SEARCH · Search NASA

Results for “chaotic states”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

All sources NASA NTRS DOE OSTI

NASA NTRS1995

A FFT Method for the Quasiclassical Selection of Initial Ro-Vibrational States of Triatomic Molecules

This paper describes the use of an exact fast Fourier transform (FFT) method to prepare specified vibrational-rotational states of triatomic molecules. The method determines the Fourier coefficients needed to describe the coordinates and momenta of a vibrating-rotating triatomic molecule. Once the Fourier coefficients of a particular state are determined, it is possible to easily generate as many random sets of initial cartesian coordinates and momenta as desired. All the members of each set will correspond to the particular vibrational-rotational state selected. For example, in the case of the ground vibrational state of a non-rotating water molecule, the calculated actions of 100 sets of initial conditions produced actions within 0.001 h(bar) of the specified quantization values and energies within 5 cm(sup -1) of the semiclassical eigenvalue. The numerical procedure is straightforward for states in which all the fundamental frequencies are independent. However for states for which the fundamental frequencies become commensurate (resonance states), there are additional complications. In these cases it is necessary to determine a new set of "fundamental" frequencies and to modify the quantization conditions. Once these adjustments are made, good results are obtained for resonance states. The major problems are in labelling the large number of Fourier coefficients and the presence of regions of chaotic motion. Results are presented for the vibrational states of H2O and HCN and the ro-vibrational states of H2O.

Eaker, Charles W.↗

DOE OSTI2026

Chaos as the cause of randomness in tearing mode onset times in DIII-D ITER baseline scenario plasmas

The first evidence of widespread chaotic plasma dynamics relevant to the onset of disruptive tearing modes is found in DIII-D tokamak discharges. This evidence is obtained by calculating positive maximal Lyapunov exponents from Mirnov signals using the Rosenstein algorithm, implying the chaotic growth and/or rotation of magnetohydrodynamic modes in DIII-D [Luxon, Nucl. Fusion 42, 614 (2002)] plasmas. Such chaotic dynamics offer an explanation for the random tearing mode onset times previously observed in ITER baseline scenario discharges. Further, the Lyapunov timescales associated with this chaos could inhibit reliable prediction of tearing mode onset beyond the angular momentum confinement timescale; this constraint should inform the design of plasma control systems on ITER.

Chaotic dynamics↗

NASA NTRS1995

Controlling Chaotic Lasers

Irregular fluctuations in intensity have long plagued the operation of a wide variety of solid-state lasers. We are exploring the possibility of exploiting rather than avoiding a laser's chaotic output. As an important step in that direction, we have applied a novel control technique to stabilize a solid state laser. By making small periodic changes in only one input parameter of the laser, we are able to stabilize complex periodic waveforms and steady state behavior in the laser output. We demonstrate the application of this approach in a diode pumped Nd:/YAG laser system.

Gills, Zelda↗

NASA NTRS2016

Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.

Blonigan, Patrick J.↗

NASA NTRS1990

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗

NASA NTRS1991

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

Yee, H. C.↗

DOE OSTI2021

Random Matrix Theory in Cd isotopes

Random matrix theory (RMT) is used to provide a measure of the chaoticity (q) of calculated results for the spectra for various Cd isotopes. Here, the goal is to gain a better understanding of the internal dynamics in play; namely, whether it tracks with regular or irregular (chaotic) behavior as determined through an RMT analyses of calculated spectra. The basis-state configurations used to determine the spectra includes all positive, negative, natural (J π = 1 – , 2 + , ...), and unnatural parity configurations (J π = 0 – , 1 + , 2 – , ...), unless suppressed for comparative purposes. The results show that when intruder-state configurations are in play, regular behavior emerges, but when not in play, chaotic behavior seems to dominate the dynamics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1994

Chaotic dynamics of corotating magnetospheric convection

The corotating plasma convection system of the Jovian magnetosphere is analyzed. The macroscopic (mhd) model introduced by Summers and Mu, (1992) that incorporates the effects of microdiffusion is extended by including previously neglected density effects. We reduce the governing partial differential equations to a third-order ordinary differential system by the Galerkin technique of mode truncation. We carry out such a severe truncation partly in the interests of tractability, and leave open the question of the efficacy of adding additional modes. Exhaustive numerical integrations are carried out to calculate the long-term solutions, and we discover that a rich array of plasma motions is possible, dependent on the value of the height-integrated ionospheric Pederson conductivity Sigma. If Sigma is less than a certain critical value Sigma(sub c), then plasma motion can be expected to be chaotic (or periodic), while if Sigma is greater than Sigma(sub c), then steady state convection is expected. In the former case, whether the plasma motion is chaotic or periodic (and, if periodic, the magnitude of the period) can be very sensitive to the value of Sigma. The value of Sigma(sub c), which is a function of a parameter q that occurs in the assumed form of the stationary radial profile (varies as L(exp -q) of the plasma mass per unit magnetic flux, lies well within the accepted range of values of Sigma for Jupiter, i.e. Sigma greater than or equal to 0.1 mho and less than or equal to 10 mho.

Summers, Danny↗

NASA NTRS2002

Phase Synchronization and Desynchronization of Structural Response Induced by Turbulent and External Sound

Acoustic and turbulent boundary layer flow loadings over a flexible structure are used to study the spatial-temporal dynamics of the response of the structure. The stability of the spatial synchronization and desynchronization by an active external force is investigated with an array of coupled transducers on the structure. In the synchronous state, the structural phase is locked, which leads to the formation of spatial patterns while the amplitude peaks exhibit chaotic behaviors. Large amplitude, spatially symmetric loading is superimposed on broadband, but in the desynchronized state, the spectrum broadens and the phase space is lost. The resulting pattern bears a striking resemblance to phase turbulence. The transition is achieved by using a low power external actuator to trigger broadband behaviors from the knowledge of the external acoustic load inducing synchronization. The changes are made favorably and efficiently to alter the frequency distribution of power, not the total power level. Before synchronization effects are seen, the panel response to the turbulent boundary layer loading is discontinuously spatio-temporally correlated. The stability develops from different competing wavelengths; the spatial scale is significantly shorter than when forced with the superimposed external sound. When the external sound level decreases and the synchronized phases are lost, changes in the character of the spectra can be linked to the occurrence of spatial phase transition. These changes can develop broadband response. Synchronized responses of fuselage structure panels have been observed in subsonic and supersonic aircraft; results from two flights tests are discussed.

Maestrello, Lucio↗

DOE OSTI2021

Data-Driven Exploration of Climate Attractor Manifolds For Long-Term Predictability

Focal Area: This white paper responds to Focal Area 3. We seek to gain insight into decadal-scale climate predictability by applying novel manifold-finding probabilistic AI techniques to the complex data produced by Earth System models (ESMs) such as E3SM. The associated portfolio of research activities leverages DOE’s asset mix of HPC platforms, climate expertise, climate simulation codes, and AI expertise. Science Challenge: Climate and climate models are dynamical systems exhibiting properties that are interpretable through chaos theory. The theory contains an important concept that is relevant to multi-decade-scale climate prediction: a chaotic attractor. While the space containing all the possible states of the Earth’s atmosphere and ocean, the possible weather, is large, the realized states tend to stay near the smaller-dimensioned attractor. This behavior is responsible for the “order behind the irregularity” [1] of climate phenomena. Climate change can be thought of as a change in the properties of the attractor, and predicting the climate over years to decades is equivalent to predicting how those properties will change. To date, the attractor has been a useful conceptual tool, but has not been amenable to direct characterization. A new development is the advent of efficient high-dimensional manifold-finding probabilistic AI techniques, which permit a data-driven characterization of the ESM attractor and its probability distribution over weather states. Such a characterization would result in a natural dimensional reduction — a “non-linear Principal Components Analysis (PCA) adapted to climate simulation data” — leading to important advances in scenario-based long-term climate prediction, long-term prediction of water cycle extremes, ESM verification, inter-model comparison, and process model development.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Estimating time in quantum chaotic systems and black holes

We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation". Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time values. Intuitively, it should become increasingly difficult to estimate the precise value of time by making measurements on the state. We use a quantity called the Fisher information from quantum metrology to quantify the minimum uncertainty in estimating time. Due to unitarity, the uncertainty in the time estimate does not grow with time if we have access to optimal measurements on the full system. Restricting the measurements to act on a small subsystem or to have low computational complexity leads to results expected from equilibration, where the time uncertainty becomes large at late times. With optimal measurements on a subsystem larger than half of the system, we regain the ability to estimate the time very precisely, even at late times. Hawking's calculation for the reduced density matrix of the black hole radiation in semiclassical gravity contradicts our general predictions for unitary quantum chaotic systems. Hawking's state always has a large uncertainty for attempts to estimate the time using the radiation, whereas our general results imply that the uncertainty should become small after the Page time. This gives a new version of the black hole information loss paradox in terms of the time estimation task. By restricting to simple measurements on the radiation, the time uncertainty becomes large. This indicates from a new perspective that the observations of computationally bounded agents are consistent with the semiclassical effective description of gravity.

Black holes↗

DOE OSTI2021

How do intermittency and simultaneous processes obfuscate the Arctic influence on midlatitude winter extreme weather events?

Abstract Pronounced changes in the Arctic environment add a new potential driver of anomalous weather patterns in midlatitudes that affect billions of people. Recent studies of these Arctic/midlatitude weather linkages, however, state inconsistent conclusions. A source of uncertainty arises from the chaotic nature of the atmosphere. Thermodynamic forcing by a rapidly warming Arctic contributes to weather events through changing surface heat fluxes and large-scale temperature and pressure gradients. But internal shifts in atmospheric dynamics—the variability of the location, strength, and character of the jet stream, blocking, and stratospheric polar vortex (SPV)—obscure the direct causes and effects. It is important to understand these associated processes to differentiate Arctic-forced variability from natural variability. For example in early winter, reduced Barents/Kara Seas sea-ice coverage may reinforce existing atmospheric teleconnections between the North Atlantic/Arctic and central Asia, and affect downstream weather in East Asia. Reduced sea ice in the Chukchi Sea can amplify atmospheric ridging of high pressure near Alaska, influencing downstream weather across North America. In late winter southward displacement of the SPV, coupled to the troposphere, leads to weather extremes in Eurasia and North America. Combined tropical and sea ice conditions can modulate the variability of the SPV. Observational evidence for Arctic/midlatitude weather linkages continues to accumulate, along with understanding of connections with pre-existing climate states. Relative to natural atmospheric variability, sea-ice loss alone has played a secondary role in Arctic/midlatitude weather linkages; the full influence of Arctic amplification remains uncertain.

Environmental Sciences & Ecology↗

DOE OSTI2023

Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov–Maxwell equilibria

The construction of kinetic equilibrium states is important for studying stability and wave propagation in collisionless plasmas. Thus, many studies over the past decades have been focused on calculating Vlasov–Maxwell equilibria using analytical and numerical methods. However, the problem of kinetic equilibrium of hybrid models is less studied, and self-consistent treatments often adopt restrictive assumptions ruling out cases with irregular and chaotic behaviour, although such behaviour is observed in spacecraft observations of space plasmas. In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov–Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is expressed in terms of the vector potential components through the quasineutrality condition. The equilibrium states are calculated upon solving an inhomogeneous Beltrami equation that determines the magnetic field, where the inhomogeneous term is the current density of the kinetic ions and the homogeneous term represents the electron current density. We show that the corresponding 1-D system is Hamiltonian, with position playing the role of time, and its trajectories have a regular, periodic behaviour for ion distribution functions that are symmetric in the two conserved particle canonical momenta. For asymmetric distribution functions, the system is nonintegrable, resulting in irregular and chaotic behaviour of the fields. The electron current density can modify the magnetic field phase space structure, inducing orbit trapping and the organization of orbits into large islands of stability. Thus, the electron contribution can be responsible for the emergence of localized electric field structures that induce ion trapping. We also provide a paradigm for the analytical construction of hybrid equilibria using a rotating two-dimensional harmonic oscillator Hamiltonian, enabling the calculation of analytic magnetic fields and the construction of the corresponding distribution functions in terms of Hermite polynomials.

Kaltsas, Dimitrios A. (ORCID:0000000300769015)↗

DOE OSTI2025

A Practical Probabilistic Benchmark for AI Weather Models

Since the weather is chaotic, it is necessary to forecast an ensemble of future states. Recently, multiple AI weather models have emerged claiming breakthroughs in deterministic skill. Unfortunately, it is hard to fairly compare ensembles of AI forecasts because variations in ensembling methodology become confounding and the baseline data volume is immense. We address this by scoring lagged initial condition ensembles—whereby an ensemble can be constructed from a library of deterministic hindcasts. This allows the first parameter‐free intercomparison of leading AI weather models' probabilistic skill against an operational baseline. Lagged ensembles of the two leading AI weather models, GraphCast and Pangu, perform similarly even though the former outperforms the latter in deterministic scoring. These results are elaborated upon by sensitivity tests showing that commonly used multiple time‐step loss functions damage ensemble calibration.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1989

Inhibition of quantum transport due to 'scars' of unstable periodic orbits

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.

Jensen, R. V.↗

NASA NTRS1986

Orbital resonances, unusual configurations and exotic rotation states among planetary satellites

The origin of orbital resonances is shown in the demonstration of the evolution of a pair of planetary satellites through a commensurability of the mean motions by a sequence of diagrams of constant energy curves in a two-dimensional phase space; the closed curve corresponding to the motion in each successive diagram is identified by its adiabatically conserved area. It is found that two-body resonances serve as a basis in the solution of the problem of the origin and evolution of the three-body Laplace resonance among the Galilean satellites of Jupiter. The unusual rotation state of Saturn's satellite Hyperion which is expected to tumble chaotically for an indefinite amount of time is discussed.

Peale, S. J.↗

NASA NTRS2011

Radiolysis of Sulfuric Acid, Sulfuric Acid Monohydrate, and Sulfuric Acid Tetrahydrate and Its Relevance to Europa

We report laboratory studies on the 0.8 MeV proton irradiation of ices composed of sulfuric acid (H2SO4), sulfuric acid monohydrate (H2SO4 H2O), and sulfuric acid tetrahydrate (H2SO4 4H2O) between 10 and 180 K. Using infrared spectroscopy, we identify the main radiation products as H2O, SO2, (S2O3)x, H3O+, HSO4(exp -), and SO4(exp 2-). At high radiation doses, we find that H2SO4 molecules are destroyed completely and that H2SO4 H2O is formed on subsequent warming. This hydrate is significantly more stable to radiolytic destruction than pure H2SO4, falling to an equilibrium relative abundance of 50% of its original value on prolonged irradiation. Unlike either pure H2SO4 or H2SO4 H2O, the loss of H2SO4 4H2O exhibits a strong temperature dependence, as the tetrahydrate is essentially unchanged at the highest irradiation temperatures and completely destroyed at the lowest ones, which we speculate is due to a combination of radiolytic destruction and amorphization. Furthermore, at the lower temperatures it is clear that irradiation causes the tetrahydrate spectrum to transition to one that closely resembles the monohydrate spectrum. Extrapolating our results to Europa s surface, we speculate that the variations in SO2 concentrations observed in the chaotic terrains are a result of radiation processing of lower hydration states of sulfuric acid and that the monohydrate will remain stable on the surface over geological times, while the tetrahydrate will remain stable in the warmer regions but be destroyed in the colder regions, unless it can be reformed by other processes, such as thermal reactions induced by diurnal cycling.

Loeffler, M. J.↗

NASA NTRS1990

An investigation of chaotic Kolmogorov flows

A two dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number (Re) varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with non-ergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Kaplan-Yorke dimension.

Platt, N.↗