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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 325 records · Page 18
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DOE OSTI2011

Predator prey oscillations in a simple cascade model of drift wave turbulence

A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separation for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

EJECTION AND CAPTURE DYNAMICS IN RESTRICTED THREE-BODY ENCOUNTERS

We study the tidal disruption of binaries by a massive point mass (e.g., the black hole at the Galactic center), and we discuss how the ejection and capture preference between unequal-mass binary members depends on which orbit they approach the massive object. We show that the restricted three-body approximation provides a simple and clear description of the dynamics. The orbit of a binary with mass m around a massive object M should be almost parabolic with an eccentricity of |1 - e| {approx}< (m/M){sup 1/3} << 1 for a member to be captured, while the other is ejected. Indeed, the energy change of the members obtained for a parabolic orbit can be used to describe non-parabolic cases. If a binary has an encounter velocity much larger than (M/m){sup 1/3} times the binary rotation velocity, it would be abruptly disrupted, and the energy change at the encounter can be evaluated in a simple disruption model. We evaluate the probability distributions for the ejection and capture of circular binary members and for the final energies. In principle, for any hyperbolic (elliptic) orbit, the heavier member has more chance to be ejected (captured), because it carries a larger fraction of the orbital energy. However, if the orbital energy is close to zero, the difference between the two members becomes small, and there is practically no ejection and capture preferences. The preference becomes significant when the orbital energy is comparable to the typical energy change at the encounter. We discuss its implications to hypervelocity stars and irregular satellites around giant planets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

CONTRIBUTIONS OF THE ELASTICITY TO THE PRECESSION OF A TWO-LAYER EARTH MODEL

We focus on the updating of a specific contribution to the precession of the equator in longitude, usually named as “second order.” It stems from the crossing of certain terms of the lunisolar gravitational potential. The IAU2006 precession theory assigns it the value of −46.8 mas/cy that was derived for a rigid Earth model. Instead of that model, we consider a two-layer Earth composed of an elastic mantle and a liquid core, working out the problem within the Hamiltonian framework developed by Getino and Ferrándiz. The targeted effect is obtained without further simplifying assumptions through Hori’s canonical perturbation method applied up to the second order of perturbation. On account of using a more realistic Earth model, the revised value of the second-order contribution is significantly changed and reaches −55.29 mas/cy. That variation of the second-order contribution is larger than other contributions included in IAU2006. It must be compensated with an increase of −8.51 mas/cy in the value of the lunisolar first-order component p{sub A}{sup ′} of the precession of the equator rate, which is derived from the total rate by subtracting the remaining contributions accounted for in IAU2006 precession. The updating of the second-order contribution implies that the p{sub A}{sup ′} parameter has to be changed, from 5040684.593 to 5040693.104 mas/cy in absence of potential revisions of other contributions. It entails a proportional variation of Earth’s dynamical ellipticity H{sub d}, for which the estimation associated with IAU2006, 0.00327379448, should be updated to 0.00327380001, about 1.7 ppm larger.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Electromagnetically induced absorption and electromagnetically induced transparency for optical transitions F{sub g} → F{sub e} in the field of elliptically polarized waves

Nonlinear laser spectroscopy is considered in the scheme of two collinear waves with arbitrary elliptical polarizations. Emphasis is placed on investigating the nonlinear corrections in the absorption spectrum of one of the waves. The spontaneous transfer of low-frequency Zeeman coherence is shown to affect the sign of the subnatural-width resonance. For a closed transition, the direction of the resonance profile has been found to depend only on the angular momenta F{sub e} and F{sub g}. On this basis, a classification has been developed for various transitions by the direction of the subnatural-width resonance profile.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Efficient Bayesian inference with latent Hamiltonian neural networks in No-U-Turn Sampling

When sampling for Bayesian inference, one popular approach in the computational field is to use Hamiltonian Monte Carlo (HMC) and specifically the No-U-Turn Sampler (NUTS), which automatically decides the end time of the Hamiltonian trajectory. However, HMC and NUTS can require numerous numerical gradients of the target density and can prove slow in practice when relying on computationally expensive forward models. We propose Latent Hamiltonian neural networks (L-HNNs) with HMC and NUTS for solving Bayesian inference problems. Once trained, L-HNNs do not require numerical gradients of the target density during sampling, and hence numerous evaluations of the forward computational model. Moreover, L-HNNs satisfy important properties such as perfect time reversibility and Hamiltonian conservation, making them well-suited for use within HMC and NUTS because stationarity can be shown. We also propose the integration of L-HNNs in an online error monitoring scheme, in which numerical gradients of the target density are used for a few samples whenever the L-HNNs prediction errors are large. This online error monitor scheme prevents sample degeneracy in regions of low probability density and ensures robust uncertainty quantification. We demonstrate L-HNNs in NUTS with online error monitoring on several analytical examples involving complex, heavy-tailed, and high-local-curvature probability densities. We then demonstrate the applicability of L-HNNs in NUTS to two computational case studies, namely the Allen-Cahn stochastic partial differential equation and an elliptic partial differential equation with 25 and 50 inference parameters, respectively. Overall, the L-HNNs in NUTS with online error monitoring satisfactorily inferred these probability densities. In conclusion, compared to traditional NUTS, L-HNNs in NUTS with online error monitoring required 1–2 orders of magnitude fewer numerical gradients of the target density and improved the effective sample size (ESS) per gradient (which is a measure of both the sampling quality and the computational expense) by an order of magnitude.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

ABOUT THE LINEARITY OF THE COLOR-MAGNITUDE RELATION OF EARLY-TYPE GALAXIES IN THE VIRGO CLUSTER

We revisit the color-magnitude relation of Virgo Cluster early-type galaxies in order to explore its alleged nonlinearity. To this aim, we reanalyze the relation already published from data obtained within the ACS Virgo Cluster Survey of the Hubble Space Telescope and perform our own photometry and analysis of the images of 100 early-type galaxies observed as part of this survey. In addition, we compare our results with those reported in the literature from data of the Sloan Digital Sky Survey. We have found that when the brightest galaxies and untypical systems are excluded from the sample, a linear relation arises in agreement with what is observed in other groups and clusters. The central regions of the brightest galaxies also follow this relation. In addition, we notice that Virgo contains at least four compact elliptical galaxies besides the well-known object VCC 1297 (NGC 4486B). Their locations in the ({mu}{sub eff})-luminosity diagram define a trend different from that followed by normal early-type dwarf galaxies, setting an upper limit in effective surface brightness and a lower limit in the effective radius for their luminosities. Based on the distribution of different galaxy sub-samples in the color-magnitude and ({mu}{sub eff})-luminosity diagrams, we draw some conclusions on their formation and the history of their evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Vortex equations governing the fractional quantum Hall effect

An existence theory is established for a coupled non-linear elliptic system, known as “vortex equations,” describing the fractional quantum Hall effect in 2-dimensional double-layered electron systems. Via variational methods, we prove the existence and uniqueness of multiple vortices over a doubly periodic domain and the full plane. In the doubly periodic situation, explicit sufficient and necessary conditions are obtained that relate the size of the domain and the vortex numbers. For the full plane case, existence is established for all finite-energy solutions and exponential decay estimates are proved. Quantization phenomena of the magnetic flux are found in both cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

The 21 cm signature of a cosmic string loop

Cosmic string loops lead to nonlinear baryon overdensities at early times, even before the time which in the standard LCDM model corresponds to the time of reionization. These overdense structures lead to signals in 21 cm redshift surveys at large redshifts. In this paper, we calculate the amplitude and shape of the string loop-induced 21 cm brightness temperature. We find that a string loop leads to a roughly elliptical region in redshift space with extra 21 cm emission. The excess brightness temperature for strings with a tension close to the current upper bound can be as high as 1deg K for string loops generated at early cosmological times (times comparable to the time of equal matter and radiation) and observed at a redshift of z+1 = 30. The angular extent of these predicted 'bright spots' is x{sup '}. These signals should be detectable in upcoming high redshift 21 cm surveys. We also discuss the application of our results to global monopoles and primordial black holes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Nonlinear modulation of an extraordinary wave under the conditions of parametric decay

A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of 'slow' equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period, is used to describe steady-state nonlinear oscillations in plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

A Probabilistic Approach to Interior Regularity of Fully Nonlinear Degenerate Elliptic Equations in Smooth Domains

We consider the value function of a stochastic optimal control of degenerate diffusion processes in a domain D. We study the smoothness of the value function, under the assumption of the non-degeneracy of the diffusion term along the normal to the boundary and an interior condition weaker than the non-degeneracy of the diffusion term. When the diffusion term, drift term, discount factor, running payoff and terminal payoff are all in the class of C{sup 1,1}( D-bar ) , the value function turns out to be the unique solution in the class of C{sub loc}{sup 1,1}(D) Intersection C{sup 0,1}( D-bar ) to the associated degenerate Bellman equation with Dirichlet boundary data. Our approach is probabilistic.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

On the Post-Keplerian Corrections to the Orbital Periods of a Two-body System and Their Application to the Galactic Center

We perform detailed numerical analyses of the orbital motion of a test particle around a spinning primary, with the aim of investigating the possibility of using the post-Keplerian (pK) corrections to the orbiter’s periods (draconitic, anomalistic, and sidereal) as a further opportunity to perform new tests of post-Newtonian gravity. As a specific scenario, the S-stars orbiting the massive black hole (MBH) supposedly lurking in Sgr A* at the center of the Galaxy are adopted. We first study the effects of the pK Schwarzchild, Lense–Thirring, and quadrupole moment accelerations experienced by a target star for various possible initial orbital configurations. It turns out that the results of the numerical simulations are consistent with the analytical ones in the small eccentricity approximation for which almost all the latter ones were derived. For highly elliptical orbits, the sizes of the three pK corrections considered turn out to increase remarkably. The periods of the observed S2 and S0-102 stars as functions of the MBH’s spin axis orientation are considered as well. The pK accelerations lead to corrections of the orbital periods of the order of 1–100 days (Schwarzschild), 0.1–10 hr (Lense–Thirring), and 1–10{sup 3} s (quadrupole) for a target star with a = 300–800 au and e ≈ 0.8, which could be measurable with future facilities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Dark halos and elliptical galaxies as marginally stable dynamical systems

The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold of particle positions—a context in which subtle spurious effects originating from the singularity in the two-body potential become particularly clear. We focus on the case of spherical systems, which support only regular orbits in the collisionless limit, despite the persistence of local exponential instability of N-body trajectories in the anomalous case of discrete point particle representation even as N → ∞. When the singularity in the potential is removed, this apparent contradiction disappears. In the absence of fluctuations, equilibrium configurations generally correspond to positive scalar curvature and thus support stable trajectories. A null scalar curvature is associated with an effective, averaged equation of state describing dynamically relaxed equilibria with marginally stable trajectories. The associated configurations are quite similar to those of observed elliptical galaxies and simulated cosmological halos and are necessarily different from the systems dominated by isothermal cores, expected from entropy maximization in the context of the standard theory of violent relaxation. It is suggested that this is the case because a system starting far from equilibrium does not reach a 'most probable state' via violent relaxation, but that this process comes to an end as the system finds and (settles in) a configuration where it can most efficiently wash out perturbations. We explicitly test this interpretation by means of direct simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Nonlinear birefringence in plasmas: Polarization dynamics, vector modulational instability, and vector solitons

The propagation of an elliptically polarized intense laser pulse in an unmagnetized collisionless uniform plasma is considered. A multiple scale perturbation theory is employed to show that in a weakly relativistic regime, evolution of the components of vector potential is governed by two coherently coupled nonlinear Schrödinger (NLS) equations. A set of equations describing the evolution of Stokes parameters is derived within the continuous wave approximation and the dynamics of components of field amplitude is studied. The polarization dynamics of a pulse is investigated by means of numerical solution of the coupled NLS equations. A detailed analysis of vector modulational instability is presented and the possibility for occurrence of various kinds of vector solitary waves is addressed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Confocal Annular Josephson Tunnel Junctions with Large Eccentricity

Confocal annular Josephson tunnel junctions (CAJTJs), which are the natural generalization of the circular annular Josephson tunnel junctions, have a rich nonlinear phenomenology due to the intrinsic non-uniformity of their planar tunnel barrier delimited by two closely spaced confocal ellipses. In the presence of a uniform magnetic field in the barrier plane, the periodically changing width of the elliptical annulus generates a asymmetric double-well for a Josephson vortex trapped in a long and narrow CAJTJ. The preparation and readout of the vortex pinned in one of the two potential minima, which are important for the possible realization of a vortex qubit, have been numerically and experimentally investigated for CAJTJs with the moderate aspect ratio 2:1. In this work, we focus on the impact of the annulus eccentricity on the properties of the vortex potential profile and study the depinning mechanism of a fluxon in more eccentric samples with aspect ratio 4:1. We also discuss the effects of the temperature-dependent losses as well as the influence of the current and magnetic noise.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2018

On quasiconformal maps and semilinear equations in the plane

Assume that Ω is a domain in the complex plane ℂ and A(z) is a symmetric 2×2 matrix function with measurable entries, detA = 1; and such that 1/K|ξ|{sup 2} ≤ 〈A(z)ξ, ξ〉 ≤ K|ξ|{sup 2}, ξ ∈ ℝ{sup 2}, 1 ≤ K < ∞ . In particular, for semilinear elliptic equations of the form div (A(z)∇u(z)) = f(u(z)) in Ω; we prove a factorization theorem that asserts that every weak solution u to the above equation can be expressed as the composition u = To𝜔; where 𝜔 : Ω → G stands for a K−quasiconformal homeomorphism generated by the matrix function A(z); and T(w) is a weak solution of the semilinear equation ∇T(w) = J(w)f(T(w)) in G: Here, the weight J(w) is the Jacobian of the inverse mapping 𝜔{sup −1}: Similar results hold for the corresponding nonlinear parabolic and hyperbolic equations. Some applications of these results to anisotropic media are given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

NONLINEAR COLOR-METALLICITY RELATIONS OF GLOBULAR CLUSTERS. IV. TESTING THE NONLINEARITY SCENARIO FOR COLOR BIMODALITY VIA HST/WFC3 u-BAND PHOTOMETRY OF M84 (NGC 4374)

Color distributions of globular clusters (GCs) in most massive galaxies are bimodal. Assuming linear color-to-metallicity conversions, bimodality is viewed as the presence of merely two GC subsystems with distinct metallicities, which serves as a critical backbone of various galaxy formation theories. Recent studies, however, revealed that the color-metallicity relations (CMRs) often used to derive GC metallicities (e.g., CMRs of g - z, V - I, and C - T{sub 1}) are in fact inflected. Such inflection can create bimodal color distributions if the underlying GC metallicity spread is simply broad as expected from the hierarchical merging paradigm of galaxy formation. In order to test the nonlinear-CMR scenario for GC color bimodality, the u-band photometry is proposed because the u-related CMRs (e.g., CMRs of u - g and u - z) are theoretically predicted to be least inflected and most distinctive among commonly used optical CMRs. Here, we present Hubble Space Telescope (HST)/WFC3 F336W (u-band) photometry of the GC system in M84, a giant elliptical in the Virgo galaxy cluster. Combining the u data with the existing HST ACS/WFC g and z data, we find that the u - z and u - g color distributions are different from the g - z distribution in a very systematic manner and remarkably consistent with our model predictions based on the nonlinear-CMR hypothesis. The results lend further confidence to the validity of the nonlinear-CMR scenario as an explanation for GC color bimodality. There are some GC systems showing bimodal spectroscopic metallicity, and in such systems the inflected CMRs often create stronger bimodality in the color domain.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Cosmic-Ray Feedback Heating of the Intracluster Medium

Active galactic nuclei (AGNs) play a central role in solving the decades-old cooling-flow problem. Although there is consensus that AGNs provide the energy to prevent catastrophically large star formation, one major problem remains: How is the AGN energy thermalized in the intracluster medium (ICM)? We perform a suite of three-dimensional magnetohydrodynamical adaptive mesh refinement simulations of AGN feedback in a cool core cluster including cosmic rays (CRs). CRs are supplied to the ICM via collimated AGN jets and subsequently disperse in the magnetized ICM via streaming, and interact with the ICM via hadronic, Coulomb, and streaming instability heating. We find that CR transport is an essential model ingredient at least within the context of the physical model considered here. When streaming is included, (i) CRs come into contact with the ambient ICM and efficiently heat it, (ii) streaming instability heating dominates over Coulomb and hadronic heating, (iii) the AGN is variable and the atmosphere goes through low-/high-velocity dispersion cycles, and, importantly, (iv) CR pressure support in the cool core is very low and does not demonstrably violate observational constraints. However, when streaming is ignored, CR energy is not efficiently spent on the ICM heating and CR pressure builds up to a significant level, creating tension with the observations. Overall, we demonstrate that CR heating is a viable channel for the AGN energy thermalization in clusters and likely also in ellipticals, and that CRs play an important role in determining AGN intermittency and the dynamical state of cool cores.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin

Different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are simulated numerically for fully nonlinear 'one-dimensional' potential water waves in a finite-depth flume between two vertical walls. In such systems, the FPU recurrence is closely related to the dynamics of coherent structures approximately corresponding to solitons of the integrable Boussinesq system. A simplest periodic solution of the Boussinesq model, describing a single soliton between the walls, is presented in analytic form in terms of the elliptic Jacobi functions. In the numerical experiments, it is observed that depending on the number of solitons in the flume and their parameters, the FPU recurrence can occur in a simple or complicated manner, or be practically absent. For comparison, the nonlinear dynamics of potential water waves over nonuniform beds is simulated, with initial states taken in the form of several pairs of colliding solitons. With a mild-slope bed profile, a typical phenomenon in the course of evolution is the appearance of relatively high (rogue) waves, while for random, relatively short-correlated bed profiles it is either the appearance of tall waves or the formation of sharp crests at moderate-height waves.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗