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Results for “Fractional derivative”

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.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Structure and chemistry of Orion S

We present interferometric observations of the SiO J = 2-1, H13CO(+) J = 1-0, HC3N J = 11-10, CH3OH J(K) = 2(0)-1(0), and SO2 J(KpK0) = 8(17)-8(08) transitions along with the 3.1 mm continuum toward the young stellar object Orion S. The HC3N and H13CO(+) emission trace similar spatial and velocity distributions which are extended and follow the Orion molecular ridge. The SiO emission is more spatially confined, peaking to the west of the 3.1 mm continuum source, while the CH3OH emission peaks to the southwest. Weak SO2 emission was detected southeast of the continuum source position. Column densities and fractional abundances are derived for each species at different positions in the region. In general, the molecular abundances near the continuum source are similar to those in the quiescent material near IRc 2, but the abundances decrease toward the continuum source position indicating localized depletions of at least a factor of three. The presence of strong SiO emission with much weaker SO2 emission is interpreted as resulting from high-velocity shock interactions between the outflow from Orion S and the surrounding cloud.

Mcmullin, Joseph P.↗
NASA NTRS1993

Isotopic fractionation of hydrogen in planetary exospheres due to ionosphere-exosphere coupling - Implications for Venus

The paper considers isotopic hydrogen fractionation processes in the Venusian exosphere due to ionosphere-exosphere coupling by addressing two deficiencies in the present theory of differential escape. First, a set of D/H isotopic fractionation curves is derived for the ion-neutral interactions of charge and collisional momentum transfer, and these are compared with the results of Gurwell and Yung (1993) for hot O collisional ejection. Then, the question of the relative importance of collisional ejection in atmospheric escape is reexamined using two simple exosphere models. It is shown that O-O collisions suppress the high energy component of the hot O distribution by more than a factor of 10. Moreover, the ballistic trajectories of fast O atoms that reach the nighttime reservoir of exospheric hydrogen favor downward scatter of D and H rather than their escape. It is concluded that, due to severe limits placed on the effectiveness of collisional ejection, the differential escape of D and H from Venus is determined by charge exchange interactions rather than the collisional ejection.

Hodges, R. R., Jr.↗
NASA NTRS1994

One milliarcsecond precision studies in the regions of Delta Equulei and Chi(sup 1) Orionis

Trigonometric parallaxes for stars in the regions of the binary stars Delta Equulei (HR 8123) and Chi(sup l) Orionis (HR 2047) are derived from data collected with the Multichannel Astrometric Photometer (MAP) and the Thaw Refractor of the University of Pittsburgh's Allegheny Observatory. The weighted mean parallax of all trigonometric studies of delta Equ is now +5.42 +/- 0.93 mas, corresponding to absolute magnitudes of 3.87 +/- 0.04 and 3.95 +/- 0.04 mag, respectively, for the primary and secondary. Using the Popper and Dworetsky orbit we find a photocentric semimajor axis of 2.9 +/- 0.8 mas and individual masses of 1.21 +/- 0.090 and 1.19 +/- 0.088 solar masses, respectively, for the primary and secondary components. The weighted mean trigonometric parallax of all studies of the binary star Chi(sup l) Ori is +111.0 +/- 0.92 mas, implying an absolute visual magnitude for the dominant GO V primary of 4.63 +/- 0.018 mag. The photocentric semimajor axis, derived from a fraction of the orbit, is 96.9 +/- 5.4 mas.

Gatewood, George↗
NASA NTRS1994

The circumstellar environment of IRAS 05338-0624

Millimeter continuum and spectral line observations with 10 sec, 30 sec, and 60 sec resolution are used to characterize the structure and chemistry of the gas around the young, embedded star, IRAS 05338-0624. On arcminute scales, emission from dense gas tracers outline an isolated condensation centered on the IRAS source position. The condensation is characterized by a size of approximately 60 sec, a density of 2 x 10(exp 5)/cc, and a virial mass of 40 solar mass. Interferometric CS J = 2-1 observations show two peaks, one toward the continuum peak and the other toward a position 14 sec west and 8 sec south. Single-dish maps of SO, CH3OH, and SiO show pronounced wing emission to the west of the IRAS source, which interferometer observations reveal to be a compact region of outflow activity. CS emission at redshifted and blueshifted velocities reveals a bipolar outflow oriented with a position angle of 45 deg, while SiO emission appears to be tracing a fast shock interaction region at the CS red-lobe peak, 14 sec west and 8 sec south of the IRAS source. Finally, H(13)CO(+) emission traces clumps of quiescent gas toward the IRAS source and adjacent to the blue lobe of the outflow. Column densities and molecular fractional abundances are derived to explore the interaction between the surrounding condensation and the young stellar object. We find evidence for gas phase depletions within the overall condensation in several gas tracers (CO, CS, HCN, SO) but not in the region immediately around the young stellar object. Enhanced abundances of SO, CH3OH, and SiO (by factors of 4, greater than 100, greater than 1000, respectively) are observed in the shocked gas; these enhancements may be explained in terms of a nondissociative shock liberating mantle materials that contain some amount of refractory materials, a moderate velocity dissociative shock in which only minor sputtering of Si occurs, or a shock that impacts surrounding material with a range of speeds.

Mcmullin, Joseph P.↗
NASA NTRS2011

Dynamics of Vegetatin Indices in Tropical and Subtropical Savannas Defined by Ecoregions and Moderate Resolution Imaging Spectoradiometer (MODIS) Land Cover

In this study, we explored the capacity of vegetation indices derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) reflectance products to characterize global savannas in Australia, Africa and South America. The savannas were spatially defined and subdivided using the World Wildlife Fund (WWF) global ecoregions and MODIS land cover classes. Average annual profiles of Normalized Difference Vegetation Index, shortwave infrared ratio (SWIR32), White Sky Albedo (WSA) and the Structural Scattering Index (SSI) were created. Metrics derived from average annual profiles of vegetation indices were used to classify savanna ecoregions. The response spaces between vegetation indices were used to examine the potential to derive structural and fractional cover measures. The ecoregions showed distinct temporal profiles and formed groups with similar structural properties, including higher levels of woody vegetation, similar forest savanna mixtures and similar grassland predominance. The potential benefits from the use of combinations of indices to characterize savannas are discussed.

Hill, Michael J.↗
NASA NTRS2012

Evaluating the Contribution of NASA Remotely-Sensed Data Sets on a Convection-Allowing Forecast Model

The Short-term Prediction Research and Transition (SPoRT) Center is a collaborative partnership between NASA and operational forecasting partners, including a number of National Weather Service forecast offices. SPoRT provides real-time NASA products and capabilities to help its partners address specific operational forecast challenges. One challenge that forecasters face is using guidance from local and regional deterministic numerical models configured at convection-allowing resolution to help assess a variety of mesoscale/convective-scale phenomena such as sea-breezes, local wind circulations, and mesoscale convective weather potential on a given day. While guidance from convection-allowing models has proven valuable in many circumstances, the potential exists for model improvements by incorporating more representative land-water surface datasets, and by assimilating retrieved temperature and moisture profiles from hyper-spectral sounders. In order to help increase the accuracy of deterministic convection-allowing models, SPoRT produces real-time, 4-km CONUS forecasts using a configuration of the Weather Research and Forecasting (WRF) model (hereafter SPoRT-WRF) that includes unique NASA products and capabilities including 4-km resolution soil initialization data from the Land Information System (LIS), 2-km resolution SPoRT SST composites over oceans and large water bodies, high-resolution real-time Green Vegetation Fraction (GVF) composites derived from the Moderate-resolution Imaging Spectroradiometer (MODIS) instrument, and retrieved temperature and moisture profiles from the Atmospheric Infrared Sounder (AIRS) and Infrared Atmospheric Sounding Interferometer (IASI). NCAR's Model Evaluation Tools (MET) verification package is used to generate statistics of model performance compared to in situ observations and rainfall analyses for three months during the summer of 2012 (June-August). Detailed analyses of specific severe weather outbreaks during the summer will be presented to assess the potential added-value of the SPoRT datasets and data assimilation methodology compared to a WRF configuration without the unique datasets and data assimilation.

Zavodsky, Bradley T.↗
NASA NTRS2019

100-kHz Rate Rayleigh Imaging for Combustion and Flow Diagnostics

Two-dimensional (2D) Rayleigh scattering (RS) imaging at an ultrahigh repetition rate of 100 kHz is demonstrated in non-reacting and reacting flows employing a high-energy burst-mode laser system. Image sequences of flow mixture fraction were directly derived from high-speed RS images. Additionally, a 2D instantaneous flow velocity field at 100 kHz was obtained through optical-flow-based analysis of the RS images. The technique was also applied to study turbulent flames having a near-constant Rayleigh cross section. The demonstrated high-speed RS technique in conjunction with optical-flow-based analysis provides non-intrusive, simultaneous measurements of the flow mixing and velocity field, extending the measurement capability of the RS technique to high-speed non-reacting and reacting flows.

Jiang, Naibo↗
NASA NTRSDate not supplied

Tomography Analysis of Orion Artemis 1 Heatshield Sample

The Orion spacecraft, under NASA's Artemis program, is an integral step in humanity's ambitions of deep space exploration, including our return to the Moon and subsequent mission to Mars. The performance of Orion's heatshield is central to ensuring the safety and success of such missions. This presentation offers a comprehensive overview of the process used in and findings derived from tomography scans of an Artemis 1 heatshield sample executed at the Lawrence Berkeley National Laboratory's Advanced Light Source. These tomography scans captured high-resolution X-Ray images of the heatshield's microstructure, allowing advanced imaging to be employed for 3D image segmentation and visualization of the sample. The Porous Media Analysis (PuMA) software stands central to our analysis, offering robust computational algorithms and methodologies to digitally compute properties of the heatshield material. The presentation discusses the following derived metrics: - Volume fractions, representing the spatial distribution and amounts of various components throughout the heatshield’s depth. - Porosity and crack distributions, offering insights into the void space within the material, critical for understanding the heatshield's structural integrity. - Fiber orientation, detailing the alignment and arrangement of fibers, significant for material orthotropy. - Permeability estimates, quantifying the passage of gas through the material, relevant for re-entry conditions and pyrolysis gasses. One distinctive feature of this study is the comparative evaluation against data obtained from tomography scans of the Exploration Flight Test-1 (EFT-1) heatshield. Such a comparison offers multiple insights, including evaluation of the consistency and repeatability of manufacturing processes as well as understanding of any evolutionary changes in heatshield design or material properties.

Micro-tomography↗
NASA NTRS2023

Petrological Traverse of the Olivine Cumulate Séítah Formation at Jezero Crater, Mars: A Perspective From SuperCam Onboard Perseverance

Séítah is the stratigraphically lowest formation visited by Perseverance in the Jezero crater floor. We present the data obtained by SuperCam: texture by imagery, chemistry by Laser-Induced Breakdown Spectroscopy, and mineralogy by Supercam Visible and Infrared reflectance and Raman spectroscopy. The Séítah formation consists of igneous, weakly altered rocks dominated by millimeter-sized grains of olivine with the presence of low-Ca and high-Ca pyroxenes, and other primary minerals (e.g., plagioclase, Cr-Fe-Ti oxides, phosphates). Along a ∼140 m long section in Séítah, SuperCam analyses showed evidence of geochemical and mineralogical variations, from the contact with the overlying Máaz formation, going deeper in the formation. Bulk rock and olivine Mg#, grain size, olivine content increase gradually further from the contact. Along the section, olivine Mg# is not in equilibrium with the bulk rock Mg#, indicating local olivine accumulation. These observations are consistent with Séítah being the deep ultramafic member of a cumulate series derived from the fractional crystallization and slow cooling of the parent magma at depth. Possible magmatic processes and exhumation mechanisms of Séítah are discussed. Séítah rocks show some affinity with some rocks at Gusev crater, and with some Martian meteorites suggesting that such rocks are not rare on the surface of Mars. Séítah is part of the Nili Fossae regional olivine-carbonate unit observed from orbit. Future exploration of Perseverance on the rim and outside of the crater will help determine if the observations from the crater floor can be extrapolated to the whole unit or if this unit is composed of distinct sub-units with various origins.

Mars 2020↗
NASA NTRS1992

Top-of-atmosphere radiative fluxes - Validation of ERBE scanner inversion algorithm using Nimbus-7 ERB data

The ERBE algorithm is applied to the Nimbus-7 earth radiation budget (ERB) scanner data for June 1979 to analyze the performance of an inversion method in deriving top-of-atmosphere albedos and longwave radiative fluxes. The performance is assessed by comparing ERBE algorithm results with appropriate results derived using the sorting-by-angular-bins (SAB) method, the ERB MATRIX algorithm, and the 'new-cloud ERB' (NCLE) algorithm. Comparisons are made for top-of-atmosphere albedos, longwave fluxes, viewing zenith-angle dependence of derived albedos and longwave fluxes, and cloud fractional coverage. Using the SAB method as a reference, the rms accuracy of monthly average ERBE-derived results are estimated to be 0.0165 (5.6 W/sq m) for albedos (shortwave fluxes) and 3.0 W/sq m for longwave fluxes. The ERBE-derived results were found to depend systematically on the viewing zenith angle, varying from near nadir to near the limb by about 10 percent for albedos and by 6-7 percent for longwave fluxes. Analyses indicated that the ERBE angular models are the most likely source of the systematic angular dependences. Comparison of the ERBE-derived cloud fractions, based on a maximum-likelihood estimation method, with results from the NCLE showed agreement within about 10 percent.

Suttles, John T.↗
NASA NTRS1995

Comparison of simulated cloud cover with satellite obsrvations over the Western United States

Satellite imagery datasets and regional climate model results are intercompared for evaluation of model accuracy in the simulation of cloud cover. Both monthly average individual simulation times are analyzed. To provide a consistent comparison, satellite data are first mapped into the model's geographic projection, grid domain, and resolution. It is found that September 1988 monthly average cloud fraction results from the modeled simulations correspond to observations, in both spatial pattern and magnitude, with bias less than +/- 20% cloud fraction over the entire inland West. Agreement in the pattern of cloud fraction also is evident for monthly average cloud fraction in July, but there is no negative bias of 10%-30% cloud fraction in the model diagnosis of cloud cover. Correlations between the spatial distributions of model-derived and observed cloud fractions are found to exceed 0.80 for certain geographic regions of the West, and these correlations are largest over mountainous areas during summer. Case studies of a series of daily cloud cover demonstrate the ability of the model to simulate the effects of frontal passage on cloud distribution. The ability of the RegCM1 to simulate daily cloud fraction and diurnal cloud evolution is somewhat weak for the summer convective season. It is anticipated that a more recent version of the regional climate model may improve the simulation of summer season cloud cover, through changes in cloud parameterization and improvements in model resolution.

Wetzel, Melanie A.↗
NASA NTRS2003

Algorithms for the Fractional Calculus: A Selection of Numerical Methods

Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

Diethelm, K.↗
NASA NTRS1993

Incompressible spectral-element method: Derivation of equations

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

Deanna, Russell G.↗
NASA NTRS2003

On the Exploitation of Sensitivity Derivatives for Improving Sampling Methods

Many application codes, such as finite-element structural analyses and computational fluid dynamics codes, are capable of producing many sensitivity derivatives at a small fraction of the cost of the underlying analysis. This paper describes a simple variance reduction method that exploits such inexpensive sensitivity derivatives to increase the accuracy of sampling methods. Three examples, including a finite-element structural analysis of an aircraft wing, are provided that illustrate an order of magnitude improvement in accuracy for both Monte Carlo and stratified sampling schemes.

Cao, Yanzhao↗
NASA NTRS1999

The Sunyaev-Zel'dovich Effect in Abell 370

We present interferometric measurements of the Sunyaev-Zel'dovich (SZ) effect towards the galaxy cluster Abell 370. These measurements, which directly probe the pressure of the cluster's gas, show the gas is strongly aspherical, on agreement with the morphology revealed by x-ray and gravitational lensing observations. We calculate the cluster's gas mass fraction by comparing the gas mass derived from the SZ measurements to the lensing-derived gravitational mass near the critical lensing radius. We also calculate the gas mass fraction from the SZ data by deriving the total mass under the assumption that the gas is in hydrostatic equilibrium (HSE). We test the assumptions in the HSE method by comparing the total cluster mass implied by the two methods. The Hubble constant derived for this cluster, when the known systematic uncertainties are included, has a very wide range of values and therefore does not provide additional constraints on the validity of the assumptions. We examine carefully the possible systematic errors in the gas fraction measurement. The gas fraction is a lower limit to the cluster's baryon fraction and so we compare the gas mass fraction, calibrated by numerical simulations to approximately the virial radius, to measurements of the global mass fraction of baryonic matter, OMEGA(sub B)/OMEGA(sub matter). Our lower limit to the cluster baryon fraction is f(sub B) = (0.043 +/- 0.014)/h (sub 100). From this, we derive an upper limit to the universal matter density, OMEGA(sub matter) <= 0.72/h(sub 100), and a likely value of OMEGA(sub matter) <= (0.44(sup 0.15, sub -0.12)/h(sub 100).

Grego, Laura↗
NASA NTRS1989

Solar abundances as derived from solar energetic particles

Recent studies have shown that there are well defined average abundances of heavy (Z above 2) solar energetic particles (SEPs), with variations in the acceleration and propagation producing a systematic flare-to-flare fractionation that depends on the charge per unit mass of the ion. Correcting the average SEP abundances for this fractionation yields SEP-derived coronal abundances for 20 elements. High-resolution SEP studies have also provided isotopic abundances for five elements. SEP-derived abundances indicate that elements with high first ionization potentials (greater than 10 eV) are depleted in the corona relative to the photosphere and provide new information on the solar abundance of C and Ne-22.

Stone, E. C.↗
NASA NTRS1991

Fragments of quartz monzodiorite and felsite in Apollo 14 soil particles

Samples of 'evolved' lithologies, felsite, quartz monzodiorite (QMD), and whitlockite-rich quartz monzodiorite, were identified compositionally and petrographically among 2-4-mm soil particles from Apollo 14. Fragments of QMD were found to be extremely rare in the Apollo 14 samples. Felsite is similar to previously reported samples. QMD 14161,7069 is similar to 15405 QMD and has ITE concentrations in KREEP-like concentration ratios of about twice the ITE concentrations of average high-K KREEP. QMD cumulate has the highest measured REE concentrations of any lunar sample to date with the exception of individual whitlockite grains. Felsite and whitlockite-rich lithologies appear to be petrogenetically related and have complementary compositions representing separated fractions of the QMD or KREEP-like parental melt. Felsite is a silica-rich fraction of the residual liquid or it is a derivative of the silica-rich fraction. Felsite or lunar granite of this type results from residual liquid separation following crystal-liquid separation of a QMD-like parent melt with concentration ratios of ITEs similar to those of KREEP.

Jolliff, B. L.↗