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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.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Seismic Excitation of the Polar Motion, 1977-1993

The mass redistribution in the earth as a result of an earthquake faulting changes the earth's inertia tensor, and hence its rotation. Using the complete formulae developed by CHAO and GROSS (1987) based on the normal mode theory, we calculated the earthquake-induced polar motion excitation for the largest 11,015 earthquakes that occurred during 1977.0-1993.6. The seismic excitations in this period are found to be two orders of magnitude below the detection threshold even with today's high precision earth rotation measurements. However, it was calculated that an earthquake of only one tenth the size of the great 1960 Chile event, if happened today, could be comfortably detected in polar motion observations. Furthermore, collectively these seismic excitations have a strong statistical tendency to nudge the pole towards approximately 140deg E, away from the actual observed polar drift direction. This non-random behavior, similarly found in other earthquake-induced changes in earth rotation and low-degree gravitational field by CHAO and GROSS (1987), manifests some geodynamic behavior yet to be explored.

Chao, Benjamin Fong↗
NASA NTRS1996

Seismic Excitation of the Polar Motion

The mass redistribution in the earth as a result of an earthquake faulting changes the earth's inertia tensor, and hence its rotation. Using the complete formulae developed by Chao and Gross (1987) based on the normal mode theory, we calculated the earthquake-induced polar motion excitation for the largest 11,015 earthquakes that occurred during 1977.0-1993.6. The seismic excitations in this period are found to be two orders of magnitude below the detection threshold even with today's high precision earth rotation measurements. However, it was calculated that an earthquake of only one tenth the size of the great 1960 Chile event, if happened today, could be comfortably detected in polar motion observations. Furthermore, collectively these seismic excitations have a strong statistical tendency to nudge the pole towards approx. 140 deg E, away from the actually observed polar drift direction. This non-random behavior, similarly found in other earthquake-induced changes in earth rotation and low-degree gravitational field by Chao and Gross (1987), manifests some geodynamic behavior yet to be explored.

Chao, Benjamin Fong↗
DOE OSTI2020

Many-Body Level Statistics of Single-Particle Quantum Chaos

We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q = 2 complex Sachdev-Ye-Kitaev model)—a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Smooth periodic gauge satisfying crystal symmetry and periodicity to study high-harmonic generation in solids

Intense lasers can easily drive nonadiabatic transitions of excited electron wave packets across the Brillouin zones, thus transition dipole moments (TDM) between energy bands of solids should be continuous, satisfying crystal symmetry, and periodic at zone boundaries. While current ab initio algorithms are powerful in calculating band structures of solids, they all introduced random phases into the eigenfunctions at each crystal momentum k. In this work, we show how to choose a “smooth-periodic” gauge where TDMs can be smooth versus k, preserving crystal symmetry, as well as maintaining periodic at boundaries. The symmetry properties of TDMs with respect to k ensure the absence of even-order harmonics from MgO with inversion symmetry, while the TDM in the “smooth-periodic” gauge for broken-symmetry ZnO is responsible for even harmonics that were underestimated in previous simulations. These results reveal the importance of correctly treating the complex TDMs that satisfy crystal symmetry and continuous across zone boundaries in nonlinear laser-solid interactions, which has been elusive in most theories so far.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Constraining chaos: Enforcing dynamical invariants in the training of reservoir computers

Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants—such as the Lyapunov exponent spectrum and the fractal dimension—in the systems of interest, enabling longer and more stable forecasts when operating with limited data. The technique is demonstrated in detail using reservoir computing, a specific kind of recurrent neural network. Finally, results are given for the Lorenz 1996 chaotic dynamical system and a spectral quasi-geostrophic model of the atmosphere, both typical test cases for numerical weather prediction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Approximating the linear response of physical chaos

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Generation of arbitrary probability distributions from chaotic dynamics

A framework is developed to derive nonlinear dynamical systems that chaotically generate arbitrary multivariate probability distributions with smooth, deterministic trajectories. Herein, the ideas are used to extend the Nosé-Hoover thermostat methodology to three-dimensional cases where the momentum distribution is nonisotropic and/or non-Gaussian. Toy models that generate several well-known distributions in physics are given as pedagogical examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

Analysis of regional deformation and strain accumulation data adjacent to the San Andreas fault

A new approach to the understanding of crustal deformation was developed under this grant. This approach combined aspects of fractals, chaos, and self-organized criticality to provide a comprehensive theory for deformation on distributed faults. It is hypothesized that crustal deformation is an example of comminution: Deformation takes place on a fractal distribution of faults resulting in a fractal distribution of seismicity. Our primary effort under this grant was devoted to developing an understanding of distributed deformation in the continental crust. An initial effort was carried out on the fractal clustering of earthquakes in time. It was shown that earthquakes do not obey random Poisson statistics, but can be approximated in many cases by coupled, scale-invariant fractal statistics. We applied our approach to the statistics of earthquakes in the New Hebrides region of the southwest Pacific because of the very high level of seismicity there. This work was written up and published in the Bulletin of the Seismological Society of America. This approach was also applied to the statistics of the seismicity on the San Andreas fault system.

Turcotte, Donald L.↗
NASA NTRS1987

Application of non-linear dynamics to the characterization of cardiac electrical instability

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

NASA Discipline Cardiopulmonary↗
DOE OSTI2021

Reinforcement Learning Configuration Interaction

Selected configuration interaction (sCI) methods exploit the sparsity of the full configuration interaction (FCI) wave function, yielding significant computational savings and wave function compression without sacrificing the accuracy. Despite recent advances in sCI methods, the selection of important determinants remains an open problem. Furthermore, we explore the possibility of utilizing reinforcement learning approaches to solve the sCI problem. By mapping the configuration interaction problem onto a sequential decision-making process, the agent learns on-the-fly which determinants to include and which to ignore, yielding a compressed wave function at near-FCI accuracy. This method, which we call reinforcement-learned configuration interaction, adds another weapon to the sCI arsenal and highlights how reinforcement learning approaches can potentially help solve challenging problems in electronic structure theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2002

Geology and Origin of Europa's Mitten Feature (Murias Chaos)

The "Mitten" (provisionally named Murias Chaos by the International Astronomical Union) is a region of elevated chaos-like terrain in the leading hemisphere of Europa. Its origin had been explained under the currently debated theories of melting through a thin lithosphere or convection within a thick one. Galileo observations reveal several characteristics that suggest that the Mitten is distinct from typical chaos terrain and point to a different formational process. Photoclinometric elevation estimates suggest that the Mitten is slightly elevated with respect to the surrounding terrain; geologic relations indicate that it must have raised significantly from the plains in its past, resembling disrupted domes on Europa's trailing hemisphere. Moreover, the Mitten material appears to have extruded onto the plains and flowed for tens of kilometers. The area subsequently subsided as a result of isostatic adjustment, viscous relaxation, and/or plains loading. Using plate flexure models, we estimated the elastic lithosphere in the area to be several kilometers thick. We propose that the Mitten originated by the ascent and extrusion of a large thermal diapir. Thermal-mechanical modeling shows that a Mitten-sized plume would remain sufficiently warm and buoyant to pierce through the crust and flow unconfined on the surface. Such a diapir probably had an initial radius between 5 and 8 km and an initial depth of 20-40 km, consistent with a thick-lithosphere model. In this scenario the Mitten appears to represent the surface expression of the rare ascent of a large diapir, in contrast to lenticulae and chaos terrain, which may form by isolated and clustered small diapirs, respectively.

Figueredo, P. H.↗
DOE OSTI2022

Quantum chaos and unitary black hole evaporation

The formation and evaporation of small AdS black holes in a theory with a holographic dual is governed by the usual rules of quantum mechanics. The eigenstate thermalization hypothesis explains the validity of semiclassical gravity for local bulk observables and can be used to quantify the magnitude of quantum corrections to the semi-classical approximation. The holographic dual produces a basis of black hole states with finite energy width, and observables that are smooth functions on the classical phase space will self-average over a large number of energy eigenstates, exponential in the Bekenstein-Hawking entropyS, leading to results that are consistent with semiclassical gravity up to small corrections of order e –S/2 . As expected, the semiclassical description breaks down for transition amplitudes that reflect the unitary evolution of the holographic theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Approximate CFTs and random tensor models

Abstract A key issue in both the field of quantum chaos and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints of conformal symmetry and locality, allowing the definition of ensembles of ‘CFT data’. These ensembles take on the same role as the ensembles of random Hamiltonians in more conventional quantum ergodic phases of many-body quantum systems. To describe individual members of the ensembles, we introduce the notion of approximate CFT, defined as a collection of ‘CFT data’ satisfying the usual CFT constraints approximately, i.e. up to small deviations. We show that they generically exist by providing concrete examples. Ensembles of approximate CFTs are very natural in holography, as every member of the ensemble is indistinguishable from a true CFT for low-energy probes that only have access to information from semi-classical gravity. To specify these ensembles, we impose successively higher moments of the CFT constraints. Lastly, we propose a theory of pure gravity in AdS 3 as a random matrix/tensor model implementing approximate CFT constraints. This tensor model is the maximum ignorance ensemble compatible with conformal symmetry, crossing invariance, and a primary gap to the black-hole threshold. The resulting theory is a random matrix/tensor model governed by the Virasoro 6j-symbol.

Physics↗
DOE OSTI2021

Nonlinear dynamics and quantum chaos of a family of kicked p -spin models

Herein we introduce kicked p-spin models describing a family of transverse Ising-like models for an ensemble of spin-1/2 particles with all-to-all p-body interaction terms occurring periodically in time as delta-kicks. This is the natural generalization of the well-studied quantum kicked top (p = 2) [Haake, Kus', and Scharf, Z. Phys. B 65, 381 (1987)]. We fully characterize the classical nonlinear dynamics of these models, including the transition to global Hamiltonian chaos. The classical analysis allows us to build a classification for this family of models, distinguishing between p = 2 and p > 2, and between models with odd and even p's. Quantum chaos in these models is characterized in both kinematic and dynamic signatures. For the latter, we show numerically that the growth rate of the out-of-time-order correlator is dictated by the classical Lyapunov exponent. Finally, we argue that the classification of these models constructed in the classical system applies to the quantum system as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

Predicting chaos for infinite dimensional dynamical systems: The Kuramoto-Sivashinsky equation, a case study

The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

Smyrlis, Yiorgos S.↗
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↗
DOE OSTI2022

GenMod: A generative modeling approach for spectral representation of PDEs with random inputs

Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.

97 MATHEMATICS AND COMPUTING↗