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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 − q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.

chaos aEuro" galaxies:↗
DOE OSTI2023

Fractal dimensions of jammed packings with power-law particle size distributions in two and three dimensions

Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent -β. Here, the static structure factor exhibits diverging power-law behavior for small wave numbers, allowing us to identify a structural fractal dimension d f . In three dimensions, d f ≈ 2.0 for 2.5≤ β ≤ 3.8, such that each of the structure factors can be collapsed onto a universal curve. In two dimensions, we instead find 1.0≲ d f ≲1.34 for 2.1≤ β ≤ 2.9. Furthermore, we show that the fractal behavior persists when rattler particles are removed, indicating that the long-wavelength structural properties of the packings are controlled by the large particle backbone conferring mechanical rigidity to the system. A numerical scheme for computing structure factors for triclinic unit cells is presented and employed to analyze the jammed packings.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

Correlations of Power-law Spectral and QPO Features In Black Hole Candidate Sources

Recent studies have shown that strong correlations are observed between low frequency QPO s and the spectral power law index for a number of black hole candidate sources (BHCs), when these sources exhibit quasi-steady hard x-ray emission states. The dominant long standing interpretation of QPO's is that they are produced in and are the signature of the thermal accretion disk. Paradoxically, strong QPO's are present even in the cases where the thermal component is negligible. We present a model which identifies the origin of the QPO's and relates them directly to the properties of a compact coronal region which is bounded by the adjustment from Kepleriaa to sub-Kelperian inflow into the BH, and is primarily responsible for the observed power law spectrum. The model also predicts the relationship between high and low frequency QPO's and shows how BH's can be unique identified from observations of the soft states of NS's and BHC's.

Fiorito, Ralph↗
DOE OSTI2021

Spatiotemporal spread of perturbations in power-law models at low temperatures: Exact results for classical out-of-time-order correlators

Here, we present exact results for the classical version of the out-of-time-order commutator (OTOC) for a family of power-law models consisting of N particles in one dimension and confined by an external harmonic potential. These particles are interacting via power-law interaction of the form ∝ $Σ_{i,j=(i≠j)}^{N}$ |x i -x j | -k for every k>1 where x i is the position of the i th particle. We present numerical results for the OTOC for finite N at low temperatures and short enough times so that the system is well approximated by the linearized dynamics around the many-body ground state. In the large-N limit, we compute the ground-state dispersion relation in the absence of external harmonic potential exactly and use it to arrive at analytical results for OTOC. We find excellent agreement between our analytical results and the numerics. We further obtain analytical results in the limit where only linear and leading nonlinear (in momentum) terms in the dispersion relation are included. The resulting OTOC is in agreement with numerics in the vicinity of the edge of the “light cone.” We find remarkably distinct features in OTOC below and above k=3 in terms of going from non-Airy behavior (1 < k < 3) to an Airy universality class (k>3). We present certain additional rich features for the case k=2 that stem from the underlying integrability of the Calogero-Moser model. We present a field theory approach that also assists in understanding certain aspects of OTOC such as the sound speed. Our findings are a step forward towards a more general understanding of the spatiotemporal spread of perturbations in long-range interacting systems.

1-dimensional systems↗
NASA NTRS1979

Modified power law equations for vertical wind profiles

In an investigation of windpower plant siting, equations are presented and evaluated for a wind profile model which incorporates both roughness and wind speed effects, while retaining the basic simplicity of the Hellman power law. These equations recognize the statistical nature of wind profiles and are compatible with existing analytical models and recent wind profile data. Predictions of energy output based on the proposed profile equations are 10% to 20% higher than those made with the 1/7 power law. In addition, correlation between calculated and observed blade loads is significantly better at higher wind speeds when the proposed wind profile model is used than when a constant power model is used.

Spera, D. A.↗
NASA NTRS1989

Creep substructure formation in sodium chloride single crystals in the power law and exponential creep regimes

Creep tests conducted on NaCl single crystals in the temperature range from 373 to 1023 K show that true steady state creep is obtained only above 873 K when the ratio of the applied stress to the shear modulus is less than or equal to 0.0001. Under other stress and temperature conditions, corresponding to both power law and exponential creep, the creep rate decreases monotonically with increasing strain. The transition from power law to exponential creep is shown to be associated with increases in the dislocation density, the cell boundary width, and the aspect ratio of the subgrains along the primary slip planes. The relation between dislocation structure and creep behavior is also assessed.

Raj, S. V.↗
DOE OSTI2021

Lieb-Robinson Light Cone for Power-Law Interactions

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1 / r α at distance r ? Here, we present a definitive answer to this question for all exponents α > 2 d and all spatial dimensions d . Schematically, information takes time at least r min { 1 , α - 2 d } to propagate a distance r . As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1981

On syntheses of the X-ray background with power-law sources

The conditions under which the combined emission from power law sources can mimic the X-ray background (XRB) spectrum in the 3-50 keV range are considered in view of HEAO 1 A-2 experiment measurements, and it is confirmed that a good fit may be obtained. The required spectral properties of the component sources differ, however, from those observed for local active galactic nuclei. Constraints are deduced for both the low luminosity extension and evolution of such local objects, and it is shown that any other class of sources contributing to the X-ray background must be characterized by an energy spectral index lower than about 0.4, which is the mean index of the XRB, and exhibit sleeper spectra at higher energies.

Dezotti, G.↗
DOE OSTI2022

Power-law inflation satisfies Penrose’s Weyl curvature hypothesis

Based on entropy considerations and the arrow of time Penrose argued that the Universe must have started in a special initial singularity with vanishing Weyl curvature. This is often interpreted to be at odds with inflation. Here we argue just the opposite, that Penrose’s persuasions are in fact consistent with inflation. Using the example of power law inflation, we show that inflation begins with a past null singularity, where Weyl tensor vanishes when the metric is initially exactly conformally flat. This initial state precisely obeys Penrose’s conditions. The initial null singularity breaks T-reversal spontaneously and picks the arrow of time. It can be regulated and interpreted as a creation of a universe from nothing, initially fitting in a bubble of Planckian size when it materializes. Penrose’s initial conditions are favored by the initial O(4) symmetry of the bubble, selected by extremality of the regulated Euclidean action. The predicted observables are marginally in tension with the data, but they can fit if small corrections to power law inflation kick in during the last 60⁢e-folds.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1973

Power law time dependence of river flood decay and its relationship to long term discharge frequency distribution

Investigations have continued into the possibility that significant information on stream flow rates can be obtained from aerial and satellite imagery of river meander patterns by seeking a correlation between the meander and discharge spectra of rivers. Such a correlation could provide the basis for a simple and inexpensive technique for remote sensing of the water resources of large geographical areas, eliminating the need for much hydrologic recording. The investigation of the nature of the meander and discharge spectra and their interrelationship can also contribute to a more fundamental understanding of the processes of both river meander formation and drainage of large basins. It has been found that floods decay with an inverse power law dependence on time. The exponent of this dependence varies from river to river and even from station to station along the same river. This power law time dependence makes possible the forecasting of river discharge with an uncertainty of about 5% for as long as a month following the flood peak.

Schubert, G.↗
DOE OSTI2024

Cracked Gridline Wear Out Follows a Power Law

Cracks can form in Silicon solar cells in photovoltaic modules due to mechanical stresses arising from various extrinsic factors like handling and weather. While the immediate performance degradation may be minor, continuous loading overtime will degrade module performance. One probable reason is gridline surface wear across the cracked silicon with increased cyclic loading. In this work we propose a method to correlate gridline wear to module electrical degradation. We begin by conducting cyclic four-point bending tests on laminated silicon solar cells with a single crack and 22 intact gridlines for 10,000 cycles. We measure the progressive change in resistance during each loading cycle. We correlate it to a length scale called critical crack opening displacement (CCOD) that signifies failure of individual gridlines. By employing Weibull analysis, we determine the characteristic CCOD for all cycles and fit this data to a modified version of a wear power law. We observe that this i ts the data well. We also propose to study the effect of individual parameters in the power law equation and extend the equation to include material properties.

bending↗
NASA NTRS2008

So You Think the Crab is Described by a Power-Law Spectrum

X-ray observations of the Crab Nebula and its pulsar have played a prominent role in the history of X-ray astronomy. Discoveries range from the detection of the X-ray Nebula and pulsar and the measurement of the Nebula-averaged X-ray polarization, to the observation of complex X-ray morphology, including jets emanating from the pulsar and the ring defining the shocked pulsar wind. The synchrotron origin of much of the radiation has been deduced by detailed studies across the electromagnetic spectrum, yet has fooled many X-ray astronomers into believing that the integrated spectrum from this system ought to be a power law. In many cases, this assumption has led observers to adjust the experiment response function(s) to guarantee such a result. We shall discuss why one should not observe a power-law spectrum, and present simulations using the latest available response matrices showing what should have been observed for a number of representative cases including the ROSAT IPC, XMM-Newton, and RXTE. We then discuss the implications, if any, for current calibrations.

Weisskopf, Martin C.↗
NASA NTRS2006

Power Spectra, Power Law Exponents, and Anisotropy of Solar Wind Turbulence at Small Scales

The Wind spacecraft provides simultaneous solar wind velocity and magnetic field measurements with 3- second time resolution, roughly an order of magnitude faster than previous measurements, enabling the small scale features of solar wind turbulence to be studied in unprecedented detail. Almost the entire inertial range can now be explored (the inertial range extends from approximately 1 to 10(exp 3) seconds in the spacecraft frame) although the dissipation range of the velocity fluctuations is still out of reach. Improved measurements of solar wind turbulence spectra at 1 AU in the ecliptic plane are presented including spectra of the energy and cross-helicity, the magnetic and kinetic energies, the Alfven ratio, the normalized cross-helicity, and the Elsasser ratio. Some recent observations and theoretical challenges are discussed including the observation that the velocity and magnetic field spectra often show different power law exponents with values close to 3/2 and 5/3, respectively; the energy (kinetic plus magnetic) and cross-helicity often have approximately equal power law exponents with values intermediate between 3/2 and 5/3; and the Alfven ratio, the ratio of the kinetic to magnetic energy spectra, is often a slowly increasing function of frequency increasing from around 0.4 to 1 for frequencies in the inertial range. Differences between high- and low-speed wind are also discussed. Comparisons with phenomenological turbulence theories show that important aspects of the physics are yet unexplained.

Podesta, J. J.↗
NASA NTRS1982

On syntheses of the X-ray background with power-law sources

The conditions under which the combined emission from power-law sources can mimic the X-ray background (XRB) spectrum in the 3-50 keV range are considered in view of HEAO 1 A-2 experiment measurements, and it is confirmed that a good fit may be obtained. The required spectral properties of the component sources differ, however, from those observed for local active galactic nuclei. Constraints are deduced for both the low-luminosity extension and evolution of such local objects, and it is shown that any other class of sources contributing to the X-ray background must be characterized by an energy spectral index lower than about 0.4, which is the mean index of the XRB, and exhibit steeper spectra at higher energies.

De Zotti, G.↗
NASA NTRS1974

Second-order small disturbance theory for hypersonic flow over power-law bodies

A mathematical method for determining the flow field about power-law bodies in hypersonic flow conditions is developed. The second-order solutions, which reflect the effects of the second-order terms in the equations, are obtained by applying the method of small perturbations in terms of body slenderness parameter to the zeroth-order solutions. The method is applied by writing each flow variable as the sum of a zeroth-order and a perturbation function, each multiplied by the axial variable raised to a power. The similarity solutions are developed for infinite Mach number. All results obtained are for no flow through the body surface (as a boundary condition), but the derivation indicates that small amounts of blowing or suction through the wall can be accommodated.

Townsend, J. C.↗
NASA NTRS2011

Power-Law Template for IR Point Source Clustering

We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217,353,545 and 857 GHz, over angular scales 100 < I < 2200), the Balloonborne Large-Aperture Submillimeter Telescope (BLAST; 250, 350 and 500 microns; 1000 < I < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fit by a simple power law of the form C_l\propto I(sup -n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, nu(sup beta) B(nu,T_eff), with a single emissivity index beta = 2.20 +/- 0.07 and effective temperature T_eff= 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha_150-220 = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in Cosmic Microwave Background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.

Addison, Graeme E.↗
NASA NTRS2012

Power-Law Template for Infrared Point-Source Clustering

We perform a combined fit to angular power spectra of unresolved infrared (IR) point sources from the Planck satellite (at 217, 353, 545, and 857 GHz, over angular scales 100 approx < l approx < 2200), the Balloon-borne Large-Aperture Submillimeter Telescope (BLAST; 250, 350, and 500 micron; 1000 approx < l approx < 9000), and from correlating BLAST and Atacama Cosmology Telescope (ACT; 148 and 218 GHz) maps. We find that the clustered power over the range of angular scales and frequencies considered is well fitted by a simple power law of the form C(sup clust)(sub l) varies as l (sub −n) with n = 1.25 +/- 0.06. While the IR sources are understood to lie at a range of redshifts, with a variety of dust properties, we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody, ν(sup Beta)B(ν, T(sub eff) ), with a single emissivity index Beta = 2.20 +/- 0.07 and effective temperature T(sub eff) = 9.7 K. Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz, as is our prediction for the effective dust spectral index, which we find to be alpha(sub 150-220) = 3.68 +/- 0.07 between 150 and 220 GHz. Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in cosmic microwave background anisotropy measurements. The combined Planck and BLAST data also rule out a linear bias clustering model.

cosmic background radiation↗