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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
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↗
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↗
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↗
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↗
DOE OSTI2022

Fourier analysis of continuous fractional diffusion synthetic acceleration schemes in slab geometry

We propose two fractional extensions of continuous diffusion synthetic acceleration (DSA) with fractional derivative order α varying over the interval 2 ≥ α ≥ 1 . We investigate the spectral properties of the corresponding continuous families of fractional preconditioners by performing Fourier analysis for a model infinite homogeneous medium problem in slab geometry. The first family results in a fractional acceleration scheme, FrDSAo, that reduces to traditional DSA for .α = 2 and scattering ratio c limiting to a unit value (c → 1) but is otherwise optimized via the Fourier analysis, to obtain the smallest possible spectral radius, for c < 1 and 2 ≥ α ≥ 1. The second family corresponds to a fractional acceleration scheme, FrDSAs, that reduces to traditional DSA for α = 2 for all values of c. The latter scheme is not optimized but has the advantage of lending itself to a more straightforward implementation. For high values of c, the results of the Fourier analysis point to the existence of an interval 2 > α > ∼1.8 where both FrDSAo and FrDSAs can achieve a lower spectral radius than DSA. For example, DSA has a spectral radius of ∼0.2246 for c = 0.9999 while FrDSAo produces a value of ∼0.1616 at α = 1.92 and FrDSAs results in ∼0.2116 at α =1.93. (author)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Discovery of a Natural Product That Binds to the Mycobacterium tuberculosis Protein Rv1466 Using Native Mass Spectrometry

Elucidation of the mechanism of action of compounds with cellular bioactivity is important for progressing compounds into future drug development. In recent years, phenotype-based drug discovery has become the dominant approach to drug discovery over target-based drug discovery, which relies on the knowledge of a specific drug target of a disease. Still, when targeting an infectious disease via a high throughput phenotypic assay it is highly advantageous to identifying the compound’s cellular activity. A fraction derived from the plant Polyalthia sp. showed activity against Mycobacterium tuberculosis at 62.5 μge/μL. A known compound, altholactone, was identified from this fraction that showed activity towards M. tuberculosis at an minimum inhibitory concentration (MIC) of 64 μM. Retrospective analysis of a target-based screen against a TB proteome panel using native mass spectrometry established that the active fraction was bound to the mycobacterial protein Rv1466 with an estimated pseudo-Kd of 42.0 ± 6.1 µM. Our findings established Rv1466 as the potential molecular target of altholactone, which is responsible for the observed in vivo toxicity towards M. tuberculosis .

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

A general non-Fourier Stefan problem formulation that accounts for memory effects

The Stefan problem is the classical model of a melting phase change. In heterogeneous systems, such phase changes can exhibit non-Fourier (anomalous) behaviors, where the advance of the melt interface does not follow the expected time scaling. These situations can be modeled by replacing the derivatives, in the governing partial differential equations, with fractional order derivatives. In particular, replacing the time derivatives leads to non-Fourier models that account for memory effects in the system. In this work, by using appropriate time convolution integrals, a general thermodynamic balance statement for melting phase problems, explicitly accounting for memory effects, is developed. From this balance, a general model formulation applicable to problems involving melting over a temperature range (i.e., a mushy region) is derived. A key component in this model is the representation of memory effects through the use of fractional derivative based constitutive models of the enthalpy and heat flux. Further, on shrinking the mushy region to a single isotherm, a general sharp interface melting model is obtained. Here, in contrast to the classic Stefan problem, the fractional derivatives induce a natural regularization, such that the constitutive models for enthalpy and heat flux are continuous at the melt interface; a result confirmed through numerical simulation. To further support the theoretical findings, a physical example of a non-Fourier Stefan problem is presented. Overall the development and results in this paper underscore the importance of explicitly relating the development of fractional calculus models to the appropriate thermodynamic balance statements.

42 ENGINEERING↗
DOE OSTI2022

The X-ray view of optically selected dual AGN

We present a study of optically selected dual Active Galactic Nuclei (AGN) with projected separations of 3–97 kpc. Using multiwavelength (MWL) information (optical, X-ray, mid-IR), we characterized the intrinsic nuclear properties of this sample and compared them with those of isolated systems. Among the 124 X-ray-detected AGN candidates, 52 appear in pairs and 72 as single X-ray sources. Through MWL analysis, we confirmed the presence of the AGN in >80 per cent of the detected targets in pairs (42 out of 52). X-ray spectral analysis confirms the trend of increasing AGN luminosity with decreasing separation, suggesting that mergers may have contributed to triggering more luminous AGN. Through X-ray/mid-IR ratio versus X-ray colours, we estimated a fraction of Compton-thin AGN (with 10 22 cm −2 < N H < 10 24 cm −2 ) of about 80 per cent, while about 16 per cent are Compton-thick sources (with N H > 10 24 cm −2 ). These fractions of obscured sources are larger than those found in samples of isolated AGN, confirming that pairs of AGN show higher obscuration. This trend is further confirmed by comparing the de-reddened [O III ] emission with the observed X-ray luminosity. However, the derived fraction of Compton-thick sources in this sample at the early stages of merging is lower than that reported for late-merging dual-AGN samples. Comparing N H from X-rays with that derived from E(B − V ) from narrow-line regions, we found that the absorbing material is likely to be associated with the torus or broad-line regions. We also explored the X-ray detection efficiency of dual-AGN candidates, finding that, when observed properly (at on-axis positions and with long exposures), X-ray data represent a powerful way to confirm and investigate dual-AGN systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Tackling the curse of dimensionality in fractional and tempered fractional PDEs with physics-informed neural networks

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence; in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions.

42 ENGINEERING↗
DOE OSTI2020

Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: Parametric Study

Pipe flow is one of the most commonly used models to describe fluid dynamics. The concept of fractional derivative has been recently found very useful and much more accurate in predicting dynamics of viscoelastic fluids compared with classic models. In this paper, we capitalize on our previous study and consider space-time dynamics of flow velocity and stress for fractional Maxwell, Zener, and Burgers models. We demonstrate that the behavior of these quantities becomes much more complex (compared to integer-order classical models) when adjusting fractional order and elastic parameters. We investigate mutual influence of fractional orders and consider their limiting value combinations. Finally, we show that the models developed can be reduced to classical ones when appropriate fractional orders are set.

Gritsenko, Dmitry (ORCID:0000000248181512)↗
DOE OSTI2025

PAVC Gridded 20m Alaska NGEE Tier3 PFTs v1.0

These 20-meter spatial resolution gridded products provide per-pixel fractional cover (%) of Next Generation Ecosystem Experiments (NGEE) Arctic Plant Functional Types (PFTs) Tier 3 across Alaska, north of the boreal treeline. The products were developed for the NGEE Arctic project, which is improving Arctic vegetation representation and parameterization of the E3SM Land Model. This dataset includes 8 files containing fractional cover for NGEE Tier 3 PFTs (https://data.ess-dive.lbl.gov/view/doi:10.15485/2529470): (1) bryophytes; (2) lichens; (3) non-vascular plants, i.e., the sum of lichens and bryophytes; (4) deciduous shrubs, (5) evergreen shrubs, (6) forbs, (7) graminoids, and a non-PFT class, (8) litter. Each pixel contains the percent cover (expressed as a fraction of total ground cover) that was predicted by random-forest regression models. The random-forest models were trained on cover data collected at 978 plots from 2010 to 2021, of which are archived in the Pan-Arctic Vegetation Cover (PAVC) database (https://data.ess-dive.lbl.gov/datasets/doi:10.15485/2483557). The plot cover was linked to 20-meter spatial resolution, satellite-derived predictor variables: Sentinel-2 spectra and Sentinel-1 polarizations averaged over the 2019 growing season, as well as topographical features derived from ArcticDEM. Then, spatio-temporally anomalous plot data that introduced large variability to the regression outcomes were dropped using the Cook’s distance outlier detection method, and the models were re-created using high-quality plots and their associated satellite derived explanatory variables per each PFT. The correlations between plot-observed and satellite-derived fractional cover for all PFTs were well correlated (R2 = 0.69–0.95 and 0.5 for litter) and had low RMSE bias (0.02–0.11). This research was performed as a part of the NGEE Arctic project. The NGEE Arctic project was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Polyakov’s confinement mechanism for generalized Maxwell theory

We study fractional-derivative Maxwell theory, as appears in effective descriptions of, for example, large N f QED 3 , graphene, and some types of surface defects. We argue that when the theory is realized on a lattice, monopole condensation leads to a confining phase via the Polyakov confinement mechanism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Borate-assisted alkaline extraction of hemicellulose from switchgrass with enhanced structural stability and purity

Valorization of non-cellulosic polysaccharides is crucial for enhancing the economic competitiveness of biorefinery processes. In this study, a mixture of boric acid and sodium hydroxide was employed to efficiently extract hemicellulose from holocellulose switchgrass. Borate-assisted alkaline extraction resulted in a higher xylan content (59.5 %) compared to conventional alkaline extraction. Here, the hemicellulose fractions derived from the borate-alkaline treatment exhibited a higher molecular weight (M w = 51.2 kDa) and a relatively lower degree of polydispersity (1.28), indicating improved structural stability. The presence of borate had a protective effect against chain scission, preserving glucuronic acid residues and increasing galactose content. Additionally, borate improved hemicellulose purity, with up to 74.1 % of the extracted hemicellulose being suitable for further enzymatic applications. Extended extraction time further enhanced hemicellulose recovery, reaching 97.9 % under NaOH/boric acid conditions while maintaining structural integrity, as confirmed by SEM, FTIR and 2D HSQC NMR analyses. These findings provide insights into the role of borate in optimizing hemicellulose extraction and improving its potential for bioconversion processes.

Borate alkaline↗