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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Harmonic analysis of discrete tracers of large-scale structure

It is commonplace in cosmology to analyze fields projected onto the celestial sphere, and in particular density fields that are defined by a set of points e.g. galaxies. When performing an harmonic-space analysis of such data (e.g. an angular power spectrum) using a pixelized map one has to deal with aliasing of small-scale power and pixel window functions. We compare and contrast the approaches to this problem taken in the cosmic microwave background and large-scale structure communities, and advocate for a direct approach that avoids pixelization. We describe a method for performing a pseudo-spectrum analysis of a galaxy data set and show that it can be implemented efficiently using well-known algorithms for special functions that are suited to acceleration by graphics processing units (GPUs). The method returns the same spectra as the more traditional map-based approach if in the latter the number of pixels is taken to be sufficiently large and the mask is well sampled. The method is readily generalizable to cross-spectra and higher-order functions. It also provides a convenient route for distributing the information in a galaxy catalog directly in harmonic space, as a complement to releasing the configuration-space positions and weights, and a route to spectral apodization. Finally, we make public a code enabling the application of our method to existing and upcoming datasets.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1977

Lunar gravity - A harmonic analysis

A sixteenth-degree and sixteenth-order spherical harmonic lunar gravity field has been derived from the long-term Keplerian variations in the orbits of the Apollo subsatellites and Lunar Orbiter 5. This model resolves the major mascon gravity anomalies of the lunar near side and is in very good agreement with line-of-sight acceleration results. The far-side map shows the major ringed basins to be strong localized negative anomalies located in broad regions of positive gravity which correspond closely to the highlands. The rms pressure levels calculated from equivalent-surface height variations show that the moon and earth support nearly equal pressures, whereas Mars is appreciably stronger. The moon appears to support larger loads than earth owing to its weaker central gravity field and perhaps a colder upper lithosphere. Significant differences between the low-degree gravity and topography spectra indicate that the longer-wavelength topographic features are isostatically compensated.

Ferrari, A. J.↗
NASA NTRS1990

Harmonic analysis of nonlinear devices on spacecraft power systems

A nonlinear device modeling algorithm (NOLID) has been developed for use in spacecraft power system analysis. This algorithm is designed to explore the effects of nonlinear devices and loads on a spacecraft power system. Application of this harmonic modeling algorithm in spacecraft power system management programs such as harmonic power flow analysis packages is discussed. It is shown that the NOLID algorithm can be applied in conjunction with a harmonic power flow to give a more accurate description of system state.

Williamson, Frank↗
DOE OSTI2014

Harmonic analysis for the characterization and correction of geometric distortion in MRI

Purpose: Magnetic resonance imaging (MRI) is gaining widespread use in radiation therapy planning, patient setup verification, and real-time guidance of radiation delivery. Successful implementation of these technologies relies on the development of simple and efficient methods to characterize and monitor the geometric distortions arising due to system imperfections and gradient nonlinearities. To this end, the authors present the theory and validation of a novel harmonic approach to the quantification of system-related distortions in MRI. Methods: The theory of spatial encoding in MRI is applied to demonstrate that the 3D distortion vector field (DVF) is given by the solution of a second-order boundary value problem (BVP). This BVP is comprised of Laplace’s equation and a limited measurement of the distortion on the boundary of a specified region of interest (ROI). An analytical series expansion solving this BVP within a spherical ROI is obtained, and a statistical uncertainty analysis is performed to determine how random errors in the boundary measurements propagate to the ROI interior. This series expansion is then evaluated to obtain volumetric DVF mappings that are compared to reference data obtained on a 3 T full-body scanner. This validation is performed within two spheres of 20 cm diameter (one centered at the scanner origin and the other offset +3 cm along each of the transverse directions). Initially, a high-order mapping requiring measurements at 5810 boundary points is used. Then, after exploring the impact of the boundary sampling density and the effect of series truncation, a reduced-order mapping requiring measurements at 302 boundary points is evaluated. Results: The volumetric DVF mappings obtained from the harmonic analysis are in good agreement with the reference data. Following distortion correction using the high-order mapping, the authors estimate a reduction in the mean distortion magnitude from 0.86 to 0.42 mm and from 0.93 to 0.39 mm within the central and offset ROIs, respectively. In addition, the fraction of points with a distortion magnitude greater than 1 mm is reduced from 35.6% to 2.8% and from 40.4% to 1.5%, respectively. Similarly, following correction using the reduced-order mapping, the mean distortion magnitude reduces to 0.45–0.42 mm within the central and offset ROIs, and the fraction of points with a distortion magnitude greater than 1 mm is reduced to 2.8% and 1.5%, respectively. Conclusions: A novel harmonic approach to the characterization of system-related distortions in MRI is presented. This method permits a complete and accurate mapping of the DVF within a specified ROI using a limited measurement of the distortion on the ROI boundary. This technique eliminates the requirement to exhaustively sample the DVF at a dense 3D array of points, thereby permitting the design of simple, inexpensive phantoms that may incorporate additional modules for auxiliary quality assurance objectives.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1992

Spherical harmonic analysis of steady photospheric flows. II

The use of the spherical harmonic functions to analyze the nearly steady flows in the solar photosphere is extended to situations in which B(0) the latitude at disk center, is nonzero and spurious velocities are present. The procedures for extracting the rotation profile and meridional circulation are altered to account for the seasonal tilt of the sun's rotation axis toward and away from the observer. A more robust and accurate method for separating the limb shift and meridional circulation signals is described. The analysis procedures include the ability to mask out areas containing spurious velocities (velocity-like signals that do not represent true flow velocities in the photosphere). The procedures are shown to work well in extracting the various flow components from realistic artificial data with a broad, continuous spectrum for the supergranulation. The presence of this supergranulation signal introduces errors of a few m/s in the measurements of the rotation profile, meridional circulation, and limb shift from a single Doppler image.

Hathaway, David H.↗
NASA NTRS1985

Venus gravity - A harmonic analysis and geophysical implications

An improved theoretical model of Venusian global gravity has been obtained by fitting a tenth degree spherical harmonic series to 78 orbital arcs of Doppler tracking data from the Pioneer Venus Orbiter. Maps of the free-air anomaly and its formal error are presented. Isostatic anomaly and 'Geoid' maps are also presented, and their geophysical implications are discussed in details. Comparison with equivalent resolution topographic models reveals a strong correlation between long wavelength gravity and the topography of Venus. Analysis of the second degree harmonics showed two aspects of the orientation of the inertial axes of Venus: (1) a significant (about three degrees) departure of the axis of greatest inertia from the rotational axis; and (2) a near alignment of the axis of least inertia with the location of the subterrestrial point at the time of the next inferior conjunction with earth (December 16, 2101). A series of contour maps of the Venusian free-air anomalies is provided.

Mottinger, N. A.↗
NASA NTRS1985

Venus topography - A harmonic analysis

A model of Venusian global topography has been obtained by fitting an eighteenth-degree harmonic series to Pioneer Venus orbiter radar altimeter data. The mean radius is (6051.45 + or - 0.04) km. The corresponding mean density is (5244.8 + or 0.5) kg/cu m. The center of figure is displaced from the center of mass by (0.339 + or - 0.088) km towards (6.6 + or 10.1) deg N, (148. 8 + or - 7.7) deg. The figure of Venus is distinctly triaxial, but the orientation and magnitudes of the principal topographic axes correlate rather poorly with the gravitational principal axes. However, the higher-degree harmonics of topography and gravity are significantly correlated. The topographic variance spectrum of Venus is very similar in form to those of the moon, Mars, and especially earth. It is suggested that this spectral similarity simply reflects a statistical balance between constructional and degradational geomorphic proceses. Venus and earth are particularly similar (and differ from the moon and Mars) in that the larger bodies both exhibit a significant low degree deficit (relative to the extrapolated trend of the higher harmonics).

Bills, B. G.↗
NASA NTRS1980

A harmonic analysis of lunar gravity

An improved model of lunar global gravity has been obtained by fitting a sixteenth-degree harmonic series to a combination of Doppler tracking data from Apollo missions 8, 12, 15, and 16, and Lunar Orbiters 1, 2, 3, 4, and 5, and laser ranging data to the lunar surface. To compensate for the irregular selenographic distribution of these data, the solution algorithm has also incorporated a semi-empirical a priori covariance function. Maps of the free-air gravity disturbance and its formal error are presented, as are free-air anomaly and Bouguer anomaly maps. The lunar gravitational variance spectrum has the form V(G; n) = O(n to the -4th power), as do the corresponding terrestrial and martian spectra. The variance spectra of the Bouguer corrections (topography converted to equivalent gravity) for these bodies have the same basic form as the observed gravity; and, in fact, the spectral ratios are nearly constant throughout the observed spectral range for each body. Despite this spectral compatibility, the correlation between gravity and topography is generally quite poor on a global scale.

Bills, B. G.↗
NASA NTRS1987

Spherical harmonic analysis of steady photospheric flows

A technique is presented in which full disk Doppler velocity measurements are analyzed using spherical harmonic functions to determine the characteristics of the spectrum of spherical harmonic modes and the nature of steady photospheric flows. Synthetic data are constructed in order to test the technique. In spite of the mode mixing due to the lack of information about the motions on the backside of the sun, solar rotation and differential rotation can be accurately measured and monitored for secular changes, and meridional circulations with small amplitudes can be measured. Furthermore, limb shift measurements can be accurately obtained, and supergranules can be fully resolved and separated from giant cells by their spatial characteristics.

Hathaway, David H.↗
NASA NTRS1987

Venus gravity - A harmonic analysis

An improved model of Venusian global gravity has been obtained by fitting an eighteenth-degree and eighteenth-order spherical harmonic series to 78 orbital arcs of high altitude (950-1350 km at periapsis) tracking data and 351 orbital arcs of lower-altitude (150-200 km at periapsis) data from the Pioneer Venus Orbiter (PVO). Compared to a recently published tenth-degree model of Mottinger et al. (1985), which is based on the 78 high-altitude arcs only, the current model provides a significant improvement in resolution and fidelity. As a measure of this improvement, it is noted that for the low-altitude arcs alone, the variance of the residuals for the present model is reduced to 19 percent of the data variance, compared to 51 percent for the tenth-degree model. Venus differs significantly from the earth in that it exhibits a significant correlation between long-wavelength topography and gravity. The gravity/topography spectral admittances are inconsistent with either Airy or Pratt isostasy, but are consistent with dynamic support by mantle convection.

Bills, Bruce G.↗
NASA NTRS1982

A harmonic analysis method for unsteady transonic flow and its application to the flutter of airfoils

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. A study is presented of the shock motion associated with an oscillating airfoil and its representation by the harmonic procedure. The effects of the shock motion and the resulting pressure pulse are shown to be included in the harmonic pressure distributions and the corresponding generalized forces. Analytical and experimental pressure distributions for the NACA 64A010 airfoil are compared for Mach numbers of 0.75, 0.80 and 0.842. A typical section, two-degree-of-freedom flutter analysis of a NACA 64A010 airfoil is performed. The results show a sharp transonic bucket in one case and abrupt changes in instability modes.

Ehlers, F. E.↗
DOE OSTI2015

Quantum efficiency harmonic analysis of exciton annihilation in organic light emitting diodes

Various exciton annihilation processes are known to impact the efficiency roll-off of organic light emitting diodes (OLEDs); however, isolating and quantifying their contribution in the presence of other factors such as changing charge balance continue to be a challenge for routine device characterization. Here, we analyze OLED electroluminescence resulting from a sinusoidal dither superimposed on the device bias and show that nonlinearity between recombination current and light output arising from annihilation mixes the quantum efficiency measured at different dither harmonics in a manner that depends uniquely on the type and magnitude of the annihilation process. We derive a series of analytical relations involving the DC and first harmonic external quantum efficiency that enable annihilation rates to be quantified through linear regression independent of changing charge balance and evaluate them for prototypical fluorescent and phosphorescent OLEDs based on the emitters 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran and platinum octaethylporphyrin, respectively. We go on to show that, in most cases, it is sufficient to calculate the needed quantum efficiency harmonics directly from derivatives of the DC light versus current curve, thus enabling this analysis to be conducted solely from standard light-current-voltage measurement data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1989

Harmonic analysis of spacecraft power systems using a personal computer

The effects that nonlinear devices such as ac/dc converters, HVDC transmission links, and motor drives have on spacecraft power systems are discussed. The nonsinusoidal currents, along with the corresponding voltages, are calculated by a harmonic power flow which decouples and solves for each harmonic component individually using an iterative Newton-Raphson algorithm. The sparsity of the harmonic equations and the overall Jacobian matrix is used to an advantage in terms of saving computer memory space and in terms of reducing computation time. The algorithm could also be modified to analyze each harmonic separately instead of all at the same time.

Williamson, Frank↗
DOE OSTI2015

Full sky harmonic analysis hints at large ultra-high energy cosmic ray deflections

The full-sky multipole coefficients of the ultra-high energy cosmic ray (UHECR) flux have been measured for the first time by the Pierre Auger and Telescope Array collaborations using a joint data set with E > 10 EeV. We calculate these harmonic coefficients in the model where UHECR are protons and sources trace the local matter distribution, and compare our results with observations. We find that the expected power for low multipoles (dipole and quadrupole, in particular) is sytematically higher than in the data: the observed flux is too isotropic. We then investigate to which degree our predictions are influenced by UHECR deflections in the regular Galactic magnetic field. It turns out that the UHECR power spectrum coefficients C{sub l} are quite insensitive to the effects of the Galactic magnetic field, so it is unlikely that the discordance can be reconciled by tuning the Galactic magnetic field model. On the contrary, a sizeable fraction of uniformly distributed flux (representing for instance an admixture of heavy nuclei with considerably larger deflections) can bring simulations and observations to an accord.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Harmonic Analysis of Electric Vehicle Loadings on Distribution System

With the increasing number of Electric Vehicles (EV) in this age, the power system is facing huge challenges of the high penetration rates of EVs charging stations. Therefore, a technical study of the impact of EVs charging on the distribution system is required. This paper is applied with PSCAD software and aimed to analyzing the Total Harmonic Distortion (THD) brought by Electric Vehicles charging stations in power systems. The paper starts with choosing IEEE34 node test feeder as the distribution system, building electric vehicle level two charging battery model and other four different testing scenarios: overhead transmission line and underground cable, industrial area, transformer and photovoltaic (PV) system. Then the statistic method is used to analyze different characteristics of THD in the plug-in transient, plug-out transient and steady-state charging conditions associated with these four scenarios are taken into the analysis. Finally, the factors influencing the THD in different scenarios are found. The analyzing results lead the conclusion of this paper to have constructive suggestions for both Electric Vehicle charging station construction and customers' charging habits.

Xu, Yijun A↗
NASA NTRS1983

Autoregressive harmonic analysis of the earth's polar motion using homogeneous International Latitude Service data

The homogeneous set of 80-year-long (1900-1979) International Latitude Service (ILS) polar motion data is analyzed using the autoregressive method (Chao and Gilbert, 1980), which resolves and produces estimates for the complex frequency (or frequency and Q) and complex amplitude (or amplitude and phase) of each harmonic component in the data. The ILS data support the multiple-component hypothesis of the Chandler wobble. It is found that the Chandler wobble can be adequately modeled as a linear combination of four (coherent) harmonic components, each of which represents a steady, nearly circular, prograde motion. The four-component Chandler wobble model 'explains' the apparent phase reversal during 1920-1940 and the pre-1950 empirical period-amplitude relation. The annual wobble is shown to be rather stationary over the years both in amplitude and in phase, and no evidence is found to support the large variations reported by earlier investigations. The Markowitz wobble is found to be marginally retrograde and appears to have a complicated behavior which cannot be resolved because of the shortness of the data set.

Chao, B. F.↗
DOE OSTI2022

On extraction of twist-two Compton form factors from DVCS observables through harmonic analysis

We investigate the exercise of locally extracting the real and imaginary parts of the four twist-2 Compton form factors (CFFs) {$\mathcal{H,E,\tilde H,\tilde E}$} which arise in the deeply virtual Compton scattering (DVCS) process e + p → e + p + y. Neglecting dynamical higher-twist contributions, we find that there are a sufficient number of DVCS observables and degrees of freedom to extract all 8 leading quantities model-independently, exploiting the azimuthal dependence of the absolute cross sections across all possible beam and target polarizations at a common kinematical point in {Q, t,x b , y}. As an example, for typical JLab lab-frame kinematics, we simplify the reduced DVCS observables to their dominant terms, providing a sufficient number of equations for local determination of the twist-2 CFFs. We demonstrate the feasibility using harmonic fitting to both cross sections and beam spin asymmetries with both real and pseudo-data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗