Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Spherical harmonic analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Magnectic Probing of Core Geodynamics

To better understand geomagnetic theory and observation, we can use spatial magnetic spectra for the main field and secular variation to test core dynamical hypotheses against seismology. The hypotheses lead to theoretical spectra which are fitted to observational spectra. Each fit yields an estimate of the radius of Earth s core and uncertainty. If this agrees with the seismologic value, then the hypotheses pass the test. A new way to obtain theoretical spectra extends the hydromagnetic scale analysis of Benton to scale-variant field and flow. For narrow scale flow and a dynamically weak field by the top of Earth s core, this yields a JGR-PI, and a secular variation spectrum modulated by a cubic polynomial in spherical harmonic degree n. The former passes the tests. The latter passes many tests, but does not describe rapid dipole decline and quadrupole rebound; some tests suggest it is a bit hard, or rich in narrow scale change.In a core geodynamo, motion of the fluid conductor does work against the Lorentz force. This converts kinetic into magnetic energy which, in turn, is lost to heat via Ohmic dissipation. In the analysis at length- scale l/k, if one presumes kinetic energy is converted in either eddy- overturning or magnetic free-decay time-scales, then Kolmogorov or other spectra in conflict with observational spectra can result. Instead, the rate work is done roughly balances the dissipation rate, which is consistent with small scale flow. The conversion time-scale depends on dynamical constraints. These are summarized by the magneto- geostrophic vertical vorticity balance by the top of the core, which includes anisotropic effects of rotation, the magnetic field, and the core-mantle boundary. The resulting theoretical spectra for the core- source field and its SV are far more compatible with observation. The conversion time-scale of order 120 years is pseudo-scale-invariant. Magnetic spectra of other planets may differ; however, if a transition to non-conducting fluid hydrogen in Jupiter acts as barrier to vertical flow, as well as current, then the shape of the jovi-magnetic spectrum could be remarkably Earth-like.

Voorhies, Coerte↗
NASA NTRS1982

Electrostatic disturbance forces on a 3-axis drag-free sensor

The electrostatic analysis of a multiple-capacitance 3-axis drag-free sensor is presented in this paper. The instrument consists of a proof-mass (a dense metallic ball) floating freely inside a spherical cavity enclosed by the sensor plates and the shield. Since the ball and the cavity are not necessarily concentric, the problem in three-dimensional potential theory for electrostatics is solved by the method of boundary perturbations and specifically in terms of spherical harmonics. The capacitance outputs of the instrument and the electrostatic forces acting on the system are derived as non-linear functions of the ball position, ball charge and the sensor plate potentials. The instrument sensitivity and cross-coupling effects are discussed. The analysis may also be useful for electrostatic gyros and suspensions.

Hagstrom, T.↗
DOE OSTI2022

Efficient computation of N -point correlation functions in D dimensions

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have $\mathscr O$(n N ) complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity $\mathscr O$(n 2 ) or $\mathscr O$(n g log n g ) if evaluated using a Fast Fourier Transform on a grid of size n g . Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the (D – 1) sphere and are intrinsically related to angular momentum operators. Concatenation of (N – 1) such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

A new method of presentation the large-scale magnetic field structure on the Sun and solar corona

The large-scale photospheric magnetic field, measured at Stanford, has been analyzed in terms of surface harmonics. Changes of the photospheric field which occur within whole solar rotation period can be resolved by this analysis. For this reason we used daily magnetograms of the line-of-sight magnetic field component observed from Earth over solar disc. We have estimated the period during which day-to-day full disc magnetograms must be collected. An original algorithm was applied to resolve time variations of spherical harmonics that reflect time evolution of large-scale magnetic field within solar rotation period. This method of magnetic field presentation can be useful enough in lack of direct magnetograph observations due to sometimes bad weather conditions. We have used the calculated surface harmonics to reconstruct the large-scale magnetic field structure on the source surface near the sun - the origin of heliospheric current sheet and solar wind streams. The obtained results have been compared with spacecraft in situ observations and geomagnetic activity. We tried to show that proposed technique can trace shon-time variations of heliospheric current sheet and short-lived solar wind streams. We have compared also our results with those obtained traditionally from potential field approximation and extrapolation using synoptic charts as initial boundary conditions.

Ponyavin, D. I.↗
NASA NTRS1994

Radiation from advanced solid rocket motor plumes

The overall objective of this study was to develop an understanding of solid rocket motor (SRM) plumes in sufficient detail to accurately explain the majority of plume radiation test data. Improved flowfield and radiation analysis codes were developed to accurately and efficiently account for all the factors which effect radiation heating from rocket plumes. These codes were verified by comparing predicted plume behavior with measured NASA/MSFC ASRM test data. Upon conducting a thorough review of the current state-of-the-art of SRM plume flowfield and radiation prediction methodology and the pertinent data base, the following analyses were developed for future design use. The NOZZRAD code was developed for preliminary base heating design and Al2O3 particle optical property data evaluation using a generalized two-flux solution to the radiative transfer equation. The IDARAD code was developed for rapid evaluation of plume radiation effects using the spherical harmonics method of differential approximation to the radiative transfer equation. The FDNS CFD code with fully coupled Euler-Lagrange particle tracking was validated by comparison to predictions made with the industry standard RAMP code for SRM nozzle flowfield analysis. The FDNS code provides the ability to analyze not only rocket nozzle flow, but also axisymmetric and three-dimensional plume flowfields with state-of-the-art CFD methodology. Procedures for conducting meaningful thermo-vision camera studies were developed.

Farmer, Richard C.↗
NASA NTRS1977

Onboard magnetic field modeling for Solar Maximum Mission /SMM/

Analysis and simulation results are presented for magnetic field models for use in attitude acquisition onboard Solar Maximum Mission (SMM). A study was made of the degree of the spherical harmonic expansion of the magnetic field required, considering mission requirements, modeling errors, and magnetometer quantization and biases. It is shown that a fifth-degree field is sufficient to provide two-degree roll angle determination accuracy with a residual magnetic bias of 10 milligauss. Also, a spherical harmonic expansion for the McIlwain L-parameter is included for the first time. This parameter will be telemetered to ground with experimental data. The fifth-degree expansion will provide the L-parameter to within two percent of accepted values. The additional onboard computational burden is the storage of 36 coefficients and an increase of about 15% in computation time. Prototype flight code was developed which is anticipated to require about 2000 bytes of core storage and 30 milliseconds of computation time per orbit point on the NSSC-1 computer.

Headrick, R. D.↗
NASA NTRS1981

Voyager 1 assessment of Jupiter's planetary magnetic field

An estimate of Jupiter's planetary magnetic field is obtained from the Voyager 1 observations of the Jovian magnetosphere. An explicit model for the magnetodisc current system is combined with a spherical harmonic model of the planetary field with both sets of parameters determined simultaneously using a nonlinear generalized inverse methodology. The resulting model fits the observations extremely well throughout the analysis interval (r 20 Jovian radii). The Jovian internal field model obtained from the Voyager 1 data is very similar to the octopole Pioneer 11 models. The best fitting magnetodisc lies in the centrifugal equator, 2/3 of the way between the rotational and magnetic equators, as appropriate for centrifugal loading of the magnetosphere by a cold plasma.

Connerney, J. E. P.↗
NASA NTRS1983

Inference of variations in the gravity field from satellite-to-satellite range rate

An analytic scheme for inferring variations of the gravity field from satellite-to-satellite range rate (low-low) is developed. As a test, it is applied to a pair of satellites in polar orbit, at altitude 160 km and spacing 100 km, with 72 data points per revolution. An assumed gravity field of tesseral spherical harmonics up to the eighth degree is completely recovered in three iterations over 64 revolutions. It is apparent that data points at regular intervals enable the use of data analysis techniques that avoid massive matrix inversions.

Kaula, W. M.↗
NASA NTRS1999

An Improved 360 Degree and Order Model of Venus Topography

We present an improved 360 degree and order spherical harmonic solution for Venus' topography. The new model uses the most recent set of Venus altimetry data with spacecraft positions derived from a recent high resolution gravity model. Geometric analysis indicates that the offset between the center of mass and center of figure of Venus is about 10 times smaller than that for the Earth, the Moon, or Mars. Statistical analyses confirm that the RMS topography follows a power law over the central part of the spectrum. Compared to the previous topography model, the new model is more highly correlated with Venus' harmonic gravity field.

Rappaport, Nicole J.↗
NASA NTRS2004

Magnetic Probing of Core Geodynamics

To better understand geomagnetic theory and observation, we can use spatial magnetic spectra for the main field and secular variation to test core dynamical hypotheses against seismology. The hypotheses lead to theoretical spectra which are fitted to observational spectra. Each fit yields an estimate of the radius of Earth's core and uncertainty. If this agrees with the seismologic value, then the hypothesis passes the test. A new way to obtain theoretical spectra extends the hydromagnetic scale analysis of Benton to scale-variant field and flow. For narrow scale flow and a dynamically weak field by the top of Earth's core, this yields a generalized Stevenson-McLeod spectrum for the core-source field, and a secular variation spectrum modulated by a cubic polynomial in spherical harmonic degree n. The former passes the tests. The latter passes many tests, but does not describe rapid dipole decline and quadrupole rebound; some tests suggest it is a bit hard, or rich in narrow scale range. In a core geodynamo, motion of the fluid conductor does work against the Lorentz force. This converts kinetic into magnetic energy which, in turn, is lost to heat via Ohmic dissipation. In the analysis at length-scale 1/k, if one presumes kinetic energy is converted in either eddy-overturning or magnetic free-decay time-scales, then Kolmogorov or other spectra in conflict with observational spectra can result. Instead, the rate work is done roughly balances the dissipation rate, which is consistent with small-scale flow. The conversion time-scale depends on dynamical constraints. These are summarized by the magnetogeostrophic vertical vorticity balance by the top of the core, which includes anisotropic effects of rotation, the magnetic field, and the core-mantle boundary. The resulting theoretical spectra for the core-source field and its SV are far more compatible with observation. The conversion time-scale of order 120 years is pseudo-scale-invariant. Magnetic spectra of other planets may differ; however, if a transition to non-conducting fluid hydrogen in Jupiter acts as a barrier to vertical flow, as well as current, then the shape of the jovi-magnetic spectrum could be remarkably Earth-like.

Voorhies, Coerte V.↗
NASA NTRS2004

Magnetic Probing of Core Geodynamics

To better understand geomagnetic theory and observation, we can use spatial magnetic spectra for the main field and secular variation to test core dynmcal hypotheses against seismology. The hypotheses lead to theoretical spectra which are fitted to observational spectra. Each fit yields an estimate of the radius of Earth's core and uncertainty. If this agrees with the seismologic value, then the hypothes pass the test. A new way to obtain theoretical spectra extends the hydromagnetic scale analysis of Benton to scale-variant field and flow. For narrow scale flow and a dynamically weak field by the top of Earth's core, this yields a generalized Stevenson-McLeod spectrum for the core-source field, and a secular variation spectrum modulated by a cubic polynomial in spherical harmonic degree n. The former passes the tests. The latter passes many tests, but does not describe rapid dipole decline and quadrupole rebound; some tests suggest it is a bit hard, or rich in narrow scale change. In a core geodynamo, motion of the fluid conductor does work against the Lorentz force. This converts kinetic into magnetic energy which, in turn, is lost to heat via Ohmic dissipation. In the analysis at lentgh-scale l/k, if one presumes kinetic energy is converted in either eddy- overturning or magnetic free-decay time-scales, then Kolmogorov or other spectra in conflict with observational spectra can result. Instead, the rate work is done roughly balances the dissipation rate, which is consistent with small scale flow. The conversion time-scale depends on dynamical constraints. These are summarized by the magneto-geostrophic vertical vorticity balance by the top of the core, which includes anisotropic effects of rotation, the magnetic field, and the core- mantle boundary. The resulting theoretical spectra for the core-source field and its SV are far more compatible with observation. The conversion time-scale of order l20 years is pseudo-scale-invarient. Magnetic spectra of other planets may differ; however, if a transition to non-conductmg fluid hydrogen in Jupiter acts as barrier to vertical flow, as well as current, then the shape of the jovi-magnetic spectrum could be remarkably Earth-like.

Voorhies, Coerte V.↗
NASA NTRS2010

High-Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

It has been known for some time that Taylor series (TS) integration is among the most efficient and accurate numerical methods in solving differential equations. However, the full benefit of the method has yet to be realized in calculating spacecraft trajectories, for two main reasons. First, most applications of Taylor series to trajectory propagation have focused on relatively simple problems of orbital motion or on specific problems and have not provided general applicability. Second, applications that have been more general have required use of a preprocessor, which inevitably imposes constraints on computational efficiency. The latter approach includes the work of Berryman et al., who solved the planetary n-body problem with relativistic effects. Their work specifically noted the computational inefficiencies arising from use of a preprocessor and pointed out the potential benefit of manually coding derivative routines. In this Engineering Note, we report on a systematic effort to directly implement Taylor series integration in an operational trajectory propagation code: the Spacecraft N-Body Analysis Program (SNAP). The present Taylor series implementation is unique in that it applies to spacecraft virtually anywhere in the solar system and can be used interchangeably with another integration method. SNAP is a high-fidelity trajectory propagator that includes force models for central body gravitation with N X N harmonics, other body gravitation with N X N harmonics, solar radiation pressure, atmospheric drag (for Earth orbits), and spacecraft thrusting (including shadowing). The governing equations are solved using an eighth-order Runge-Kutta Fehlberg (RKF) single-step method with variable step size control. In the present effort, TS is implemented by way of highly integrated subroutines that can be used interchangeably with RKF. This makes it possible to turn TS on or off during various phases of a mission. Current TS force models include central body gravitation with the J2 spherical harmonic, other body gravitation, thrust, constant atmospheric drag from Earth's atmosphere, and solar radiation pressure for a sphere under constant illumination. The purpose of this Engineering Note is to demonstrate the performance of TS integration in an operational trajectory analysis code and to compare it with a standard method, eighth-order RKF. Results show that TS is 16.6 times faster on average and is more accurate in 87.5% of the cases presented.

Scott, James R.↗
NASA NTRS1979

Development and analysis of a twelfth degree and order gravity model for Mars

Satellite geodesy techniques previously applied to artificial earth satellites have been extended to obtain a high-resolution gravity field for Mars. Two-way Doppler data collected by 10 Deep Space Network (DSN) stations during Mariner 9 and Viking 1 and 2 missions have been processed to obtain a twelfth degree and order spherical harmonic model for the martian gravitational potential. The quality of this model was evaluated by examining the rms residuals within the fit and the ability of the model to predict the spacecraft state beyond the fit. Both indicators show that more data and higher degree and order harmonics will be required to further refine our knowledge of the martian gravity field. The model presented shows much promise, since it resolves local gravity features which correlate highly with the martian topography. An isostatic analysis based on this model, as well as an error analysis, shows rather complete compensation on a global (long wavelength) scale. Though further model refinements are necessary to be certain, local (short wavelength) features such as the shield volcanos in Tharsis appear to be uncompensated. These are interpreted to place some bounds on the internal structure of Mars.

Christensen, E. J.↗
NASA NTRS1971

Lunar gravity derived from long-period satellite motion, a proposed method

A method was devised to determine the spherical harmonic coefficients of the lunar gravity field. The method consists of a two-step data reduction and estimation process. Pseudo-Doppler data were generated simulating two different lunar orbits. The analysis included the perturbing effects of the L1 lunar gravity field, the earth, the sun, and solar radiation pressure. Orbit determinations were performed on these data and long-period orbital elements were obtained. The Kepler element rates from these solutions were used to recover L1 lunar gravity coefficients. Overall results of the experiment show that lunar gravity coefficients can be accurately determined and that the method is dynamically consistent with long-period perturbation theory.

Ferrari, A. J.↗
NASA NTRS1979

Global accuracy estimates of point and mean undulation differences obtained from gravity disturbances, gravity anomalies and potential coefficients

Through the method of truncation functions, the oceanic geoid undulation is divided into two constituents: an inner zone contribution expressed as an integral of surface gravity disturbances over a spherical cap; and an outer zone contribution derived from a finite set of potential harmonic coefficients. Global, average error estimates are formulated for undulation differences, thereby providing accuracies for a relative geoid. The error analysis focuses on the outer zone contribution for which the potential coefficient errors are modeled. The method of computing undulations based on gravity disturbance data for the inner zone is compared to the similar, conventional method which presupposes gravity anomaly data within this zone.

Jekeli, C.↗
DOE OSTI2022

Dark Energy Survey Year 3 results: A 2.7% measurement of baryon acoustic oscillation distance scale at redshift 0.835

We present angular diameter measurements obtained by measuring the position of baryon acoustic oscillations (BAO) in an optimized sample of galaxies from the first three years of Dark Energy Survey data (DES Y3). The sample consists of 7 million galaxies distributed over a footprint of 4100 deg 2 with 0.6 < z photo < 1.1 and a typical redshift uncertainty of 0.03 ( 1 + z ) . The sample selection is the same as in the BAO measurement with the first year of DES data, but the analysis presented here uses three times the area, extends to higher redshift, and makes a number of improvements, including a fully analytical BAO template, the use of covariances from both theory and simulations, and an extensive preunblinding protocol. We used two different statistics; angular correlation function and power spectrum, and validate our pipeline with an ensemble of over 1500 realistic simulations. Both statistics yield compatible results. We combine the likelihoods derived from angular correlations and spherical harmonics to constrain the ratio of comoving angular diameter distance D M at the effective redshift of our sample to the sound horizon scale at the drag epoch. We obtain D M ( z eff = 0.835 ) / r d = 18.92 ± 0.51 , which is consistent with, but smaller than, the Planck prediction assuming flat Λ CDM , at the level of 2.3 σ . The analysis was performed blind and is robust to changes in a number of analysis choices. It represents the most precise BAO distance measurement from imaging data to date, and is competitive with the latest transverse ones from spectroscopic samples at z > 0.75 . When combined with DES 3 x 2 pt + SNIa , they lead to improvements in H 0 and Ω m constraints by ∼ 20 % .

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1989

High resolution analysis of satellite gradiometry

Satellite gravity gradiometry is a technique now under development which, by the middle of the next decade, may be used for the high resolution charting from space of the gravity field of the earth and, afterwards, of other planets. Some data analysis schemes are reviewed for getting detailed gravity maps from gradiometry on both a global and a local basis. It also presents estimates of the likely accuracies of such maps, in terms of normalized spherical harmonics expansions, both using gradiometry alone and in combination with data from a Global Positioning System (GPS) receiver carried on the same spacecraft. It compares these accuracies with those of current and future maps obtained from other data (conventional tracking, satellite-satellite tracking, etc.), and also with the spectra of various signals of geophysical interest.

Colombo, O. L.↗
NASA NTRS1994

The isostatic state of Mead crater

We have analyzed high-resolution Magellan Doppler tracking data over Mead crater, using both line-of-sight and spherical harmonic methods, and have found a negative gravity anomaly of about 4-5 mgal (at spacecraft altitude, 182 km). This is consistent with no isostatic compensation of the present topography; the uncertainty in the analysis allows perhaps as much as 30% compensation at shallow dpeths (approximately 25 km). This is similar to observations of large craters on Earth, which are not generally compensated, but contrasts with at least some lunar basins which are inferred to have large Moho uplifts and corresponding positive Bouguer anomalies. An uncompensated load of this size requires a lithosphere with an effective elastic lithosphere thickness greater than 30 km. In order for the crust-mantle boundary not to have participated in the deformation associated with the collapse of the transient cavity during the creation of the crater, the yield strength near the top of the mantle must have been significantly higher on Earth and Venus than on the Moon at the time of basin formation. This might be due to increased strength against frictional sliding at the higher confining pressures within the larger planets. Alternatively, the thinner crusts of Earth and Venus compared to that of the Moon may result in higher creep strength of the upper mantle at shallower depths.

Banerdt, W. B.↗