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At least 433 records · Page 24

Accuracy of a class of concurrent algorithms for transient finite element analysis

The accuracy of a new class of concurrent procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.

Ortiz, Michael↗

Flight dynamics facility operational orbit determination support for the ocean topography experiment

The Ocean Topography Experiment (TOPEX/POSEIDON) mission is designed to determine the topography of the Earth's sea surface across a 3 yr period, beginning with launch in June 1992. The Goddard Space Flight Center Dynamics Facility has the capability to operationally receive and process Tracking and Data Relay Satellite System (TDRSS) tracking data. Because these data will be used to support orbit determination (OD) aspects of the TOPEX mission, the Dynamics Facility was designated to perform TOPEX operational OD. The scientific data require stringent OD accuracy in navigating the TOPEX spacecraft. The OD accuracy requirements fall into two categories: (1) on orbit free flight; and (2) maneuver. The maneuver OD accuracy requirements are of two types; premaneuver planning and postmaneuver evaluation. Analysis using the Orbit Determination Error Analysis System (ODEAS) covariance software has shown that, during the first postlaunch mission phase of the TOPEX mission, some postmaneuver evaluation OD accuracy requirements cannot be met. ODEAS results also show that the most difficult requirements to meet are those that determine the change in the components of velocity for postmaneuver evaluation.

Bolvin, D. T.↗

Doppler Global Velocimetry at NASA Glenn Research Center: System Discussion and Results

A ruggedized Doppler Global Velocimetry system has been built and tested at NASA Glenn Research Center. One component of planar velocity measurements of subsonic and supersonic flows from an under-expanded free jet are reported, which agree well with predicted values. An error analysis evaluates geometric and spectral error terms, and characterizes speckle noise in isotropic data. A multimode, fused fiber optic bundle is demonstrated to couple up to 650 mJ/pulse of laser light without burning or fiber ablation, and without evidence of Stimulated Brillouin Scattering or other spectral-broadening problems. Comparisons are made between spinning wheel data using illumination by freespace beam propagation and fiber optic beam delivery. The fiber bundle illumination is found to provide more spatially even and stable illumination than is typically available from pulsed Nd:YAG laser beams. The fiber bundle beam delivery is also a step toward making remote measurements and automatic real-time plume sectioning feasible in wind tunnel environments.

Lant, Christian T.↗

Dose variations caused by setup errors in intracranial stereotactic radiotherapy: A PRESAGE study

Stereotactic radiotherapy (SRT) requires tight margins around the tumor, thus producing a steep dose gradient between the tumor and the surrounding healthy tissue. Any setup errors might become clinically significant. To date, no study has been performed to evaluate the dosimetric variations caused by setup errors with a 3-dimensional dosimeter, the PRESAGE. This research aimed to evaluate the potential effect that setup errors have on the dose distribution of intracranial SRT. Computed tomography (CT) simulation of a CIRS radiosurgery head phantom was performed with 1.25-mm slice thickness. An ideal treatment plan was generated using Brainlab iPlan. A PRESAGE was made for every treatment with and without errors. A prescan using the optical CT scanner was carried out. Before treatment, the phantom was imaged using Brainlab ExacTrac. Actual radiotherapy treatments with and without errors were carried out with the Novalis treatment machine. Postscan was performed with an optical CT scanner to analyze the dose irradiation. The dose variation between treatments with and without errors was determined using a 3-dimensional gamma analysis. Errors are clinically insignificant when the passing ratio of the gamma analysis is 95% and above. Errors were clinically significant when the setup errors exceeded a 0.7-mm translation and a 0.5° rotation. The results showed that a 3-mm translation shift in the superior-inferior (SI), right-left (RL), and anterior-posterior (AP) directions and 2° couch rotation produced a passing ratio of 53.1%. Translational and rotational errors of 1.5 mm and 1°, respectively, generated a passing ratio of 62.2%. Translation shift of 0.7 mm in the directions of SI, RL, and AP and a 0.5° couch rotation produced a passing ratio of 96.2%. Preventing the occurrences of setup errors in intracranial SRT treatment is extremely important as errors greater than 0.7 mm and 0.5° alter the dose distribution. The geometrical displacements affect dose delivery to the tumor and the surrounding normal tissues.

61 RADIATION PROTECTION AND DOSIMETRY↗

Effects of flight instrumentation errors on the estimation of aircraft stability and control derivatives

An error analysis program based on an output error estimation method was used to evaluate the effects of sensor and instrumentation errors on the estimation of aircraft stability and control derivatives. A Monte Carlo analysis was performed using simulated flight data for a high performance military aircraft, a large commercial transport, and a small general aviation aircraft for typical cruise flight conditions. The effects of varying the input sequence and combinations of the sensor and instrumentation errors were investigated. The results indicate that both the parameter accuracy and the corresponding measurement trajectory fit error can be significantly affected. Of the error sources considered, instrumentation lags and control measurement errors were found to be most significant.

Bryant, W. H.↗

Analysis of discretization errors in LES

All numerical simulations of turbulence (DNS or LES) involve some discretization errors. The integrity of such simulations therefore depend on our ability to quantify and control such errors. In the classical literature on analysis of errors in partial differential equations, one typically studies simple linear equations (such as the wave equation or Laplace's equation). The qualitative insight gained from studying such simple situations is then used to design numerical methods for more complex problems such as the Navier-Stokes equations. Though such an approach may seem reasonable as a first approximation, it should be recognized that strongly nonlinear problems, such as turbulence, have a feature that is absent in linear problems. This feature is the simultaneous presence of a continuum of space and time scales. Thus, in an analysis of errors in the one dimensional wave equation, one may, without loss of generality, rescale the equations so that the dependent variable is always of order unity. This is not possible in the turbulence problem since the amplitudes of the Fourier modes of the velocity field have a continuous distribution. The objective of the present research is to provide some quantitative measures of numerical errors in such situations. Though the focus of this work is LES, the methods introduced here can be just as easily applied to DNS. Errors due to discretization of the time-variable are neglected for the purpose of this analysis.

Ghosal, Sandip↗

Neutron ages computed from experimental activation data

Computer program reduces time manually required to compute neutron age and to provide definite plan of procedural choices. Program allows convenient comparison of several fitting and error analysis procedures. Program code provides for error estimation of various integration options.

Semler, T. T.↗

The Stanford gyroscope experiment

Gyroscopes in motion about a massive body are found to have two main effects: (1) geodetic effect, solely due to motion of the gyroscope about the earth and (2) motional effect, due to earth rotation. An experiment is proposed to measure the precession rate of one or more gyroscopes, mounted either on earth or in a satellite, with respect to the axis of a telescope pointing at a suitable fixed star. The procedures and apparatus to be used in this experiment are outlined; the error analysis is summarized. The relation of error to size, speed, and mechanical properties of rotor is presented, along with the design requirements for accuracy of 10 to the -16th power rad/s.

Everitt, C. W. F.↗

A Ganymede lander mission

The paper addresses the dynamical problem and question of technical feasibility associated with delivering a simple, semi-hard lander to one of the Galilean satellites, Ganymede. Emphasis is placed on the identification of a viable, not necessarily optimal, baseline trajectory and maneuver sequence. Simplicity is stressed in the lander's use of two fixed-impulse solid rockets for landing maneuvers. It is shown through an error analysis that navigation and maneuver execution errors can be compensated on the baseline descent trajectory by controlling just the thrust direction. Finally, specific subsystem capabilities needed on the lander to achieve a successful touchdown within a specific performance envelope are also identified.

Boain, R. J.↗

Mathematical Models for Doppler Measurements

Error analysis increases precision of navigation. Report presents improved mathematical models of analysis of Doppler measurements and measurement errors of spacecraft navigation. To take advantage of potential navigational accuracy of Doppler measurements, precise equations relate measured cycle count to position and velocity. Drifts and random variations in transmitter and receiver oscillator frequencies taken into account. Mathematical models also adapted to aircraft navigation, radar, sonar, lidar, and interferometry.

Lear, William M.↗

An investigation of error characteristics and coding performance

The performance of forward error correcting coding schemes on errors anticipated for the Earth Observation System (EOS) Ku-band downlink are studied. The EOS transmits picture frame data to the ground via the Telemetry Data Relay Satellite System (TDRSS) to a ground-based receiver at White Sands. Due to unintentional RF interference from other systems operating in the Ku band, the noise at the receiver is non-Gaussian which may result in non-random errors output by the demodulator. That is, the downlink channel cannot be modeled by a simple memoryless Gaussian-noise channel. From previous experience, it is believed that those errors are bursty. The research proceeded by developing a computer based simulation, called Communication Link Error ANalysis (CLEAN), to model the downlink errors, forward error correcting schemes, and interleavers used with TDRSS. To date, the bulk of CLEAN was written, documented, debugged, and verified. The procedures for utilizing CLEAN to investigate code performance were established and are discussed.

Ebel, William J.↗

Derivation of terrain slope from SAR interferometric phase gradient

The relationship between the gradient of the interferometric phase and the terrain slope, which, it is thought, would allow a derivation of the terrain slopes without phase unwrapping, is presented. A linear relationship between the interferometric phase gradient and the terrain slopes was found. A quantitative error analysis showed that only very small errors are introduced by these approximations for orbital Synthetic Aperture Radar (SAR) geometries. An example of a slope map for repeat pass interferometry from ERS-1 SAR data is given. A number of direct and indirect applications of the terrain slope are indicated: erosion and avalanche hazard studies, radiometric calibration of SAR data, and normalization of the interferometric correlation coefficient.

Wegmueller, Urs↗

Cirrus cloud retrieval using infrared sounding data: Multilevel cloud errors

In this study we perform an error analysis for cloud-top pressure retrieval using the High-Resolution Infrared Radiometric Sounder (HIRS/2) 15-microns CO2 channels for the two-layer case of transmissive cirrus overlying an overcast, opaque stratiform cloud. This analysis includes standard deviation and bias error due to instrument noise and the presence of two cloud layers, the lower of which is opaque. Instantaneous cloud pressure retrieval errors are determined for a range of cloud amounts (0.1-1.0) and cloud-top pressures (850-250 mb). Large cloud-top pressure retrieval errors are found to occur when a lower opaque layer is present underneath an upper transmissive cloud layer in the satellite field of view (FOV). Errors tend to increase with decreasing upper-cloud effective cloud amount and with decreasing cloud height (increasing pressure). Errors in retrieved upper-cloud pressure result in corresponding errors in derived effective cloud amount. For the case in which a HIRS FOV has two distinct cloud layers, the difference between the retrieved and actual cloud-top pressure is positive in all cases, meaning that the retrieved upper-cloud height is lower than the actual upper-cloud height. In addition, errors in retrieved cloud pressure are found to depend upon the lapse rate between the low-level cloud top and the surface. We examined which sounder channel combinations would minimize the total errors in derived cirrus cloud height caused by instrument noise and by the presence of a lower-level cloud. We find that while the sounding channels that peak between 700 and 1000 mb minimize random errors, the sounding channels that peak at 300-500 mb minimize bias errors. For a cloud climatology, the bias errors are most critical.

Baum, Bryan A.↗

Spectral Analysis of Forecast Error Investigated with an Observing System Simulation Experiment

The spectra of analysis and forecast error are examined using the observing system simulation experiment (OSSE) framework developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASAGMAO). A global numerical weather prediction model, the Global Earth Observing System version 5 (GEOS-5) with Gridpoint Statistical Interpolation (GSI) data assimilation, is cycled for two months with once-daily forecasts to 336 hours to generate a control case. Verification of forecast errors using the Nature Run as truth is compared with verification of forecast errors using self-analysis; significant underestimation of forecast errors is seen using self-analysis verification for up to 48 hours. Likewise, self analysis verification significantly overestimates the error growth rates of the early forecast, as well as mischaracterizing the spatial scales at which the strongest growth occurs. The Nature Run-verified error variances exhibit a complicated progression of growth, particularly for low wave number errors. In a second experiment, cycling of the model and data assimilation over the same period is repeated, but using synthetic observations with different explicitly added observation errors having the same error variances as the control experiment, thus creating a different realization of the control. The forecast errors of the two experiments become more correlated during the early forecast period, with correlations increasing for up to 72 hours before beginning to decrease.

OSSE↗

Continued investigation of potential application of Omega navigation to civil aviation

Major attention is given to an analysis of receiver repeatability in measuring OMEGA phase data. Repeatability is defined as the ability of two like receivers which are co-located to achieve the same LOP phase readings. Specific data analysis is presented. A propagation model is described which has been used in the analysis of propagation anomalies. Composite OMEGA analysis is presented in terms of carrier phase correlation analysis and the determination of carrier phase weighting coefficients for minimizing composite phase variation. Differential OMEGA error analysis is presented for receiver separations. Three frequency analysis includes LOP error and position error based on three and four OMEGA transmissions. Results of phase amplitude correlation studies are presented.

Baxa, E. G., Jr.↗

Variational fast forwarding for quantum simulation beyond the coherence time

Abstract Trotterization-based, iterative approaches to quantum simulation (QS) are restricted to simulation times less than the coherence time of the quantum computer (QC), which limits their utility in the near term. Here, we present a hybrid quantum-classical algorithm, called variational fast forwarding (VFF), for decreasing the quantum circuit depth of QSs. VFF seeks an approximate diagonalization of a short-time simulation to enable longer-time simulations using a constant number of gates. Our error analysis provides two results: (1) the simulation error of VFF scales at worst linearly in the fast-forwarded simulation time, and (2) our cost function’s operational meaning as an upper bound on average-case simulation error provides a natural termination condition for VFF. We implement VFF for the Hubbard, Ising, and Heisenberg models on a simulator. In addition, we implement VFF on Rigetti’s QC to demonstrate simulation beyond the coherence time. Finally, we show how to estimate energy eigenvalues using VFF.

97 MATHEMATICS AND COMPUTING↗

Chemistry of the Sagittarius dwarf galaxy: A top-light initial mass function, outflows, and the R-process

From chemical abundance analysis of stars in the Sagittarius dwarf spheroidal galaxy (Sgr), we conclude that the α-element deficiencies cannot be due to the Type Ia supernova (SN Ia) time-delay scenario of Tinsley. Instead, the evidence points to low [α/Fe] ratios resulting from an initial mass function (IMF) deficient in the highest mass stars. The critical evidence is the 0.4 dex deficiency of [O/Fe], [Mg/Fe], and other hydrostatic elements, contrasting with the normal trend of r-process [Eu/Fe] {sub r} with [Fe/H]. Supporting evidence comes from the hydrostatic element (O, Mg, Na, Al, Cu) [X/Fe] ratios, which are inconsistent with iron added to the Milky Way (MW) disk trends. Also, the ratio of hydrostatic to explosive (Si, Ca, Ti) element abundances suggests a relatively top-light IMF. Abundance similarities with the LMC, Fornax, and IC 1613 suggest that their α-element deficiencies also resulted from IMFs lacking the most massive SNe II. The top-light IMF, as well as the normal trend of r-process [Eu/Fe] {sub r} with [Fe/H] in Sgr, indicates that massive SNe II (≳30 M {sub ☉}) are not major sources of r-process elements. High [La/Y] ratios, consistent with leaky-box chemical evolution, are confirmed but ∼0.3 dex larger than theoretical asymptotic giant branch (AGB) predictions. This suggests that a substantial increase in the theoretical {sup 13}C pocket in low-mass AGB stars is required. Sgr has the lowest [Rb/Zr] ratios known, consistent with pollution by low-mass (≲2 M {sub ☉}) AGB stars near [Fe/H] = –0.6, likely resulting from leaky-box chemical evolution. The [Cu/O] trends in Sgr and the MW suggest that Cu yields increase with both metallicity and stellar mass, as expected from Cu production by the weak s-process in massive stars. Finally, we present an updated hyperfine splitting line list, an abundance analysis of Arcturus, and further develop our error analysis formalism.

79 ASTRONOMY AND ASTROPHYSICS↗