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 127 records · Page 7

TPSAS-NF1676L-11084-DND

The solar radiation must be considered as the primary factor when we study the climatic system because it provides almost all energy that drives the climatic system and most atmospheric phenomena. The solar radiation at the TOA is partially transferred, transformed into other forms of energy that are eventually dissipated by the general circulation of the atmosphere and oceans, and partially used in chemical and biological processes. The absorption of solar energy in the atmosphere (Acol) plays a key role in the climate system, not only because it affects the amount of solar energy absorbed by the Earth system, but also because it changes the vertical distribution of absorbed energy, which in turn impacts surface evaporation, atmospheric convection and precipitation. To investigate Acol, we have collected the collocated satellite-surface observations over the 35 selected BSRN surface sites during the period 2000-2004. The surface radiation budgets are averaged from the BSRN Shortwave (SW) observations over a 1-hour interval centered at the time of the NASA Terra and Aqua satellites overpass, and the TOA radiation budgets are averaged from the closest FOV satellite data to the BSRN stations. Then the atmospheric column SW absorption will be inferred from the satellite TOA albedo and BSRN surface absorption (through the estimated surface albedo). Monthly means of Acol, TOA albedo, and surface absorption have been calculated under both clear- and all-sky conditions over the 35 selected BSRN sites which represent different climate regimes. To evaluate the GCM simulations, we have collected the ECHAM5-HAM simulated surface, TOA and atmospheric radiation budgets by researchers at ETH Zurich and compared those simulations with observations. The preliminary comparisons have shown that the ECHAM5 simulated clear-sky surface absorption, TOA albedo, and ACOL agree very well (1-3%) with observations. Under all-sky conditions, they have strong correlations with CERES-derived cloud fraction. The simulated surface absorption is lower and TOA albedo is higher than those under clear skies, but ACOL does not increase too much. However, there are relatively large differences over some regions and months. A further study is needed.

X. Dong↗

Helicity in the Large-Scale Galactic Magnetic Field

We search for observational signatures of magnetic helicity in data from all-sky radio polarization surveys of the Milky Way Galaxy. Such a detection would help confirm the dynamo origin of the field and may provide new observational constraints for its shape. We compare our observational results to simulated observations for both a simple helical field, and for a more complex field that comes from a solution to the dynamo equation. Our simulated observations show that the large-scale helicity of a magnetic field is reflected in the large-scale structure of the fractional polarization derived from the observed synchrotron radiation and Faraday depth of the diffuse Galactic synchrotron emission. Comparing the models with the observations provides evidence for the presence of a quadrupolar magnetic field with a vertical component that is pointing away from the observer in both hemispheres of the Milky Way Galaxy. Since there is no reason to believe that the Galactic magnetic field is unusual when compared to other galaxies, this result provides further support for the dynamo origin of large-scale magnetic fields in galaxies.

J. L. West↗

A two-equation soot-in-flamelet modeling approach applied under Spray A conditions

Soot production (including formation and oxidation) is studied in the transient, high-pressure and turbulent n-dodecane Spray A flames from the Engine Combustion Network (ECN) using computational fluid dynamics (CFD) simulations. A two-equation soot-in-flamelet modeling approach is applied within the framework of the Unsteady Flamelet Progress Variable (UFPV) model and results are validated against experimental data. Equations for soot mass fraction and soot number density derived in the mixture fraction space are solved in the context of detailed flamelet calculations. Source terms for the different steps in the soot chemistry are tabulated and incorporated in the flamelet manifold. For the reference condition, the modeling approach based on the tabulated flamelet manifold reduces the computational cost of a CFD calculation by approximately 40 times compared to a non-tabulated well-mixed (WM) modeling approach. The soot-in-flamelet approach is then extended to study the effect of ambient oxygen concentration, ambient mixture composition and ambient temperature on soot production. Results show that the modeling approach is able to capture the experimental trends for the soot volume fraction (SVF) with good quantitative agreement, especially in the soot ramp-up region.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effective-field-theory model for the fractional quantum Hall effect

Starting directly from the microscopic Hamiltonian, a field-theory model is derived for the fractional quantum Hall effect. By considering an approximate coarse-grained version of the same model, a Landau-Ginzburg theory similar to that of Girvin (1986) is constructed. The partition function of the model exhibits cusps as a function of density. It is shown that the collective density fluctuations are massive.

Zhang, S. C.↗

Transfer hydrogenation of heavy hydrocarbons with hydrogen-donor solvents

Processes for converting the coal-derived heavy-oil fraction of syncrude to polyols are described. The processes involve mixing a feed stream comprising the coal-derived heavy-oil fraction with an alcohol and aqueous sulfuric acid, heating the mixture, reacting the coal-derived heavy-oil fraction with ozone, and reacting the ozonated heavy-oil fraction with glycerin to form the polyol. In some cases, the ozonated heavy-oil fraction can be neutralized before reacting the ozonated heavy-oil fraction with the glycerin.

Chauhan, Satya P.↗

Exceptional Thermal Properties of Polymer-Derived Ceramic Composites Reinforced with High Volume Fractions of Boron Nitride Nanotube at Elevated Temperature

We report for the first time the synthesis of boron nitride nanotube (BNNT) reinforced ceramic composites using the polymer derived ceramic (PDC) processing route. The nanocomposites had a BNNT loading of up to 35.4 vol.%. TGA results showed that the nanocomposites have good thermal stability up to 900 oC in air. BNNTs in the nanocomposites survived in an oxidizing environment up to 900 oC, revealing that the nanocomposites can be used for high temperature applications. Thermal conductivity of PDC reinforced with 35.4 vol.% BNNT was measured as 4.123 W/(m·K) at room temperature, which is a 2100 % increase compared to that of pristine PDC. The thermal conductivity value increases with the increase of BNNT content. A thermal conductivity percolation phenomenon appeared when the BNNT content increased to 36±5 vol.%. The results of this study showed that BNNTs could effectively improve the thermal conductivity of PDC materials. BNNT reinforced PDC could be used as thermal structural materials in a harsh environment at the temperature up to 900 deg C.

Yujun Jia↗

Origin of picritic green glass magmas by polybaric fractional fusion

A preliminary presentation is given of a model which explains the picritic lunar mare green glass compositions as composites or magmas derived by polybaric fractional melting. The model accommodates changes in source composition and solidus temperature. As in the Klein and Langmuir model, the final compositions of the melts signify only average depths of melting. The onset of melting is deeper, final segregation is shallower.

Longhi, John↗

Generalized fractional approach to solving partial differential equations with arbitrary dispersion relations

The dynamics of physical systems are typically modeled by partial differential equations (PDEs). Because of the complexity in physical systems, PDE models rely on approximations or limiting cases. To model the full complexity of physical systems, it is necessary to use multiscale approaches where appropriate models are used at each level. Alternatively, complexity can be directly tackled by fractional integrodifferential equations that must be derived for each system. Here, we argue that complexity can be restored in PDEs by describing them from a fractional calculus perspective. Rather than deriving a fractional integrodifferential equation, we reinterpret the dispersion relation of the system by use of the Riesz definition, which contains the required information relating the energy and momentum space of the system and thus fully describes their dynamics. The approach is demonstrated by two examples: the Landau–Lifshitz equation in a 1D ferromagnetic chain and a modified KdV equation supporting surface gravity waves or Euler dispersion. The presented approach is applicable to fluids, soft matter, and solid-state matter and can be readily generalized to higher dimensions and more complex systems. While numerical calculations are needed to determine the fractional operator, the approach is analytical and can be utilized to determine analytical solutions and investigate nonlinear problems.

97 MATHEMATICS AND COMPUTING↗

Composite interstellar grains

The possibility that interstellar grains are composite collections of very small particles, loosely attached to one another, is investigated. The grains are assumed to include a substantial proportion of vacuum along with solid particles. The optical properties of the composite grains are calculated with the approximate 'Bruggeman mixing rule', and the extinction of the grain is calculated wih standard Mie theory. The derived cross sections are close to those of hollow spheres in which the constituents occupy the proper volume fractions, and the derived optical constants of the mixture also obey the Kramers-Kroenig relations. The calculated interstellar extinction law shows reasonable agreement with observations of the diffuse ISM over the 1500-0.12 micron wavelength range. The predicted albedo is 0.5-0.6. It is predicted that the visual extinction per H nucleus should increase slightly with R(V).

Mathis, John S.↗

Predicting Bone Mechanical State During Recovery After Long-Duration Skeletal Unloading Using QCT and Finite Element Modeling

During long-duration missions at the International Space Station, astronauts experience weightlessness leading to skeletal unloading. Unloading causes a lack of a mechanical stimulus that triggers bone cellular units to remove mass from the skeleton. A mathematical system of the cellular dynamics predicts theoretical changes to volume fractions and ash fraction in response to temporal variations in skeletal loading. No current model uses image technology to gather information about a skeletal site s initial properties to calculate bone remodeling changes and then to compare predicted bone strengths with the initial strength. The goal of this study is to use quantitative computed tomography (QCT) in conjunction with a computational model of the bone remodeling process to establish initial bone properties to predict changes in bone mechanics during bone loss and recovery with finite element (FE) modeling. Input parameters for the remodeling model include bone volume fraction and ash fraction, which are both computed from the QCT images. A non-destructive approach to measure ash fraction is also derived. Voxel-based finite element models (FEM) created from QCTs provide initial evaluation of bone strength. Bone volume fraction and ash fraction outputs from the computational model predict changes to the elastic modulus of bone via a two-parameter equation. The modulus captures the effect of bone remodeling and functions as the key to evaluate of changes in strength. Application of this time-dependent modulus to FEMs and composite beam theory enables an assessment of bone mechanics during recovery. Prediction of bone strength is not only important for astronauts, but is also pertinent to millions of patients with osteoporosis and low bone density.

Chang, Katarina L.↗

Derivation and Testing of Consumptive Water Use Fraction for Specialty Crops

The Crop Consumptive Use Fraction (CCUF) expresses beneficial water use in the form of seasonal evapotranspiration of applied water (ETAW), relative to total irrigation volume. The metric is an indicator of the efficiency of agricultural water use and is a recommended component for preparation of agricultural water management plans in California. An FAO-56 based web application has been developed to facilitate retrospective evaluation of ETAW, and hence CCUF, at field level. The current application is optimized for prevailing climate in four of the state’s main growing regions: San Joaquin Valley, Sacramento Valley, Central Coast, and North Coast. User inputs include crop type, soil texture, irrigation method, daily irrigation volume, daily rainfall, and seasonal start/stop dates to define the analysis period. Time series of fractional green canopy cover (Fc), based on Landsat and Sentinel-2 Earth-resource satellite observations, are imported from NASA’s Satellite Irrigation Management Support (SIMS) system. Grass reference evapotranspiration (ETo) time series are accessed from Spatial CIMIS (California Irrigation Management Information System). Daily crop height (h) is estimated as a simple function of typical maximum height for the given crop type (from FAO-56) and Fc. A vegetation density coefficient (Kd) is derived from Fc and h. Stomatal control factors during mid-and late-season are applied to tree and vine crops. Typical values for minimum daily relative humidity and mean daily windspeed, derived from historical CIMIS weather data, are used to correct for regional deviations from standard climate (defined as RHmin=45%, windspeed =2m/s). The resulting daily basal crop coefficient (Kcb) represents the ET of a well-watered crop with minimal soil evaporation, relative to ETo. A soil water balance sub-model for the top 0.1 m is used to calculate daily evaporation coefficients (Ke). A second sub-model applies to the root zone to calculate crop water stress coefficients (Ks) and effective precipitation (Pe), which is the fraction of rainfall that is available for crop use. Those coefficients are combined with Kcb and ETo to calculate daily ETc. ETAW is then derived as cumulative ETc less cumulative Pe. For verification purposes, sensor installations were used to measure seasonal ETc in commercial fields for several annual and perennial specialty crops by soil water balance and energy balance methods. Model estimates of seasonal ETc show mean absolute error of <10% compared to the ground measurements.

Derivation↗

Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits

Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.

Atmospheric Turbulence Modeling↗

Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits

Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.

Kopasakis, George↗

Sequential Precipitation Input Tagging (SPIT) to Estimate Water Transit Times and Hydrologic Tracer Dynamics Within Water‐Tagging Enabled Hydrologic Models

Determining the age distribution of water exiting a catchment is important for understanding groundwater storage and mixing. New water-tagging capabilities within models track precipitation events as they move through simulated storages, yet forward modeling of individual events may not systematically capture the full transit time distribution (TTD). Here, we present a “sequential precipitation input tagging” (SPIT) framework to tag all input precipitation at regular intervals during extended model simulations. Monthly tags over 7 years were applied at six National Ecological Observatory Network sites to calculate TTDs and derive mean virtual tracer age, $\overline{T_{V}}$, fractions of young water, F yw , and hydrologic tracer concentrations (water isotopes δ 18 O and δ 2 H) within a tagging enabled version of the Weather Research and Forecast hydrologic model (WRF-Hydro). Throughout seven simulation years, the fraction of simulated discharge derived from tagged events, F tag , increased each year, with the final year's F tag ranging from 66% to 100% and highlights the need to apply SPIT over many years to understand TTDs. When the F tag was >75%, simulated $\overline{T_{V}}$ ranged 179–923 days and F yw 0.6%–23.9%, with daily values exhibiting a power-law relationship with precipitation, discharge, and groundwater. Through implementation of SPIT, we find this hydrologic model configuration performs poorly in estimation of $\overline{T_{V}}$ and F yw (root mean squared error of 469 days and 14.4% respectively), suggesting it misrepresents subsurface mixing. Thus, the SPIT framework provides a reproducible approach to calculate watershed transit times within tagging enabled models and thereby assess and improve representation of hydrologic processes.

fraction of young water↗

Analyses of Cometary Silicate Crystals: DDA Spectral Modeling of Forsterite

Comets are the Solar System's deep freezers of gases, ices, and particulates that were present in the outer protoplanetary disk. Where comet nuclei accreted was so cold that CO ice (approximately 50K) and other supervolatile ices like ethane (C2H2) were preserved. However, comets also accreted high temperature minerals: silicate crystals that either condensed (greater than or equal to 1400 K) or that were annealed from amorphous (glassy) silicates (greater than 850-1000 K). By their rarity in the interstellar medium, cometary crystalline silicates are thought to be grains that formed in the inner disk and were then radially transported out to the cold and ice-rich regimes near Neptune. The questions that comets can potentially address are: How fast, how far, and over what duration were crystals that formed in the inner disk transported out to the comet-forming region(s)? In comets, the mass fractions of silicates that are crystalline, f_cryst, translate to benchmarks for protoplanetary disk radial transport models. The infamous comet Hale-Bopp has crystalline fractions of over 55%. The values for cometary crystalline mass fractions, however, are derived assuming that the mineralogy assessed for the submicron to micron-sized portion of the size distribution represents the compositional makeup of all larger grains in the coma. Models for fitting cometary SEDs make this assumption because models can only fit the observed features with submicron to micron-sized discrete crystals. On the other hand, larger (0.1-100 micrometer radii) porous grains composed of amorphous silicates and amorphous carbon can be easily computed with mixed medium theory wherein vacuum mixed into a spherical particle mimics a porous aggregate. If crystalline silicates are mixed in, the models completely fail to match the observations. Moreover, models for a size distribution of discrete crystalline forsterite grains commonly employs the CDE computational method for ellipsoidal platelets (c:a:b=8.14x8.14xl in shape with geometrical factors of x:y:z=1:1:10, Fabian et al. 2001; Harker et al. 2007). Alternatively, models for forsterite employ statistical methods like the Distribution of Hollow Spheres (Min et al. 2008; Oliveira et al. 2011) or Gaussian Random Spheres (GRS) or RGF (Gielen et al. 200S). Pancakes, hollow spheres, or GRS shapes similar to wheat sheaf crystal habit (e.g., Volten et al. 2001; Veihelmann et al. 2006), however, do not have the sharp edges, flat faces, and vertices seen in images of cometary crystals in interplanetary dust particles (IDPs) or in Stardust samples. Cometary forsterite crystals often have equant or tabular crystal habit (J. Bradley). To simulate cometary crystals, we have computed absorption efficiencies of forsterite using the Discrete Dipole Approximation (DDA) DDSCAT code on NAS supercomputers. We compute thermal models that employ a size distribution of discrete irregularly shaped forsterite crystals (nonspherical shapes with faces and vertices) to explore how crystal shape affects the shape and wavelength positions of the forsterite spectral features and to explore whether cometary crystal shapes support either condensation or annealing scenarios (Lindsay et al. 2012a, b). We find forsterite crystal shapes that best-fit comet Hale-Bopp are tetrahedron, bricks or brick platelets, essentially equant or tabular (Lindsay et al. 2012a,b), commensurate with high temperature condensation experiments (Kobatake et al. 2008). We also have computed porous aggregates with crystal monomers and find that the crystal resonances are amplified. i.e., the crystalline fraction is lower in the aggregate than is derived by fitting a linear mix of spectral features from discrete subcomponents, and the crystal resonances 'appear' to be from larger crystals (Wooden et al. 2012). These results may indicate that the crystalline mass fraction in comets with comae dominated by aggregates may be lower than deduced by popular methods that only emoy ensembles of discrete crystals.

Wooden, Diane↗

Spectral energy distributions of the brightest Palomar-Green quasars at intermediate redshifts

We have combined low-dispersion International Ultraviolet Explorer (IUE) spectra with the optical/near-IR spectrophotometry of Neugebauer et al. (1987) in order to study the spectral energy distributions of seven of the brightest Palomar-Green (PG) quasars at intermediate redshifts (Z(sub em) greater than or equal to 0.9 and less than or equal to 1.5). Some of these PG quasars are barely detectable in long IUE exposures, so we have used the Gaussian Extraction (GEX) technique to maximize the signal-to-noise of the IUE data, and we have co-added all spectra available from the IUE archive for each QSO unless the ultraviolet spectra varied significantly from one exposure to the next. We have corrected the spectral energy distributions for Milky Way reddening using the observed neutral hydrogen column densities on each sight line and the gas-to-dust relation recently derived by Diplas & Savage. Six of the seven quasars are detected down to lambda much less than 700 A in the rest frame, and consequently continuum reddening due to dust in the immediate vicinity of the quasar can have a dramatic effect on the spectral energy distributions. In order to explore the possible importance of intrinsic continuum reddening, we have assembled a heuristic extinction curve which extends to lambda much less than 912 A. Using this heuristic extinction curve, we derive reasonable upper limits on the intrinsic E(B-V) for each quasar. We briefly discuss some of the implications of the derived intrinsic continuum reddening limits. We use geometrically thin accretion disk models to derive the black hole masses and accretion rates implied by the spectral energy distributions. Even if we neglect intrinsic reddening, we find that a large fraction of the quasars require super-Eddington accretion rates (which is not consistent with the thin disk assumption). Comparison of the data in this paper to a large body of data from the literature on the accretion disk M(sub BH) - M dot grid calculated by Wandel & Petrosian reveals that our quasars are among the brightest in the sky at 1450 A, and ostensibly suggests that the fraction of quasars which require super-Eddington accretion rates is much smaller than the fraction that we derive from our data alone. However, intrinsic continuum reddening has been ignored in this comparison, and a small amount of intrinsic reddening will push more of the quasars into the super-Eddington regime. We also plot the recent reverberation monitoring results on NGC 5548 and NGC 3783 on the Wandel & Petrosian grid, and we find that these Seyfert galaxies appear to vary along lines of constant M(sub BH). Continuum flux from two of the quasars in our main sample, PG 1338+416 and PG 1630+377, is detected at lambda(sub rest) less than 584 A. These quasars can in principle be used for the He I Gunn-Peterson test, but the S/N of IUE spectra of individual objects is usually too low to place interesting limits on the Gunn-Peterson optical depth. In order to improve the S/N, we have formed a composite spectrum from the spectra of five quasars detected with IUE at lambda(sub rest) less than 584 A, and we have used this composite spectrum to place a tighter limit on tau(sub GP, He I). We briefly discuss intermediate-redshift Lyman limit systems (Z(sub LL) greater than or equal to 0.5 and less than or equal to 1.6) detected in the IUE spectra of five quasars, including lower limits on N(H I) in each Lyman limit system.

Tripp, Todd M.↗

Numerical analysis of discrete fractional integrodifferential structural dampers

This paper develops solution algorithms enabling the handling of the dynamic response of nonlinear structures contained discretely attached dampers modeled by fractional integrodifferential operators of the Grunwald-Liouville-Riemann type. The development consists of two levels of formulation, namely: (1) numerical approximations of fractional operators and, (2) the establishment of global level implicit schemes enabling the solution to nonlinear structural formulations. To generalize the overall results, error estimates are derived for the fractional operator approximation algorithm. These enable an ongoing optimization of solution efficiency for a given error tolerance. To benchmark the scheme, the results of several numerical experiments are presented. These illustrate the numerical characteristics of the overall formulation.

Padovan, Joseph↗

Assessing Arctic low-level clouds and precipitation from above – a radar perspective

Most Arctic clouds occur below 2 km altitude as revealed by CloudSat satellite observations. However, recent studies suggest that the relatively coarse spatial resolution, low sensitivity, and blind zone of the radar installed on CloudSat may not enable it to comprehensively document low-level clouds. We investigate the impact of these limitations on the Arctic low- level cloud fraction, which is the amount of cloudy points with respect to all points as a function of height, derived from CloudSat radar observations. For this purpose, we leverage highly resolved vertical profiles of low-level cloud fraction derived from downlooking Microwave Radar/radiometer for Arctic Clouds (MiRAC) radar reflectivity measurements. MiRAC has been operated during four aircraft campaigns taking place in the vicinity of Svalbard during different times of the year and covering more than 25,000 km. This allows us to study the dependence of CloudSat limitations on different synoptic and surface conditions.

54 ENVIRONMENTAL SCIENCES↗