Search NASA⌕ Search

SEARCH · Search NASA

Results for “Root %N”

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 217 records · Page 12

A fast, preconditioned conjugate gradient Toeplitz solver

A simple factorization is given of an arbitrary hermitian, positive definite matrix in which the factors are well-conditioned, hermitian, and positive definite. In fact, given knowledge of the extreme eigenvalues of the original matrix A, an optimal improvement can be achieved, making the condition numbers of each of the two factors equal to the square root of the condition number of A. This technique is to applied to the solution of hermitian, positive definite Toeplitz systems. Large linear systems with hermitian, positive definite Toeplitz matrices arise in some signal processing applications. A stable fast algorithm is given for solving these systems that is based on the preconditioned conjugate gradient method. The algorithm exploits Toeplitz structure to reduce the cost of an iteration to O(n log n) by applying the fast Fourier Transform to compute matrix-vector products. Matrix factorization is used as a preconditioner.

Pan, Victor↗

The Influence of Observation Errors on Analysis Error and Forecast Skill Investigated with an Observing System Simulation Experiment

The Global Modeling and Assimilation Office (GMAO) observing system simulation experiment (OSSE) framework is used to explore the response of analysis error and forecast skill to observation quality. In an OSSE, synthetic observations may be created that have much smaller error than real observations, and precisely quantified error may be applied to these synthetic observations. Three experiments are performed in which synthetic observations with magnitudes of applied observation error that vary from zero to twice the estimated realistic error are ingested into the Goddard Earth Observing System Model (GEOS-5) with Gridpoint Statistical Interpolation (GSI) data assimilation for a one-month period representing July. The analysis increment and observation innovation are strongly impacted by observation error, with much larger variances for increased observation error. The analysis quality is degraded by increased observation error, but the change in root-mean-square error of the analysis state is small relative to the total analysis error. Surprisingly, in the 120 hour forecast increased observation error only yields a slight decline in forecast skill in the extratropics, and no discernable degradation of forecast skill in the tropics.

Observation Error↗

Necklaces, symmetries and self-reciprocal polynomials

The connection between a certain class of necklaces and self-reciprocal polynomials over finite fields is shown. For equal to or greater than 2, self-reciprocal polynomials of degree 2n arising from monic irreducible polynomials of degree n are shown to be either irreducible or the product of two irreducible factors which are necessarily reciprocal polynomials. DeBruijn's (1959) method is used to count the number of necklaces in this class and hence obtain a formula for the number of irreducible self-reciprocal polynomials, showing that they exist for every even degree. Thus every extension of a finite field of even degree can be obtained by adjoining a root of an irreducible self-reciprocal polynomial.

Miller, R. L.↗

Finite element analysis of notch behavior using a state variable constitutive equation

The state variable constitutive equation of Bodner and Partom was used to calculate the load-strain response of Inconel 718 at 649 C in the root of a notch. The constitutive equation was used with the Bodner-Partom evolution equation and with a second evolution equation that was derived from a potential function of the stress and state variable. Data used in determining constants for the constitutive models was from one-dimensional smooth bar tests. The response was calculated for a plane stress condition at the root of the notch with a finite element code using constant strain triangular elements. Results from both evolution equations compared favorably with the observed experimental response. The accuracy and efficiency of the finite element calculations also compared favorably to existing methods.

Dame, L. T.↗

Sub-Femto-g Free Fall for Space-Based Gravitational Wave Observatories: LISA Pathfinder Results

We report the first results of the LISA Pathfinder in-flight experiment. The results demonstrate that two free-falling reference test masses, such as those needed for a space-based gravitational wave observatory like LISA, can be put in free fall with a relative acceleration noise with a square root of the power spectral density of 5.2 +/- 0.1 fm s(exp -2)/square root of Hz, or (0.54 +/- 0.01) x 10(exp -15) g/square root of Hz, with g the standard gravity, for frequencies between 0.7 and 20 mHz. This value is lower than the LISA Pathfinder requirement by more than a factor 5 and within a factor 1.25 of the requirement for the LISA mission, and is compatible with Brownian noise from viscous damping due to the residual gas surrounding the test masses. Above 60 mHz the acceleration noise is dominated by interferometer displacement readout noise at a level of (34.8 +/- 0.3) fm square root of Hz, about 2 orders of magnitude better than requirements. At f less than or equal to 0.5 mHz we observe a low-frequency tail that stays below 12 fm s(exp -2)/square root of Hz down to 0.1 mHz. This performance would allow for a space-based gravitational wave observatory with a sensitivity close to what was originally foreseen for LISA.

space science↗

Theory of the control of structures by low authority controllers

The novel idea presented is based on the observation that if a structure is controlled by distributed systems of sensors and actuators with limited authority, i.e., if the controller is allowed to modify only moderately the natural modes and frequencies of the structure, then it should be possible to apply root perturbation techniques to predict analytically the behavior of the total system. Attention is given to the root perturbation formula first derived by Jacobi for infinitesimal perturbations which neglect the induced eigenvector perturbation, a more general form of Jacobi's formula, first-order structural equations and modal state vectors, state-space equations for damper-augmented structures, and modal damping prediction formulas.

Aubrun, J. N.↗

Benchmark notch test for life prediction

The laser Interferometric Strain Displacement Gage (ISDG) was used to measure local strains in notched Inconel 718 test bars subjected to six different load histories at 649 C (1200 F) and including effects of tensile and compressive hold periods. The measurements were compared to simplified Neuber notch analysis predictions of notch root stress and strain. The actual strains incurred at the root of a discontinuity in cyclically loaded test samples subjected to inelastic deformation at high temperature where creep deformations readily occur were determined. The steady state cyclic, stress-strain response at the root of the discontinuity was analyzed. Flat, double notched uniaxially loaded fatigue specimens manufactured from the nickel base, superalloy Inconel 718 were used. The ISDG was used to obtain cycle by cycle recordings of notch root strain during continuous and hold time cycling at 649 C. Comparisons to Neuber and finite element model analyses were made. The results obtained provide a benchmark data set in high technology design where notch fatigue life is the predominant component service life limitation.

Domas, P. A.↗

Infrared temperature measurements over bare soil and vegetation - A HAPEX perspective

Preliminary analyses of aircraft and ground measurements made in France during the HAPEX experiment show that horizontal radiometric surface temperature variations, as viewed by aircraft, can reflect the vertical profile of soil moisture (soil versus root zone) because of horizontal variations in vegetation density. Analyses based on one day's data show that, although horizontal variations in soil moisture were small, the vertical differences between a dry surface and a wet root zone were large. Horizontal temperature differences between bare soil, corn and oats reflect differences in the fractional vegetation cover, as seen by the radiometer. On the other hand, these horizontal variations in radiometric surface temperature seem to reflect real horizontal variations in surface turbulent energy fluxes.

Carlson, Toby N.↗

Analysis of the Performance Characteristics of the Five-Channel Microtops II Sun Photometer for Measuring Aerosol Optical Thickness and Precipitable Water Vapor

Five Microtops II sun photometers were studied in detail at the NASA Goddard Space Flight Center (GSFC) to determine their performance in measuring aerosol optical thickness (AOT or Tau(sub alphalambda) and precipitable column water vapor (W). Each derives Tau(sub alphalambda) from measured signals at four wavelengths lambda (340, 440, 675, and 870 nm), and W from the 936 nm signal measurements. Accuracy of Tau(sub alphalambda) and W determination depends on the reliability of the relevant channel calibration coefficient (V(sub 0)). Relative calibration by transfer of parameters from a more accurate sun photometer (such as the Mauna-Loa-calibrated AERONET master sun photometer at GSFC) is more reliable than Langley calibration performed at GSFC. It was found that the factory-determined value of the instrument constant for the 936 nm filter (k= 0.7847) used in the Microtops' internal algorithm is unrealistic, causing large errors in V(sub 0(936)), Tau(sub alpha936), and W. Thus, when applied for transfer calibration at GSFC, whereas the random variation of V(aub 0) at 340 to 870 nm is quite small, with coefficients of variation (CV) in the range of 0 to 2.4%, at 936 nm the CV goes up to 19%. Also, the systematic temporal variation of V(sub 0) at 340 to 870 nm is very slow, while at 936 nm it is large and exhibits a very high dependence on W. The algorithm also computes Tau(sub alpha936) as 0.91Tau(sub alpha870), which is highly simplistic. Therefore, it is recommended to determine Tau(sub alpha936) by logarithmic extrapolation from Tau(sub alpha675) and Tau(sub alpha 870. From the operational standpoint of the Microtops, apart from errors that may result from unperceived cloud contamination, the main sources of error include inaccurate pointing to the Sun, neglecting to clean the front quartz window, and neglecting to calibrate correctly. If these three issues are adequately taken care of, the Microtops can be quite accurate and stable, with root mean square (rms) differences between corresponding retrievals from clean calibrated Microtops and the AERONET sun photometer being about +/-0.02 at 340 nm, decreasing down to about +/-0.01 at 870 nm.

Ichoku, Charles↗

Validation of Soil Moisture Data Products from the NASA SMAP Mission

The National Aeronautics and Space Administration (NASA)Soil Moisture Active Passive(SMAP) mission has been validatingits soil moisture (SM) products since the start of data production onMarch 31, 2015. Prior to launch, the mission defined a set of criteria for core validation sites (CVS) that enable the testing of the key mission SM accuracy requirement(unbiased root-mean-square error <0.04 m3/m3). Thevalidation approach also includes other (“sparse network”) in situSM measurements, satellite SM products, model-based SM products, and field experiments. Over the past six years, the SMAP SM products have been analyzed with respect to thesereference data,and the analysis approaches themselves have been scrutinizedin an effort to best understand the products’ performance. Validation of themost recent SMAP Level 2 and 3 SMretrievalproducts (R17000) shows that the L-band (1.4 GHz) radiometer-based SM record continues to meet mission requirements. The products aregenerallyconsistentwith SM retrievals from the European Space Agency (ESA)Soil Moisture Ocean Salinity mission, althoughthere aredifferencesin some regions. The high-resolution (3-km) SM retrieval product,generated by combining Copernicus Sentinel-1 data with SMAP observations,performswithin expectations. Currently, however,there is limited availability of3-kmCVSdatato support extensive validation at this spatial scale. The most recent (version 5)SMAP Level4 SMdata assimilation productprovidingsurface and root-zone SM with complete spatio-temporal coverageat 9-km resolution also meets performance requirements. The SMAP SM validation program will continue throughout the mission life; futureplans include expanding ittoforestedand high-latituderegions

SMAP↗

Mutations in a new Arabidopsis cyclophilin disrupt its interaction with protein phosphatase 2A

The heterotrimeric protein phosphatase 2A (PP2A) is a component of multiple signaling pathways in eukaryotes. Disruption of PP2A activity in Arabidopsis is known to alter auxin transport and growth response pathways. We demonstrated that the regulatory subunit A of an Arabidopsis PP2A interacts with a novel cyclophilin, ROC7. The gene for this cyclophilin encodes a protein that contains a unique 30-amino acid extension at the N-terminus, which distinguishes the gene product from all previously identified Arabidopsis cyclophilins. Altered forms of ROC7 cyclophilin with mutations in the conserved DENFKL domain did not bind to PP2A. Unlike protein phosphatase 2B, PP2A activity in Arabidopsis extracts was not affected by the presence of the cyclophilin-binding molecule cyclosporin. The ROC7 transcript was expressed to high levels in all tissues tested. Expression of an ROC7 antisense transcript gave rise to increased root growth. These results indicate that cyclophilin may have a role in regulating PP2A activity, by a mechanism that differs from that employed for cyclophilin regulation of PP2B.

NASA Discipline Plant Biology↗

Use of thermal infrared and colour infrared imagery to detect crop moisture stress

The author has identified the following significant results. In the presence of variable plant cover (primarily percent cover) and variable available water content, the remotely sensed apparent temperatures correlate closely with plant cover and poorly with soil water. To the extent that plant cover is not systematically related to available soil water, available water in the root zone values may not be reliably predicted from the thermal infrared data. On the other hand, if plant cover is uniform and the soil surface is shown in a minor way, the thermal data indicate plant stress and consequently available water in the soil profile.

Mckenzie, R. C.↗

Tabulation of Mie scattering calculation results for microwave radiative transfer modeling

In microwave radiative transfer model simulations, the Mie calculations usually consume the majority of the computer time necessary for the calculations (70 to 86 percent for frequencies ranging from 6.6 to 183 GHz). For a large array of atmospheric profiles, the repeated calculations of the Mie codes make the radiative transfer computations not only expensive, but sometimes impossible. It is desirable, therefore, to develop a set of Mie tables to replace the Mie codes for the designated ranges of temperature and frequency in the microwave radiative transfer calculation. Results of using the Mie tables in the transfer calculations show that the total CPU time (IBM 3081) used for the modeling simulation is reduced by a factor of 7 to 16, depending on the frequency. The tables are tested by computing the upwelling radiance of 144 atmospheric profiles generated by a 3-D cloud model (Tao, 1986). Results are compared with those using Mie quantities computed from the Mie codes. The bias and root-mean-square deviation (RMSD) of the model results using the Mie tables, in general, are less than 1 K except for 37 and 90 GHz. Overall, neither the bias nor RMSD is worse than 1.7 K for any frequency and any viewing angle.

Yeh, Hwa-Young M.↗

Micromachined electron tunneling infrared sensors

The development of an improved Golay cell is reported. This new sensor is constructed entirely from micromachined silicon components. A silicon oxynitride (SiO(x)N(y)) membrane is deflected by the thermal expansion of a small volume of trapped gas. To detect the motion of the membrane, an electron tunneling transducer is used. This sensor detects electrons which tunnel through the classically forbidden barrier between a tip and a surface; the electron current is exponentially dependent on the separation between the tip and the surface. The sensitivity of tunneling transducers constructed was typically better than 10(exp -3) A/square root of Hz. Through use of the electron tunneling transducer, the scaling laws which have prevented the miniaturization of the Golay cell are avoided. This detector potentially offers low cost fabrication, compatibility with silicon readout electronics, and operation without cooling. Most importantly, this detector may offer better sensitivity than any other uncooled infrared sensor, with the exception of the original Golay cell.

Kenny, T. W.↗

Surface Turbulent Fluxes Over Pack Ice Inferred from TOVS Observations

A one-dimensional, atmospheric boundary layer model is coupled to a thermodynamic ice model to estimate the surface turbulent fluxes over thick sea ice. The principal forcing parameters in this time-dependent model are the air temperature, humidity, and wind speed at a specified level (either at 2 m or at 850 mb) and the downwelling surface radiative fluxes. The free parameters. are the air temperature, humidity, and wind speed profiles below the specified level, the surface skin temperature, the ice temperature profile, and the surface turbulent fluxes. The goal is to determine how well we can estimate the turbulent surface heat and momentum fluxes using forcing parameters from atmospheric temperatures and radiative fluxes retrieved from the TIROS-N Operational Vertical Sounder (TOVS) data. Meteorological observations from the Lead Experiment (LeadEx, April 1992) ice camp are used to validate turbulent fluxes computed with the surface observations and the results are used to compare with estimates based on radio-sonde observations or with estimates based on TOVS data. We find that the TOVS-based estimates of the stress are significantly more accurate than those found with a constant geostrophic drag coefficient, with a root-mean-square error about half as large. This improvement is due to stratification effects included in the boundary layer model. The errors in the sensible heat flux estimates, however, are large compared to the small mean values observed during the field experiment.

Lindsay, R. W.↗

Structural tailoring of aircraft engine blade subject to ice impact constraints

In this paper, results are presented for the minimum weight design of SR2 unswept blade made of (Titanium/Graphite-Epoxy/Titanium)s fiber composite. The blade which is rotating at high RPM is subject to ice impact. The root chord length, blade thicknesses at five stations, and graphite-epoxy ply orientation are chosen as design variables. The design constraints are placed on the behavior variables: leading edge strain and root damage parameter due to ice impact, maximum post-impact bending stress at the root due to rotation, first three natural frequencies and resonance margin after impact. The method of feasible directions is employed to solve the inequality constrained minimization problem. The effect of ice speed and the ice impact location on the final design are discussed.

Reddy, E. S.↗

Angular Distribution Models for Top-of-Atmosphere Radiative Flux Estimation from the Clouds and the Earth's Radiant Energy System Instrument on the Tropical Rainfall Measuring Mission Satellite: Validation - Part II

Top-of-atmosphere (TOA) radiative fluxes from the Clouds and the Earth s Radiant Energy System (CERES) are estimated from empirical angular distribution models (ADMs) that convert instantaneous radiance measurements to TOA fluxes. This paper evaluates the accuracy of CERES TOA fluxes obtained from a new set of ADMs developed for the CERES instrument onboard the Tropical Rainfall Measuring Mission (TRMM). The uncertainty in regional monthly mean reflected shortwave (SW) and emitted longwave (LW) TOA fluxes is less than 0.5 W/sq m, based on comparisons with TOA fluxes evaluated by direct integration of the measured radiances. When stratified by viewing geometry, TOA fluxes from different angles are consistent to within 2% in the SW and 0.7% (or 2 W/sq m) in the LW. In contrast, TOA fluxes based on ADMs from the Earth Radiation Budget Experiment (ERBE) applied to the same CERES radiance measurements show a 10% relative increase with viewing zenith angle in the SW and a 3.5% (9 W/sq m) decrease with viewing zenith angle in the LW. Based on multiangle CERES radiance measurements, 18 regional instantaneous TOA flux errors from the new CERES ADMs are estimated to be 10 W/sq m in the SW and, 3.5 W/sq m in the LW. The errors show little or no dependence on cloud phase, cloud optical depth, and cloud infrared emissivity. An analysis of cloud radiative forcing (CRF) sensitivity to differences between ERBE and CERES TRMM ADMs, scene identification, and directional models of albedo as a function of solar zenith angle shows that ADM and clear-sky scene identification differences can lead to an 8 W/sq m root-mean-square (rms) difference in 18 daily mean SW CRF and a 4 W/sq m rms difference in LW CRF. In contrast, monthly mean SW and LW CRF differences reach 3 W/sq m. CRF is found to be relatively insensitive to differences between the ERBE and CERES TRMM directional models.

Loeb, N. G.↗

Top-of-Atmosphere Shortwave Broadband Observed Radiance and Estimated Irradiance over Polar Regions from Clouds and the Earth's Radiant Energy System (CERES) Instruments on Terra

Empirical angular distribution models for estimating top-of-atmosphere shortwave irradiances from radiance measurements over permanent snow, fresh snow and sea ice are developed using CERES measurements on Terra. Permanent snow angular distribution models depend on cloud fraction, cloud optical thickness, and snow brightness. Fresh snow and sea ice angular distribution models depend on snow and sea ice fraction, cloud fraction, cloud optical thickness, and snow and ice brightness. These classifications lead to 10 scene types for permanent snow and 25 scene types for fresh snow and sea ice. The average radiance over clear-sky permanent snow is more isotropic with satellite viewing geometry than that over overcast permanent snow. On average, the albedo of clear-sky permanent snow varies from 0.65 to 0.68 for solar zenith angles between 60$logical and\circ$ and 80 deg, while the corresponding albedo of overcast scenes varies from 0.70 to 0.73. Clear-sky permanent snow albedos over Antarctica estimated from two independent angular distribution models are consistent to within 0.6%, on average. Despite significant variability in sea ice optical properties with season, the estimated mean relative albedo error is -1 % for very dark sea ice and 0.1% for very bright sea ice when albedos derived from different viewing angles are averaged. The estimated regional root-mean-square (RMS) relative albedo error is 5.6% and 2.6% when the sea ice angular distribution models are applied to a region that contains very dark and very bright sea ice, respectively. Similarly, the estimated relative albedo bias error for fresh snow is -0.1% for very dark snow.

Kato, S.↗