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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Variations of the Milankovitch frequencies in time

The sensitivity of the amplitudes and frequencies in the development of the Earth's orbital and rotational elements involved in the astronomical theory of paleoclimates (eccentricity, obliquity, and climate precession), to the Earth-Moon distance and consequently to the length of the day and to the dynamical ellipticity of the Earth has been discussed for the last billions of years. The shortening of the Earth-Moon distance and of the length of the day, as well as the lengthening of the dynamical ellipticity of the Earth back in time induce a shortening of the fundamental astronomical periods for precession and obliquity. At the same time, the amplitudes of the different terms in the development of the obliquity are undergoing a relative enlargement of about 50 percent at 2 x 10(exp 9) yr BP but the independent term is increasing very weakly (less than 0.1 percent). In other words, the value of the obliquity, which lies within a range of 21.7 to 24.9 deg over the Quarternary was restricted to a range of 22.5 to 24.1 deg at 2 x 10(exp 9) yr BP. On the other hand, the amplitudes in the development of the climatic precession do not change. Moreover, these changes in the frequencies and amplitudes for both obliquity and climatic precession are larger for longer period terms. Finally, the periods in the eccentricity development are not influenced by the variation of the lunar distance. But the motion of the solar system, especially of the inner planets, was shown to be chaotic. It means that it is impossible to compute the exact motion of the planets over more than about 100 Myr, and the fundamental frequencies of the systems are not fixed quantities, but are slowly varying with time. As long as we consider the most important terms, the maximum deviation from the present-day value of the 19-kyr precessional period due to the chaotic motion of the solar system only does not reach more than a few tens of years around 80 Myr BP. Therefore the shortening of the obliquity and climatic precession periods is mostly driven by the change in the lunar distance and the consequent variations in the dynamical ellipticity of the Earth's angular speed. At first sight, the deviation in the period for the eccentricity can be neglected, as the chaotic behavior of the solar system implies a relative change of the main periods by less than 0.2 percent, 1.4 percent, and 1.9 percent respectively, this maximum change being achieved around 80 Myr BP. This implies, in particular, that the eccentricity periods for Quarternary climate studies may be considered more or less constant for pre-Quaternay times and equal to their Quaternary values.

Loutre, Marie-France↗
NASA NTRS1994

Some recent results of nonlinear acoustics in combustion chambers

The chief purpose of this paper is to provide a brief review of some recent work on nonlinear acoustics applicable to combustion instabilities, largely in the framework of an approximate analysis. Some connections will be made with the modern theory of nonlinear dynamical systems, including very recent and incomplete attempts by others to assess the possible chaotic behavior observed in laboratory tests.

Culick, F. E. C.↗
NASA NTRS2008

Fomalhaut's Debris Disk and Planet: Constraining the Mass of Formalhaut B from Disk Morphology

Following the optical imaging of exoplanet candidate Fomalhaut b (Fom b), we present a numerical model of how Fomalhaut's debris disk is gravitationally shaped by a single interior planet. The model is simple, adaptable to other debris disks, and can be extended to accommodate multiple planets. If Fom b is the dominant perturber of the belt, then to produce the observed disk morphology it must have a mass M(sub pl) < 3M(sub J), an orbital semimajor axis a(sub pl) > 101.5AU, and an orbital eccentricity e(sub pl) = 0.11 - 0.13. These conclusions are independent of Fom b's photometry. To not disrupt the disk, a greater mass for Fom b demands a smaller orbit farther removed from the disk; thus, future astrometric measurement of Fom b's orbit, combined with our model of planet-disk interaction, can be used to determine the mass more precisely. The inner edge of the debris disk at a approximately equals 133AU lies at the periphery of Fom b's chaotic zone, and the mean disk eccentricity of e approximately equals 0.11 is secularly forced by the planet, supporting predictions made prior to the discovery of Fom b. However, previous mass constraints based on disk morphology rely on several oversimplifications. We explain why our constraint is more reliable. It is based on a global model of the disk that is not restricted to the planet's chaotic zone boundary. Moreover, we screen disk parent bodies for dynamical stability over the system age of approximately 100 Myr, and model them separately from their dust grain progeny; the latter's orbits are strongly affected by radiation pressure and their lifetimes are limited to approximately 0.1 Myr by destructive grain-grain collisions. The single planet model predicts that planet and disk orbits be apsidally aligned. Fomalhaut b's nominal space velocity does not bear this out, but the astrometric uncertainties are difficult to quantify. Even if the apsidal misalignment proves real, our calculated upper mass limit of 3 M(sub J) still holds. Parent bodies are evacuated from mean-motion resonances with Fom b; these empty resonances are akin to the Kirkwood gaps opened by Jupiter. The belt contains at least 3M(sub Earth) of solids that are grinding down to dust, their velocity dispersions stirred so strongly by Fom b that collisions are destructive. Such a large mass in solids is consistent with Fom b having formed in situ.

Chiang, E.↗
DOE OSTI2022

Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80-D bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2D and 3D pseudo-phase-space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is resumed back to a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

36 MATERIALS SCIENCE↗
NASA NTRS2003

Probable Disastrous Consequences of Collision Between Unknown Small (100 m) Asteroids with Known (Approximately 1 km) Near Earth Orbiting (NEO) Asteroids

The long-term stability of the Solar System is not well understood. Ironically its stability is taken for granted even though our knowledge of all the constituents [comets, asteroids. (The Asteroid Belt between Mars and Jupiter, Trojan Asteroids, Kuiper belt, Ort Cloud), planetoids, planets, moons, etc], and its long-term dynamics cannot be easily computed. At best one might say that the solar system is chaotic, but much of the time it seems to exists near a quasi-stationary state. An asteroid that passes near the Earth regularly returns with clock-like precision. Taking into account every known detail of its path through the solar system, its orbit is calculated forward thousands of years with no untoward calamity on the horizon. And then one day, this passive visitor slams into the Earth during a sunny afternoon picnic! Can this happen? Unfortunately, this is a real possibility in the ordinary history of the solar system. In fact our knowledge of the solar system in the small is sketchy, as will be pointed out. Events, which lie outside our awareness, can precipitate disasters that we may perceive when it's too late to launch effective counter measures. In this work, one such scenario is described and the direct consequences for the Earth are calculated.

Smalley, Larry↗
DOE OSTI2020

Fast dynamic aperture optimization with forward-reversal integration

A fast dynamic aperture (DA) optimization method for storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symmetry, a numerical forward integration differs from its reversal. For a chaotic trajectory, cumulative round-off errors are scaled, which results in an exponential growth on the difference. The exponential effect is a generic chaos indicator which represents the sensitivity of the chaotic motion to its initial condition. The chaos indicator of the charged particle motion can be obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. “backward integrations.” The indicator is observable even through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. Finally, the DA of the National Synchrotron Light Source II storage ring, and another test diffraction-limited light source ring, were optimized using this method for the purpose of demonstration.

43 PARTICLE ACCELERATORS↗
NASA NTRS2018

Mission analysis for the EM-1 CubeSats EQUULEUS and OMOTENASHI

EQUULEUS is a Lunar L2 orbiter and a 6-Unit CubeSat by JAXA and the University of Tokyo. OMOTENASHI is a 6-Unit CubeSat by JAXA, the world’s smallest Lunar lander. EQUULEUS and OMOTENASHI are among the 13 secondary payloads selected by NASA to be launched with Exploration Mission-1 in 2019. Despite their limited size and cost, EQUULEUS and OMOTENASHI are challenging missions, especially in terms of trajectory design and control. EQUULEUS exploits the Earth-Sun-Moon chaotic dynamics and enter a libration point orbit around the L2 of the Earth-Moon system, using a new water propulsion system with low thrust and little propellant. This “Orbit Control Experiment” is one of the main objectives of the mission. OMOTENASHI executes a semi-hard landing that requires breaking the spacecraft to a stop just a few-hundred meters above the Moon’s surface. Both missions present new and unique challenges, where the design of the nominal trajectory is mainly driven by the constrains on orbital control capabilities, and operational and robustness considerations. This paper presents the current baselines, and give an overview of the new techniques developed for their design.

Oshima, Kenta↗
DOE OSTI2024

Accurate data-driven surrogates of dynamical systems for forward propagation of uncertainty

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. Here, this work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.

42 ENGINEERING↗
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.↗
DOE OSTI2024

Local Poincaré algebra from quantum chaos

The local two-dimensional Poincaré algebra near the horizon of an eternal AdS black hole, or in proximity to any bifurcate Killing horizon, is generated by the Killing flow and outward null translations on the horizon. In holography, this local Poincaré algebra is reflected as a pair of unitary flows in the boundary Hilbert space whose generators under modular flow grow and decay exponentially with a maximal Lyapunov exponent. This is a universal feature of many geometric vacua of quantum gravity. To explain this universality, we show that a two-dimensional Poincaré algebra emerges in any quantum system that has von Neumann subalgebras associated with half-infinite modular time intervals (modular future and past subalgebras) in a limit analogous to the near-horizon limit. In ergodic theory, quantum dynamical systems with future or past algebras are called quantum K-systems. The surprising statement is that modular K-systems are always maximally chaotic. Interacting quantum systems in the thermodynamic limit and large N theories above the Hawking-Page phase transition are examples of physical theories with future/past subalgebras. We prove that the existence of (modular) future/past von Neumann subalgebras also implies a second law of (modular) thermodynamics and the exponential decay of (modular) correlators. We generalize our results from the modular flow to any dynamical flow with a positive generator and interpret the positivity condition as quantum detailed balance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Fast Dynamic Aperture Optimization with Reversal Integration

A fast method for dynamic aperture (DA) optimization of storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symme- try, a numerical forward integration di ers from its reversal. For chaotic trajectories, cumulative round-o errors are scaled, which results in an exponential growth in the di erence. The exponential e ect, intrinsically associated with the Lyapunov exponent, is a generic indicator of chaos because it represents the sensitivity of chaotic motion to an initial condition. A chaos indicator of the charged particle motion is then obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. \backward integrations." The indicator was con rmed to be ob- servable through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. The DA of the National Synchrotron Light Source II storage ring, and another test di raction-limited light source ring, were optimized using this method for the purpose of demonstration.

36 MATERIALS SCIENCE↗
NASA NTRS1986

Determining Chaotic Instabilities in Mechanical Systems

Theoretical developments enable suppression of chaotic structual motions. Theory enables prediction, avoidance, and suppression of chaotic vibrations in structures, especially using dynamic feedback stabilization. In new formulation, motion both repeatable and predictable.

Zak, M. A.↗
DOE OSTI2023

Online real-time learning of dynamical systems from noisy streaming data

Abstract Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by physical sensors, it is natural that the obtained data is corrupted by measurement noise. In this paper, we present a novel algorithm for online real-time learning of dynamical systems from noisy time-series data, which employs the Robust Koopman operator framework to mitigate the effect of measurement noise. The proposed algorithm has three main advantages: (a) it allows for online real-time monitoring of a dynamical system; (b) it obtains a linear representation of the underlying dynamical system, thus enabling the user to use linear systems theory for analysis and control of the system; (c) it is computationally fast and less intensive than the popular extended dynamic mode decomposition (EDMD) algorithm. We illustrate the efficiency of the proposed algorithm by applying it to identify the Van der Pol oscillator, the chaotic attractor of the Henon map, the IEEE 68 bus system, and a ring network of Van der Pol oscillators.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

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.↗
DOE OSTI2020

Investigation of flow regimes in arc plasma–gas interactions using a two-temperature arc in crossflow model

The perpendicular impingement of a gas stream on an electric arc, a configuration known as the arc in crossflow, is of primary relevance in the study of plasma-gas interactions, as well as in industrial applications such as circuit breakers and wire-arc spraying. The flow dynamics in the arc in crossflow are the result of coupled fluid-thermal-electromagnetic phenomena accompanied by large property gradients, which can produce significant deviations from Local Thermodynamic Equilibrium (LTE) among electrons and gas species. These characteristics can lead to the establishment of distinct flow regimes depending on the relative values of the controlling parameters of the system, such as inflow velocity, arc current, and inter-electrode spacing. A two-temperature non-LTE (NLTE) model is used to investigate the arc dynamics and the establishment of flow regimes in the arc in crossflow. The plasma flow model is implemented within a nonlinear Variational Multiscale (VMS) numerical discretization approach that is less dissipative, and hence better suited to capture unstable behavior, than traditional VMS methods commonly used in computational fluid dynamics simulations. The Reynolds and the Enthalpy dimensionless numbers, characterizing the relative flow strength and arc strength, respectively, are chosen as the controlling parameters of the system. Simulation results reveal the onset of dynamic behavior and the establishment of steady, periodic, quasi-periodic, and chaotic or potentially turbulent, regimes, as identified by distinct spatiotemporal fluctuations. The computational findings reveal the role of increasing the relative arc strength on enhancing flow stability by delaying the growth of fluctuating and unstable flow behavior.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

The kinematics of buoyancy induced mixing

A model problem to study mixing driven by buoyancy flow fields due to a time dependent body force which consists of a steady and an oscillatory component is considered. Flow fields generated by a time dependent body force, which consists of a steady and an oscillatory component from vibrations or g-jitter, mix two fluids inside a cavity by stretching and folding the interface into various morphological patterns. These patterns show two basic structures depending on the dominant components of the body force. These structures are whirls and tendrils, corresponding to the dominance of either the steady or oscillatory component, respectively. A combination of these structures also occurs in the interaction region. In this region the effect of the steady component opposes the oscillatory component and the result is to smooth the interface, and prevent breakup of the interface. For the parametric range considered, two basic flow regimes occur: convective and chaotic. In the convective regime, the morphological patterns are topological. In the chaotic regime, mixing occurs by a repetitive sequence of bubble formation, necking, and breakup which spreads the concentration field throughout the cavity. The length stretch of the interface increases exponentially with time. The dynamical system characteristics show that in the convective regime, at a point in space, the flow field is oscillatory with elliptical phase space trajectories, and its power spectrum indicates that the flow field responds to the corresponding input frequency. Whereas, in the chaotic regime, the flow field is aperiodic, the phase space trajectories show irregular patterns, and the power spectrum shows a broadband distribution.

Duval, Walter M. B.↗
DOE OSTI2020

Holographic map for cosmological horizons

Here, we propose a holographic map between Einstein gravity coupled to matter in a de Sitter background and large N quantum mechanics of a system of spins. Holography maps a spin model with a finite-dimensional Hilbert space defined on a version of the stretched horizon into bulk gravitational dynamics. The full Hamiltonian of the spin model contains a nonlocal piece which generates chaotic dynamics, widely conjectured to be a necessary part of quantum gravity, and a local piece which recovers the perturbative spectrum in the bulk.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗