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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

A comparison of GPS broadcast and DMA precise ephemerides

We compare the broadcast ephemerides from Global Positioning Satellites (GPS) to the postprocessed ephemerides from the Defense Mapping Agency (DMA). We find significant energy in the spectrum of the residuals at 1 cycle/day and higher multiples. We estimate the time variance of the residuals and show that the short term residuals, from 15 min, exhibit power law processes with greater low frequency perturbations than white phase modulation. We discuss the significance of these results for the performance of the GPS Kalman filter which estimates the broadcast orbits.

Weiss, Marc A.↗
NASA NTRS2005

The development of a Kalman filter clock predictor

A Kalman filter based clock predictor is developed, and its performance evaluated using both simulated and real data. The clock predictor is shown to possess a neat to optimal Prediction Error Variance (PEV) when the underlying noise consists of one of the power law noise processes commonly encountered in time and frequency measurements. The predictor's performance is the presence of multiple noise processes is also examined. The relationship between the PEV obtained in the presence of multiple noise processes and those obtained for the individual component noise processes is examined. Comparisons are made with a simple linear clock predictor. The clock predictor is used to predict future values of the time offset between pairs of NPL's active hydrogen masers.

clock predictor↗
NASA NTRS1990

Coarsening in binary solid-liquid mixtures

A theory of Ostwald ripening has been developed for a solid-liquid mixture cosisting of a low volume fraction array of spherical solid particles in a liquid wherein the coarsening process proceeds via the transport of both heat and mass. It is found that the simultaneous transport of heat and mass during ripening does not alter the exponents of the temporal power laws governing the ripening process from their classical values but does alter the amplitudes of these power laws. The growth rate of the cube of the average particle radius, the rate constant, is found to depend both on the alloy solute concentration and the ratio of the thermal to solutal diffusivities. In most metallic systems, a large decrease in the rate constant can be expected with small additions of solute to a pure metal. Possible extensions of this theory to the analogous problem of ripening in isothermal ternary alloys are also discussed.

Voorhees, P. W.↗
NASA NTRS1984

Empirical relations for cavitation and liquid impingement erosion processes

A unified power-law relationship between average erosion rate and cumulative erosion is presented. Extensive data analyses from venturi, magnetostriction (stationary and oscillating specimens), liquid drop, and jet impact devices appear to conform to this relation. A normalization technique using cavitation and liquid impingement erosion data is also presented to facilitate prediction. Attempts are made to understand the relationship between the coefficients in the power-law relationships and the material properties.

Rao, P. V.↗
NASA NTRS2003

Characterization of the Crab Pulsar's Timing Noise

We present a power spectral analysis of the Crab pulsar's timing noise, mainly using radio measurements from Jodrell Bank taken over the period 1982-1989, an interval bounded by sparse data sampling and a large glitch. The power spectral analysis is complicated by nonuniform data sampling and the presence of a steep red power spectrum that can distort power spectra measurement by causing severe power 'leakage'. We develop a simple windowing method for computing red noise power spectra of uniformly sampled data sets and test it on Monte Carlo generated sample realizations of red power-law noise. We generalize time-domain methods of generating power-law red noise with even integer spectral indices to the case of noninteger spectral indices. The Jodrell Bank pulse phase residuals are dense and smooth enough that an interpolation onto a uniform time series is possible. A windowed power spectrum is computed revealing a periodic or nearly periodic component with a period of 568 +/- 10 days and a l/f(exp 3) power-law noise component in pulse phase with a noise strength S(sub infinity)=(1.24 +/- 0.067) x 10(exp 16) cycles(exp 2)/sec(exp 2) over the analysis frequency range f=0.003- 0.1 cycles/day. This result deviates from past analyses which characterized the pulse phase timing residuals as either l/f(sub 4) power-law noise or a quasiperiodic process. The analysis was checked using the Deeter polynomial method of power spectrum estimation that was developed for the case of nonuniform sampling, but has lower spectral resolution. The timing noise is consistent with a torque noise spectrum rising with analysis frequency as f implying blue torque noise, a result not predicted by current models of pulsar timing noise. If the periodic or nearly periodic component is due to a binary companion, we find a mass function f(M) = (6.8 +/- 2.4) x 10(exp -16) solar mass and a companion mass, M(sub c) is greater than or equal to 3.2 solar mass assuming a Crab pulsar mass of 1.4 solar mass.

Scott, D. M.↗
NASA NTRS1989

Size distribution of dust grains: A problem of self-similarity

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space.

Henning, TH.↗
NASA NTRS2018

Power-Law Statistics of Driven Reconnection in the Magnetically Closed Corona

Numerous observations have revealed that power-law distributions are ubiquitous in energetic solar processes. Hard X-rays, soft X-rays, extreme ultraviolet radiation, and radio waves all display power-law frequency distributions. Since magnetic reconnection is the driving mechanism for many energetic solar phenomena, it is likely that reconnection events themselves display such power-law distributions. In this work, we perform numerical simulations of the solar corona driven by simple convective motions at the photospheric level. Using temperature changes, current distributions, and Poynting fluxes as proxies for heating, we demonstrate that energetic events occurring in our simulation display power-law frequency distributions, with slopes in good agreement with observations. We suggest that the braiding-associated reconnection in the corona can be understood in terms of a self-organized criticality model driven by convective rotational motions similar to those observed at the photosphere.

Knizhnik, K. J.↗
NASA NTRS2011

Heliospheric Observations of Energetic Particles

Heliospheric observations of energetic particles have shown that, on long time averages, a consistent v^-5 power-law index arises even in the absence of transient events. This implies an ubiquitous acceleration process present in the solar wind that is required to generate these power-law tails and maintain them against adiabatic losses and coulomb-collisions which will cool and thermalize the plasma respectively. Though the details of this acceleration process are being debated within the community, most agree that the energy required for these tails comes from fluctuations in the magnetic field which are damped as the energy is transferred to particles. Given this source for the tail, is it then reasonable to assume that the turbulent LISM should give rise to such a power-law tail as well? IBEX observations clearly show a power-law tail of index approximately -5 in energetic neutral atoms. The simplest explanation for the origins of these ENAs are that they are energetic ions which have charge-exchanged with a neutral atom. However, this would imply that energetic ions possess a v^-5 power-law distribution at keV energies at the source of these ENAs. If the source is presumed to be the LISM, it provides additional options for explaining the, so called, IBEX ribbon. This presentation will discuss some of these options as well as potential mechanisms for the generation of a power-law spectrum in the LISM.

Summerlin, Errol J.↗
NASA NTRS2019

Electron Scattering by Low-frequency Whistler Waves at Earth’s Bow Shock

Electrons are accelerated to nonthermal energies at shocks in space and astrophysical environments. While shock drift acceleration (SDA) has been considered a key process of electron acceleration at Earth’s bow shock, it has also been recognized that SDA needs to be combined with an additional stochastic process to explain the observed power-law energy spectra. Here, we show mildly energetic (∼0.5 keV) electrons are locally scattered (and accelerated while being confined) by magnetosonic-whistler waves within the shock transition layer, especially when the shock angle is large (θ(sub Bn) approximately equal or greater than 70°). When measured by the Magnetospheric Multiscale mission at a high cadence, ∼0.5 keV electron flux increased exponentially in the shock transition layer. However, the flux profile was not entirely smooth and the fluctuation showed temporal/spectral association with large-amplitude (δB/B ~ 0.3), low-frequency (approximately equal or less than 0.1 Ω(sub ce) where Ω(sub ce) is the cyclotron frequency), obliquely propagating (θ(sub kB) ~ 30°–60°, where θ(sub kB) is the angle between the wave vector and background magnetic field) whistler waves, indicating that the particles were interacting with the waves. Particle simulations demonstrate that, although linear cyclotron resonances with ∼0.5 keV electrons are unlikely due to the obliquity and low frequencies of the waves, the electrons are still scattered beyond 90° pitch angle by (1) resonant mirroring (transit-time damping), (2) non-resonant mirroring, and (3) subharmonic cyclotron resonances. Such coupled nonlinear scattering processes are likely to provide the stochasticity needed to explain the power-law formation.

Oka, M.↗
NASA NTRS1991

Relaxation processes in a low-order three-dimensional magnetohydrodynamics model

The time asymptotic behavior of a Galerkin model of 3D magnetohydrodynamics (MHD) has been interpreted using the selective decay and dynamic alignment relaxation theories. A large number of simulations has been performed that scan a parameter space defined by the rugged ideal invariants, including energy, cross helicity, and magnetic helicity. It is concluded that time asymptotic state can be interpreted as a relaxation to minimum energy. A simple decay model, based on absolute equilibrium theory, is found to predict a mapping of initial onto time asymptotic states, and to accurately describe the long time behavior of the runs when magnetic helicity is present. Attention is also given to two processes, operating on time scales shorter than selective decay and dynamic alignment, in which the ratio of kinetic to magnetic energy relaxes to values 0(1). The faster of the two processes takes states initially dominant in magnetic energy to a state of near-equipartition between kinetic and magnetic energy through power law growth of kinetic energy. The other process takes states initially dominant in kinetic energy to the near-equipartitioned state through exponential growth of magnetic energy.

Stribling, Troy↗
NASA NTRS2024

Double Power-law Formation by Sequential Particle Acceleration

Spectral double power laws are common in solar high-energy phenomena such as flares and interplanetary energetic-electron events. However, the physical mechanism that produces the changes in power-law index within a single spectrum is unclear. We developed a fully analytical method of forming single power-law spectra from sequential acceleration of particles orbiting inside and hopping between simulated large-scale magnetic islands formed by flare reconnection. Here, we extend the analytical method to the formation of double power-law spectra by assuming sequential acceleration in two successive regions with different acceleration and particle-transport rates. The resulting spectral distribution is continuous and smooth, with a flattening at low energies, two power-law regions at mid-energies, and a steep rollover at high energies. The model provides analytical expressions for the spectral indices, all energy breaks, and normalization constants as functions of just three physical parameters of each acceleration region: (1) the energy gain in each accelerator, (2) the percentage of particles transferred between accelerators, and (3) the number of accelerators visited. One of the most salient predictions of our work is that the spectral index at high (low) energies is determined by the parameters of the first "seed" (second) acceleration region. By constructing the spectral distribution through an iterative analytical process, the evolution toward a double power law is easily characterized and explained. Our analytical model provides tools to interpret space- and ground-based observations from RHESSI, FOXSI, NuSTAR, Solar Orbiter/STIX, EOVSA, and future high-energy missions.

Solar flares↗
NASA NTRS1993

Spectral evidence for stirring scales and two-dimensional turbulence in the auroral ionosphere

Electric field power spectra from two auroral sounding rocket flights show evidence of a distinct scale size regime for injection of energy into the auroral oval. The signature of this process is a broad plateau in the spectrum, with power law dependences at both shorter and longer scale sizes. We argue that the spectral properties at high k are dominated by processes occurring near the edges of inverted-V electron precipitation regions (auroral arcs). We see no compelling reason to conclude that a linear local plasma instability is occurring but rather, that nonlinear mixing and forward cascade yield the observed velocity field. The spectra of simultaneously observed density irregularities are quite different from those of the electric field, implying that the plasma density does not behave as a passive scalar in the auroral zone during active conditions. At low-k values we show that the rocket spectra are consistent with the power spectra of magnetospheric electric fields measured by the DE, AE-C, and Hilat stallites.

Earle, G. D.↗
NASA NTRS1980

A power law fit to oxygen absorption at 60 GHz and its application to remote sensing of atmospheric temperature

The paper presents an empirical study of the oxygen spectrum near 60 GHz with reference to its applicability to the remote sensing of the tropospheric and lower stratospheric temperature. It is demonstrated that the absorption coefficient of oxygen at 60 GHz can be fitted to the power law form with a relative rms error of about 8%. The power law form, when used in conjunction with the weighting function, permits the definition of some basic quantities in the passive remote sensing of the atmospheric temperature. It is shown how the power law form has been utilized in processing data from the Nimbus 5 microwave spectrometer experiment. The algorithm presented can be applied to spectrometer experiments at infrared frequencies.

Poon, R. K. L.↗
NASA NTRS1980

Thermal models for solar hard X-ray bursts

Thermal models for hard X-ray bursts consisting of a one-dimensional flux tube whose central electrons are heated to about 400 million K are examined. It is found that the evolution of a thermal X-ray source is a sensitive function of the electron-ion thermal coupling and the state of the plasma into which the source expands. When this coupling is weak, the heated electrons separate into a region of high temperature of about 400 million K and a region of lower temperature of about 100 million K, a process which leads to a power-law X-ray spectrum. In the case of strong coupling there is only one dominant temperature, about 200 million K, and the X-ray spectrum resembles a true thermal spectrum.

Smith, D. F.↗
NASA NTRS1992

Soft gamma rays from black holes versus neutron stars

The recent launches of GRANAT and GRO provide unprecedented opportunities to study compact collapsed objects from their hard x ray and gamma ray emissions. The spectral range above 100 keV can now be explored with much higher sensitivity and time resolution than before. The soft gamma ray spectral data is reviewed of black holes and neutron stars, radiation, and particle energization mechanisms and potentially distinguishing gamma ray signatures. These may include soft x ray excesses versus deficiencies, thermal versus nonthermal processes, transient gamma ray bumps versus power law tails, lines, and periodicities. Some of the highest priority future observations are outlines which will shed much light on such systems.

Liang, Edison P.↗
NASA NTRSDate not supplied

Projecting the Performance of a Continuous Bosch Carbon Dioxide Reduction System

Kinetic studies using a subscale reactor were used to develop power-law rate equations for the two primary reactions contributing to the Bosch carbon dioxide reduction process: the reverse water-gas shift reaction and the carbon monoxide hydrogenation reaction. An alloy catalyst in bead form was used in these studies, which investigated both the dependence on gas composition and the dependence on time as the beads gradually disintegrate during carbon formation. Bead disintegration impacts both the rates and the relative activities of the two primary reactions. Although the kinetic testing was conducted in a single-pass mode, the target Bosch application requires operation in a recycle mode to achieve high conversion. Further, the proposed design concept for a full-scale carbon dioxide reduction system would allow carbon to be removed continuously in contrast to previous Bosch processes that required replacement of expendable catalyst cartridges. The developed power-law kinetic rate equations were used in conjunction with a reactor model to project the operating conditions, performance, and sizing of a continuous Bosch system.

carbon dioxide reduction↗
NASA NTRS1994

Gamma-ray emission and electron acceleration in solar flares

Recent observations have extended the spectra of the impulsive phase of flares to the GeV range. Such high-energy photons can be produced either by electron bremsstrahlung or by decay of pions produced by accelerated protons. In this paper we investigate the effects of processes which become important at high energies. We examine the effects of synchrotron losses during the transport of electrons as they travel from the acceleration region in the corona to the gamma-ray emission sites deep in the chromosphere and photosphere, and the effects of scattering and absorption of gamma rays on their way from the photosphere to space instruments. These results are compared with the spectra from so-called electron-dominated flares, observed by GRS on the Solar Maximum Mission, which show negligible or no detectable contribution from accelerated protons. The spectra of these flares show a distinct steepening at energies below 100 keV and a rapid falloff at energies above 50 MeV. Following our earlier results based on lower energy gamma-ray flare emission we have modeled these spectra. We show that neither the radiative transfer effects, which are expected to become important at higher energies, nor the transport effects (Coulomb collisions, synchrotron losses, or magnetic field convergence) can explain such sharp spectral deviations from a simple power law. These spectral deviations from a power law are therefore attributed to the acceleration process. In a stochastic acceleration model the low-energy steepening can be attributed to Coulomb collision and the rapid high-energy steepening can result from synchrotron losses during the acceleration process.

Petrosian, Vahe↗
NASA NTRS1991

Compton reflection in active galactic nuclei and the cosmic X-ray background

This paper discusses further the model of Fabian et al. (1990) for the cosmic X-ray background (XRB) spectrum, in which the emission is due to AGNs at large redshifts. Each AGN emits a power-law spectrum modified by Compton reflection from cold gas. It is found that the model provides an excellent fit to the XRB from 3 to 500 keV if the sources radiate from a maximum redshift of at least 3.75, if their comoving emissivity varies like (1 + z) exp beta, with beta between 1.8 and 3.3, and if the intrinsic power-law energy index is between 0.9 and 1.2. About 90 percent of the power-law radiation in each AGN must be processed by Compton reflection. The model predicts that the intensity of the XRB below 3 keV is significantly above that extrapolated from observations above 3 keV, without requiring contributions from other types of source.

Rogers, R. D.↗