SEARCH · Search NASA

Results for “divided differences”

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.

SourceResearch connectionFrom yearThrough year

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

At least 55 records · Page 3

All sources NASA NTRS DOE OSTI

NASA NTRS2016

Electric Field Quantitative Measurement System and Method

A method and system are provided for making a quantitative measurement of an electric field. A plurality of antennas separated from one another by known distances are arrayed in a region that extends in at least one dimension. A voltage difference between at least one selected pair of antennas is measured. Each voltage difference is divided by the known distance associated with the selected pair of antennas corresponding thereto to generate a resulting quantity. The plurality of resulting quantities defined over the region quantitatively describe an electric field therein.

Generazio, Edward R.↗

NASA NTRS2021

Best Practices Identified Through the Completion of UAS Flight Demonstrations

After several years of research into Detect and Avoid (DAA) and Command and Control (C2) systems for Unmanned Aircraft Systems (UAS), the National Aeronautics and Space Administration’s (NASA) UAS Integration into the National Airspace System project initiated a focused two-year effort along with the Federal Aviation Administration (FAA) and three industry partners to investigate remaining issues in the specification, test, certification and airspace integration to allow UAS operations in non-segregated airspace. The approach taken had the industry partners propose a flight demonstration approximating a commercial operation, while NASA helped, as needed, the partners through design and test phases and NASA observed interactions with the FAA. During this effort NASA collected best practices intended to be of value to similar UAS endeavors. These best practices can be divided into different sets, including practices that describe the relationship between business considerations to UAS design or describe several UAS development challenges. Another set includes best practices focused on navigating the UAS design and type certification processes. A third set includes best practices that relate to the design of the DAA system. Deploying DAA systems in this timeframe posed unique challenges. Commercial off-the-shelf DAA systems do not exist, necessitating custom development and, for two of the partners, the use of low-size, -weight, and -power (SWaP) sensors not completely specified for DAA. A fourth set of best practices relates to lost-link contingency planning. The final set of best practices relates to the design and testing of C2 systems and obtaining spectrum licenses. The UAS demonstrations were piloted remotely, and for all aspects of flight safety, a C2 system was required to communicate DAA and other UAS subsystem data to the remote pilot and to allow the pilot to issue commands to the vehicle. Throughout the course of this effort, the partners integrated prototype DAA and C2 systems into unmanned aircraft, tested those systems, and laid the groundwork for type certification programs that are expected to continue.

NASA↗

DOE OSTI2025

Comparison of multi-stage air treatment process divided by the same temperature and enthalpy difference

The multi-stage air treatment system has been proposed recently, and lower grade chilled/hot water could be used and energy efficiency could be improved. However, it has not been studied which division method of air treatment processes has higher energy efficiency. In this study, the model to calculate the energy consumption of multi-stage air treatment process is introduced, and the effects of two division methods, i.e. multi-stage air treatment process divided by the same temperature difference (ST method) or same enthalpy difference (SE method) between inlet and outlet at each stage, under 9 different air inlet parameters in the 2-stage and 3-stage air treatment processes are analysed and compared. The results show that (1) the system energy consumption of the SE method is generally lower than that of the ST method; (2) there is generally a larger energy consumption reduction rate of SE method when the air relative humidity is 70% compared to relative humidity of 50% and 90%; (3) the difference between ST method and SE method is not great, so both methods can be used for the design of multi-stage treatment system although SE method is normally recommended.

Wang, Wentao↗

DOE OSTI2023

(U) A General-Purpose Code for Correlated Sampling Using Batch Statistics with MCNP6 for Fixed-Source Problems

Correlated sampling can be used to reduce the uncertainty of a difference of tallies by taking advantage of the negative covariance term in the sandwich formula. Booth first showed how correlated sampling can be applied with batch statistics using MCNP’s tally fluctuation chart (TFC) to reduce the uncertainty of a difference of tallies in fixed-source problems. Booth presented a problem in which a 1273% uncertainty in a difference was reduced to 8% by accounting for correlations. Researchers He and Su recently studied correlated sampling using the TFC in MCNP version 5. They determined that the code did not print enough digits in the TFC tally means for accurate batch statistics in some cases. After modifying the source code, they concluded that “correlated sampling can yield a standard deviation of about one magnitude smaller than that predicted by the direct, un-correlated simulation when the changes in system response are small (say about 1%), which is equivalent to saving in CPU time by a factor of 100. Such saving [sic] becomes less significant as the change in system response becomes larger.” He and Su provided the formulas needed to apply batch statistics to compute the correlated uncertainty of a difference of tallies. In this report, we follow up on their work by providing the formulas needed to apply batch statistics to compute the correlated uncertainty of a ratio of tallies and of a difference of two tallies divided by a third tally. We extend these formulas to differences and ratios of ratios. These formulas are applied to reduce the uncertainty associated with calculating a relative sensitivity. He and Su did not investigate the accuracy of their correlated sampling uncertainty estimates. We use their test problems and evaluate the accuracy of the uncertainty estimates by comparing with results obtained from random sampling, and, in simple cases, with theoretical values of the “exact” uncertainties. We find that the uncertainties obtained from batch statistics are accurate as long as at least 100 batches are used. We present a new computer code, COSUBS (COrrelated Sampling Using Batch Statistics), that reads MCNP6 TFCs and applies correlated sampling using batch statistics for the tally combinations that the user specifies. COSUBS is a very general tool that compares all TFCs for a base case and one or two perturbed cases. It computes uncertainties for ratios if given only a base case. This report is organized as follows. The equations to apply batch statistics to the difference of random tallies are reviewed in Sec. II. Section III presents the equations for applying batch statistics to a ratio of random tallies; this is useful for computing relative sensitivities using a one-sided finite difference and the relative sensitivity using the differential operator method. Section IV presents the equations for applying batch statistics to a difference of two random tallies divided by a third; this is useful for computing a relative sensitivities using a central difference. Section V presents the equations for applying batch statistics to a difference of two ratios with four random tallies. Section VI presents the equations for applying batch statistics to a one-sided finite difference estimate of the relative sensitivity of a ratio (this uses four random tallies). Section VII presents the equations for applying batch statistics to a central difference estimate of the relative sensitivity of a ratio (this uses six random tallies). Section VIII presents the equations for applying batch statistics to a sum of random tallies. Section IX discusses how to apply batch statistics using MCNP6. Section X presents COSUBS, describing its command-line options and logic. Sections XI through XVI present numerical results for various test problems. Section XVII is a summary and conclusions. Appendix A derives the theoretical Monte Carlo tally variance given certain assumptions; these variances are used to verify the batch statistics for some of the problems. Appendix B lists the MCNP6 input for the unperturbed example problem. Appendix C presents modifications made to MCNP6.3 to support this work.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Quantum Divide and Compute: Exploring the Effect of Different Noise Sources

Abstract Our recent work (Ayral et al. in Proceedings of IEEE computer society annual symposium on VLSI, ISVLSI, pp 138–140, 2020. 10.1109/ISVLSI49217.2020.00034 ) showed the first implementation of the Quantum Divide and Compute (QDC) method, which allows to break quantum circuits into smaller fragments with fewer qubits and shallower depth. This accommodates the limited number of qubits and short coherence times of quantum processors. This article investigates the impact of different noise sources—readout error, gate error and decoherence—on the success probability of the QDC procedure. We perform detailed noise modeling on the Atos Quantum Learning Machine, allowing us to understand tradeoffs and formulate recommendations about which hardware noise sources should be preferentially optimized. We also describe in detail the noise models we used to reproduce experimental runs on IBM’s Johannesburg processor. This article also includes a detailed derivation of the equations used in the QDC procedure to compute the output distribution of the original quantum circuit from the output distribution of its fragments. Finally, we analyze the computational complexity of the QDC method for the circuit under study via tensor-network considerations, and elaborate on the relation the QDC method with tensor-network simulation methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2014

X-Ray Properties of K-Selected Galaxies at 0.5 Less than z Less than 2.0: Investigating Trends with Stellar Mass, Redshift and Spectral Type

We examine how the total X-ray luminosity correlates with stellar mass, stellar population, and redshift for a K-band limited sample of approximately 3500 galaxies at 0.5 < z < 2.0 from the NEWFIRM Medium Band Survey in the COSMOS field. The galaxy sample is divided into 32 different galaxy types, based on similarities between the spectral energy distributions. For each galaxy type, we further divide the sample into bins of redshift and stellar mass, and perform an X-ray stacking analysis using the Chandra COSMOS data. We find that full band X-ray luminosity is primarily increasing with stellar mass, and at similar mass and spectral type is higher at larger redshifts. When comparing at the same stellar mass, we find that the X-ray luminosity is slightly higher for younger galaxies (i.e., weaker 4000 angstrom breaks), but the scatter in this relation is large. We compare the observed X-ray luminosities to those expected from low- and high-mass X-ray binaries (XRBs). For blue galaxies, XRBs can almost fully account for the observed emission, while for older galaxies with larger 4000 angstrom breaks, active galactic nuclei (AGN) or hot gas dominate the measured X-ray flux. After correcting for XRBs, the X-ray luminosity is still slightly higher in younger galaxies, although this correlation is not significant. AGN appear to be a larger component of galaxy X-ray luminosity at earlier times, as the hardness ratio increases with redshift. Together with the slight increase in X-ray luminosity this may indicate more obscured AGNs or higher accretion rates at earlier times.

Properties↗

DOE OSTI2020

Non-monotonic behavior of the lateral diffusivity in an adsorbate as a function of the surface coverage

Diffusion dynamics of adsorbate particles confined on a surface strongly depends on the adsorbate surface coverage. Our molecular dynamics simulation reveals that the average lateral diffusivity of the Lennard-Jones adsorbate on a flat substrate varies non-monotonically with the surface coverage. Given that the adsorbate becomes stratified into distinct layers, we propose a novel approach to analyze the lateral diffusion of the adsorbate particles in different layers, via dividing the total lateral diffusion into consecutive lateral diffusion processes, separated by the layer boundary crossing events. A new definition of the lateral diffusivity in the specific layer has been introduced, and it is revealed that the total lateral diffusivity is equal to the sum of lateral diffusivities in different layers. Furthermore, the non-monotonic behavior of the average lateral diffusivity with the surface coverage is found to result from the difference in behavior of the lateral diffusivity between the first and other layers.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Are Milky-Way-like galaxies like the Milky Way? A view from SDSS-IV/MaNGA

ABSTRACT In this paper, we place the Milky Way (MW) in the context of similar-looking galaxies in terms of their star-formation and chemical evolution histories. We select a sample of 138 Milky Way analogues (MWAs) from the SDSS-IV/MaNGA survey based on their masses, Hubble types, and bulge-to-total ratios. To compare their chemical properties to the detailed spatially-resolved information available for the MW, we use a semi-analytic spectral fitting approach, which fits a self-consistent chemical-evolution and star-formation model directly to the MaNGA spectra. We model the galaxies’ inner and outer regions assuming that some of the material lost in stellar winds falls inwards. We also incorporate chemical enrichment from type II and Ia supernovae to follow the alpha-element abundance at different metallicities and locations. We find some MWAs where the stellar properties closely reproduce the distribution of age, metallicity, and alpha enhancement at both small and large radii in the MW. In these systems, the match is driven by the longer time-scale for star formation in the outer parts, and the inflow of enriched material to the central parts. However, other MWAs have very different histories. These divide into two categories: self-similar galaxies where the inner and outer parts evolve identically; and centrally-quenched galaxies where there is very little evidence of late-time central star formation driven by material accreted from the outer regions. We find that, although selected to be comparable, there are subtle morphological differences between galaxies in these different classes, and that the centrally-quenched galaxies formed their stars systematically earlier.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1973

The application of NASTRAN at Sperry Univac Holland

Very divergent problems arising with different calculations indicate that NASTRAN is not always accessible for common use. Problems with engineering, modelling, and use of the program system are analysed and a way of solution is outlined. Related to this, some supplementary modifications are made at Sperry Univac Holland to facilitate the program for the less skilled user. The implementation of a new element also gives an insight into the use of NASTRAN at Sperry Univac Holland. As the users of Univac computers are from very different kinds of industries like shipbuilders, petrochemical industries, and building industries, the variety of problems coming from these users is very large. This variety results in experience not with one special kind of calculation nor one special kind of construction, but with a wide area of problems arising in the use of NASTRAN. These problems can roughly be divided into three different groups: (1) recognition of what is to be calculated and how, (2) construction of a model, and (3) handling the NASTRAN program. These are the basic problems for every less skilled user of NASTRAN and the Application/Research Department of Sperry Univac has to give reasonable answers to these questions.

Koopmans, G.↗

NASA NTRS1983

The importance of geobotany in geological remote sensing applications

A description of the different effects of variations in ground cover vegetation on remote sensing data in geological and prospecting applications is presented. The different variations are divided into three categories: structural; taxonomic and spectral. Structural variations include changes in the physical appearance of ground cover which may be detectable by a remote sensing instrument. Taxonomic variations occur in those plant communities which are associated with specific geological regions. Spectral variations are due to specific geochemical stresses which may be useful in characterizing geological features at a site. The need for a general scheme for the interpretation of geobotanical remote sensing data is discussed: Geosat data for the field reflectance spectra of different tree species in West Virginia are presented as examples.

Mouat, D. A.↗

NASA NTRS1994

Modeling tropical Pacific sea surface temperature with satellite-derived solar radiative forcing

Two independent datasets for the solar radiation at the surface derived from satellites are compared. The data derived from the Earth Radiation Budget Experiment (ERBE) is for the net solar radiation at the surface whereas the International Satellite Cloud Climatology Project (ISCCP) data is for the downward flux only and was corrected with a space- and time-varying albedo. The ISCCP net flux is at all times higher than the ERBE flux. The difference can be divided into an offset that decreases with latitude and another component that correlates with high tropical cloud cover. With this latter exception the two datasets provide spatial patterns of solar flux that are very similar. A tropical Pacific Ocean model is forced with these two datasets and observed climatological winds. The upward heat flux is parameterized taking into account separately the longwave radiative, latent, and sensible heat fluxes. Best fit values for the uncertain parameters are found using an optimization procedure that seeks to minimize the difference between model and observed SST by varying the parameters within a reasonable range of uncertainty. The SST field the model produces with the best fit parameters is the best the model can do. If the differences between the model and data are larger than can be accounted for by remaining uncertainties in the heat flux parameterization and forcing data then the ocean model must be held to be at fault. Using this method of analysis, a fundamental model fault is identified. Inadequate treatment of mixed layer/entrainment processes in upwelling regions of the eastern tropical Pacific leads to a large and seasonally varying error in the model SST. Elsewhere the model SST is insufficiently different from observed to be able to identify model errors.

Seager, Richard↗

NASA NTRS1991

Wavelength independent interferometer

A polychromatic interferometer utilizing a plurality of parabolic reflective surfaces to properly preserve the fidelity of light wavefronts irrespective of their wavelengths as they pass through the instrument is disclosed. A preferred embodiment of the invention utilizes an optical train which comprises three off-axis parabolas arranged in conjunction with a beam-splitter and a reference mirror to form a Twyman-Green interferometer. An illumination subsystem is provided and comprises a pair of lasers at different preselected wavelengths in the visible spectrum. The output light of the two lasers is coaxially combined by means of a plurality of reflectors and a grating beam combiner to form a single light source at the focal point of the first parabolic reflection surface which acts as a beam collimator for the rest of the optical train. By using visible light having two distinct wavelengths, the present invention provides a long equivalent wavelength interferogram which operates at visible light wherein the effective wavelength is equal to the product of the wavelengths of the two laser sources divided by their difference in wavelength. As a result, the invention provides the advantages of what amounts to long wavelength interferometry but without incurring the disadvantage of the negligible reflection coefficient of the human eye to long wavelength frequencies which would otherwise defeat any attempt to form an interferogram at that low frequency using only one light source.

Hochberg, Eric B.↗

DOE OSTI2020

An analysis of the spatio-temporal resolution of the immersed boundary method with direct forcing

The immersed boundary method (IBM) with direct forcing is very popular in the simulation of rigid particulate flows. In the IBM, an interaction force is introduced at the interface between fluid and particle in order to approximate the no-slip boundary condition. The interaction force is calculated through dividing the velocity difference (or error) between fluid and particle at the interface by the time step. Here, a dynamic equation for the velocity difference is derived. Additionally, analyses on the dynamic equation provide a few new findings: (i) The interaction force is the solution of a least-squares error problem, with the direct implication that the Lagrangian marker distribution has no effect on the large scale flow structure once the distribution of Lagrangian markers become saturated along the interface (i.e., each marker remains properly correlated with all its neighbors); (ii) The Lagrangian volume-weight is a relaxation factor to control how fast the velocity error decays to the ideal value of zero; (iii) The optimal choice of the Lagrangian volume-weight is the largest value permissible by a stability condition. A comprehensive convergence analysis with regard to the spatial and temporal resolution is presented for the velocity error and also for the shear-stress and surface pressure. In three simple canonical problems, it is analytically and numerically shown that the IBM results converge to the theoretical solutions obtained with precise imposition of no-slip and no-penetration boundary conditions. It is observed that it is not necessary to match the Lagrangian marker volume-weight to that of the local Eulerian cell volume and in fact this matching leads to lower than optimal computational efficiency. However, it is found that extremely high Eulerian grid resolution and small time step have to be used to obtain high precision simulation results. Especially, the time step should be inversely proportional to the particle Reynolds number for low Reynolds number flows. For high frequency oscillation problems, the grid size needs to be reduced by a factor of the square root of the frequency, and the time step to be reduced by a factor of the frequency. The theoretical findings here can be used to alleviate the technical difficulties in simulating non-spherical particles by not requiring the Lagrangian marker distribution to match the Eulerian grids and also in the implementation of IBM on non-uniform Eulerian grids. The present work also provides simple practical guidance on the choice of temporal and spatial resolution so as to control the simulation error a priori.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Effects of Atwood and Reynolds numbers on the evolution of buoyancy-driven homogeneous variable-density turbulence

The evolution of buoyancy-driven homogeneous variable-density turbulence (HVDT) at Atwood numbers up to 0.75 and large Reynolds numbers is studied by using high-resolution direct numerical simulations. To help understand the highly non-equilibrium nature of buoyancy-driven HVDT, the flow evolution is divided into four different regimes based on the behaviour of turbulent kinetic energy derivatives. The results show that each regime has a unique type of dependence on both Atwood and Reynolds numbers. It is found that the local statistics of the flow based on the flow composition are more sensitive to Atwood and Reynolds numbers compared to those based on the entire flow. It is also observed that, at higher Atwood numbers, different flow features reach their asymptotic Reynolds-number behaviour at different times. The energy spectrum defined based on the Favre fluctuations momentum has less large-scale contamination from viscous effects for variable-density flows with constant properties, compared to other forms used previously. The evolution of the energy spectrum highlights distinct dynamical features of the four flow regimes. Thus, the slope of the energy spectrum at intermediate to large scales evolves from -7/3 to -1 , as a function of the production-to-dissipation ratio. The classical Kolmogorov spectrum emerges at intermediate to high scales at the highest Reynolds numbers examined, after the turbulence starts to decay. Finally, the similarities and differences between buoyancy-driven HVDT and the more conventional stationary turbulence are discussed and new strategies and tools for analysis are proposed.

42 ENGINEERING↗

DOE OSTI2022

Pre-production results from ATLAS ITk Strip Sensors Quality Assurance Testchip

The production of strip sensors within the framework of the ATLAS Inner Tracker (ITk) development is a process which requires continuous evaluation during the full production period (about 4 years). Such an evaluation is divided into two different parts: Quality Control (QC), which focuses on the final product (the actual sensors) and tries to identify possible defects once the fabrication is completed, and Quality Assurance (QA), which aims to prevent deviations in the manufacturing process and uses specifically-designed test structures. The initial sensor pre-production consists of 5% (1041 sensors) of the total number of sensors expected during production. As part of pre-production, the collaboration has measured key parameters from miniature strip sensors (minis), monitor diodes (MD8), and the ATLAS Testchip, before and after irradiation. In this contribution we focus on the analysis of the results of the MD8 and the Testchip. All parameters have been obtained from the test structures (MD8, bias resistors, interdigitated structures, field oxide capacitors, coupling capacitors, punch-through protection structures and cross-bridge resistors) measured at the different test sites (KEK/Tsukuba, Birmingham, Toronto, Ljubljana, Valencia, Carleton, Prague, CNM-Barcelona). The results are compared to predefined pre- and post-irradiation specifications for each tested parameter.

47 OTHER INSTRUMENTATION↗

NASA NTRS1981

Picture gallery: A structured presentation of OAO-2 photometric data supported by UBV, ANS, and TD1 observations

Stellar fluxes for 531 stars in the wavelength range lambda 5500-1330A lambda are presented in the form of graphs. The stars are divided into 52 different categories on the basis of their spectral types and objects within one category are shown together. The agreement between the various ultraviolet photometric systems for early type stars is generally better than 0.10 mag. Stars with known and/or observed variability have been grouped separately. A list of stars with observed photometric properties which are indicative of stellar or interstellar anomalies is also provided.

Koornneed, J.↗

NASA NTRS1984

Applications of a conservative zonal scheme to transient and geometrically complex problems

A conservative zoning technique, wherein the flow field for a finite-difference calculation is divided into several regions to simplify grid generation, is discussed and is applied in the solution of a two-dimensional problem of complex topology. Calculations are performed on two zonal, or patched, grid systems for the supersonic flow over a double-airfoil configuration. The solution is smooth and continuous across the zonal interfaces, and shock waves pass through the boundaries without distortion. In addition, the time-accuracy of the zonal-boundary method is verified by a two-zone cyclinder calculation with a stationary inner and a rotating outer mesh.The feasibility of the zonal approach for use in the solution of geometrically complex and unsteady problems is thus demonstrated.

Hessenius, K. A.↗

NASA NTRS1985

Moving target, distributed, real-time simulation using Ada

Research on a precompiler solution is described for the moving target compiler problem encountered when trying to run parallel simulation algorithms on several microcomputers. The precompiler is under development at NASA-Lewis for simulating jet engines. Since the behavior of any component of a jet engine, e.g., the fan inlet, rear duct, forward sensor, etc., depends on the previous behaviors and not the current behaviors of other components, the behaviors can be modeled on different processors provided the outputs of the processors reach other processors in appropriate time intervals. The simulator works in compute and transfer modes. The Ada procedure sets for the behaviors of different components are divided up and routed by the precompiler, which essentially receives a multitasking program. The subroutines are synchronized after each computation cycle.

Collins, W. R.↗