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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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15 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Data-Driven Closures and Assimilation for Stiff Multiscale Random Dynamics

Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Kaon gluon parton distribution and momentum fraction from 2+1+1 lattice QCD with high statistics

We present a high-statistics lattice-QCD determination of the kaon gluon parton distribution function and gluon momentum fraction. We use clover valence fermion action to take 1,296,640 kaon-correlator measurements on a highly improved staggered quark ensemble with 𝑎 ≈ 0.12 fm and 310-MeV pion mass generated by the MILC Collaboration. A detailed investigation into the impact of gauge-link smearing on the gluonic matrix elements indicates that five steps of hypercubic smearing offer an effective balance between signal quality and preservation of long-distance physics. We report a nonperturbatively renormalized kaon gluon momentum fraction of Math output error at 𝜇 = 2 GeV in the Math output error scheme. Using reduced pseudo-Ioffe-time-distribution matrix elements and pseudo-parton-distribution-function (PDF) matching, we extract the kaon gluon PDF and compare with the prediction from the Dyson-Schwinger equation and with the pion PDF obtained from the same ensemble.

First-principles calculations↗
DOE OSTI2025

Voltage Probability Density Function Shaping Control Strategy Considering Grid Operational Uncertainties

It is well-known that power systems operation always affected by various uncertainties which make the bus voltage a random process that can be characterized by its probability density function (PDF) at any time instant. In this context, this paper presents a novel PDF-based voltage control framework for power systems. By modeling voltage as a stochastic process, we formulate a stochastic differential equationthat captures grid uncertainties. The associated Fokker-Planck-Kolmogorov equation is derived to describe the evolution of the voltage PDF, which enables the formulation of a PDF-shaping control strategy. To simplify the PDF control formulation, a B-spline neural network is introduced for real-time estimation and regulation of the voltage distribution. The proposed PDF control law updates voltage references for energy storage systems and synchronous generators using real-time PDF measurements and feedback signals. The proposed method is validated on a modified Kundur’s two-area system. Simulation results demonstrate that the controller can significantly improve the voltage stability under stochastic conditions, highlighting its effectiveness in modern inverter-rich grids.

Gui, Yonghao [ORNL] (ORCID:0000000250435534)↗
DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Closure models for the feedback of energetic particles on plasma turbulence

Energetic particles interact with the plasma surrounding them, resonating with certain types of plasma waves to stabilize them while destabilizing others, and changing the character of the background turbulence in ways that have not been fully quantified or understood. Interaction with the turbulent background plasma is key to the acceleration of many types of energetic particles including high-energy cosmic rays, solar energetic particles, and pick-up ions. The acceleration of particles is a process that would ideally be described by a kinetic model, a type of model that follows a probability distribution function (PDF) for all particles in 7-dimensional (x, y, z, v x , v y , v z , t) space. Because of the high dimensionality of a kinetic model, simulations that solve kinetic equations use the largest computational resources currently available, and are yet unable to simulate a realistic number of particles, reach the large scales necessary for astrophysical problems, and use high-precision numerical methods. Two available alternatives to kinetic plasma models have been explored for this problem, with limited success. One is a multi-fluid model produced by a cumulant discarding closure, which evolves coupled equations for the velocity, magnetic field, and internal energy for both the background plasma and the fluid of energetic particles. However, simulations that solve multi-fluid magnetohydrodynamic (MHD) equations are able to include the interaction with energetic particles only in crude ways, typically as an add-on pressure term. The second alternative is to use a hybrid method to couple a fluid description of the background plasma to a kinetic model or a Fokker–Planck model for the energetic particles. These methods are hampered by the physical modeling of the coupling. In this work, we develop a new model, which follows the PDF for all particles; this can be viewed as a step toward physical realism above a multi-fluid MHD model, while also being more computationally efficient than a kinetic model. The equations we develop model both the background plasma and the energetic particles self-consistently. Over the last decade, similar PDF methods have been developed to a high level of sophistication to model reactive flows and turbulent combustion for engineering applications. For treatment of the feedback of the energetic particles on a background plasma, a PDF closure approach should evaluate the mean characteristics, including the density, with better statistical quality than will particle-sampling procedures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

RAIS Preliminary Remediation Goals for Chemicals

Chemical preliminary remediation goals (PRGs) (https://rais.ornl.gov/cgibin/prg/PRG_search?select=chem) are calculated by selecting the applicable chemical(s) together with the applicable media, land use, and exposure route combination. If “site-specific” is selected as the PRG type, the following page will show the equations and exposure parameters used for deriving the PRGs, and some of the parameter values may be changed as necessary. If “default” is selected as the PRG type, the RAIS will proceed directly to the results page. Multiple chemicals can be selected. Results can be downloaded in .xlsx or .pdf formats. Additionally, the session inputs for the PRG calculator can be saved for future use and recalled by the PRG calculator. The derivation of the selected PRG and the applicable equations and exposure parameters can be reviewed in more detail using the RAIS Chemical PRG Calculator User Guide (https://rais.ornl.gov/tools/rais_chemical_prg_guide.html).

Manning, Karessa [Oak Ridge National Laboratory (O↗
DOE OSTI2024

RAIS Preliminary Remediation Goals for Radionuclides

Radionuclide PRGs (https://rais.ornl.gov/cgi-bin/prg/PRG_search?select=rad) are calculated by selecting the applicable radionuclide(s) together with the applicable media, land use, and exposure route combination. If “site-specific” is selected as the PRG type, the following page will show the equations and exposure parameters used for deriving the PRGs, and some of the parameter values may be changed as necessary. If “default” is selected as the PRG type, the RAIS will proceed directly to the results page. Multiple radionuclides can be selected with this tool. Results can be downloaded in .xlsx or .pdf formats. Additionally, the session inputs for the PRG calculator can be saved for future use and recalled by the PRG calculator. The derivation of the selected PRG(s) and the applicable equations and exposure parameters can be reviewed in more detail using the RAIS Radionuclide PRG Calculator User Guide available here: https://rais.ornl.gov/tools/rais_rad_prg_guide.html. html.

Manning, Karessa [Oak Ridge National Laboratory (O↗
DOE OSTI2025

A tale of two polarization paradoxes: The diamagnetic polarization paradox

An accurate calculation of the total polarization charge density in a plasma is essential for a self-consistent determination of the electric field. Yet, the “diamagnetic polarization paradox” refers to the fact that there is a paradoxical factor of 1/2 difference between the pressure-driven “diamagnetic polarization” density calculated using real space drift theory vs action-angle space guiding center and gyrokinetic theory that has not been explained before. Here, we show that both results can be made consistent with one another. Half of the diamagnetic polarization is due to the transformation from the guiding center density to the real space density. The other half is due to the fact that, within the drift kinetic ordering assumptions, the guiding center density should be expressed as the gyroaverage of the density in the limit of vanishing Larmor radius. A comprehensive review of polarization is presented to complete the derivation, and then we derive results that are required for the polarization calculations to agree. Expressions for the diamagnetic polarization density are given that are accurate to first order in amplitude and all orders in gyroradius within the gyrokinetic theory for a constant magnetic field. Applications to Maxwell–Boltzmann particle distribution functions (PDFs), including anisotropic temperature, are presented. Local invariants, like total energy and toroidal momentum, do not generate net polarization effects; the electric and thermodynamic polarizations must precisely cancel. In contrast, anisotropic dependence on the magnetic moment generates a net polarization proportional to the temperature anisotropy. Finally, when sources are present, the equilibrium PDF is approximately the ratio of two orbit averages.

adiabatic theory↗
DOE OSTI2025

Hot Droughts and Forest Tree Dynamics in the Amazon - Statistical Models, Scripts, Data, and Outputs

This package contains data, outputs, equations, and R scripts for analyses for manuscript entitled "Hot droughts in the Amazon: A window to a future hypertropical climate" by J. Chambers et al., in particular it contains statistical models and analyses for the INPA BIONTE tree mortality study. The Models folder contains details for all statistical models in PDF files. The Scripts folder contains the R scripts for Bayesian Hierarchical Models (two text files) and SEMs (one text file) are separate and reasonably annotated. All data associated with these scripts are in the data folder. The Data folder contains two of the three CSV files used for the analyses and are called by the R scripts. Two of them are part of published datasets (`BIONTE_mortality-rates.csv` from Lima et al. 2024, DOI:10.15486/ngt/1898910 and `SPEI.csv` from Pastorello et al. 2023 DOI:10.15486/ngt/1958257) and also provided in this package for convenience (please see the corresponding datasets for usage and citation terms). The third dataset (`BIONTE_gapfilled_wd.csv`) contains sensitive information and can be obtained by contacting the manuscript lead author. The Outputs folder contains the two output files that provide extra information about the analyses. The file `figuresFeb2025d.pdf` contains all the figures from the manuscript - captions are in the manuscript. The file `ChambersMS.pdf` contains primary results from Bayesian statistical models, regression analyses, and validation steps applied to the tree mortality data from the INPA experiments. The document includes visual summaries, model diagnostics, and leave-one-out (LOO) validation results. A breakdown of file contents can be found in the README file that is part of this package.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Investigating the Transverse Structure of Hadrons Using Parton Pseudodistributions

Within the pseudo-PDF framework, we investigate the perturbative contributions to correlators that are used to study transverse momentum dependent parton distributions (TMDs) on the lattice. Our results contain the full perturbative corrections which arise as artifacts from performing the calculation for a Euclidean separation between the parton fields, as well as the corrections which yield the evolution equations for the TMDs. This gives a path to extraction of the genuine non-perturbative features of the three-dimensional structure of the hadrons from lattice calculations.

Santiago, Melvin Gabriel [Old Dominion Univ., Norf↗
DOE OSTI2025

Effects of threshold resummation for large-x PDF in large momentum effective theory

Parton distribution functions (PDFs) at large x are challenging to extract from experimental data, yet they are essential for understanding hadron structure and searching for new physics beyond the Standard Model. Within the framework of the large momentum P z expansion of lattice quasi-PDFs, we investigate large x PDFs, where the matching coefficient is factorized into the hard kernel, related to the active quark momentum xP z , and the threshold soft function, associated with the spectator momentum (1 − x)P z . The renormalization group equation of the soft function enables the resummation of the threshold double logarithms α k ln 2k (1 − x), which is crucial for a reliable and controllable calculation of large x PDFs. Our analysis with pion valence PDFs indicates that perturbative matching breaks down when the spectator momentum (1 − x)P z approaches Λ QCD , but remains valid when both xP z and (1 − x)P z are much larger than Λ QCD . Additionally, we incorporate leading renormalon resummation within the threshold framework, demonstrating good perturbative convergence in the region where both spectator and active quark momenta are perturbative scales.

factorization↗
DOE OSTI2025

First study of polarized proton-proton scattering with small-𝑥 helicity evolution

We perform a phenomenological study of helicity-dependent parton distribution functions (PDFs) using small-𝑥 helicity evolution equations, incorporating for the first time single-inclusive jet production data in polarized proton-proton (𝑝⁢𝑝) scattering at parton momentum fractions 𝑥 <0.1. We also simultaneously include double-longitudinal spin asymmetries in inclusive and semi-inclusive deep-inelastic scattering probing 𝑥 <0.1. Employing the polarized small-𝑥 pure-glue calculation of 𝑝⁢𝑝 → 𝑔⁡𝑋 for the jet production cross section, we modify the large-𝑁 𝑐 &𝑁 𝑓 KPS-CTT evolution equations by setting 𝑁 𝑓 = 0 to replicate the large-𝑁𝑐 (pure-glue) limit, while retaining external quark flavors for the spinor field operators. We find that the 𝑝⁢𝑝 data have a considerable impact on the helicity PDFs at small 𝑥, reducing their uncertainties and leading to a total quark and gluon helicity in the proton for 𝑥 < 0.1 of −0.04 ±0.23. Combining our analysis with a recent JAM helicity PDF analysis of the world polarized data, which includes 𝑥 > 0.1, we find a total quark and gluon helicity contribution for 𝑥 >10 −7 of between 0.02 and 0.51.

Adamiak, Daniel [Michigan State University] (ORCID↗
DOE OSTI2026

Gluon splitting at small x: a unified derivation for the JIMWLK, DGLAP and CSS equations

We revisit the calculation of the next-to-leading order (NLO) corrections to dijet production in electron-ion collisions at small x. We focus on the back-to-back configuration where the relative transverse momentum P ⊥ of the measured jets is much larger than both their momentum imbalance K ⊥ and the target saturation momentum Q s (x, A). In this regime, we present for the first time a complete calculation of the real NLO corrections, associated with gluon emissions outside the jet cones, at leading power in 1/P ⊥ . Our result exhibits TMD factorisation, with the same hard factor as at tree-level and a NLO correction to the Weiszäcker-Williams (WW) gluon transverse momentum dependent (TMD) distribution which involves four Wilson-line operators. By studying different kinematical regimes for K ⊥ and for the radiated gluon, we recover all the quantum evolutions that were previously identified for this process at NLO: the B-JIMWLK high-energy evolution and the CSS evolution of the gluon WW TMD, and the DGLAP evolution of the gluon PDF. When both K ⊥ and the transverse momentum transferred by the target are large compared to Q s , all the Wilson-line operators boil down to the unintegrated gluon distribution and our NLO result for the gluon TMD can be used to isolate the transverse-momentum dependent gluon splitting function.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Bayesian quantification of observability and equation of state of twin stars

The possibility of discovering twin stars, two neutron stars (NSs) with the same mass but different radii, is usually studied in forward modelings by using a restricted number of NS matter equations of state (EOSs) encapsulating a first-order phase transition from hadronic to quark matter (QM). Informing our likelihood function with the NS radius data from GW170817 and using a metamodel with nine parameters capable of mimicking most NS EOSs available in the literature, we conduct a Bayesian quantification of the observability and underlying EOSs of twin stars. Of the accepted EOSs, between 12 and 18% yield twin stars, depending on the restrictions we place on the second branch. The possibility of twin stars remains robust even under recent observational constraints. Here, we show that many of these twin star scenarios are observable with currently available levels of accuracy in measuring NS radii. We also present the marginalized posterior probability density functions (PDFs) of every EOS parameter for each of four mass-radius correlation topologies. We find that the inferred EOS depends sensitively on not only whether twin stars are present, but also the category of twin stars, indicating that the observation of twin stars would provide a strong constraint on the underlying EOS. In particular, for two coexisting hybrid stars having QM cores at different densities, the PDF for QM speed of sound squared 𝑐$^2_{qm}$ has two peaks, one below and another above the conformal limit 𝑐$^2_{qm}$ = 1/3 predicted by perturbative QCD.

QCD in nuclear reactions↗
DOE OSTI2025

SPRUCE Root Production Assessed with Manual Minirhizotrons Resolved to Plant Functional Type, 2015-2021

This dataset contains raw root length and diameter for individual roots and estimated root population production measurements from the Spruce and Peatland Responses Under Changing Environments (SPRUCE) experimental site within the Marcell Experimental Forest in northern Minnesota, USA. Measurements started at the beginning of whole ecosystem warming manipulations in 2015 through 2021 (2015-05-26 to 2021-09-01). Root morphology and estimated production were quantified throughout the peat profile with manual minirhizotrons deployed within SPRUCE plots. Images were processed using commercial software to quantify the length and diameter of individual roots. Roots were visually assigned to a plant functional type (PFT) of either (ericaceous) shrub, herb (sedges and Maianthemum trifolium), or tree (Larix laricina, Picea mariana) based on expert opinion. The biomass of individual roots was estimated using PFT-specific allometric equations (Iversen et al., 2018). Production per day was estimated as the length of new roots produced between imaging sessions, divided by the number of days between imaging sessions. These values were placed on a m2 aboveground area basis and scaled to a standard depth of 1m (roots are not evenly distributed with depth, do not interpret value as being on a m3 basis). Maximum and average (weighted by production length) depth of each PFT were also estimated within each minirhizotron tube. Annual production was interpolated as the average of four methods to scale these data (see Weber et al, 2026). Standing crop of roots was estimated for each tube as the maximum visible amount (both length and mass) of roots of that PFT for that year. These data expand the ability of researchers to accurately estimate the belowground dynamics of peatland vegetation, as well as the role that fine roots may play in impacting the fluxes of carbon within peatlands. This dataset contains three data files in comma-separate values (*.csv) format. This dataset contains one data file in comma-separate values (.csv) format. Additional metadata are provided: three data dictionaries and a file-level metadata file in comma-separate values (.csv) format and a user guide in PDF (*.pdf) format.

54 ENVIRONMENTAL SCIENCES↗