotic' associated with nonlinear interactions of the large-scale circulation-regardless of any allowance for year-to-year variations in external forcing mechanisms. Titles of papers presented at scientific conferences and a manuscript to be submitted to the scientific literature are provided. An overview of a areas for further investigation is also presented.

Hollingsworth, Jeffery L.↗