Search NASA⌕ Search

SEARCH · Search NASA

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.

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

At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Multilayer sea ice in the Arctic - Model- and satellite-derived

The behavior of sea ice is a strong function of ice strength which, in the central Arctic, depends on the relative fractions of multiyear and first-year ice coverage. A dynamic-thermodynamic sea ice model has been configured to include both multiyear and first-year ice. The model has been run for a 7-year period, 1979-1985, for which a satellite microwave record of multiyear sea ice coverage is available. The simulated concentrations of multiyear ice are slightly higher than the satellite-derived concentrations, although the total coverage of simulated multiyear ice agrees well with the satellite-derived coverage. Both the simulated and the satellite-derived coverages in the early 1980s show large interannual variations that represent potentially large perturbations in the mass balance of Arctic pack ice. These fluctuations are generally consistent in the model and satellite data, and they are generally consistent with year-to-year differences in the large-scale wind forcing. In at least some cases the wintertime distribution of multiyear ice is influenced by the pattern of ice drift as far back as the previous summer. The late December coverage of multiyear ice in the Alaskan region appears to foreshadow summer ice conditions in the same region. The short-term response to an intense synoptic system is considerably larger in the satellite data than in the model results.

Walsh, John E.↗
NASA NTRS1982

The tropospheric gas composition of Jupiter's north equatorial belt (NH3, PH3, CH3D, GeH4, H2O) and the Jovian D/H isotropic ratio

The gas composition of the troposphere of Jupiter in the clearest regions of the North Equatorial Belt (NEB) was derived from the Voyager 1 IRIS data. The infrared spectrum for this homogeneous cloud free region was modeled to infer altitude profiles for NH3, PH3, GeH4 and H2O. The Profiles for NH3 and PH3 were found to be depleted in the upper troposphere but otherwise in agreement with their solar values at the 1 bar level. The mole fraction for CH3D was determined to be 3.5(+1.0 or -1.3) x 10 to the minus 7th power. The GeH4 mole fraction of 7+ or -2 x 10 to the minus 10th power at the 2 to 3 bar level is a factor of 10 lower than the solar value. The H2O mole fraction is approximately 1 x 0.00001 at the 2.5 bar level and is increasing to approximately 3 x 0.00001 at 4 bars where it is a factor of 30 lower than solar. Using IRIS infrared values for the mole fractions of CH3D and CH4 a value of D/H = 3.6(+1.0 or -1.4)x 0.00001 is derived. Assuming this Jovian D/H ratio is representative of the protosolar nebula, and correcting for chemical galactic evolution, yields a value of 5.5 - 9.0 x 0.00001 for the primordial D/H ratio and an upper limit of 1.8 to 2.4 x 10 to the minus 31st power cu cm for the present day baryon density.

Kunde, V.↗
NASA NTRS1983

Spectral properties of mixtures of montmorillonite and dark grains - Implications for remote sensing minerals containing chemically and physically adsorbed water

The spectral properties from 0.4 to 3 microns of montmorillonite plus dark carbon grains (called opaques) of various sizes are studied as a function of the weight fraction of opaques present. The reflectance level and band depths of the 1.4-, 1.9-, 2.2-, and 2.8-micron water and/or OH absorption features are analyzed using derived empirical relationships and scattering theory. It is found that the absorption band depths and reflectance level are a very nonlinear function of the weight fraction of opaques present but can be predicted in many cases by simple scattering theory. The 2.8-micron bound water fundamental band is the most difficult absorption feature to suppress. The overtone absorptions are suppressed a greater amount than the fundamental but are still apparent even when 10-20 wt pct opaques are present. The relationships observed and the simple scattering theory presented show that quantitative compositional remote sensing studies are feasible for surfaces containing complex mineral mixtures.

Clark, R. N.↗
DOE OSTI2025

Formation and Evolution Simulations of Saturn, Including Composition Gradients and Helium Immiscibility

In this paper, the formation of Saturn is modeled by detailed numerical simulations according to the core-nucleated accretion scenario. Previous models are enhanced to include the dissolution of accreting planetesimals, composed of water ice, rock, and iron, in the gaseous envelope of the planet, leading to a nonuniform composition with depth. The immiscibility of helium in metallic hydrogen layers is also considered. The calculations start at a mass of 0.5 Earth masses and are extended to the present day. At 4.57 Gyr, the model, proceeding outward, has the following structure: (i) a central core composed of 100% heavy elements and molecules, (ii) a region with a decreasing heavy-element mass fraction, down to a value of 0.1, (iii) a layer of uniform composition with the helium mass fraction Y enhanced over the primordial value, (iv) a helium rain region with a gradient in Y, (v) an outer convective, adiabatic region with uniform composition in which Y is reduced from the primordial value, and (vi) the very outer layers where cloud condensation of the heavy elements occurs. Models of the distribution of heavy elements as a function of radius are compared with those derived to fit the observations of the Cassini mission, with rough qualitative agreement. The helium mass fraction in Saturn’s outer layers is estimated to be around 20%. Models are found that provide good agreement with Saturn’s intrinsic luminosity and radius.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2013

The CACAO Method for Smoothing, Gap Filling, and Characterizing Seasonal Anomalies in Satellite Time Series

Consistent, continuous, and long time series of global biophysical variables derived from satellite data are required for global change research. A novel climatology fitting approach called CACAO (Consistent Adjustment of the Climatology to Actual Observations) is proposed to reduce noise and fill gaps in time series by scaling and shifting the seasonal climatological patterns to the actual observations. The shift and scale CACAO parameters adjusted for each season allow quantifying shifts in the timing of seasonal phenology and inter-annual variations in magnitude as compared to the average climatology. CACAO was assessed first over simulated daily Leaf Area Index (LAI) time series with varying fractions of missing data and noise. Then, performances were analyzed over actual satellite LAI products derived from AVHRR Long-Term Data Record for the 1981-2000 period over the BELMANIP2 globally representative sample of sites. Comparison with two widely used temporal filtering methods-the asymmetric Gaussian (AG) model and the Savitzky-Golay (SG) filter as implemented in TIMESAT-revealed that CACAO achieved better performances for smoothing AVHRR time series characterized by high level of noise and frequent missing observations. The resulting smoothed time series captures well the vegetation dynamics and shows no gaps as compared to the 50-60% of still missing data after AG or SG reconstructions. Results of simulation experiments as well as confrontation with actual AVHRR time series indicate that the proposed CACAO method is more robust to noise and missing data than AG and SG methods for phenology extraction.

LAI↗
DOE OSTI2025

Effect of particle size and moisture on flow performance of loblolly pine anatomical fractions: Experimental findings and model predictions

The rising energy demand has highlighted biomass as a promising next-generation energy source. However, commercializing biomass-derived energy faces challenges, particularly in handling biomass feedstock. Factors like particle size, shape, moisture content, and surface roughness significantly impact biomass flowability. This study addresses a crucial knowledge gap by examining the effects of particle size and moisture content on the flow behavior and shear properties of different anatomical fractions of loblolly pine (Pinus taeda). The bulk shear behavior was examined using a Schulze ring shear tester, while flow performance was tested through gravity-driven flow experiments in a variable wedge-shape hopper. Results were incorporated into empirical and machine learning-based flow prediction models to evaluate their accuracy and limitations. The study found that samples with higher moisture content show higher unconfined yield strength. The critical arching distance increased with particle size, e.g., from approximately 13 and 33 mm for 2- and 6-mm whole chips, respectively at a 32-degree inclination angle. Conversely, the flow rate decreased for a given hopper opening as particle size increased. For instance, at a 60-mm hopper opening and a 32-degree inclination angle, the mass flow rates for 2- and 6-mm whole chips were 7.83 and 6.42 tonne/h, respectively. The empirical model consistently overpredicted the mass flow rate for all anatomical fractions, while the machine learning model more accurately predicted the central tendency of flow rate but was insensitive to varying tissue proportions. These novel findings provide comprehensive characterization of anatomical fractions, reveal significant combined effects of particle size and moisture content on biomass flow behavior, and demonstrate a better predictive accuracy of a machine learning model, all of which are useful for optimizing material handling strategies and biomass utilization technologies in the industry.

09 - BIOMASS FUELS↗
DOE OSTI2021

A search for the decays of stopped long-lived particles at $ \sqrt{\mathrm{s}} $ = 13 TeV with the ATLAS detector

A search for long-lived particles, which have come to rest within the ATLAS detector, is presented. The subsequent decays of these particles can produce high-momentum jets, resulting in large out-of-time energy deposits in the ATLAS calorimeters. These de- cays are detected using data collected during periods in the LHC bunch structure when collisions are absent. The analysed dataset is composed of events from proton-proton collisions produced by the Large Hadron Collider at a centre-of-mass energy of s = 13 TeV and recorded by the ATLAS experiment during 2017 and 2018. The dataset used for this search corresponds to a total live time of 579 hours. The results of this search are used to derive lower limits on the mass of gluino R -hadrons, assuming a branching fraction $ \mathcal{B}\left(\overset{\sim }{g}\to q\overline{q}{\chi}_1^0\right) $ B g ~ → q q ¯ χ 1 0 = 100%, with masses of up to 1 . 4 TeV excluded for gluino lifetimes of 10 - 5 to 10 3 s.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Thermomechanical conversion in metals: dislocation plasticity model evaluation of the Taylor-Quinney coefficient

Using a partitioned-energy thermodynamic framework which assigns energy to that of atomic configurational stored energy of cold work and kinetic-vibrational, in this study we derive an important constraint on the Taylor-Quinney coefficient, which quantifies the fraction of plastic work that is converted into heat during plastic deformation. Associated with the two energy contributions are two separate temperatures – the ordinary temperature for the thermal energy and the effective temperature for the configurational energy. We show that the Taylor-Quinney coefficient is a function of the thermodynamically defined effective temperature that measures the atomic configurational disorder in the material. Finite-element analysis of recently published experiments on the aluminum alloy 6016-T4 [1], using the thermodynamic dislocation theory (TDT), shows good agreement between theory and experiment for both stress-strain behavior and temporal evolution of the temperature. The simulations include both conductive and convective thermal energy loss during the experiments, and significant thermal gradients exist within the simulation results. Computed values of the differential Taylor-Quinney coefficient are also presented and suggest a value which differs between materials and increases with increasing strain.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Tool-workpiece stick-slip conditions and their effects on torque and heat generation rate in the friction stir welding

Friction stir welding (FSW) has found increased applications in automotive and aerospace industries due to its advantages of solid-state bonding, no fusion and melting, and versatility in various working conditions and material combinations. However, the relationship among processing parameters, material properties, and bonding extent and fidelity remains largely empirical, primarily because of the lack of the mechanistic understanding of the tool-workpiece frictional behavior that affects our subsequent understanding of microstructural evolution and interface bonding formation. While the tool-workpiece stick-slip condition is believed to dictate the resulting torque and heat generation rate during the welding process, it remains rare and elusive to conduct a quantitative experimental measurement of such interfacial field. On the other hand, numerical simulations based on Computational Fluid Dynamics (CFD) rely on ad hoc assumptions of interfacial pressure and shear-stress conditions, but predictions can only be validated via the medium- and far-range temperature field which is known to be insensitive to the interfacial frictional behavior. This work first presents a comparison among two CFD-based simulation methodologies and the Coupled Eulerian Lagrangian (CEL) model in finite element method, the last of which uses the Coulomb friction so that the stick-slip is naturally developed. Based on the Hill-Bower similarity relationship in the contact analysis, an analytical model is developed here to prove why a constant stick-slip fraction will be developed in the steady state, to correlate the stick-slip fraction to processing parameters such as the tool spin rate, and further to derive dimensionless functions for torque and heat-generation-rate predictions. Pros and cons of various numerical approaches in predicting stick-slip are discussed, and our analytical model has been found to agree well with our numerical simulation and literature experimental results. These analyses provide the critical strain-rate and temperature fields that are needed for the bonding analysis in our future work.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Cost-constrained adaptive simulations of transient spray combustion in a gas turbine combustor

Predictive high-fidelity simulations of turbulent spray combustion must capture the combined effects of complex chemistry, multiphase evaporating flow and spray-flame interactions to achieve physical accuracy. Finite-rate chemistry (FRC) combined with a realistic chemical mechanism is a combustion model well-suited for this purpose, but has a high computational cost due to the large number and stiffness of transported chemical species. In contrast, flamelet-based models achieve lower cost by transporting a small number of quantities of reduced stiffness, but assumptions regarding local flame topology, boundary conditions and inter-phase coupling limit their physical accuracy. Recently, the Pareto-efficient combustion (PEC) framework was developed to dynamically assign combustion models based on local cost and accuracy metrics in gas-phase reacting flows. In this work, we extend this PEC framework to spray combustion through the rigorous analysis of the multiphase coupling terms in the governing equations. The derivation shows that spray evaporation causes errors in the prediction of species mass fractions for flamelet-based models due to the sensitivity of the local thermo-chemical state to changes in composition caused by fuel vaporization across combustion regimes present in practical spray combustion devices. Sub-model assignment is formulated as a multiple-choice knapsack problem, where computational cost is directly controlled through the fraction of the domain assigned to the FRC sub-model. The extended PEC formulation is applied to the simulation of a realistic rich-quench-lean gas turbine combustor at steady-state conditions, as well as transient operation resulting in lean blow-out (LBO). Analysis of transient simulations during LBO demonstrates the extended PEC formulation’s capacity to dynamically adapt to changing conditions within the combustor. Transient combustor dynamics are shown to approach convergence with limited increases in computational cost, while retaining substantial computational cost reduction compared to monolithic FRC simulations. Through PEC simulations with increasing fractions of the domain assigned to FRC, monolithic flamelet simulations are shown to over-predict flame stability during LBO. Finally, the extended PEC formulation is thus shown to overcome deficiencies of monolithic models by controlling modeling error for multiphase combustion modeling.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Three-dimensional mapping of mineral in intact shark centra with energy dispersive x-ray diffraction

The centra of shark vertebrae consist of cartilage mineralized by a bioapatite similar to bone's carbonated hy-droxyapatite, and, without a repair mechanism analogous to remodeling in bone, these structures still survive millions of cycles of high-strain loading. The main structures of the centrum are an hourglass-shaped double cone and the intermedialia which supports the cones. Little is known about the nanostructure of shark centra, spe-cifically the relationship between bioapatite and cartilage fibers, and this study uses energy dispersive diffraction (EDD) with polychromatic synchrotron x-radiation to study the spatial organization of the mineral phase and its crystallographic texture. The unique energy-sensitive detector array at beamline 6-BM-B, the Advanced Photon Source, enables EDD to quantify the texture within each sampling volume with one exposure while constructing 3D maps via specimen translation across the sampling volume. Herein this study maps a centrum from two shark orders, a carcharhiniform and a lamniform, with different intermedialia structures. In the blue shark (Prionace glauca, Carcharhiniformes), the bioapatite's c-axes are oriented laterally within the centrum's cone walls but axially within the wide wedges of the intermedialia; the former is interpreted to resist lateral deformation, the latter to support axial loads. In the shortfin mako (Isurus oxyrinchus, Lamniformes), there is some tendency for c-axis variation with position, but the situation is unclear because one dimension of the sampling volume is consid-erably larger than the thickness and spacing of the intermedialia's radially-oriented lamellae. Because elastic modulus in collagen plus bioapatite mineralized tissues varies significantly with both volume fraction of bio-apatite and crystallographic texture, the present 3D EDD-derived maps should inform future 3D numerical models of shark centra under applied load.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Astrophysical Explosions Revisited: Collisionless Coupling of Debris to Magnetized Plasma

The coupling between a rapidly expanding cloud of ionized debris and an ambient magnetized plasma is revisited with a hybrid (kinetic ion/fluid electron) simulation code that allows a study over a wide range of plasma parameters. Over a specified range of hypothetical conditions, simple scaling laws in terms of the total debris mass and explosion speed are derived and verified for the maximal size of the debris cloud and the fraction of debris that free-streams from the burst along the magnetic field. Furthermore, the amount of debris that escapes from the burst with minimal coupling to the background magnetic field increases with the debris gyroradius. Test cases with two different debris species—including a heavy minority species with a relatively large gyroradius—highlight how the collisionless coupling of the debris depends on the single particle trajectories as well as the overall conservation of energy and momentum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Here we analyze a plurality of epidemiological models through the lens of physics-informed neural networks (PINNs) that enable us to identify time-dependent parameters and data-driven fractional differential operators. In particular, we consider several variations of the classical susceptible-infectious-removed (SIR) model by introducing more compartments and fractional-order and time-delay models. We report the results for the spread of COVID-19 in New York City, Rhode Island and Michigan states and Italy, by simultaneously inferring the unknown parameters and the unobserved dynamics. For integer-order and time-delay models, we fit the available data by identifying time-dependent parameters, which are represented by neural networks. In contrast, for fractional differential models, we fit the data by determining different time-dependent derivative orders for each compartment, which we represent by neural networks. We investigate the structural and practical identifiability of these unknown functions for different datasets, and quantify the uncertainty associated with neural networks and with control measures in forecasting the pandemic.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Physical implications of the extrapolation and statistical bootstrap of nucleon structure function ratios F 2 n F 2 p for mirror nuclei He 3 and H 3

A nuclear physics example of statistical bootstrap is used on the MARATHON nucleon structure function ratio data in the quark momentum fraction regions x B → 0 and x B → 1. The extrapolated F 2 ratio as quark momentum fraction x B → 1 is $\frac{F^n_2}{F^p_2}$ → 0.4 ± 0.05 and this value is compared to theoretical predictions. The extrapolated ratio when x B → 0 favors the simple model of isospin symmetry with the complete dominance of sea quarks at low momentum fraction. At high- x B , the proton quark distribution function ratio d/u is derived from the F 2 ratio and found to be d/u → 1/6. Our extrapolated values for both the $\frac{F^n_2}{F^p_2}$ ratio and the d/u parton distribution function ratio are within uncertainties of perturbative QCD values from quark counting, helicity conservation arguments, and a Dyson-Schwinger equation with a contact interaction model. In addition, it is possible to match the statistical bootstrap value to theoretical predictions by allowing two compatible models to act simultaneously in the nucleon wave function. Finally, one such example is nucleon wave functions composed of a linear combination of a quark-diquark state and a three-valence quark correlated state with coefficients that combine to give the extrapolated F 2 ratio at x B = 1.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1972

Comparative petrology of Apollo 16 sample 68415 and Apollo 14 samples 14276 and 14310.

Petrographic and electron microprobe studies of Apollo 16 igneous rock 68415 and Apollo 14 rocks 14276 and 14310 show that all three samples differ from the mare basalts and are characterized by plagioclase as the first liquidus phase and by the abundance of plagioclase which is in part cumulate in origin. Major and minor element abundances and isotopic data prohibit the derivation of rocks like any of these samples from one another by magmatic fractionation during their crystallization. They could have originated by partial melting of an old, more Al-rich source material without isotopic equilibration with the residuum, by complete melting of three independent sources, or by contamination with old radiogenic material. The existence of such feldspathic basalts indicates that the generation of Al-rich magmas may have been an important and widespread lunar process.

Gancarz, A. J.↗
NASA NTRS1975

Approximate solutions of radiative transfer in dusty nebulae. 2: Hydrogen and helium

The ionization structure of hydrogen and helium in dusty nebulae is discussed. The general equations for pure hydrogen nebulae are modified to include helium. An approximate analytic solution is presented for Stroemgren radii of hydrogen and helium in the absence of dust. It is shown that these results, with simple modifications, are also applicable to dusty nebulae where the effective absorption cross section of dust grains varies slowly with frequency in the 1000 to 200A range. No analytic solutions are possible if this cross section varies rapidly with frequency. In this case, however, simple coupled differential equations are derived. Approximate analytic expressions are presented for evaluation of the variation of the fraction of ionizing radiation absorbed by dust and the ratio of the volume emission measures of He II to H II regions with the spectrum of the ionizing source, helium abundance, and absorption properties of dust. The effects of dust on the He III zone are discussed. Results are restricted to spherically symmetric nebulae, but nonuniform gas and dust distributions and clumpiness can be taken into account.

Dana, R. A.↗
NASA NTRS1976

Equilibrium properties of chemically reacting gases

The equilibrium energy, enthalpy, entropy, specific heat at constant volume and constant pressure, and the equation of state of the gas are all derived for chemically reacting gas mixtures in terms of the compressibility, the mol fractions, the thermodynamic properties of the pure gas components, and the change in zero point energy due to reaction. Results are illustrated for a simple diatomic dissociation reaction and nitrogen is used as an example. Next, a gas mixture resulting from combined diatomic dissociation and atomic ionization reactions is treated and, again, nitrogen is used as an example. A short discussion is given of the additional complexities involved when precise solutions for high-temperature air are desired, including effects caused by NO produced in shuffle reactions and by other trace species formed from CO2, H2O and Ar found in normal air.

Source record↗
NASA NTRS1979

Apollo 12 feldspathic basalts 12031, 12038 and 12072 - Petrology, comparison and interpretations

The paper presents the petrology of Apollo 12 feldspathic basalts. Modal and chemical data indicate that basalts 12072, 12038, and 12031 cannot be related to the other Apollo rock types; 12072 contains phenocrysts of olivine and pigeonite, 12038 is a multiply saturated equigranular basalt, and 12031 is a coarse-grained rock with granular to graphic intergrowths of pyroxene and plagioclase. The bulk compositions indicate that these basalts could not have been derived from the Apollo 12 olivine or ilmenite basalts by crystal-liquid fractionation, and their petrologic similarities suggest that they were produced in the same or similar source regions.

Beaty, D. W.↗