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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Reaching a burning plasma and ignition using smaller capsules/ Hohlraums , higher radiation temperatures, and thicker ablator/ice on the national ignition facility

In indirect-drive implosions, the final core hot spot energy and pressure and, hence, neutron yield attainable in 1D increase with increasing laser peak power and, hence, radiation drive temperature at the fixed capsule and Hohlraum size. Here we present simple analytic scalings validated by 1D simulations that quantify the improvement in performance and use this to explain existing data and simulation trends. Extrapolating to the 500 TW National Ignition Facility peak power limit in a low gas-fill 5.4 mm diameter Hohlraum based on existing high adiabat implosion data at 400 TW, 1.3 MJ and 1 × 10 16 yield, we find that a 2–3 × 10 17 yield (0.5–0.7 MJ) is plausible using only 1.8 MJ of laser energy. Based on existing data varying deuterium–tritium (DT) fuel thickness and dopant areal density, further improvements should be possible by increasing DT fuel areal density, and hence confinement time and yield amplification.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Constructing Data-Driven Predictions at the Far Detector for NOvA's Neutrino Oscillation Analysis.

NOvA, is a two-detector, long-baseline neutrino oscillation experiment located at Fermilab, Batavia, IL, USA. It is designed primarily to constrain neutrino oscillation parameters using $\nu_\mu \ (\bar{\nu}_\mu)$ disappearance and $\nu_e \ (\bar{\nu}_e)$ appearance data. The Neutrinos at Main Injector (NuMI) beamline at Fermilab provides a high purity 900 KW intense beam of neutrinos and anti-neutrinos to NOvA. The NOvA Near Detector, located 100m underground and 1km away from the beam source, observes the un-oscillated $\nu_\mu \ (\bar{\nu}_\mu)$ and beam $\nu_e \ (\bar{\nu}_e)$ event spectrum. The Far Detector, located in Ash River, MN, USA, is 809 km from the ND and records the oscillated $\nu_e \ (\bar{\nu}_e)$ and the un-oscillated $\nu_\mu \ (\bar{\nu}_\mu)$ event spectrum. NOvA uses a data-driven technique called extrapolation to predict the expected number of $\nu_\mu \ (\bar{\nu}_\mu)$ and $\nu_e \ (\bar{\nu}_e)$ events at the Far Detector using the Near Detector data. The use of data from a functionally equivalent Near Detector provides a powerful constraint on the systematic uncertainties in NOvA neutrino oscillation analyses. As NOvA continues to add data statistics, a robust constraint on systematics becomes more crucial for neutrino oscillation analysis. The details of the NOvA neutrino oscillation analysis framework and how it constrains dominant systematic uncertainties using the Near Detector data will be discussed in this poster.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Unveiling the transferability of PLSR models for leaf trait estimation: lessons from a comprehensive analysis with a novel global dataset

Leaf traits are essential for understanding many physiological and ecological processes. Partial least squares regression (PLSR) models with leaf spectroscopy are widely applied for trait estimation, but their transferability across space, time, and plant functional types (PFTs) remains unclear. We compiled a novel dataset of paired leaf traits and spectra, with 47 393 records for >700 species and eight PFTs at 101 globally distributed locations across multiple seasons. Using this dataset, we conducted an unprecedented comprehensive analysis to assess the transferability of PLSR models in estimating leaf traits. While PLSR models demonstrate commendable performance in predicting chlorophyll content, carotenoid, leaf water, and leaf mass per area prediction within their training data space, their efficacy diminishes when extrapolating to new contexts. Specifically, extrapolating to locations, seasons, and PFTs beyond the training data leads to reduced R 2 (0.12–0.49, 0.15–0.42, and 0.25–0.56) and increased NRMSE (3.58–18.24%, 6.27–11.55%, and 7.0–33.12%) compared with nonspatial random cross-validation. The results underscore the importance of incorporating greater spectral diversity in model training to boost its transferability. These findings highlight potential errors in estimating leaf traits across large spatial domains, diverse PFTs, and time due to biased validation schemes, and provide guidance for future field sampling strategies and remote sensing applications.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Unifying and benchmarking state-of-the-art quantum error mitigation techniques

Error mitigation is an essential component of achieving a practical quantum advantage in the near term, and a number of different approaches have been proposed. In this work, we recognize that many state-of-the-art error mitigation methods share a common feature: they are data-driven, employing classical data obtained from runs of different quantum circuits. For example, Zero-noise extrapolation (ZNE) uses variable noise data and Clifford-data regression (CDR) uses data from near-Clifford circuits. We show that Virtual Distillation (VD) can be viewed in a similar manner by considering classical data produced from different numbers of state preparations. Observing this fact allows us to unify these three methods under a general data-driven error mitigation framework that we call UNIfied Technique for Error mitigation with Data (UNITED). In certain situations, we find that our UNITED method can outperform the individual methods (i.e., the whole is better than the individual parts). Specifically, we employ a realistic noise model obtained from a trapped ion quantum computer to benchmark UNITED, as well as other state-of-the-art methods, in mitigating observables produced from random quantum circuits and the Quantum Alternating Operator Ansatz (QAOA) applied to Max-Cut problems with various numbers of qubits, circuit depths and total numbers of shots. We find that the performance of different techniques depends strongly on shot budgets, with more powerful methods requiring more shots for optimal performance. For our largest considered shot budget (10 10 ), we find that UNITED gives the most accurate mitigation. Hence, our work represents a benchmarking of current error mitigation methods and provides a guide for the regimes when certain methods are most useful.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Photoelectric absorption cross section of silicon near the bandgap from room temperature to sub-Kelvin temperature

The use of cryogenic silicon as a detector medium for dark matter searches is gaining popularity. Many of these searches are highly dependent on the value of the photoelectric absorption cross section of silicon at low temperatures, particularly near the silicon bandgap energy, where the searches are most sensitive to low mass dark matter candidates. While such cross section data have been lacking from the literature, previous dark matter search experiments have attempted to estimate this parameter by extrapolating it from higher temperature data. However, discrepancies in the high temperature data have led to order-of-magnitude differences in the extrapolations. In this paper, we resolve these discrepancies by using a novel technique to make a direct, low temperature measurement of the photoelectric absorption cross section of silicon at energies near the bandgap (1.2 eV–2.8 eV).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Modular machine learning-based elastoplasticity: Generalization in the context of limited data

The development of highly accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions and from the viewpoint of data availability, verification, and validation. Recently, data-driven modeling approaches have been proposed that aim to establish stress-evolution laws that avoid user-chosen functional forms by relying on machine learning representations and algorithms. However, these approaches not only require a significant amount of data but also need data that probes the full stress space with a variety of complex loading paths. Furthermore, they rarely enforce all necessary thermodynamic principles as hard constraints. Hence, they are in particular not suitable for low-data or limited-data regimes, where the first arises from the cost of obtaining the data and the latter from the experimental limitations of obtaining labeled data, which is commonly the case in engineering applications. In this work, we discuss a hybrid framework that can work on a variable amount of data by relying on the modularity of the elastoplasticity formulation where each component of the model can be chosen to be either a classical phenomenological or a data-driven model depending on the amount of available information and the complexity of the response. The method is tested on synthetic uniaxial data coming from simulations as well as cyclic experimental data for structural materials. The discovered material models are found to not only interpolate well but also allow for accurate extrapolation in a thermodynamically consistent manner far outside the domain of the training data. This ability to extrapolate from limited data was the main reason for the early and continued success of phenomenological models and the main shortcoming in machine learning-enabled constitutive modeling approaches. Training aspects and details of the implementation of these models into Finite Element simulations are discussed and analyzed.

42 ENGINEERING↗
DOE OSTI2021

Experimental workflow to estimate model parameters for evaluating long term viscoelastic response of CO2 storage caprocks

Understanding the time-dependent behavior of reservoir and sealing formations is critical to assessing risks associated with geological carbon storage since time-dependent deformation strongly influences mechanical responses of some rock types. Many studies have evaluated the risk of CO2 leakage and induced seismicity by assuming poroelastic rheology in sealing formations. Few have considered viscoelastic or other time-dependent responses, where the existing literature adopts 1D models to represent long-term time-dependent responses. This is primarily because to date, the general form of a reasonable 3D time-dependent model for rocks remains unclear. In this paper, we address this unclear issue by proposing a new workflow to select constitutive modeling parameters to evaluate if a 3D viscoelastic model is reasonable using several-hour-long experimental data and a power-law response to extrapolate to the decades-long time frames of interest in geologic carbon storage. To provide experimental data, we conducted multi-level loading/unloading triaxial relaxation tests with four rock types. The experimental results showed that the maximum load relaxation observed is approximately 49%, with some rock types showing as little as 1.4%. Using a simple linear viscoelastic model, parameters were chosen such that a maximum deviation of 1.5 MPa in axial stress and 7 MPa in radial stress was attained with the extrapolated 30-year data. We found that a reasonable parameter range for the normalized elastic modulus is 0.1~2 for rocks with significant time-dependent responses and 0.01~0.06 for those with small time-dependent responses. No matter how significant time-dependent responses are for rocks considered, our results showed that the relaxation time has a general range of 1~10^10 s, whose time scale can be one or two orders higher than a time frame typically envisioned for CO2 injection projects.

Stress relaxation, 3D time-dependent model, viscoe↗
DOE OSTI2026

Towards fully predictive gyrokinetic full- f simulations: validation and triangularity studies in TCV

Designing economical magnetic confinement fusion power plants motivates computational tools that can estimate plasma behavior from engineering parameters without direct reliance on experimental measurement of the plasma profiles. In this work, we present full-f global long-wavelength gyrokinetic simulations of edge and scrape-off layer turbulence in tokamaks that use only magnetic geometry, heating power, and particle inventory as inputs. Unlike many modeling approaches that employ free parameters fitted to experimental data, raising uncertainties when extrapolating to reactor scales. This approach directly simulates turbulence and resulting profiles through gyrokinetics without such empirical adjustments. This is achieved via an adaptive sourcing algorithm in Gkeyll that strictly controls energy injection and emulates particle sourcing due to neutral recycling. We show that the simulated kinetic profiles compare reasonably well with Thomson scattering and Langmuir probe data for Tokamak á Configuration Variable (TCV) discharge #65125, and that the simulations reproduce characteristic features such as blob transport and self-organized electric fields. Applying the same framework to study triangularity effects suggests mechanisms contributing to the improved confinement reported for negative triangularity (NT). Simulations of TCV discharges #65125 and #65130 indicate that NT increases the E x B flow shear (by about 20% in these cases), which correlates with reduced turbulent losses and a modest change in the distribution of power exhaust to the vessel wall. While the physical models contain approximations that can be refined in future work, the predictive capability demonstrated here, evolving multiple profile relaxation times with kinetic electron and ion models in hundreds of GPU hours, indicates the feasibility of using Gkeyll to support design studies of fusion devices.

Hoffmann, Antoine Cyril David [Princeton Plasma Ph↗
DOE OSTI2025

Thermophysical Properties of Ti3SiC2 MAX Phase Composites with SiC Reinforcement

In the present work, dense (∼100%) Ti 3 SiC 2 composites (TSC) are processed along with 20 vol% of SiC reinforcement (TSC20) via spark plasma sintering at 1400°C, 40 MPa, 15 min, and dynamic vacuum environment. Thermal expansion of both the composites increases from RT to 1273 K and linear fitting of data yields coefficient of thermal expansion (CTE) of 9.4 × 10 −6 K −1 for TSC which decreases to 8.3 × 10 −6 K −1 for TSC20. With increase in temperature from RT to 773 K, specific heat for both TSC and TSC20 composites is observed to increase from 598-850 J.kg −1 .K −1 , whereas thermal diffusivity and thermal conductivity values decrease with testing temperature. SiC reinforcement in Ti 3 SiC 2 resulted in improved thermal diffusivity from 12.7 to 18.7 mm 2 .s −1 and thermal conductivity from ∼57 to ∼79 W.m −1 .K −1 at RT. However, with increase in temperature (773 K), thermal diffusivity and conductivity decrease, and values get closer for both TSC and TSC20 composites. Further extrapolation of thermal conductivity data showed cross-over at ∼973 K due to domination of phonon-phonon scattering and thus lower values of thermal conductivity for TSC20 than TSC. Therefore, reduced CTE and higher thermal conductivity of TSC20 make it a viable choice for applications in high temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Machine learning for seismic low-frequency extrapolation

The cycle-skipping problem that plagues full waveform inversion (FWI) can be at least partially mitigated if low frequencies (which encode the kinematics of wave propagation in seismic data) are recorded. However, seismic sources and receivers are band-limited, so seismic data does not generally include signals down to 0 Hz. To improve our ability to solve the seismic inverse problem, one can synthesize this missing low-frequency (LF) content from the recorded high-frequency (HF) data using machine learning (ML) models. Deep learning models such as convolutional neural networks (CNNs) demonstrate impressive ability to perform low frequency extrapolation. However, such models require powerful hardware (GPU machines) and careful training. We assess the extrapolation capabilities of three different ML models that do not require GPU machines, namely, random forest, Gaussian process regression and gradient boosting, on both synthetic and real data. Experimental results on two synthetic data sets (generated from a low velocity lens embedded in a homogeneous medium, and the Marmousi model) demonstrate that FWI applied to the extrapolated data consistently improves inversion accuracy relative to FWI applied to the original data sets that do not contain low frequencies. Application of low-frequency extrapolation to real data from the Northwest Shelf of Australia demonstrates that tree-based ML models such as gradient boosting can outperform CNNs in terms of both accuracy and computational cost on non-GPU architectures.

58 GEOSCIENCES↗
DOE OSTI2021

Deep-freeze graph training for latent learning

Scientific and engineering advances are primarily driven by multi-tier conceptual constructs and conditional theoretical frameworks. The theories allow predictions of hypothetical system responses, given a set of approximate conditions (ranges of applicability) imposed on latent parameters that cannot be measured directly. Learning to estimate the latent variables (Latent Learning) helps to pinpoint the anticipated range-edge anomalies and improves the confidence in interpretation, interpolation and extrapolation of limited experimental data. Due to high dimensionality and extreme non-linearity of the materials science problems, very large datasets are typically required for conventional data-driven model development. The vital experimental data collection, particularly on microstructural phases, is very challenging, which makes it difficult to compile a high-quality database. Incorporation of the domain knowledge into the computational graph structure, initialization and optimization processes presents a viable mechanism for developing accurate models, with limited datasets. Furthermore, this study successfully utilized the approach to build the Deep Freeze Graph (DeepFreG) by mapping known causality relationships and by digitizing empirical domain knowledge for Latent Learning (LL), with specific applications in materials science.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Machine learning in materials research: Developments over the last decade and challenges for the future

The number of studies that apply machine learning (ML) to materials science has been growing at a rate of approximately 1.67 times per year over the past decade. In this review, I examine this growth in various contexts. First, I present an analysis of the most commonly used tools (software, databases, materials science methods, and ML methods) used within papers that apply ML to materials science. The analysis demonstrates that despite the growth of deep learning techniques, the use of classical machine learning is still dominant as a whole. It also demonstrates how new research can effectively build upon past research, particular in the domain of ML models trained on density functional theory calculation data. Next, I present the progression of best scores as a function of time on the matbench materials science benchmark for formation enthalpy prediction. In particular, a dramatic improvement of 7 times reduction in error is obtained when progressing from feature-based methods that use conventional ML (random forest, support vector regression, etc.) to the use of graph neural network techniques. Finally, I provide views on future challenges and opportunities, focusing on data size and complexity, extrapolation, interpretation, access, and relevance.

36 MATERIALS SCIENCE↗
DOE OSTI2026

The solubility of NdPO 4 and DyPO 4 and stability of Nd and Dy chloride and hydroxyl complexes as a function of pH and salinity to 450 °C

The mobility of rare earth elements (REE) in geological systems is often controlled by the stability of monazite and xenotime, which are important hosts for the light and heavy REE. These REE phosphates constitute important resources and provide information on ore formation conditions and timing due to their uses as geothermometers and geochronometers. While the thermodynamic properties for these minerals are well-established up to high temperature and pressure, the properties for the aqueous REE complexes are not well constrained with limited information up to 300 °C. In this study, the solubility of synthetic NdPO 4 and DyPO 4 endmembers were measured in hydrothermal sub- to supercritical NaCl-bearing aqueous solutions from 350 at saturated water vapor pressure to 450 °C at 700 bar. The speciation of Nd and Dy was determined in acidic to alkaline solutions (pH 25 °C values from 2 to 10), and indicates that the hydroxyl species REE(OH) 2 + and REE(OH) 3 0 predominate at low salinity (0.01 mol/kg NaCl) with some contribution of REE chloride species REECl 2+ and REECl 2 + in acidic fluids. The REE phosphate solubility measured in these experiments is up to two orders of magnitude higher than predicted using existing thermodynamic properties from literature for aqueous species extrapolated from lower temperature data to supercritical conditions. To address this discrepancy, the thermodynamic properties of the REE aqueous species were optimized using GEMSFITS to derive the formation constants for the REE chloride (β Cl ) and hydroxyl (β OH ) complexes in the studied temperature range. This study highlights the importance of the hydroxyl species REE(OH) 2 + and REE(OH) 3 0 over a wide range of pH and temperature. As a result, the revised thermodynamic properties for Dy and Nd chloride and hydroxyl species more accurately predict the solubility of NdPO 4 and DyPO 4 and provide insight into the speciation and mobility of the light and heavy REE in hydrothermal supercritical fluids in the crust.

58 GEOSCIENCES↗
DOE OSTI2020

Morphology of Vapor-Deposited Acetonitrile Films

Crystalline acetonitrile has two polymorphs, a high temperature (HT) phase that is stable between 217 K and its melting point at 229 K, and a low temperature (LT) phase that is stable below 217 K. Solid acetonitrile films can be prepared by vapor deposition in an ultra-high vacuum chamber. To prevent sublimation of the film temperatures are often kept below 150 K. While the LT phase is thermodynamically favored at these low temperatures, such preparation usually results in the formation of the metastable HT polymorph. In this work we use reflection adsorption infrared spectroscopy (RAIRS) and temperature programmed desorption (TPD) experiments to investigate the effects of the deposition temperature and underlying substrate on the morphology of acetonitrile films prepared with molecular beam deposition. We obtained the elusive LT phase when dosing at 120 K on a graphene substrate and on a crystalline decane layer. Dosing acetonitrile on other surfaces produced the HT phase, as did annealing of amorphous films. We used TPD experiments to determine the Gibbs energy difference between the HT and LT phases. Our ΔG values agree with extrapolation of equilibrium calorimetry data. Furthermore, we also observed that acetonitrile films were amorphous when dosed at temperatures ≤ 60 K, and porous for temperatures ≤ 50 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Reply to Comment by Peterie Et Al. on “Accelerated Fill‐Up of the Arbuckle Group Aquifer and Links to U.S. Midcontinent Seismicity”

Abstract Peterie et al. question one observation in our paper: associating pressure increases to injection volumes at distances of up to 25 km from an injection well. In this reply, we show that the comment misunderstands our analysis and the evidence that led to this conclusion. We also show that gauge‐depth‐corrected pressures, used by the authors to produce statewide pressure maps, are discrepant with the static fluid level data, provided in our original compilation and analysis. The discrepancies are a result of the pressure correction method employed, which naïvely substitutes formation pressure for bottomhole pressure to calculate wellbore fluid density. Their linearly interpolated pressure maps, based on sparse data, contain interpolation and extrapolation artifacts that contradict injection trends in the state, the Theis solution, and the superposition principle. We reiterate that pressure and static fluid level increases in Class I wells existed prior to 2013, most notably in central Kansas, where recent earthquakes are cited in the comment as evidence of a pressure plume emanating from the Kansas‐Oklahoma border, 90 km away. We show that the space‐time pattern of seismicity in this area is inconsistent with a northward propagating pressure plume and, instead, seismicity appears to be centered on and near a cluster of high‐rate injection wells, two of which are among the highest rate wells in the state. These observations, along with recent M4 + earthquakes during continued decreases in wastewater injection in southern Kansas and northern Oklahoma, question the usefulness of the comment for understanding and managing societally significant earthquakes.

Ansari, Esmail↗
DOE OSTI2023

Cooking methods and kitchen ventilation availability, usage, perceived performance and potential in Canadian homes

Cooking is a substantial contributor to air pollutant exposures in many residences. Effective use of kitchen ventilation can mitigate exposure; however, information on its availability, usage, and potential to increase its use across the population has been limited. This study aimed to obtain nationally representative information on cooking methods, kitchen ventilation availability and usage, and the potential for education to increase effective usage. An online survey was sent to a representative sample of Canadian homes to collect data on cooking methods, the presence and use of mechanical kitchen ventilation devices, perceived device performance, and willingness to implement mitigation strategies. Responses were weighted to match key demographic factors and analyzed using non-parametric statistics. Among the 4500 respondents, 90% had mechanical ventilation devices over the cooktop (66% of which were vented to the outside), and 30% reported regularly using their devices. Devices were used most often for deep-frying, followed by stir-frying, sautéing or pan-frying, indoor grilling, boiling or steaming. Almost half reported rarely or never using their ventilation devices during baking or oven self-cleaning. Only 10% were fully satisfied with their devices. More frequent use was associated with the device being vented to the outdoors, having more than two speed settings, quiet operation if only one speed, covering over half of the cooktop, and higher perceived effectiveness. After being informed of the benefits of kitchen ventilation, 64% indicated they would consider using their devices more often, preferentially using back burners with ventilation, and/or using higher ventilation device settings when needed. This study provides population-representative data on the most used cooking methods, kitchen ventilation availability and usage, and influencing factors in Canadian homes. Such data are needed for exposure assessments and evaluating the potential to mitigate cooking-related pollutant exposures via more effective use of kitchen ventilation. The data can be reasonably extrapolated to the United States, given the similarities in residential construction practices and cultural norms between the two countries.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

The Sensitivity of Variational Bayesian Neural Network Performance to Hyperparameters

In scientific applications, predictive modeling is often of limited use without accurate uncertainty quantification (UQ) to indicate when a model may be extrapolating or when more data needs to be collected. Bayesian Neural Networks (BNNs) produce predictive uncertainty by propagating uncertainty in neural network (NN) weights and offer the promise of obtaining not only an accurate predictive model but also accurate UQ. However, in practice, obtaining accurate UQ with BNNs is difficult due in part to the approximations used for model training (such as those made in variational inference) and in part to the need to choose a suitable set of hyperparameters; these hyperparameters outnumber those needed for traditional NNs and often have opaque effects on the results. We aim to shed light on the effects of hyperparameter choices for variational BNNs by performing a global sensitivity analysis of variational BNN performance under varying hyperparameter settings. Our results indicate that many of the hyperparameters interact with each other to affect both predictive accuracy and UQ. For improved usage of variational BNNs in real-world applications, we suggest that thorough hyperparameter tuning, including tuning of prior hyperparameters and loss function parameters, is essential for accurate UQ in variational BNNs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Gluon distributions and their applications to Ioffe-time distributions

We investigate unpolarized and polarized gluon distributions and their applications to the Ioffe-time distributions, which are related to lattice QCD calculations of parton distribution functions. Guided by the counting rules based on the perturbative QCD at large momentum fraction x and the color coherence of gluon couplings at small x, we parametrize gluon distributions in the helicity basis. By fitting the unpolarized gluon distribution, the inferred polarized gluon distribution from our parametrization agrees with the one from global analysis. A simultaneous fit to both unpolarized and polarized gluon distributions is also performed to explore the model uncertainty. The agreement with the global analysis supports the (1 - x) power suppression of the helicity-antialigned distribution relative to the helicity-aligned distribution. The corresponding Ioffe-time distributions and their asymptotic expansions are calculated from the gluon distributions. Our results of the Ioffe-time distributions can provide guidance to the extrapolation of lattice QCD data to the region lacking precise gluonic matrix elements. Therefore, they can help regulate the ill-posed inverse problem associated with extracting the gluon distributions from discrete data from first-principle calculations, which are available in a limited range of the nucleon momentum and the spatial separation between the gluonic currents. Given various limitations in obtaining lattice QCD data at large Ioffe time, phenomenological approaches can provide important complementary information to extract the gluon distributions in the entire momentum fraction region, especially at small x. The possibility of investigating higher-twist effects and other systematic uncertainties in the contemporary first-principle calculations of parton distributions from phenomenologically well-determined Ioffe-time distributions in the large Ioffe-time region is also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗