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All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Spatial power spectra of the crustal geomagnetic field and core geomagnetic field

Equations providing numerical values of the geomagnetic field spherical harmonic spatial power spectrum as defined by Lowes (1966, 1974) are obtained and this power spectrum is related to various other power spectra. Equations relating the spherical harmonic spatial power spectrum to average great circle power spectra for components of the vector magnetic field in the radial direction, along the great circle track and perpendicular to the first two directions are derived under the assumption that the sources of the field are internal. A statistical model for the crustal and core geomagnetic fields is proposed and used to derive equations for the expected main and crustal spherical harmonic power spectra. The model equations are then compared with observations to determine a scale factor which is then used to obtain an estimate for the core radius and a great circle power spectrum for the field component perpendicular to the great circle and radial directions which are in good agreement with observations. The predicted spherical harmonic power spectrum for the crustal field is found to be consistent with POGO satellite and aircraft data. Other possible models for the crustal and core geomagnetic fields are also briefly considered.

Mcleod, M. G.↗
NASA NTRS1978

Period variations in pulsating X-ray sources. II - Torque variations and stellar response

A statistical description of variations in the torque acting on a rotating neutron star is developed in terms of stationary random processes and is used to calculate the torque power spectrum, stellar response power spectrum, and the total mean square variation in the crustal angular velocity of the star. The response of a star with a finite frequency internal mode is calculated with the aid of phenomenological equations which correspond to a generalized two-component model of the star. The form of the stellar response functions is examined in a number of limiting cases of physical interest, and the dependence of the response power on both the period of observation and the time over which fluctuating torques have been acting is discussed.

Lamb, F. K.↗
NASA NTRS1998

Method and apparatus for assessing cardiovascular risk

The method for assessing risk of an adverse clinical event includes detecting a physiologic signal in the subject and determining from the physiologic signal a sequence of intervals corresponding to time intervals between heart beats. The long-time structure of fluctuations in the intervals over a time period of more than fifteen minutes is analyzed to assess risk of an adverse clinical event. In a preferred embodiment, the physiologic signal is an electrocardiogram and the time period is at least fifteen minutes. A preferred method for analyzing the long-time structure variability in the intervals includes computing the power spectrum and fitting the power spectrum to a power law dependence on frequency over a selected frequency range such as 10.sup.-4 to 10.sup.-2 Hz. Characteristics of the long-time structure fluctuations in the intervals is used to assess risk of an adverse clinical event.

Albrecht, Paul↗
NASA NTRS1993

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Buchert, T.↗
NASA NTRSDate not supplied

Helioseismic Measurements of Convective Power in Solar Cycle 24

Constraining the parameters under which convection in the solar interior operates has important implications for describing how energy is transported by plasma motions, and various physical models have been employed to provide some theoretical estimates on the expected power spectrum. Past attempts to measure the convective power distributed among large spatial scales have, however, found differing and incompatible values. Here, we present measurements of the convective power spectrum in the upper convection zone for Carrington rotations in Solar Cycle 24 obtained from the helioseismic signal corresponding to East-West flows. We also perform calibration on synthetic data using the global acoustic GALE code to make assessments of the flow velocities at various length scales without the need for performing inversions. This allows us to derive the convective power spectrum from the flow maps and to compare with the results from the raw travel times. These results are compared against predictions of convective power in global models of convection produced by the EULAG code. Finally, we show how the steps in our analysis procedure (for example data segmentation, filtering, etc.) affect our estimates of the convective power by comparing with the synthetic data from the GALE code.

Heliophysics↗
NASA NTRS1992

Large-scale structure in the Southern Sky Redshift Survey

The power spectrum from the Southern Sky Redshift Survey and the CfA samples are measured in order to explore the amplitude of fluctuation in the galaxy density. At lambda of less than or equal to 30/h Mpc the observed power spectrum is quite consistent with the standard CDM model. At larger scales the data indicate an excess of power over the standard CDM model. The observed power spectrum from these optical galaxy samples is in good agreement with that drawn from the sparsely sampled IRAS galaxies. The shape of the power spectrum is also studied by examining the relation between the genus per unit volume and the smoothing length. It is found that, over Gaussian smoothing scales from 6 to 14/h Mpc, the power spectrum has a slope of about -1. The topology of the galaxy density field is studied by measuring the shift of the genus curve from the Gaussian case. Over all smoothing scales studied, the observed genus curves are consistent with a random phase distribution of the galaxy density field, as predicted by the inflationary scenarios.

Park, Changbom↗
NASA NTRS2002

Measurement of Arcminute Scale Cosmic Microwave Background Anisotropy with the BIMA Array

We report the results of our continued study of arcminute scale anisotropy in the Cosmic Microwave Background (CMB) with the Berkeley-Illinois-Maryland Association (BIMA) array. The survey consists of ten independent fields selected for low infrared dust emission and lack of bright radio point sources. With observations from the VLA (Very Large Array) at 4.8 GHz, we have identified point sources which could act as contaminants in estimates of the CMB power spectrum and removed them in the analysis. Modeling the observed power spectrum with a single. flat band power with average multipole of l(sub eff) = 6864, we find Delta T = 14.2((sup +4.8)(sub -6.0)) micro K at 68% confidence. The signal in the visibility data exceeds the expected contribution from instrumental noise with 96.5% confidence. We have also divided the data into two bins corresponding to different spatial resolutions in the power spectrum. We find Delta T(sub 1) = 16.6((sup +5.3)(sub -5.9)) micro K at 68% confidence for CMB flat band power described by an average multipole of l(sub eff) = 5237 and Delta T(sub 2) is less than 26.5 micro K at 95% confidence for l(sub eff) = 8748.

Dawson, K. S.↗
NASA NTRS1982

Computing the Power-Density Spectrum for an Engineering Model

Computer program for calculating of power-density spectrum (PDS) from data base generated by Advanced Continuous Simulation Language (ACSL) uses algorithm that employs fast Fourier transform (FFT) to calculate PDS of variable. Accomplished by first estimating autocovariance function of variable and then taking FFT of smoothed autocovariance function to obtain PDS. Fast-Fourier-transform technique conserves computer resources.

Dunn, H. J.↗
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 NTRSDate not supplied

Global Analysis of Nonlinear Second-Mode Development in a Mach-6 Boundary Layer From High-Speed Schlieren Data

The second-mode instability on a 7◦ half-angle sharp cone at Mach 6 is analyzed using high-speed calibrated schlieren imagery at a frame rate near the expected fundamental frequency. Experiments were conducted in the NASA Langley 20-Inch Mach 6 facility at unit Reynolds number between 6.56×106 and 9.71×106 m−1. Time-resolved pixel intensity signals throughout the boundary layer are reconstructed using spatially available data in the schlieren images to recover an effective sampling rate of over 10 MHz; these are then converted to quantitative density gradients using a thin-lens-based calibration technique. A global analysis is performed on the schlieren data to investigate the nonlinear growth of the second-mode fundamental and harmonic content. Point-wise measures of the auto-bicoherence are used to identify specific triadic interactions and the locations of their highest levels of quadratic phase coupling. Significant resonance interactions between the second-mode fundamental and harmonic instabilities were found along with interactions between these and the mean flow. Bispectral mode decomposition is employed to educe the flow structures associated with these interactions. A similar analysis is performed for the power spectrum, with power spectral densities computed for each pixel’s time-series and spectral proper orthogonal decomposition employed to derive the modal structure and energy of the flow at specific frequencies. Comparisons between the bispectral quantities and second-mode power show that nonlinear interactions, particularly resonance interactions, are closely correlated with space-time modulation of disturbances during the nonlinear stage of transition.

boundary layer transition↗
NASA NTRS1994

Properties of acoustic sources in the Sun

The power spectrum of solar acoustic oscillations shows peaks extending out to frequencies much greater than the acoustic cutoff frequency of approximately 5.3 mHz, where waves are no longer trapped. Kumar & Lu (1991) proposed that these peaks arise from the interference of traveling waves which are generated by turbulent convection. According to this model, the frequencies of the peaks in the power spectrum depend on the static structure of the Sun as well as the radial location of the sources. Kumar & Lu used this idea to determine the depth of the acoustic sources. However, they ignored dissipative effects and found that the theoretically computed power spectrum was falling off much more rapidly than the observed spectrum. In this paper, we include the interaction of radiation with acoustic waves in the computation of the power spectrum. We find that the theoretically calculated power spectra, when radiative damping is included are in excellent agreement with the observed power spectra over the entire observed frequency range of 5.3 to 7.5 mHz above the acoustic cutoff frequency. Moreover, by matching the peak frequencies in the observed and theoretical spectra we find the mean depth of acoustic sources to be 140 +/- 60 km below the photosphere. We show that the spectrum of solar turbulence near the top of the solar convection zone is consistent with the Kolmogorov spectrum, and that the observed high frequency power spectrum provides strong evidence that the acoustic sources in the Sun are quadrupolar. The data, in fact, rules out dipole sources as significant contributors to acoustic wave generation in the Sun. The radial extent of the sources is poorly determined and is estimated to be less than about 550 km.

Kumar, Pawan↗
NASA NTRS1987

The effect of decay of the amplitude of oscillation on random process models for QPO X-ray stars

Random process models provide a useful mathematical framework for analysis of the quasi-periodic oscillations (QPO) recently discovered in the X-ray emission from certain luminous Galactic X-ray stars. In this paper, consideration is given to the effects of the power spectrum of the decay of the amplitude of oscillation that is expected in some physical models for the QPO phenomena. The resulting changes in the power spectrum depend on the ratio of the decay time of the amplitude of oscillation to the lifetime of the shot envelope. For values of this ratio less than about 10, it is found that incoherent QPO peaks in the power spectrum are significantly reduced in height and total power and are broadened in width, making them more difficult to detect. Coherent terms in the power spectrum, if present, are reduced in height and total power, but their width is unaffected. The red noise component remains unchanged. The present results are applied to the beat-frequency modulated accretion model in order to set constraints on the physical properties of the boundary layer between the inner edge of the accretion disk and the neutron star magnetosphere.

Shibazaki, N.↗
NASA NTRS2016

Mapping the Gas Turbulence in the Coma Cluster: Predictions for Astro-H

Astro-H will be able for the first time to map gas velocities and detect turbulence in galaxy clusters. One of the best targets for turbulence studies is the Coma cluster, due to its proximity, absence of a cool core, and lack of a central active galactic nucleus. To determine what constraints Astro-H will be able to place on the Coma velocity field, we construct simulated maps of the projected gas velocity and compute the second-order structure function, an analog of the velocity power spectrum. We vary the injection scale, dissipation scale, slope, and normalization of the turbulent power spectrum, and apply measurement errors and finite sampling to the velocity field. We find that even with sparse coverage of the cluster, Astro-H will be able to measure the Mach number and the injection scale of the turbulent power spectrum-the quantities determining the energy flux down the turbulent cascade and the diffusion rate for everything that is advected by the gas (metals, cosmic rays, etc.). Astro-H will not be sensitive to the dissipation scale or the slope of the power spectrum in its inertial range, unless they are outside physically motivated intervals. We give the expected confidence intervals for the injection scale and the normalization of the power spectrum for a number of possible pointing configurations, combining the structure function and velocity dispersion data. Importantly, we also determine that measurement errors on the line shift will bias the velocity structure function upward, and show how to correct this bias.

clusters: intracluster medium↗
NASA NTRS1990

Modeling of solar oscillation power spectra

To produce accurate estimates of the line-profile parameters of a model used to represent the spectral features in a solar oscillation power spectrum, it is necessary to (1) select the appropriate probability density function when deriving the maximum-likelihood function to be employed for the parameter estimation and (2) allow for the redistribution of spectral power caused by gaps in the data string. This paper describes a maximum-likelihood method for estimating the model parameters (based on the observed power spectrum statistics) that accounts for redistribution of spectral power caused by gaps in the data string, by convolving the model with the power spectrum of the observed window function. The accuracy and reliability of the method were tested using both artificial and authentic solar oscillation power spectrum data. A comparison of this method with various least-squares techniques is also presented.

Anderson, Edwin R.↗
NASA NTRS1975

Motion of charged particles normal to an irregular magnetic field

The motion is analyzed of charged particles in a fluctuating magnetic field which varies only in directions normal to its mean direction, such as that which would be generated by an ensemble of magnetosonic waves propagating normal to an ambient magnetic field. The appropriate generalization of gradient-drift motion is derived in terms of the power spectrum of the magnetic fluctuations, and an effective spatial diffusion coefficient is obtained. Several special cases are considered, including a Gaussian power spectrum, a power-law spectrum with a cutoff, and a general power-law spectrum. A possible magnitude is calculated for the spatial diffusion coefficient of the solar wind.

Jokipii, J. R.↗