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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Assessment of Cloud Fraction Derived from a New Geostationary Satellite Cloud Retrieval Algorithm for CERES and Progress Towards Cross-platform Continuity

For over two decades The Clouds and the Earth’s Radiant Energy System (CERES) project has produced long-term records of top-of-atmosphere (TOA) and surface irradiances for detecting changes in the Earth’s radiation budget and advancing understanding of how clouds contribute to those changes. Accurate characterization of the spatial and temporal distributions of clouds are a critical component for producing CERES datasets. The CERES Cloud Working Group (CWG) derives cloud properties from both geostationary (GEO) and low-Earth orbit (LEO) satellite sensors in order to provide complete global coverage at hourly temporal resolution. However, the use of multiple sensors to provide this spatiotemporal coverage throughout a long-term record presents some challenges, because the various sensors generally have different spectral band characteristics (e.g., spectral band width and response) and spatial resolution. These differences can result in spatial artifacts at the coverage boundary between two sensors or temporal artifacts when one sensor replaces another in the record. For the upcoming Edition 5 release of CERES products, the CWG is developing cloud retrieval algorithms which utilize only spectral bands common to most modern passive satellite radiometers and account for differences in spectral width and response. The goal with this approach is to provide global cloud properties for CERES with greater cross-platform consistency than the previous Edition 4 products and thus mitigate artifacts which are evident at the interface of two sensors. This study focuses on retrieval of total cloud fraction from various GEO sensors, and we use Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) observations to assess the accuracy of total cloud fraction derived from the various sensors. The Edition 5 cloud mask algorithm depends on estimates of cloud-free TOA spectral radiances to differentiate clear and cloudy conditions, and CALIOP is used to assess the accuracy of those estimates when cloud-free conditions are indeed observed.

CALIOP↗
NASA NTRS1993

Mapping and monitoring changes in vegetation communities of Jasper Ridge, CA, using spectral fractions derived from AVIRIS images

An important application of remote sensing is to map and monitor changes over large areas of the land surface. This is particularly significant with the current interest in monitoring vegetation communities. Most of traditional methods for mapping different types of plant communities are based upon statistical classification techniques (i.e., parallel piped, nearest-neighbor, etc.) applied to uncalibrated multispectral data. Classes from these techniques are typically difficult to interpret (particularly to a field ecologist/botanist). Also, classes derived for one image can be very different from those derived from another image of the same area, making interpretation of observed temporal changes nearly impossible. More recently, neural networks have been applied to classification. Neural network classification, based upon spectral matching, is weak in dealing with spectral mixtures (a condition prevalent in images of natural surfaces). Another approach to mapping vegetation communities is based on spectral mixture analysis, which can provide a consistent framework for image interpretation. Roberts et al. (1990) mapped vegetation using the band residuals from a simple mixing model (the same spectral endmembers applied to all image pixels). Sabol et al. (1992b) and Roberts et al. (1992) used different methods to apply the most appropriate spectral endmembers to each image pixel, thereby allowing mapping of vegetation based upon the the different endmember spectra. In this paper, we describe a new approach to classification of vegetation communities based upon the spectra fractions derived from spectral mixture analysis. This approach was applied to three 1992 AVIRIS images of Jasper Ridge, California to observe seasonal changes in surface composition.

Sabol, Donald E., Jr.↗
DOE OSTI2020

Antimicrobial Properties of Corn Stover Lignin Fractions Derived from Catalytic Transfer Hydrogenolysis in Supercritical Ethanol with a Ru/C Catalyst

Converting lignin to value-added products at high yields provides an avenue for making ethanol biorefineries more profitable while reducing the carbon footprint of products generally derived from petroleum. In this study, corn stover lignin was depolymerized by catalytic transfer hydrogenolysis (CTH) in supercritical ethanol with a Ru/C catalyst. The lignin-derived bio-oil was then sequentially extracted utilizing hexane, petroleum ether, chloroform, and ethyl acetate as solvents in order of less polar to polar, and the subsequent bio-oils were characterized using GPC, GC/MS, and HSQC NMR. In this work, results show that the monomers in the bio-oil fractions contained primarily alkylated phenols, hydrogenated hydroxycinnamic acid derivatives, syringol and guaiacol-type lignins created from reductive cleavages of ether linkages, which were sequentially extracted into groups depending on the solvent polarity. The antimicrobial properties of the bio-oils were screened against Gram-positive (Bacillus subtilis, Lactobacillus amylovorus, and Staphylococcus epidermidis) and Gram-negative (Escherichia coli) bacteria and yeast (Saccharomyces cerevisiae) by examining microbial growth inhibition. Results show that CTH-derived bio-oils inhibited all tested organisms at concentrations less than 3 mg/mL. Total monomer concentration and the presence of specific monomers (i.e., syringyl propane) showed correlations to antimicrobial activity, likely due to cell death or membrane damage. This study provides insights into using sequential extraction to fractionate lignin-derived compounds and correlations between the properties of the extracted compounds and their antimicrobial activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1983

High performance liquid chromatographic hydrocarbon group-type analyses of mid-distillates employing fuel-derived fractions as standards

Two high performance liquid chromatographic (HPLC) methods have been developed for the determination of saturates, olefins and aromatics in petroleum and shale derived mid-distillate fuels. In one method the fuel to be analyzed is reacted with sulfuric acid, to remove a substantial portion of the aromatics, which provides a reacted fuel fraction for use in group type quantitation. The second involves the removal of a substantial portion of the saturates fraction from the HPLC system to permit the determination of olefin concentrations as low as 0.3 volume percent, and to improve the accuracy and precision of olefins determinations. Each method was evaluated using model compound mixtures and real fuel samples.

Seng, G. T.↗
NASA NTRS1991

The least-squares mixing models to generate fraction images derived from remote sensing multispectral data

Constrained-least-squares and weighted-least-squares mixing models for generating fraction images derived from remote sensing multispectral data are presented. An experiment considering three components within the pixels-eucalyptus, soil (understory), and shade-was performed. The generated fraction images for shade (shade image) derived from these two methods were compared by considering the performance and computer time. The derived shade images are related to the observed variation in forest structure, i.e., the fraction of inferred shade in the pixel is related to different eucalyptus ages.

Shimabukuro, Yosio Edemir↗
NASA NTRS2004

Control of Initialized Fractional-Order Systems

Fractional-Order systems, or systems containing fractional derivatives and integrals, have been studied by many in the engineering area. Additionally, very readable discussions, devoted specifically to the subject, are presented by Oldham and Spanier, Miller and Ross, and Pudlubny (1999a). It should be noted that there are a growing number of physical systems whose behavior can be compactly described using fractional system theory. Of specific interest to electrical engineers are long lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, and chaos. With the growing number of applications, it is important to establish a theory of control for these fractional-order systems, and for the potential use of fractional-order systems as feedback compensators. This topic is addressed in this paper. The first section discusses the control of fractional-order systems using a vector space representation, where initialization is included in the discussion. It should be noted that Bagley and Calico and Padovan and Sawicki both present a fractional state-space representation, which do not include the important historic effects. Incorporation of these effects based on the initialized fractional calculus is presented . The control methods presented in this paper are based on the initialized fractional order system theory. The second section presents an input-output approach. Some of the problems encountered in these sections are: a) the need to introduce a new complex plane to study the dynamics of fractional-order systems, b) the need to properly define the Laplace transform of the fractional derivative, and c) the proper inclusion of the initialization response in the system and control formulation. Following this, the next section generalizes the proportional-plus-integral-control (PI-control) and PID-control (PI-plus- derivative) concepts using fractional integrals. This is then further generalized using general fractional- order compensators. Finally the compensator concept is generalized by the use of a continuum of fractions in the compensator via the concept of order-distributions. The last section introduces fractional feedback in discrete-time.

Hartley, Tom T.↗
DOE OSTI2025

A Region-Growing Segmentation Approach to Delineating Timberline from Satellite-Derived Tree Fractional Cover Products

Timberline marks the transitions from continuous forests to sparse forests and tundra landscapes. As the spatial distribution and dynamics of timberline are closely associated with regional energy and carbon balance, mapping timberline is important to a wide range of environmental and ecological studies. However, current timberline delineation approaches remain under-developed. We proposed an automatic timberline delineation method based on a seeded region-growing segmentation technique and satellite-derived products of tree fractional cover. We applied our approach to the West Siberian Plain and Alaska treeline regions as defined by the Circumpolar Arctic Vegetation Map. The results demonstrate the effectiveness of the proposed method for the accurate delineation of the timberlines that spatially align well with very-high-resolution satellite images. Based on the delineated timberlines, we find regional-scale tree encroachment to be not as substantial as previously reported. The proposed approach can be applied to understanding climate-induced forest responses and inform forest management practices.

Circumpolar Arctic Vegetation Map↗
DOE OSTI2020

The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

Abstract In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered.Three models are including the space-time fractional-order Boussinesq equation, space-time (2 + 1)-dimensional breaking soliton equations, and space-time fractional-order SRLW equation describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the sense of β -derivative are defined. Some fractional PDEs will convert to the considered ordinary differential equations by the help of transformation of β -derivative. These equations are analyzed utilizing an integration scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions, solitary, topological, dark soliton, periodic, kink, and rational, fall out as a by-product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so forth.

Engineering↗
NASA NTRS1992

Linear mixing model applied to coarse resolution satellite data

A linear mixing model typically applied to high resolution data such as Airborne Visible/Infrared Imaging Spectrometer, Thematic Mapper, and Multispectral Scanner System is applied to the NOAA Advanced Very High Resolution Radiometer coarse resolution satellite data. The reflective portion extracted from the middle IR channel 3 (3.55 - 3.93 microns) is used with channels 1 (0.58 - 0.68 microns) and 2 (0.725 - 1.1 microns) to run the Constrained Least Squares model to generate fraction images for an area in the west central region of Brazil. The derived fraction images are compared with an unsupervised classification and the fraction images derived from Landsat TM data acquired in the same day. In addition, the relationship betweeen these fraction images and the well known NDVI images are presented. The results show the great potential of the unmixing techniques for applying to coarse resolution data for global studies.

Holben, Brent N.↗
DOE OSTI2020

Quantifying Leaf Chlorophyll Concentration of Sorghum from Hyperspectral Data Using Derivative Calculus and Machine Learning

Leaf chlorophyll concentration (LCC) is an important indicator of plant health, vigor, physiological status, productivity, and nutrient deficiencies. Hyperspectral spectroscopy at leaf level has been widely used to estimate LCC accurately and non-destructively. This study utilized leaf-level hyperspectral data with derivative calculus and machine learning to estimate LCC of sorghum. We calculated fractional derivative (FD) orders starting from 0.2 to 2.0 with 0.2 order increments. Additionally, 43 common vegetation indices (VIs) were calculated from leaf spectral reflectance factor to make comparisons with reflectance-based data. Within the modeling pipeline, three feature selection methods were assessed: Pearson’s correlation coefficient (PCC), partial least squares based variable importance in the projection (VIP), and random forest-based mean decrease impurity (MDI). Finally, we used partial least squares regression (PLSR), random forest regression (RFR), support vector regression (SVR), and extreme learning regression (ELR) to estimate the LCC of sorghum. Results showed that: (1) increasing derivative order can show improved model performance until certain order for reflectance-based analysis; however, it is inconclusive to state that a particular order is optimal for estimating LCC of sorghum; (2) VI-based modeling outperformed derivative augmented reflectance factor-based modeling; (3) mean decrease impurity was found effective in selecting sensitive features from large feature space (reflectance-based analysis), whereas simple Pearson’s correlation coefficient worked better with smaller feature space (VI-based analysis); and (4) SVR outperformed all other models within reflectance-based analysis; alternatively, ELR with VIs from original reflectance yielded slightly better results compared to all other models.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Accelerating gradient descent and Adam via fractional gradients

Here we propose a class of novel fractional-order optimization algorithms. We define a fractional-order gradient via the Caputo fractional derivatives that generalizes integer-order gradient. We refer it to as the Caputo fractional-based gradient, and develop an efficient implementation to compute it. A general class of fractional-order optimization methods is then obtained by replacing integer-order gradients with the Caputo fractional-based gradients. To give concrete algorithms, we consider gradient descent (GD) and Adam, and extend them to the Caputo fractional GD (CfGD) and the Caputo fractional Adam (CfAdam). We demonstrate the superiority of CfGD and CfAdam on several large scale optimization problems that arise from scientific machine learning applications, such as ill-conditioned least squares problem on real-world data and the training of neural networks involving non-convex objective functions. Numerical examples show that both CfGD and CfAdam result in acceleration over GD and Adam, respectively. We also derive error bounds of CfGD for quadratic functions, which further indicate that CfGD could mitigate the dependence on the condition number in the rate of convergence and results in significant acceleration over GD.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

The effect of spatial resolution on satellite derived cloud cover

The effects of a varying sensor spatial resolution on the cloud fraction derived by reflectance threshold (RT), IR temperature threshold (IRT), hybrid bispectral threshold (HBT) and spatial coherence (SC) methods for cloud retrieval from remotely sensed data were examined experimentally. Eight subscenes from four scenes acquired with the Landsat Thematic Mapper (TM) in 1982, 1983 and 1985 were used in the trials. All cloud retrieval methods were applied to extract the cloud fraction in all the subscences for comparison with the total cloud amount determined from the TM band 4 data, which had 28.5 m resolution.

Wielicki, B. A.↗
DOE OSTI2023

Hydrodynamic theory of scrambling in chaotic long-range interacting systems

The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density. In systems with power-law interactions, the corresponding fractional-derivative FKPP equation provides an analogous mean-field theory. However, the fractional FKPP description is potentially subject to strong quantum fluctuation effects, so it is not clear a priori if it provides a suitable effective description for generic chaotic systems with power-law interactions. Here, in this work, we study this problem using a model of coupled quantum dots with interactions decaying as 1/r α , where each dot hosts N degrees of freedom. The large-N limit corresponds to the mean-field description, while quantum fluctuations contributing to the OTOC can be modeled by 1/N corrections consisting of a cutoff function and noise. Within this framework, we show that the parameters of the effective theory can be chosen to reproduce the butterfly light cone scalings previously found for N=1 and generic finite N. In order to reproduce these scalings, the fractional index μ in the FKPP equation needs to be shifted from the naïve value of μ=2⁢α–1 to a renormalized value μ=2⁢α–2. We provide supporting analytic evidence for the cutoff model and numerical confirmation for the full fractional FKPP equation with cutoff and noise.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

3D Cloud Aerosol Precipitation Experiment at kennaook Cape Grim (3D-CAPE-k) Field Campaign Report

The objective of this campaign was to complement the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) User Facility’s Cloud And Precipitation Experiment at kennaook (CAPE-k) in northwest Tasmania by deploying scanning, fixed pointing angle, and in situ aerosol, cloud, and precipitation remote-sensing instruments during the last six months of the experiment. These instruments provided a three-dimensional (3D) context to the second ARM Mobile Facility (AMF2) vertically pointing observations collected at the kennaook Cape Grim (KCG) site and captured a portion of the life cycle of the clouds before and after the passage over the AMF2 vertical column. These 3D cloud measurements will be used in the near future to 1) investigate how the vertical profiles of aerosol and cloud properties are representative of the broader area and how these properties evolve during the portion of the cloud life cycle captured by the scanning instruments, 2) quantify how accurate the cloud fraction derived with assumptions from vertically pointing observations are compared with direct 3D cloud fraction measurements, 3) evaluate cloud fraction and liquid water path in the Australian Community Climate and Earth-System Simulator–Convective-scale (ACCESS-C) forecast model, and 4) evaluate aerosol and cloud products from the European Space Agency/Japanese Aerospace Exploration Agency (ESA/JAXA) Earth Cloud Aerosol Radiation Explorer (EarthCARE) mission using the scanning measurements, offering more chances of exact collocation, thereby complementing the statistical approach we are planning to employ with AMF2 observations for that same purpose.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Antimony stable isotope fractionation during adsorption onto birnessite: A molecular perspective from X-ray absorption spectroscopy and density functional theory

Sorption of antimony (Sb) onto birnessite significantly influences the fate of Sb in oceanic and terrestrial environments and fractionates Sb isotopes. Nevertheless, little is known about Sb isotopic fractionation during its adsorption on birnessite. Here, in this study, we show the value of Δ 123 Sb adsorbed-aqueous increases from −0.398 to −0.332 ‰ in 1 h and then decreases and stabilizes at −0.384 ‰ in 72 h. The enrichment of the light Sb isotope is predominantly due to the distortion of the octahedral symmetry. X-ray absorption spectroscopy results indicate Sb first forms a double-corner-sharing complex on birnessite and then transforms to a double-edge-sharing complex during adsorption. The optimized bond distances for double-corner-sharing (3.37 Å) and double-edge-sharing (2.90 Å) complexes calculated using density functional theory (DFT) fits well with the structure (3.41 and 3.00 Å) revealed by X-ray absorption spectroscopy, respectively. The fractionation derived from reduced partition function ratios calculated using DFT aligns well with the experimental results. Therefore, the variation in Sb isotopic fractionation during adsorption is attributed to the evolving structure of Sb complexes on birnessite. Our results demonstrate the isotopic fractionation of Sb during adsorption on birnessite and provide a molecular-scale understanding of Sb behavior, contributing to the correct reconstruction of the Sb isotope composition of ancient seawater using ferromanganese crusts and nodules, and efforts to trace Sb migration in epigenetic mining environments.

Adsorption↗