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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 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The Value of Watching How Materials Grow: A Multimodal Case Study on Halide Perovskites

Material synthesis is one of the most important aspects in humankinds’ endeavor to discover and create new materials for energy applications. One strategy to tailor materials with desired functions in a rational way is by knowing how functions relate to structure, synthetic variables, arrangement of atoms and molecules, and how functions evolve during synthesis. In order to accelerate materials synthesis, discovery, and optimization by 10 times it is the right time now to integrate computational tools, synthesis, and characterization. One particular barrier to realizing this concept is the understanding of when and how phases form in real time during synthesis, which is challenging to asses by existing theoretical frameworks. In addition, transient or metastable phases with positive free energy above the lowest-free energy ground state can be revealed by such real time (in situ) measurements. Metastable materials are ubiquitous in condensed matter and can show superior properties compared to their equilibrium form. This work discusses the value of emerging multimodal in situ characterizations exemplified on hybrid halide perovskites. Finally, the ways in which the implementation of in situ measurements can advance the materials science synthesis field as well as their role to enable close-loop feedback control and autonomous synthesis are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2024

RELAP5-3D validation studies based on the High Temperature Test facility

In the spring and summer of 2019, experiments were conducted at the High Temperature Test Facility (HTTF) that form the basis of an upcoming high-temperature gas-cooled reactor (HTGR) thermal hydraulics (T/H) benchmark. HTTF is an integral effects test facility for HTGR T/H modeling validation. This paper presents RELAP5-3D models of two of those experiments: PG-27, a pressurized conduction cooldown (PCC); and PG-29, a depressurized conduction cooldown (DCC). These models used the RELAP5-3D model of HTTF originally developed by Paul Bayless as a starting point. The sensitivity analysis and uncertainty quantification code, RAVEN was used to perform calibration studies for the steady-state portion of PG-27. Here we developed four PG-27 calibrations based on steady-state conditions. These calibrations all used an effective thermal conductivity equal to 36 % of the measured thermal conductivity, but they differed with respect to the frictional pressure drops and radial conduction models. These models all captured the trends in steady-state temperature distributions and transient temperature behavior well. All four calibrations show room for improvement in predicting the transient temperature rise. The smallest error in temperature rise during the transient was a 21 % underprediction, and the largest was a 48 % underprediction. The errors in transient temperature rise are largely a result of a mismatch in power density between the RELAP5-3D model and the experiment due to the location of active heater rods along the boundary between heat structures in the model. The best of these calibrations was applied to PG-29 to model the DCC. Once again, temperatures during the transient were underpredicted but trends in temperature were captured. The RELAP5-3D model captured trends in the data but could not reproduce measured temperatures exactly. This result is not attributed to deficiencies in the experimental data or to RELAP5–3D itself. Rather, this result likely arises due to the some of the assumptions and decisions made when the RELAP5-3D model was first developed, prior to the execution of HTTF experiments. An agreement in prediction of temperature trends but challenges reproducing HTTF temperatures within measurement uncertainty is consistent with previous analyses of HTTF in the literature. Future RELAP5-3D validation activities centered around HTTF may be able to provide greater insight into the code’s capabilities for HTGR modeling with a more finely nodalized model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Delivering real-time multi-modal materials analysis with enterprise beamlines

Contemporary advancements in low-cost automation and computation, reduced barrier to entry in developing artificial intelligence/machine learning (AI/ML), and increased ability to represent complex materials in digital form have led to a number of accelerated materials discovery platforms. However, many of these approaches operate with completely rigid vertical integration in an isolated feedback loop using limited modalities. In order to make a substantial impact on discovering new energy materials, AI-driven experiments must operate collaboratively with each other and researchers and over multiple measurement modalities. Herein, we describe the potential for an “internet of things” approach to self-driving enterprise beamlines that merges core information technologies, robotics, and multi-modal AI. The approach will enable full utility of light sources, collaborate effectively with other remote materials acceleration platforms, and help stride toward the world’s energy future.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Collisional effects on resonant particles in quasilinear theory

A careful examination of the effects of collisions on resonant wave–particle interactions leads to an alternate interpretation and deeper understanding of the quasilinear operator originally formulated by Kennel & Engelmann ( Phys. Fluids , vol. 9, 1966, pp. 2377–2388) for collisionless, magnetized plasmas, and widely used to model radio frequency heating and current drive. The resonant and nearly resonant particles are particularly sensitive to collisions that scatter them out of and into resonance, as for Landau damping as shown by Johnston ( Phys. Fluids , vol. 14, 1971, pp. 2719–2726) and Auerbach ( Phys. Fluids , vol. 20, 1977, pp. 1836–1844). As a result, the resonant particle–wave interactions occur in the centre of a narrow collisional boundary when the collision frequency $\unicode[STIX]{x1D708}$ is very small compared to the wave frequency $\unicode[STIX]{x1D714}$ . The diffusive nature of the pitch angle scattering combined with the wave–particle resonance condition enhances the collision frequency by $(\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708})^{2/3}\gg 1$ , resulting in an effective resonant particle collisional interaction time of $\unicode[STIX]{x1D70F}_{\text{int}}\sim (\unicode[STIX]{x1D708}/\unicode[STIX]{x1D714})^{2/3}/\unicode[STIX]{x1D708}\ll 1/\unicode[STIX]{x1D708}$ . A collisional boundary layer analysis generalizes the standard quasilinear operator to a form that is fully consistent with Kennel–Englemann, but allows replacing the delta function appearing in the diffusivity with a simple integral (having the appropriate delta function limit) retaining the new physics associated with the narrow boundary layer, while preserving the entropy production principle. The limitations of the collisional boundary layer treatment are also estimated, and indicate that substantial departures from Maxwellian are not permitted.

Physics↗
DOE OSTI2024

Robust Tensor Hypercontraction of the Particle–Particle Ladder Term in Equation-of-Motion Coupled Cluster Theory

One method of representing a high-rank tensor as a (hyper-)product of lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et al. This strategy has been found to be useful for reducing the polynomial scaling of coupled-cluster methods by representation of a four-dimensional tensor of electron-repulsion integrals in terms of five two-dimensional matrices. Pierce et al. have already shown that the application of a robust form of THC to the particle–particle ladder (PPL) term reduces the cost of this term in couple-cluster singles and doubles (CCSD) from O(N 6 ) to O(N 5 ) with negligible errors in energy with respect to the density-fitted variant. In this work, we have implemented the least-squares variant of THC (LS-THC) which does not require a nonlinear tensor factorization, including the robust form (R-LS-THC), for the calculation of the excitation and electron attachment energies using equation-of-motion coupled cluster methods EOMEE-CCSD and EOMEA-CCSD, respectively. We have benchmarked the effect of the R-LS-THC-PPL approximation on excitation energies using the comprehensive QUEST database and the accuracy of electron attachment energies using the NAB22 database. Here, we find that errors on the order of 1 meV are achievable with a reduction in total calculation time of approximately 5x.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Engineered Silicon Carbide Three-Dimensional Frameworks through DNA-Prescribed Assembly

The ability to create nanoengineered silicon carbide (SiC) architectures is important for the diversity of optical, electronic, and mechanical applications. Here, we report a fabrication of periodic three-dimensional (3D) SiC nanoscale architectures using a self-assembled and designed 3D DNA-based framework. The assembly is followed by the templating into silica and subsequent conversion into SiC using a lower temperature pathway (<700 °C) via magnesium reduction. The formed SiC framework lattice has a unit size of about 50 nm and domains over 5 μm, and it preserves the integrity of the original 3D DNA lattice. The spectroscopic and electron microscopy characterizations reveal SiC crystalline morphology of 3D nanoarchitectured lattices, whereas electrical probing shows 2 orders of magnitude enhancements of electrical conductivity over the precursor silica framework. The reported approach offers a versatile methodology toward creating highly structured and spatially prescribed SiC nanoarchitectures through the DNA-programmable assembly and the combination of templating processes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Spatially resolved mass–metallicity relation at $z$ ~ 0.26 from the MUSE-Wide Survey

Galaxies in the local universe have a spatially resolved star-forming main sequence (rSFMS) and mass–metallicity relation (rMZR). We know that the global mass–metallicity relation (MZR) results from the integral of the rMZR, and it evolves with redshift. However, the evolution of the rMZR with redshift is still unclear because the spatial resolution and signal-to-noise ratio are low. Currently, too few observations beyond the local universe are available, and only simulations can reproduce the evolution of the rMZR with redshift. We selected ten emission-line galaxies with an average redshift of $z$ ~ 0.26 from the MUSE-Wide DR1. We obtained the spatially resolved star formation rate (SFR) and metallicity from integral field spectroscopy (IFS), as well as the stellar mass surface density from 3D-HST photometry. We derived the rSFMS and rMZR at $z$ ~ 0.26 and compared them with those of local galaxies. We find that the rSFMS of galaxies at $z$ ~ 0.26 has a slope of ~0.771. The rMZR exists at z ~ 0.26, showing a similar shape to that of the local universe, but a lower average metallicity that is about ~0.11 dex lower than the local metallicity. In addition, we also study the spatially resolved fundamental metallicity relation (rFMR) of these galaxies. However, there is no obvious evidence that an rFMR exists at $z$ ~ 0.26, and it is not an extension of rMZR at a high SFR. Similar to their global versions, the rSFMS and rMZR of galaxies also evolve with redshift. At fixed stellar mass, galaxies at higher redshift show a higher SFR and lower metallicity. In conclusion, these suggest that the evolution of the global galaxy properties with redshift may result from integrating the evolution of the spatially resolved galaxy properties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Ultraviolet spectra of extreme nearby star-forming regions: Evidence for an overabundance of very massive stars

ABSTRACT As deep spectroscopic campaigns extend to higher redshifts and lower stellar masses, the interpretation of galaxy spectra depends increasingly upon models for very young stellar populations. Here we present new HST/COS ultraviolet spectroscopy of seven nearby (<120 Mpc) star-forming regions hosting very young stellar populations (∼4–20 Myr) with optical Wolf–Rayet stellar wind signatures, ideal laboratories in which to benchmark these stellar models. We detect nebular C iii] in all seven, but at equivalent widths uniformly <10 Å. This suggests that even for very young stellar populations, the highest equivalent width C iii] emission at ≥15 Å is reserved for inefficiently cooled gas at metallicities at or below that of the SMC. The spectra also reveal strong C iv P-Cygni profiles and broad He ii emission formed in the winds of massive stars, including some of the most prominent He ii stellar wind lines ever detected in integrated spectra. We find that the latest stellar population synthesis prescriptions with improved treatment of massive stars nearly reproduce the entire range of stellar He ii wind strengths observed here. However, we find that these models cannot simultaneously match the strongest wind features alongside the optical nebular line constraints. This discrepancy can be naturally explained by an overabundance of very massive stars produced by a high incidence of binary mass transfer and mergers occurring on short ≲10 Myr time-scales, suggesting these processes may be crucial for understanding systems dominated by young stars both nearby and in the early Universe.

Senchyna, Peter↗
DOE OSTI2021

Approximation of the Frequency-Amplitude Curve Using the Homotopy Analysis Method

The Frequency-Amplitude (F-A) curve on power system oscillation under a large disturbance characterizes how a natural oscillation mode transitions to nonlinear oscillations with growing amplitudes and decaying frequencies. The existing formulation of the F-A curve is derived by solving elliptical integrals on oscillation of a single-machine-infinite-bus equivalent about the targeted oscillation mode. The formula is in a form of infinite series and needs to sum a large number of terms for satisfactory accuracy. This paper introduces an explicit, approximate expression obtained from the Homotopy Analysis Method on the F-A curve. The proposed F-A curve expression is derived from an SMIB system and verified on the IEEE 3-machine 9-bus system to show how the oscillation frequency of a dominant mode varies with oscillation amplitude under large disturbances.

frequency-amplitude (F-A) curve↗
DOE OSTI2024

Optimal Control of SOEC-Based Hydrogen Production Systems for Demand Response Using Deep Reinforcement Learning in Smart Grids

Solid oxide electrolysis cell (SOEC) hydrogen production technology can range in size from small, appliance-size equipment to large-scale, central production facilities that can be tied directly to renewable or non-greenhouse-gas-emitting forms of electricity production, making it an ideal resource for demand response (DR). The SOEC hydrogen production system is a complex integrated system that encompasses fluid dynamics, electrical dynamics, and electrochemical and thermal dynamics, all of which involve non-linearity and non-convexity. Proper control of the SOEC hydrogen production system is crucial to enable its participation in the DR program. Here, to overcome the difficulty of designing an explicit control law for such nonlinear systems with nonconvex optimization features in DR applications, deep reinforcement learning (DRL) is explored to achieve the optimal control of the SOEC system for DR participation. Specifically, a twin delayed deterministic policy gradient (TD3) control framework is applied to achieve optimal response performance during DR events by considering power tracking error and hydrogen production efficiency with a suitable reward function. Two case studies with grid connections for tracking different DR commands were investigated. The first case study involved operating conditions reaching the boundaries, while the second involved operating conditions within the boundaries. The results showed that the proposed DRL-based control for SOEC can track the DR signal in a timely manner while maintaining high energy efficiency.

08 HYDROGEN↗
DOE OSTI2021

Experimental Investigation on the Performance Loss of Cross-Linked Polymers During Photo-Oxidative Aging

Abstract Polymeric substances have seen an unprecedented integration in countless applications and fields of life, subjecting them to a broad range of environmental conditions, which can cause a form of damage to the structural and mechanical properties of these components known as aging. In this study we investigate the effects of the degradation of polymeric materials due to the extended exposure to sunlight, which can be simulated through controlled photo-oxidative aging using ultraviolet (UV) radiation as the main catalyst of this phenomenon. The effects on mechanical behavior and chemical properties of four polymeric materials with different mechanical characteristics was accordingly monitored throughout the study. The materials range in hardness with the polyurethane adhesive being the hardest and acting plastically, followed by an acrylic which exhibits greater hardening with time, a polyurethane sealant, which behaves in an elastomeric manner, and a silicon sealant, which is the softest of the set. Samples were prepared and subjected to UV radiation at three different temperatures namely 45, 60 and 80°C, for different aging periods ranging from 1 day for higher temperatures to 150 days for lower ones. The samples were then subjected to the Fourier transform Infrared spectroscopy (FTIR) test to monitor the change in the chemical composition of the materials along the aging durations and conditions. The materials were then subjected to mechanical testing along two modes of mechanical loading, which are a simple tension until failure and a double-cyclic test with progressively increasing strain limits after every two successful cycles until the sample reaches failure. The samples are loaded at constant strain rates throughout both tests. These tests revealed the change of behavior of our materials along the aging periods and conditions. The changes in mechanical behavior vary across each individual material depending on the aging temperature and period, with the changes ranging from hardening to softening, embrittlement or an increase in the maximum strain the material can endure before failure. A general trend would be that most materials become harder after photo-oxidation, however due to the range of temperatures in the aging conditions, thermo-oxidation, which causes softening in some of the polymers, has an increasingly notable effect at higher temperatures. A visible correlation can be noted between the change in mechanical behavior and a change in absorbance of Infrared Radiation (IR) in the FTIR spectrum, as the greater the crosslinking throughout the polymer matrix, the lower the absorbance of IR radiation due to the increased stiffness of the overall macro-molecular structure.

Korayem, Abd-Elrahman↗
DOE OSTI2024

Hestia SW-IFL Onroad Fossil Fuel Carbon Dioxide (FFCO2) product: Road segment-level annual FFCO2 emissions across Arizona (2017-2022), version 1.1

The SW-IFL onroad fossil fuel carbon dioxide (FFCO2) emissions data product represents CO2 emissions from the combustion of fossil fuels by motor vehicles (e.g., passenger cars, trucks, buses, motorcycles) traveling on designated roadways. The emissions are represented geographically on each road segment within the state of Arizona spanning the 2017 to 2022 time period. This data product was developed as part of the Southwest Urban Corridor Integrated Field Laboratory (SW-IFL) project, which aims to provide new knowledge and tools that address urban environmental issues by integrating high-resolution observations, modeling, and civic engagement. The emissions data are provided in CSV (input data, ONR_FFCO2_AZ_county.csv) and GeoPackage form (output polyline objects - about 786,000 road segments, XXXX_AZ_v1.1.gpkg) designated by road class (interstates, arterials, collectors, local). The metadata file (Metadata_SW-IFL_Onroad_annualFFCO2_v1.1.docx) provides details about attributes and data formats. The GeoPackage emissions data are provided separately for local roads and nonlocal roads (interstates, arterials, collectors). The method file (Methods_SW-IFL_Onroad_annualFFCO2_v1.1.docx) describes the data processing flow and data sources. Update on 2024-04-17: Updates were made to both the input emission data file (.csv) and output segment-level emission file (.gpkg). There was an update in county-level emission input data (ONR_FFCO2_AZ_county.csv) and the entire road segments were reprocessed to reflect this update.Update on 2024-04-29: Update was made to one output segment-level emission file (Nonlocal_AZ_v1.0.gpkg). There was an error in the AADT values and the data were reprocessed to reflect this update.Update on 2024-10-22: Temporal coverage was extended to include 2022. VMT values were recalculated using new AADT data and the entire road segments were reprocessed to reflect these updates.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

(U) A Theoretical Study of Asay Foil Trajectories (V.02)

We consider the trajectory of a generic Asay foil ejecta momentum diagnostic sensor, for scenarios where ejecta are produced at a planar surface and fly ballistically through a perfect vacuum to the sensor. To do so, we build upon a previously established mathematical formalism derived for the analytic study of stationary sensors (i.e., piezopins). First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source areal mass function (“source model”). This defines an integro-differential equation (IDE) for the foil trajectory. When ejecta production is instantaneous - as is generally assumed in momentum diagnostic data analyses - the IDE leads to an implicit and easily calculable closed-form solution for the foil trajectory in a perfect system, as long as the ejecta particle velocity distribution is twice-integrable. General properties of the instant-production trajectory solution indicate the existence of a boundary condition the particle velocity distribution must satisfy in order for the analytically predicted foil trajectories to be compatible with certain features commonly observed in foil data. This boundary condition is identical to one derived previously from a consideration of piezopin data. Armed with the analytic solution for instant production, we also consider various techniques used to extract time-dependent cumulative ejecta masses from foil trajectories, and derive an expression for the error imposed by using an approximated equation of motion. This analytic trajectory solution furthermore makes it possible to examine the common practice of presenting inferred cumulative ejecta masses as a function of a normalized implied velocity; we derive conditions under which this methodology is and is not meaningful. We also propose a strategy for extending the instant-production trajectory solution to time-dependent source functions.

42 ENGINEERING↗
DOE OSTI2021

USAMP Low-Cost Mg Sheet Component Development and Demonstration Project

The overarching objective of this USAMP project was to develop and demonstrate door panels made from magnesium (Mg) sheet with a cost penalty over conventional steel stampings of no more than $\$5.50$/kg saved. The technical approach integrated experiments with advanced computational tools based on Integrated Computational Materials Engineering (ICME) methods to develop new alloy chemistries and their thermomechanical processing that promise improved formability and lower forming temperatures. A penultimate task before finally forming the stampings was to incorporate actual microstructure into models that would enable formability simulations. This approach would, for the first time, account for individual magnesium grains moving in an anisotropic fashion unlike that for aluminum or steel that have isotropic properties upon which the current simulation tools are based. In separate activities, new coatings and lubricants to facilitate forming and improved corrosion protection and joining strategies, were developed to ensure that the door could be produced with stated product requirements. A technical cost model, which included parts production, assembly, and paint for a door specifically designed for Mg sheet, showed the cost penalty to be between $\$4.26$ to $\$6.60$/kg saved, which enveloped the project’s cost targets. The cost of the coated Mg sheet was identified as the key driver for the cost penalty. The mass of the Mg-intensive door was 7.9 kg, which was 54% less than the baseline steel door.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Low-Cost Magnesium Alloy Sheet Component Development and Demonstration Project

The overarching objective of this USAMP project was to develop and demonstrate door panels made from magnesium (Mg) sheet with a cost penalty over conventional steel stampings of no more than $5.50/kg saved. The technical approach integrated experiments with advanced computational tools based on Integrated Computational Materials Engineering (ICME) methods to develop new alloy chemistries and their thermomechanical processing that promise improved formability and lower forming temperatures. A penultimate task before finally forming the stampings was to incorporate actual microstructure into models that would enable formability simulations. This approach would, for the first time, account for individual magnesium grains moving in an anisotropic fashion unlike that for aluminum or steel that have isotropic properties upon which the current simulation tools are based. In separate activities, new coatings and lubricants to facilitate forming and improved corrosion protection and joining strategies, were developed to ensure that the door could be produced with stated product requirements. A technical cost model, which included parts production, assembly, and paint for a door specifically designed for Mg sheet, showed the cost penalty to be between 4.26 USD to 6.60 USD/kg saved, which enveloped the project’s cost targets. The cost of the coated Mg sheet was identified as the key driver for the cost penalty. The mass of the Mg-intensive door was 7.9 kg, which was 54% less than the baseline steel door.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Development of Quantum Computing Interconnect Based on Aerosol Jet Printing and Electrochemical Deposition of Rhenium

The electrodeposition of rhenium on to a metal seed layer on flexible substrates is presented as a means to creating superconducting flexible cable connectors in an enabling plug-and-play approach for quantum computing. Cryogenic quantum electronics are currently connected using masses of stainless-steel coaxial cables that are bulky, rigid - both in form and design - and lead to significant joule heating, thermal noise, and cross talk. Here, we present an unprecedented approach to integrate an aerosol jet printed (AJP) metal seed layer with rhenium electrodeposition on a flexible substrate in the advancement of superconducting interconnect technologies. Silver and gold were printed using the ‘Nanojet’ aerosol jet printer on Kapton films. Adhesion of gold was found to be far superior to that of silver and adhesion on roughened Kapton surpassed that of its smooth counterpart. Electrodeposition of rhenium was successful on both silver and gold and an amorphous Re film was confirmed by XRD. Results for both materials are presented however due to the poor adhesion of silver to Kapton it was ruled out as a viable candidate. Composite materials were characterized by profilometry, EDS, XRD and FIBSEM. Electrical measurements of the composite at ambient temperature showed a critical temperature (T c ), where the resistance drops to 0, of 5.8 K, well above 4.2 K, the temperature of liquid helium. Stress-strain tests of the Ag-Re and Au-Re composites on roughened and smooth Kapton were completed. Cyclic flexure testing (200 cycles) to 1.25% strain showed smooth Kapton samples reach a stress of ~16 MPa, while Kapton roughened with sandpaper, reaches ~20MPa of stress for the same 1.25% strain.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Questionnaire for Radioisotope Identification and Estimation from Gamma Spectra using PyRIID v2

Accurate targeting of radioisotope classifiers and estimators requires an understanding of the target problem space. In order to facilitate clear communication on expected model behavior and performance between practitioners and stakeholders on their problems, this questionnaire was created. Stakeholder responses form the basis of a trained model as well as the start of usage requirements for the model as it is integrated with analysis processes or detection systems. This questionnaire may also be useful to machine learning practitioners and gamma spectroscopists developing new algorithms as a starting point for characterizing their problem space, especially if they are using PyRIID.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Lattice QCD calculation of the pion generalized parton distribution

We present the results of a Lattice QCD computation of pion generalized parton distribution (GPD), employing perturbative matching up to next-to-next-to-leading order (NNLO). The computations are based on an ensemble of Nf=2+1 highly improved staggered quarks (HISQ) with a pion mass of 300 MeV and a lattice spacing of 0.04 fm. Centered on the zero-skewness limit, we utilize a recently proposed Lorentz-invariant definition of GPD, which is derived from Lorentz-invariant amplitudes. We analyze and compare these amplitudes in both Breit and non-Breit kinematic frames at comparable momentum transfers, validating their frame-independent nature. To obtain light-cone GPD, we integrate hybrid scheme renormalization with the large momentum effective theory (LaMET). Moreover, we determine the first three iso-vector generalized form factors (GFFs) of the pion using the ratio scheme renormalization and leading-twist factorization, achieving NNLO accuracy.

Ding, Heng-Tong↗