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NASA NTRS1992

A quantitative measure of the structure of gamma-ray burst time profiles

A cursory examination of cosmic gamma-ray burst time profiles indicates an inhomogeneous distribution of structure. In the first approximation, there seem to be two types of profiles; smooth ones with little structure and highly variable ones with lots of structure. To put this observation to the test, we have examined the statistical nature of the profile derivative to choose which parameter might best be called the burst 'spikiness'. We have found that a good estimator is given by a count of the number of 'spikes' (defined by a specific numerical recipe) and not by the rms deviations from either a pre-burst background or any type of moving average background. The application of this parameter to 30 burst time histories shows it to be consistent over a wide range of profile types. The analysis also reveals a preferred average time between spikes of approximately 1.5 seconds.

Lestrade, John P.↗

NASA NTRS2002

Locally-Based Kernal PLS Smoothing to Non-Parametric Regression Curve Fitting

We present a novel smoothing approach to non-parametric regression curve fitting. This is based on kernel partial least squares (PLS) regression in reproducing kernel Hilbert space. It is our concern to apply the methodology for smoothing experimental data where some level of knowledge about the approximate shape, local inhomogeneities or points where the desired function changes its curvature is known a priori or can be derived based on the observed noisy data. We propose locally-based kernel PLS regression that extends the previous kernel PLS methodology by incorporating this knowledge. We compare our approach with existing smoothing splines, hybrid adaptive splines and wavelet shrinkage techniques on two generated data sets.

Rosipal, Roman↗

NASA NTRS1992

A variational method for finite element stress recovery: Applications in one-dimension

It is well-known that stresses (and strains) calculated by a displacement-based finite element analysis are generally not as accurate as the displacements. In addition, the calculated stress field is typically discontinuous at element interfaces. Because the stresses are typically of more interest than the displacements, several procedures have been proposed to obtain a smooth stress field, given the finite element stresses, and to improve the accuracy. Hinton and Irons introduced global least squares smoothing of discrete data defined on a plane using a finite element formulation. Tessler and co-workers recently developed a conceptually similar formulation for smoothing of two-dimensional data based on a discrete least square approximation with a penalty constraint. The penalty constraint results in a stress field which is C(exp 1)-continuous, a result not previously obtained. The approach requires additional, 'smoothing' finite element analysis and for their two-dimensional application, they used a conforming C(exp 0)-continuous triangular finite element based on a conforming plate element. This paper presents the results of a detailed investigation into the application of Tessler's smoothing procedure to the smoothing of finite element stresses from one-dimensional problems. Although the one-dimensional formulation has some practical applicability, such as in truss, beam, axisymmetric mechanics, and one-dimensional heat conduction, the primary motivation for developing the one-dimensional smoothing case is to explore the characteristics of the general smoothing strategy. In particular, it is used to describe the behavior of the method and to explore the suitability of criteria proposed for the smoothing analysis. Prior to presenting numerical results, the variational formulation of the smoothing strategy is presented and a criterion for the smoothing analysis is described.

Riggs, H. Ronald↗

NASA NTRS1971

Sensitivity of the creep-rupture properties of Waspaloy sheet to sharp-edged notches in the temperature range 1000-1400 deg F.

Time-dependent notch sensitivity of Waspaloy was observed at test temperatures from 1000 to 1300 deg F. Its occurrence in this range was dependent on the heat treatment. ?Overaging' eliminated the notch sensitivity. Optimum combination of smooth and notched specimen strengths for material solution treated at 1975 deg F were obtained by aging 24 hr at 1550 deg F. Necessary conditions for time-dependent notch sensitivity were (1) the notch specimen loads had to be below the approximate 0.2 percent offset yield strength; and (2 ) test data from smooth specimens had to indicate that small amounts of creep used up large fractions of creep-rupture life. No reasons were evident why these criteria will not prove applicable to other alloys.

Wilson, D. J.↗

NASA NTRS1993

Generating Smooth Motions For Robotic Manipulators

In improved method for generating trajectory of robotic manipulator, each straight-line segment of trajectory composed of constant-velocity main portion sandwiched between smooth acceleration at start and smooth deceleration at finish. Algorithm implementing method computes velocity in each accelerating portion as sinusoidal function of position along line. This motion chosen for two reasons: closely approximates motion of human hand along straight-line trajectory, and provides very smooth transitions between constant-velocity portion and accelerated and decelerational end portions.

Bejczy, Antal K.↗

NASA NTRS2014

On a Solar Origin for the Cosmogenic Nuclide Event of 775 A.D.

We explore requirements for a solar particle event (SPE) and flare capable of producing the cosmogenic nuclide event of 775 A.D., and review solar circumstances at that time. A solar source for 775 would require a greater than 1 GV spectrum approximately 45 times stronger than that of the intense high-energy SPE of 1956 February 23. This implies a greater than 30 MeV proton fluence (F(sub 30)) of approximately 8 × 10(exp 10) proton cm(exp −2), approximately 10 times larger than that of the strongest 3 month interval of SPE activity in the modern era. This inferred F(sub 30) value for the 775 SPE is inconsistent with the occurrence probability distribution for greater than 30 MeV solar proton events. The best guess value for the soft X-ray classification (total energy) of an associated flare is approximately X230 (approximately 9 × 10(exp 33) erg). For comparison, the flares on 2003 November 4 and 1859 September 1 had observed/inferred values of approximately X35 (approximately 10(exp 33) erg) and approximately X45 (approximately 2 × 10(exp 33) erg), respectively. The estimated size of the source active region for a approximately 10(exp 34) erg flare is approximately 2.5 times that of the largest region yet recorded. The 775 event occurred during a period of relatively low solar activity, with a peak smoothed amplitude about half that of the second half of the 20th century. The approximately 1945-1995 interval, the most active of the last approximately 2000 yr, failed to witness a SPE comparable to that required for the proposed solar event in 775. These considerations challenge a recent suggestion that the 775 event is likely of solar origin.

solar particles↗

DOE OSTI2023

Evaluating route to impact convergence of the harmonic balance method for piecewise-smooth systems

Here in this work, we investigate the applicability of the harmonic balance method (HBM) to predict periodic solutions of a single degree-of-freedom forced Duffing oscillator with freeplay nonlinearity. By studying the route to impact, which refers to a parametric study as the contact stiffness increases from soft to hard, the convergence behavior of the HBM can be understood in terms of the strength of the non-smooth forcing term. HBM results are compared to time-integration results to facilitate an evaluation of the accuracy of nonlinear periodic responses. An additional contribution of this study is to perform convergence and stability analysis specifically for isolas generated by the non-smooth nonlinearity. Residual error analysis is used to determine the approximate number of harmonics required to get results accurate to a given error tolerance. Hill’s method and Floquet theory are employed to compute the stability of periodic solutions and identify the types of bifurcations in the system.

42 ENGINEERING↗

DOE OSTI2024

Coil optimization for quasi-helically symmetric stellarator configurations

Filament-based coil optimizations are performed for several quasi-helical stellarator configurations, beginning with the one from Landreman & Paul ( Phys. Rev. Lett. , vol. 128, 2022, 035001), demonstrating that precise quasi-helical symmetry can be achieved with realistic coils. Several constraints are placed on the shape and spacing of the coils, such as low curvature and sufficient plasma–coil distance for neutron shielding. The coils resulting from this optimization have a maximum curvature 0.8 times that of the coils of the Helically Symmetric eXperiment (HSX) and a mean squared curvature 0.4 times that of the HSX coils when scaled to the same plasma minor radius. When scaled up to reactor size and magnetic field strength, no fast particle losses were found in the free-boundary configuration when simulating 5000 alpha particles launched at $3.5\,\mathrm {MeV}$ on the flux surface with a normalized toroidal flux of $s=0.5$ . An analysis of the tolerance of the coils to manufacturing errors is performed using a Gaussian process model, and the coils are found to maintain low particle losses for smooth, large-scale errors up to amplitudes of approximately $0.15\,\mathrm {m}$ . Another coil optimization is performed for the Landreman–Paul configuration with the additional constraint that the coils are purely planar. Visual inspection of the Poincaré plot of the resulting magnetic field-lines reveal that the planar modular coils alone do a poor job of reproducing the target equilibrium. Additional non-planar coil optimizations are performed for the quasi-helical configuration with $5\,\%$ volume-averaged plasma beta from Landreman et al. ( Phys. Plasma , vol. 29, issue 8, 2022, 082501), and a similar configuration also optimized to satisfy the Mercier criterion. The finite beta configurations had larger fast-particle losses, with the free-boundary Mercier-optimized configuration performing the worst, losing approximately $5.5\,\%$ of alpha particles launched at $s=0.5$ .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Automating NISQ Application Design with Meta Quantum Circuits with Constraints (MQCC)

Near-term intermediate scale quantum (NISQ) computers are likely to have very restricted hardware resources, where precisely controllable qubits are expensive, error-prone, and scarce. Programmers of such computers must therefore balance trade-offs among a large number of (potentially heterogeneous) factors specific to the targeted application and quantum hardware. To assist them, we propose Meta Quantum Circuits with Constraints (MQCC), a meta-programming framework for quantum programs. Programmers express their application as a succinct collection of normal quantum circuits stitched together by a set of (manually or automatically) added meta-level choice variables, whose values are constrained according to a programmable set of quantitative optimization criteria. MQCC’s compiler generates the appropriate constraints and solves them via an SMT solver, producing an optimized, runnable program. We showcase a few MQCC’s applications for its generality including an automatic generation of efficient error syndrome extraction schemes for fault-tolerant quantum error correction with heterogeneous qubits and an approach to writing approximate quantum Fourier transformation and quantum phase estimation that smoothly trades off accuracy and resource use. We also illustrate that MQCC can easily encode prior one-off NISQ application designs-–multi-programming (MP), crosstalk mitigation (CM)—as well as a combination of their optimization goals (i.e., a combined MP-CM).

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

Nonlinear estimation theory applied to orbit determination

The development of an approximate nonlinear filter using the Martingale theory and appropriate smoothing properties is considered. Both the first order and the second order moments were estimated. The filter developed can be classified as a modified Gaussian second order filter. Its performance was evaluated in a simulated study of the problem of estimating the state of an interplanetary space vehicle during both a simulated Jupiter flyby and a simulated Jupiter orbiter mission. In addition to the modified Gaussian second order filter, the modified truncated second order filter was also evaluated in the simulated study. Results obtained with each of these filters were compared with numerical results obtained with the extended Kalman filter and the performance of each filter is determined by comparison with the actual estimation errors. The simulations were designed to determine the effects of the second order terms in the dynamic state relations, the observation state relations, and the Kalman gain compensation term. It is shown that the Kalman gain-compensated filter which includes only the Kalman gain compensation term is superior to all of the other filters.

Choe, C. Y.↗

NASA NTRS1986

Exhaust-Gas Pressure and Temperature Survey of F404-GE-400 Turbofan Engine

An exhaust-gas pressure and temperature survey of the General Electric F404-GE-400 turbofan engine was conducted in the altitude test facility of the NASA Lewis Propulsion System Laboratory. Traversals by a survey rake were made across the exhaust-nozzle exit to measure the pitot pressure and total temperature. Tests were performed at Mach 0.87 and a 24,000-ft altitude and at Mach 0.30 and a 30,000-ft altitude with various power settings from intermediate to maximum afterburning. Data yielded smooth pressure and temperature profiles with maximum jet temperatures approximately 1.4 in. inside the nozzle edge and maximum jet temperatures from 1 to 3 in. inside the edge. A low-pressure region located exactly at engine center was noted. The maximum temperature encountered was 3800 R.

Walton, James T.↗

NASA NTRS1992

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

Cannizzaro, Frank E.↗

NASA NTRS1994

Luminosity effects and the emission-line properties of quasars with 0 less than z less than 3.8

We present data and a spectral atlas for 76 quasars with 2.97 less than z less than 3.80 and for 33 quasars with z approximately 2, together with measures of 73 quasars from the IUE archives that mostly have z less than 1. The quasars provide a sampling of the luminosity-redshift plane at constant luminosity for 0 less than z less than 3.8, a range of a factor of 40 in luminosity for 3 less than z less than 3.8, and a range of 10(exp 3) in luminosity for z less than 1. We investigate the behavior of the principle emission lines from 1200-2000 A and find: (1) The Baldwin effect at z greater than 3 is definitely present in the C IV lambda 1549 line and in the other strong emission lines in varying degrees except for N v lambda-lambda(1240) and 1400, where the effect is very weak. (2) The component that varies with luminosity has a narrower full width at half maximum (FWHM) than the average line width and appears consistent with the first component of the principal component analysis of the Large Bright Quasar Survey sample by Francis et al. (1992). (3) There is no evidence for redshifted-dependent spectral changes, Baldwin or otherwise, in quasars of the same luminosity in the z approximately 2 and z greater than 3 samples. (4) The Baldwin effect in the IUE, z approximately 2, and z greater than 3 subsamples joins smoothly, although the slope of the effect steepens with increasing luminosity. (5) The results are consistent with the ionization parameter decreasing with increasing luminosity. (6) The large ratio of N v to Ly-alpha and its small change with luminosity are consistent with the arguments of Hamann & Ferland (1993a, b) that the N/C ratio is enhanced in high-luminosity quasars with z greater than 3.

Osmer, Patrick S.↗

NASA NTRS1995

Filtering Image Records Using Wavelets and the Zakai Equation

Consider the problem of detecting and localizing a faint object moving In an "essentially stationary" background, using a sequence of two-dimensional low-SNR images of the scene. A natural approach consists of "digitizing" each snapshot into a discrete set of observations, sufficiently (perhaps not exactly) matched to the object In question, then tracking the object using an appropriate stochastic filter. The tracking would be expected to make up for the low signal-to-noise ratio, this allowing one to "coherently" process successive images in order to beat down the noise and localize the object. Thus, "tracking" here does not refer to the usual notion of detecting then tracking: rather, we track in order to detect The problem then becomes one of choosing the appropriate image representation as well as the optimal (and necessarily nonlinear filter. We propose exact and approximate solutions using wavelets and the Zakai equation. The smoothness of the wavelets used is required in the derivation of the evolution equation for the conditional density giving the filter, and their orthogonality makes it possible to carry out actual computations of the Ito- and change-of-gauge-terms in the algorithm effectively.

Haddad, Ziad S.↗

NASA NTRS2001

Astrobiology Investigations at a Martian Hematite Site

Christensen et al, using data from the Mars Global Surveyor Thermal Emission Spectrometer (TES), have identified gray crystalline hematite in a 350 km by 750 km region near Sinus Meridiani. The deposit corresponds closely to the low-albedo highlands unit 'sm', mapped as a wind-eroded, ancient, subaqueous sedimentary deposit. Christensen et al interpreted the Sinus Meridiani deposit to be 'an in-place, rock-stratigraphic sedimentary unit characterized by smooth, friable layers composed primarily of basaltic sediments with approximately 10 to 15 % crystalline gray hematite.' Christensen et al discussed five possible mechanisms for the formation of this deposit: direct precipitation from standing, oxygenated, Fe-rich water; precipitation from Fe-rich hydrothermal fluids; low-temperature dissolution and precipitation through mobile groundwater leaching; surface weathering and coatings; thermal oxidation of magnetite-rich lavas. Four of these mechanisms involve the interactions of rock with water, and thus have implications in the search for evidence of microbial life.

Allen, Carlton, C.↗

NASA NTRS2003

Meridiani Planum Hematite Deposit: Potential for Preservation of Microfossils

Christensen et al., using data from the Mars Global Surveyor Thermal Emission Spectrometer (TES), have identified gray crystalline hematite in a 350 km by 750 km region near Meridiani Planum. The deposit corresponds closely to the low-albedo highlands unit sm, mapped as a wind-eroded, ancient, subaqueous sedimentary deposit. Christensen et al. interpreted the Meridiani Planum deposit to be an in-place, rock-stratigraphic sedimentary unit characterized by smooth, friable layers composed primarily of basaltic sediments with approximately 10 to 15% crystalline gray hematite. The Meridiani Planum hematite deposit has recently been designated as the prime landing site for one of the two Mars Exploration Rover (MER) spacecraft. The MER landings are scheduled for January, 2004. Christensen et al. discussed five possible mechanisms for the formation of this deposit: direct precipitation from standing, oxygenated, Fe-rich water; precipitation from Fe-rich hydrothermal fluids; low-temperature dissolution and precipitation through mobile groundwater leaching; surface weathering and coatings; thermal oxidation of magnetite-rich lavas. Four of these mechanisms involve the interactions of rock with water, and thus have implications in the search for evidence of microbial life.

C C Allen↗

NASA NTRS2014

Discovery of Finely Structured Dynamic Solar Corona Observed in the Hi-C Telescope

In the summer of 2012, the High-resolution Coronal Imager (Hi-C) flew aboard a NASA sounding rocket and collected the highest spatial resolution images ever obtained of the solar corona. One of the goals of the Hi-C flight was to characterize the substructure of the solar corona. We therefore examine how the intensity scales from AIA resolution to Hi-C resolution. For each low-resolution pixel, we calculate the standard deviation in the contributing high-resolution pixel intensities and compare that to the expected standard deviation calculated from the noise. If these numbers are approximately equal, the corona can be assumed to be smoothly varying, i.e. have no evidence of substructure in the Hi-C image to within Hi-C's ability to measure it given its throughput and readout noise. A standard deviation much larger than the noise value indicates the presence of substructure. We calculate these values for each low-resolution pixel for each frame of the Hi-C data. On average, 70 percent of the pixels in each Hi-C image show no evidence of substructure. The locations where substructure is prevalent is in the moss regions and in regions of sheared magnetic field. We also find that the level of substructure varies significantly over the roughly 160 s of the Hi-C data analyzed here. This result indicates that the finely structured corona is concentrated in regions of heating and is highly time dependent.

Winebarger, A.↗

NASA NTRS1996

Wavelet Sparse Approximate Inverse Preconditioners

There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.

Chan, Tony F.↗