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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Upper bounds for convergence rates of vector extrapolation methods on linear systems with initial iterations

The application of the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE) to a vector sequence obtained by the linear iterative technique x(sub j) + 1 = Ax(sub j) = b,j = 1,2,..., is considered. Both methods produce a two dimensional array of approximations s(sub n,k) to the solution of the system (I - A)x = b. Here, s(sub n,k) is obtained from the vectors x(sub j), n is less than or equal to j is less than or equal to n + k + 1. It was observed in an earlier publication by the first author that the sequence s(sub n,k), k = 1,2,..., for n greater than 0, but fixed, possesses better convergence properties than the sequence s(sub 0,k), k = 1,2,.... A detailed theoretical explanation for this phenomenon is provided in the present work. This explanation is heavily based on approximations by incomplete polynomials. It is demonstrated by numerical examples when the matrix A is sparse that cycling with s(sub n,k) for n greater than 0, but fixed, produces better convergence rates and costs less computationally than cycling with s(sub 0,k). It is also illustrated numerically with a convection-diffusion problem that the former may produce excellent results where the latter may fail completely. As has been shown in an earlier publication, the results produced by s(sub 0,k) are identical to the corresponding results obtained by applying the Arnoldi method or generalized minimal residual scheme (GMRES) to the system (I - A)x = b.

Sidi, Avram↗
DOE OSTI2019

Comparing smoothing techniques for extracting MOSFET threshold voltage

Measurement noise acts as a barrier to the accurate calculation of threshold voltage by derivative-based extraction methods. We examined several smoothing techniques and their effects on measurement noise in threshold voltage extracted by the linear extrapolation method and the g m /I d method. We applied these techniques on a set of SiC power MOSFET devices before and after they had undergone accelerated thermal testing. The smoothing methods examined are least-squares polynomial fitting, low-pass filtering using Butterworth and Chebyshev fillers, and differential smoothing. These methods are compared by their shift in threshold voltage compared to unsmoothed data and their standard deviation among the measurements of each device. All methods performed poorly at smoothing when extracting via the g m /I d due to the large amounts of high-magnitude subthreshold noise, mostly tending to extract threshold voltages far below the expected value. Differential smoothing provided results closest to the expected value with an absolute shift of 1.2 V on average. The smoothing methods performed better with the LE method. On a failed device, all smoothing methods except polynomial smoothing preserved the large threshold voltage anomaly for four out of five measurements. These results show that choice of smoothing method, if used must be evaluated based on the device and extraction method.

42 ENGINEERING↗
DOE OSTI2024

Development of a Full-Scale Connected U-Net for Reflectivity Inpainting in Spaceborne Radar Blind Zones

CloudSat’s Cloud Profiling Radar is a valuable tool for remotely monitoring high-latitude snowfall, but its ability to observe hydrometeor activity near the Earth’s surface is limited by a radar blind zone caused by ground clutter contamination. This study presents the development of a deeply supervised U-Net-style convolutional neural network to predict cold season reflectivity profiles within the blind zone at two Arctic locations. The network learns to predict the presence and intensity of near-surface hydrometeors by coupling latent features encoded in blind zone-aloft clouds with additional context from collocated atmospheric state variables (i.e., temperature, specific humidity, and wind speed). Results show that the U-Net predictions outperform traditional linear extrapolation methods, with low mean absolute error, a 38% higher Sørensen–Dice coefficient, and vertical reflectivity distributions 60% closer to observed values. The U-Net is also able to detect the presence of near-surface cloud with a critical success index (CSI) of 72% and cases of shallow cumuliform snowfall and virga with 18% higher CSI values compared to linear methods. An explainability analysis shows that reflectivity information throughout the scene, especially at cloud edges and at the 1.2-km blind zone threshold, along with atmospheric state variables near the tropopause, are the most significant contributors to model skill. This surface-trained generative inpainting technique has the potential to enhance current and future remote sensing precipitation missions by providing a better understanding of the nonlinear relationship between blind zone reflectivity values and the surrounding atmospheric state.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Methods for Measuring and Computing the Reference Temperature in Newton’s Law of Cooling for External Flows

Newton’s law of cooling requires a reference temperature (𝑇 𝑟𝑒𝑓 ) to define the heat-transfer coefficient (ℎ). For external flows with multiple temperatures in the freestream, obtaining 𝑇 𝑟𝑒𝑓 is a challenge. One widely used method, referred to as the adiabatic-wall (AW) method, obtains 𝑇 𝑟𝑒𝑓 by requiring the surface of the solid exposed to convective heat transfer to be adiabatic. Another widely used method, referred to as the linear-extrapolation (LE) method, obtains 𝑇 𝑟𝑒𝑓 by measuring/computing the heat flux ($𝑞^{′′}_𝑠$) on the solid surface at two different surface temperatures (𝑇 𝑠 ) and then linearly extrapolating to $𝑞^{′′}_𝑠$ = 0. A third recently developed method, referred to as the state-space (SS) method, obtains 𝑇 𝑟𝑒𝑓 by probing the temperature space between the highest and lowest in the flow to account for the effects of 𝑇 𝑠 or $𝑞^{′′}_𝑠$ on 𝑇 𝑟𝑒𝑓 . This study examines the foundation and accuracy of these methods via a test problem involving film cooling of a flat plate where $𝑞^{′′}_𝑠$ switches signs on the plate’s surface. Results obtained show that only the SS method could guarantee a unique and physically meaningful 𝑇 𝑟𝑒𝑓 where 𝑇 𝑠 =𝑇 𝑟𝑒𝑓 on a nonadiabatic surface $𝑞^{′′}_𝑠$ = 0. The AW and LE methods both assume 𝑇 𝑟𝑒𝑓 to be independent of 𝑇 𝑠 , which the SS method shows to be incorrect. Though this study also showed the adiabatic-wall temperature, 𝑇 𝐴𝑊 , to be a good approximation of 𝑇 𝑟𝑒𝑓 (<10% relative error), huge errors can occur in ℎ about the solid surface where |𝑇 𝑠 −𝑇 𝐴𝑊 | is near zero because where 𝑇 𝑠 =𝑇 𝐴𝑊 , $𝑞^{′′}_𝑠$ ≠ 0.

Newton's law of cooling↗
NASA NTRS2017

Mixed Convection Blowoff Limits as a Function of Oxygen Concentration and Upward Forced Stretch Rate for Burning Pmma Rods of Various Sizes

Normal gravity flame blowoff limits in an axisymmetric pmma rod geometry in upward axial stagnation flow are compared with microgravity Burning and Suppression of Solids II (BASS-II) results recently obtained aboard the International Space Station. This testing utilized the same BASS-II concurrent rod geometry, but with the addition of normal gravity buoyant flow. Cast polymethylmethacrylate (pmma) rods of diameters ranging from 0.635 cm to 3.81 cm were burned at oxygen concentrations ranging from 14 to 18 by volume. The forced flow velocity where blowoff occurred was determined for each rod size and oxygen concentration. These blowoff limits compare favorably with the BASS-II results when the buoyant stretch is included and the flow is corrected by considering the blockage factor of the fuel. From these results, the normal gravity blowoff boundary for this axisymmetric rod geometry is determined to be linear, with oxygen concentration directly proportional to flow speed. We describe a new normal gravity upward flame spread test method which extrapolates the linear blowoff boundary to the zero stretch limit to resolve microgravity flammability limits, something current methods cannot do. This new test method can improve spacecraft fire safety for future exploration missions by providing a tractable way to obtain good estimates of material flammability in low gravity.

blowoff↗
NASA NTRS2016

Correlation of Normal Gravity Mixed Convection Blowoff Limits with Microgravity Forced Flow Blowoff Limits

The axisymmetric rod geometry in upward axial stagnation flow provides a simple way to measure normal gravity blowoff limits to compare with microgravity Burning and Suppression of Solids - II (BASS-II) results recently obtained aboard the International Space Station. This testing utilized the same BASS-II concurrent rod geometry, but with the addition of normal gravity buoyant flow. Cast polymethylmethacrylate (PMMA) rods of diameters ranging from 0.635 cm to 3.81 cm were burned at oxygen concentrations ranging from 14 to 18% by volume. The forced flow velocity where blowoff occurred was determined for each rod size and oxygen concentration. These blowoff limits compare favorably with the BASS-II results when the buoyant stretch is included and the flow is corrected by considering the blockage factor of the fuel. From these results, the normal gravity blowoff boundary for this axisymmetric rod geometry is determined to be linear, with oxygen concentration directly proportional to flow speed. We describe a new normal gravity 'upward flame spread test' method which extrapolates the linear blowoff boundary to the zero stretch limit in order to resolve microgravity flammability limits-something current methods cannot do. This new test method can improve spacecraft fire safety for future exploration missions by providing a tractable way to obtain good estimates of material flammability in low gravity.

microgravity↗
NASA NTRS1991

Sonic boom predictions for three generic models using a solution-adaptive full-potential code

The TranAir full-potential code, which utilizes a solution-adaptive, unstructured Cartesian grid, was used to compute near-field pressure signatures of three generic supersonic configurations: a cone-cylinder, a low aspect ratio rectangular wing, and a delta-wing/body. TranAir pressure signatures are extrapolated to near- and mid-field distances using a quasi-linear extrapolation technique. Results are compared with existing wind tunnel data and, where possible, with extrapolated experimental data and quasi-linear Whitham-method results. In general, the extrapolated TranAir data is in good agreement with experimental and Whitham-method pressure signatures, but peak pressures are slightly under-predicted. It is thought that computed data obtained too near to the model was the main reason for the discrepancies. Flow-field grid structure was also found to be important in obtaining accurate offbody data.

Madson, Michael D.↗
NASA NTRS2017

CLASP2: The Chromospheric LAyer Spectro-Polarimeter

A major remaining challenge for heliophysicsis to decipher the magnetic structure of the chromosphere, due to its "large role in defining how energy is transported into the corona and solar wind" (NASA's Heliophysics Roadmap). Recent observational advances enabled by the Interface Region Imaging Spectrometer (IRIS) have revolutionized our view of the critical role this highly dynamic interface between the photosphere and corona plays in energizing and structuring the outer solar atmosphere. Despite these advances, a major impediment to better understanding the solar atmosphere is our lack of empirical knowledge regarding the direction and strength of the magnetic field in the upper chromosphere. Such measurements are crucial to address several major unresolved issues in solar physics: for example, to constrain the energy flux carried by the Alfven waves propagating through the chromosphere (De Pontieuet al., 2014), and to determine the height at which the plasma Beta = 1 transition occurs, which has important consequences for the braiding of magnetic fields (Cirtainet al., 2013; Guerreiroet al., 2014), for propagation and mode conversion of waves (Tian et al., 2014a; Straus et al., 2008) and for non-linear force-free extrapolation methods that are key to determining what drives instabilities such as flares or coronal mass ejections (e.g.,De Rosa et al., 2009). The most reliable method used to determine the solar magnetic field vector is the observation and interpretation of polarization signals in spectral lines, associated with the Zeeman and Hanle effects. Magnetically sensitive ultraviolet spectral lines formed in the upper chromosphere and transition region provide a powerful tool with which to probe this key boundary region (e.g., Trujillo Bueno, 2014). Probing the magnetic nature of the chromosphere requires measurement of the Stokes I, Q, U and V profiles of the relevant spectral lines (of which Q, U and V encode the magnetic field information).

Chromosphere↗
NASA NTRS2017

CLASP2: The Chromospheric LAyer Spectro-Polarimeter

A major remaining challenge for heliophysicsis to decipher the magnetic structure of the chromosphere, due to its 'large role in defining how energy is transported into the corona and solar wind' (NASA's Heliophysics Roadmap). Recent observational advances enabled by the Interface Region Imaging Spectrometer (IRIS) have revolutionized our view of the critical role this highly dynamic interface between the photosphere and corona plays in energizing and structuring the outer solar atmosphere. Despite these advances, a major impediment to better understanding the solar atmosphere is our lack of empirical knowledge regarding the direction and strength of the magnetic field in the upper chromosphere. Such measurements are crucial to address several major unresolved issues in solar physics: for example, to constrain the energy flux carried by the Alfven waves propagating through the chromosphere (De Pontieuet al., 2014), and to determine the height at which the plasma β = 1 transition occurs, which has important consequences for the braiding of magnetic fields (Cirtainet al., 2013; Guerreiroet al., 2014), for propagation and mode conversion of waves (Tian et al., 2014a; Straus et al., 2008) and for non-linear force-free extrapolation methods that are key to determining what drives instabilities such as flares or coronal mass ejections (e.g., De Rosa et al., 2009). The most reliable method used to determine the solar magnetic field vector is the observation and interpretation of polarization signals in spectral lines, associated with the Zeeman and Hanle effects. Magnetically sensitive ultraviolet spectral lines formed in the upper chromosphere and transition region provide a powerful tool with which to probe this key boundary region (e.g., Trujillo Bueno, 2014). Probing the magnetic nature of the chromosphere requires measurement of the Stokes I, Q, U and V profiles of the relevant spectral lines (of which Q, U and V encode the magnetic field information).

Solar; Chromosphere; Polarization↗
NASA NTRSDate not supplied

Space-based UV Spectropolarimetry for Chromospheric Magnetic Field Measurements

High-resolution observations with space-and ground-based telescopes, along with advanced numerical modeling, have highlighted the intricate coupling between the chromosphere, transition region, and corona, and the critical role the chromosphere plays in the mass and energy balance of the outer solar atmosphere. Despite these recent advances, a major impediment to better understanding the solar atmosphere is our lack of empirical knowledge regarding the direction and strength of the magnetic field in the upper chromosphere (Decadal Survey, 2012). Such measurements are crucial to address several major unresolved issues in solar physics: for example, to constrain the energy flux carried by the Alfvén waves propagating through the chromosphere, and to determine the height at which the plasma β = 1 transition occurs, which has important consequences for the braiding of magnetic fields, for propagation and mode conversion of waves and for non-linear force-free extrapolation methods that are key to determining what drives instabilities such as flares or coronal mass ejections. Probing the magnetic nature of the Sun’s atmosphere requires measurement of the Stokes I, Q, U and V profiles of relevant spectral lines (of which Q, U and V encode the magnetic field information). Many of the magnetically sensitive lines formed in the chromosphere and transition region are in the ultraviolet spectrum, necessitating observations above the absorbing terrestrial atmosphere. The Chromospheric Layer Spectro-Polarimeter (“CLASP2”) sounding rocket was flown successfully in April 2019, as a follow-on to the successful flight in September 2015 of the Chromospheric Lyman-Alpha Spectro-Polarimeter (“CLASP1”). In October of 2021, we re-flew the CLASP2 experiment with a modified observing program to further demonstrate the maturity of the UV spectropolarimetry techniques, and readiness for development into a satellite observatory. During the reflight, called “CLASP2.1”, the spectrograph slit was scanned across an active region plage to acquire a two-dimensional map of Stokes V/I, to demonstrate the ability of UV spectropolarimetry to yield chromospheric magnetic fields over a large area.

David E McKenzie↗
NASA NTRS2011

Method and System for Temporal Filtering in Video Compression Systems

Three related innovations combine improved non-linear motion estimation, video coding, and video compression. The first system comprises a method in which side information is generated using an adaptive, non-linear motion model. This method enables extrapolating and interpolating a visual signal, including determining the first motion vector between the first pixel position in a first image to a second pixel position in a second image; determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image; determining a third motion vector between the first pixel position in the first image and the second pixel position in the second image, the second pixel position in the second image, and the third pixel position in the third image using a non-linear model; and determining a position of the fourth pixel in a fourth image based upon the third motion vector. For the video compression element, the video encoder has low computational complexity and high compression efficiency. The disclosed system comprises a video encoder and a decoder. The encoder converts the source frame into a space-frequency representation, estimates the conditional statistics of at least one vector of space-frequency coefficients with similar frequencies, and is conditioned on previously encoded data. It estimates an encoding rate based on the conditional statistics and applies a Slepian-Wolf code with the computed encoding rate. The method for decoding includes generating a side-information vector of frequency coefficients based on previously decoded source data and encoder statistics and previous reconstructions of the source frequency vector. It also performs Slepian-Wolf decoding of a source frequency vector based on the generated side-information and the Slepian-Wolf code bits. The video coding element includes receiving a first reference frame having a first pixel value at a first pixel position, a second reference frame having a second pixel value at a second pixel position, and a third reference frame having a third pixel value at a third pixel position. It determines a first motion vector between the first pixel position and the second pixel position, a second motion vector between the second pixel position and the third pixel position, and a fourth pixel value for a fourth frame based upon a linear or nonlinear combination of the first pixel value, the second pixel value, and the third pixel value. A stationary filtering process determines the estimated pixel values. The parameters of the filter may be predetermined constants.

Lu, Ligang↗
NASA NTRS1961

Semiempirical Theories of the Affinities of Negative Atomic Ions

The determination of the electron affinities of negative atomic ions by means of direct experimental investigation is limited. To supplement the meager experimental results, several semiempirical theories have been advanced. One commonly used technique involves extrapolating the electron affinities along the isoelectronic sequences, The most recent of these extrapolations Is studied by extending the method to Include one more member of the isoelectronic sequence, When the results show that this extension does not increase the accuracy of the calculations, several possible explanations for this situation are explored. A different approach to the problem is suggested by the regularities appearing in the electron affinities. Noting that the regular linear pattern that exists for the ionization potentials of the p electrons as a function of Z, repeats itself for different degrees of ionization q, the slopes and intercepts of these curves are extrapolated to the case of the negative Ion. The method is placed on a theoretical basis by calculating the Slater parameters as functions of q and n, the number of equivalent p-electrons. These functions are no more than quadratic in q and n. The electron affinities are calculated by extending the linear relations that exist for the neutral atoms and positive ions to the negative ions. The extrapolated. slopes are apparently correct, but the intercepts must be slightly altered to agree with experiment. For this purpose one or two experimental affinities (depending on the extrapolation method) are used in each of the two short periods. The two extrapolation methods used are: (A) an isoelectronic sequence extrapolation of the linear pattern as such; (B) the same extrapolation of a linearization of this pattern (configuration centers) combined with an extrapolation of the other terms of the ground configurations. The latter method Is preferable, since it requires only experimental point for each period. The results agree within experimental error with all data, except with the most recent value of C, which lies 10% lower.

Edie, John W.↗
NASA NTRS1996

The Hot Bands of Methane Between 5 and 10(micro)m

Experimental line intensities of 1727 transitions arising from nine hot bands in the pentad-dyad system of methane are fitted to first and second order using the effective dipole moment expansion in the polyad scheme. The observed bands are V3-V2, V3-V4, V1-V2, V1-V4, 2V4-V4, V2+V4-V2, V2+V4-V4, 2V2-V4, and the intensities are obtained from long-path spectra recorded with the Fourier transform spectrometer located at Kitt Peak National Observatory. For the second order model, some of the 27 intensity parameters are not linearly independant, and so two methods (extrapolation and effective parameters) are propopsed to model the intensities of the hot bands.

methane hot bands dipole moment expansion Kitt Pea↗
NASA NTRS2011

Method and system for non-linear motion estimation

A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.

Lu, Ligang↗
NASA NTRS1987

An algorithm for a generalization of the Richardson extrapolation process

The paper presents a recursive method, designated the W exp (m)-algorithm, for implementing a generalization of the Richardson extrapolation process. Compared to the direct solution of the linear sytems of equations defining the extrapolation procedure, this method requires a small number of arithmetic operations and very little storage. The technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying a d-transformation to power series. In the course of development a new recursive algorithm for implementing a very general extrapolation procedure is introduced, for solving the same problem. A FORTRAN program for the W exp (m)-algorithm is also appended.

Ford, William F.↗
NASA NTRS1992

Ground signature extrapolation of three-dimensional near-field CFD predictions for several HSCT configurations

A CFD analysis of the near-field sonic boom environment of several low boom High Speed Civilian Transport (HSCT) concepts is presented. The CFD method utilizes a multi-block Euler marching code within the context of an innovative mesh topology that allows for the resolution of shock waves several body lengths from the aircraft. Three-dimensional pressure footprints at one body length below three-different low boom aircraft concepts are presented. Models of two concepts designed by NASA to cruise at Mach 2 and Mach 3 were built and tested in the wind tunnel. The third concept was designed by Boeing to cruise at Mach 1.7. Centerline and sideline samples of these footprints are then extrapolated to the ground using a linear waveform parameter method to estimate the ground signatures or sonic boom ground overpressure levels. The Mach 2 concept achieved its centerline design signature but indicated higher sideline booms due to the outboard wing crank of the configuration. Nacelles are also included on two of NASA's low boom concepts. Computations are carried out for both flow-through nacelles and nacelles with engine exhaust simulation. The flow-through nacelles with the assumption of zero spillage and zero inlet lip radius showed very little effect on the sonic boom signatures. On the other hand, it was shown that the engine exhaust plumes can have an effect on the levels of overpressure reaching the ground depending on the engine operating conditions. The results of this study indicate that engine integration into a low boom design should be given some attention.

Siclari, M. J.↗
DOE OSTI2021

Extending quantum probabilistic error cancellation by noise scaling

Here, we propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similar to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device’s noise model, e.g., avoiding gate-set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), leading to partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise-reduction factors can be further postprocessed with ZNE to better approximate the zero-noise limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1989

Quotient-difference type generalizations of the power method and their analysis

The recursion relations that were proposed by W. F. Ford and A. Sidi (Appl. Numer. Math, 4 (1988), pp. 477-489) for implementing vector extrapolation methods are used for devising generalizations of the power method for linear operators. These generalizations are shown to produce approximations to largest eigenvalues of a linear operator under certain conditions. They are similar in form to the quotient-difference algorithm and share similar convergence properties with the latter. These convergence properties also resemble those obtained for the basic LR and QR algorithms. Finally, it is shown that the convergence rate produced by one fo these generalizations is twice as fast for normal operators as it is for nonnormal operators.

Sidi, Avram↗