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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Evaluating Protection System Performance for a Real-World Weak Grid Area With High Inverter-Based Resources: Preprint

This paper evaluates an existing protection scheme implemented in a real-world weak grid area with a high penetration of inverter-based resources (IBRs). The study aims to assess the reliability and adequacy of protection schemes originally designed for traditional synchronous machine systems and determine whether they can continue to operate reliably in systems with high levels of IBRs. Hardware relays are tested using a controller-hardware-in-the-loop setup. PSCAD electromagnetic transient simulation with an IBR original equipment manufacturer black-box model is used to perform fault studies and generate COMTRADE data, which are replayed by a real-time digital simulator (RTDS) to feed input to the hardware relays. Three scenarios are analyzed: normal operation, an N-1 contingency, and an IBR-only scenario. The evaluation results reveal the following: 1) the protection scheme remains reliable under normal conditions and N-1 contingencies and 2) in IBR-only scenarios, differential protection (87L) continues to operate reliably, whereas local protection elements, such as distance and directional elements, fail because of the lack of regulated negative sequence current contributed by IBRs. These findings provide utilities with valuable insights for improving their protection systems in high-IBRs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Development of an Unbiased Future Solar Dataset for Solar Resource Adequacy Research Over CONUS

A high-resolution, long-term solar dataset is essential for capturing the variability of solar energy resources and informing strategies to ensure grid reliability and resilience in systems with high levels of solar energy integration. This study focuses on generating unbiased, high-resolution projections of solar irradiance through a statistical downscaling framework, using Earth system model (ESM) simulations obtained from the North American Coordinated Regional Climate Downscaling Experiment (NA-CORDEX). The National Solar Radiation Database (NSRDB) is used to calibrate statistical downscaling models. The newly developed dataset provides solar irradiance, surface air temperature, and surface wind speed at 4-km and hourly resolutions across the contiguous United States (CONUS), based on two future scenarios (RCP4.5 and RCP8.5). This study outlines key steps in developing the high-resolution future solar dataset, including (1) regridding ESM data to a common 20-km resolution grid, (2) correcting ESM biases using the NSRDB, and (3) applying temporal and spatial downscaling methods to generate high-resolution (4-km, hourly) solar projections. Preliminary results indicate that downscaled projections (4-km) captured reasonable spatial patterns when compared to observations across CONUS for four variables. On average across all pixels, 4-km daily-total GHI and DNI projections showed normalized bias (nBias) less than 1% and 6% for GHI and DNI against NSRDB, respectively (nBias less than 1% and 5% for daily-average surface air temperature and surface wind speed). In terms of long-term trend for GHI and DNI, there was no strong increasing or decreasing trend (when compared to surface air temperature), but it showed a very weak decreasing trend.

14 SOLAR ENERGY↗
DOE OSTI2025

WHOLESCALE - Water & Hole Observations Leverage Effective Stress Calculations And Lessen Expenses (Final Technical Report 2020 - 2024)

The WHOLESCALE acronym stands for Water & Hole Observations Leverage Effective Stress Calculations and Lessen Expenses. The goal of the WHOLESCALE project is to simulate the spatial distribution and temporal evolution of stress in the geothermal system at San Emidio in Nevada, United States. To reach this goal, the WHOLESCALE team has developed a methodology to incorporate and interpret data from four methods of measurement into a multi-physics model that couples thermal, hydrological, and mechanical (T H-M) processes. The WHOLESCALE team has applied this methodology at the San Emidio geothermal field, located ~100 km north of Reno, Nevada in the northwestern Basin and Range province. The WHOLESCALE team includes 30 individuals working at two universities, two national laboratories, and one industry partner. Two master-degree students and five post-doctoral researchers have gained professional experience and earned partial financial support via the WHOLESCALE project. The WHOLESCALE team has taken advantage of the perturbations created by changes in pumping operations during planned shutdowns in 2016, 2021, and 2022 to infer temporal changes in the state of stress in the geothermal system at San Emidio, Nevada, U.S. The WHOLESCALE results support the working hypothesis that increasing pore-fluid pressure reduces the effective normal stress acting across fault zones. During normal operations, pumping in deep production wells decreases fluid pressures and thus increases the effective normal stresses on faults, reducing microseismicity. During planned shutdowns, the cessation of production increases pore-fluid pressure and reduces effective normal stress. The WHOLESCALE products generated during the 4-year period between 2020 and 2024 include: three articles published in the open-access, peer-reviewed scientific literature, two master’s theses, 20 presentations or papers at scientific conferences, and 17 data sets available on public repositories. The WHOLESCALE project has been completed in two phases that included three performance periods separated by two Go/No-go Stage Gate Reviews. Tasks were classified by data type (i.e., Geologic Structure, Borehole, Geodesy, Hydrology, Seismology, and Modeling). The first phase of the project started July 31, 2020 and included ongoing project coordination (Task 1), a project kickoff (Task 2), analysis of existing data (Task 3), development of the initial stress model & deployment design (Task 4), and Go/No-go Decision Point #1 (Task 5). Phase II began with implementing the 2022 deployment (Task 6), followed by Go/No-go Decision Point #2 (Task 7) The remainder of Phase II consisted of analyzing data collected during deployment (Task 8), calibration of the stress model on all observations (Task 9), and the Final Review (August 23, 2024) & Reporting (Task 10).

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

TorchBraid: High-Performance Layer-Parallel Training of Deep Neural Networks with MPI and GPU Acceleration

TorchBraid is a high-performance implementation of layer-parallel training for deep neural networks (DNNs) supporting MPI-based parallelism and GPU acceleration. Layer-parallel training has been developed to overcome the serialization inherent in forward and backward propagation of DNNs that limits utilization of computational resources in the strong scaling limit. To achieve this, TorchBraid integrates the PyTorch neural network framework with the state-of-the-art XBraid time-parallel library. Furthermore, this article presents the use and performance of TorchBraid, in addition to solutions for overcoming the algorithmic challenges inherent in combining automatic differentiation with layer-parallel. Results are presented with and without GPU acceleration for the Tiny ImageNet and MNIST image classification data sets, as well as recurrent neural networks. Overall, TorchBraid enables fast training of DNNs, both in a strong and weak scaling context. In addition to the TorchBraid software, several new advances in applying layer-parallel algorithms are detailed. Integration of layer-parallel with data-parallel algorithms is presented for the first time, showing the computational advantages of the combination. Standard deep learning techniques, like batch-normalization, are developed for layer-parallel training. Finally, a new approach combining layer-parallel with spatial coarsening in order to accelerate training for 3D image classification shows roughly a 10× speedup over serial execution.

Layer-parallel↗
DOE OSTI2026

Quantifying the Impact of Metal Population Distribution in MFI-Supported Mo Catalysts for Methane Dehydroaromatization

Precise evaluation of intrinsic kinetic behavior in Mo/MFI catalysts for methane dehydroaromatization (MDA) is confounded by variations in Mo dispersion and speciation, which are influenced by metal loading and zeolite acidity. This work advances the utility of H 2 -temperature programmed reduction (H 2 -TPR) for characterizing Mo/MFI catalysts by enabling quantitative comparison of MoO x populations distinguished by reduction behavior and linked to initial catalytic performance. A comprehensive H 2 reduction pathway is established through systematic H 2 - TPR studies varying catalyst composition (1–10 wt % Mo, Si/Al = 15, 40, ∞), supplemented by UV-Raman spectroscopy, X-ray powder diffraction, N 2 physisorption, NH 3 -TPD, and advanced spectroscopic analysis (in situ XAS with principal component analysis/multivariate curve resolution—alternating least squares). Two low-temperature H 2 -TPR regions capture distinct Mo populations undergoing initial Mo(VI)→Mo(IV) reduction: a lower-temperature population (Mo-RI) associated primarily with highly dispersed, anchored MoO x species expected to predominantly reside within MFI channels, and a higher-temperature population (Mo-RII) corresponding to a broader set of MoO x species that becomes increasingly bulk-like/extrazeolitic at higher Mo loading. Quantification of these populations provides practical, kinetically relevant descriptors for comparing initial MDA rates across catalysts with varying Mo loading, Si/Al ratio, and MoO x heterogeneity. Application of lower-temperature Mo-RI estimates to kinetic measurements reveals a minimum threshold of ∼0.12 × 10 –3 mol Mo-RI/g cat , above which initial forward benzene rates normalized to this population converge despite differences in metal loading and zeolite Brønsted acidity. This threshold coincides with a transition toward a common C 2 -mediated benzene-forming regime, as indicated by approach-to-equilibrium analysis of methane-to-ethane, ethane-to-ethylene, and ethylene-to-benzene reaction steps. Above this threshold, normalized initial benzene rates are nearly invariant with increasing Mo-RII/Mo-RI population ratio, indicating that excess Mo-RII populations, including bulk-like/extrazeolitic MoO x domains present at higher loading, do not measurably suppress benzene formation associated with anchored and mostly channel-confined Mo population under the initial-rate conditions examined.

Mo/MFI↗
DOE OSTI2025

Deep Factorization Machine Learning for Disaggregation of Transmission Load Profiles with High Penetration of Behind-The-Meter Solar

The ever-growing integration of distributed energy resources (DERs), especially behind-the-meter (BTM) solar generations, poses imperative operational challenges to system operators such as regional transmission organizations (RTOs). It is important for RTOs to effectively and accurately extract actual load profiles at the transmission level for a single node with significant BTM solar injection. This paper first illustrates the necessity of disaggregating the daily actual load profile of a single node. Furthermore, by segmenting nodes with selected timeseries features, nodes with significant BTM solar generation are identified. Lastly, a bi-level framework is proposed, comprising reference node disaggregation and DeepFM nodal disaggregation, aimed at disaggregating the nodal load profiles from which system operators require more information. By adopting a hybrid Deep Factorization Machine (DeepFM) model, the model achieve accurate results by extracting both linear and nonlinear relations between nodes in the same region and the zonal load and nodal load profile. To overcome the lack of ground truth, this paper segments the load profile into daytime, nighttime, and zero-crossing points and utilizes the latter two for evaluation purposes. The proposed disaggregation procedure is validated using real world, minute-level, normalized, and anonymized nodal data in the PJM service territory.

42 ENGINEERING↗
DOE OSTI2025

Heterogeneous and Framework-Bound Copper Species Contribute to Catalytic Partial Methane Oxidation in Cu–Chabazite Zeolites

The relationship between continuous partial methane oxidation (PMO) rates and Cu site speciation in Cu-CHA zeolite catalysts is explored through differential rate measurements across a series of samples of varying compositions combined with density functional theory, first-principles thermodynamics, and statistical models that characterize Cu speciation. Under continuous PMO conditions (573 K, 0.07 kPa O 2 , 3 kPa H 2 O), Cu ions are shown to anchor to the CHA framework in both monomeric (Z 2 Cu and Z 2 CuH 2 O) and dimeric (O- and OH-bridged Cu) forms that are sensitive to the identity of the local framework anchoring site. Consequently, across the studied compositional range, Cu-CHA catalysts are predicted to contain a mixture of monomeric and dimeric Cu sites. Cu-normalized CH 3 OH formation rates extrapolated to zero conversion reflect contributions from multiple site types. Predicted CH 3 OH formation rates indicate that the Cu site reactivity toward CH 4 is influenced by zeolite composition and is likely limited by the reduction half-cycle.

03 NATURAL GAS↗
DOE OSTI2025

Uncertainties in the effects of organic aerosol coatings on polycyclic aromatic hydrocarbon concentrations and their estimated health effects

We used the CAM5 model to examine how different particle-bound polycyclic aromatic hydrocarbon (PAH) degradation approaches affect the spatial distribution of benzo(a)pyrene (BaP). Three approaches were evaluated: NOA (no effect of OA coatings state on BaP), shielded (viscous OA coatings shield BaP from oxidation under cool and dry conditions) and ROI-T (viscous OA coatings slow BaP oxidation in response to temperature and humidity). Results show that BaP concentrations vary seasonally, influenced by emissions, deposition, transport and degradation approach, all of which are influenced by meteorological conditions. All simulations predict higher population-weighted global average (PWGA) fresh BaP concentrations during December–January–February (DJF) compared to June–July–August (JJA), due to increased emissions from household activities and reduced removal processes during colder months. The shielded and ROI-T approaches, which account for OA coatings, result in 2–6 times higher BaP concentrations in DJF compared to NOA. The shielded simulation predicts the highest PWGA fresh BaP concentration (1.3 ng m −3 ), with 90 % of BaP protected from oxidation. In contrast, the ROI-T approach forecasts lower concentrations in middle to low latitudes, as it assumes less effective OA coatings under warmer, more humid conditions. Evaluations against observed BaP concentrations show the shielded approach performs best, with a normalized mean bias (NMB) within ± 20 %. The combined incremental lifetime cancer risk (ILCR) for both fresh and oxidized PAHs is similar across simulations, emphasizing the importance of considering both forms in health risk assessments. This study highlights the critical role of accurate degradation approaches in PAH modeling.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2025

Demonstration of a Novel Technology to Manage Electricity Demand in Grid-Independent Military Microgrids

This research was conducted by the National Renewable Energy Laboratory (NREL) in collaboration with the S&C Electric Inc. through funding provided by the ESTCP. The project demonstrates use of cybersecure Automated Demand Response (ADR) technology to effectively manage microgrid loads during grid-independent, also known as "islanded," operation. When military microgrids become isolated from the main electrical grid, they are required to balance electricity supply and demand locally. Given that local generation may be constrained, the prevailing strategy involves shedding all but the most critical loads by tripping smart circuit breakers, which then necessitate manual resetting. This approach is generally implemented at the building level, which means that the buildings with mission-critical activities are exempt from load management and remain fully powered, whereas those deemed non-critical can experience a complete loss of service. In this research we developed a method that allows building automation systems to selectively control their assets in response to load shedding request from a microgrid controller, avoiding total loss of service in contrast to the conventional control approach. A commercial OpenADR client server by GridFabric is used for communication between the microgrid controller and the building management system (BMS). The microgrid controller monitors both generation capacity and various assets within the microgrid and issues a demand reduction request when necessary. This request is communicated to the OpenADR server via Modbus. Upon receiving the request, the OpenADR server forwards it to the BMS utilizing the OpenADR protocol. The BMS is pre-configured with various levels of load reduction strategies based on the controllable assets available, allowing for a nuanced approach to demand reduction. Both lab and field tests were performed that considered load shedding needed to achieve closed transition into island mode and to accommodate changing loads and power source availability while islanded. A commercial microgrid controller was used for these tests with normal programming within the expected constraints of the system capabilities. That is, the solution did not require any specialized modification to the code base of the controller. Given the latency of the round-trip communication path between the microgrid controller and the various devices involved with the load shed processes, there are certain scenarios for which the demonstrated solution are appropriate and some which are not. The methods described in this report can be used for load shedding/restoration during transitions between islanded and grid-tied modes of operation, as well as accommodating normal variations in load and the need to remove a power source from operation for maintenance. These methods should not be used for scenarios that require load shedding within a second or two such as sudden and unanticipated significant load increases or loss of power sources through equipment faults.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Measurements of Angular Distributions of Drell-Yan Dimuons in $p+p$ and $p+d$ Interactions at 120 GeV/$c$

We present experimental results on the angular distributions of Drell-Yan muons produced by a 120 GeV/$c$ proton beam interacting with liquid hydrogen and deuterium targets. The dimuon angular distributions in both polar ($θ$) and azimuthal ($ϕ$) angles in the Collins-Soper frame are measured within the kinematic range of $4.5 < m_{μμ} < 10\ \mathrm{GeV}/c^2$, $0.19 < p_T < 2.24\ \mathrm{GeV}/c$, and $0 < x_F < 0.95$. Unlike the results of a previous proton-induced Drell-Yan experiment at a higher energy, the data reveal a pronounced $\cos 2ϕ$ modulation in the angular distributions. Comparison with perturbative QCD (pQCD) predictions shows statistically significant deviations, with p-values of 3.5% for the $p+p$ and 1.5% for the $p+d$ Drell-Yan processes. These results suggest the presence of nonperturbative QCD contributions.

Nagai, K. [Christian Brothers U.; Los Alamos; Taiw↗
DOE OSTI2024

Improving the National Solar Radiation Database (NSRDB) Using a Physics-Based Direct Normal Irradiance (DNI) Model: Preprint

The National Solar Radiation Database (NSRDB) is a widely used resource providing satellite-derived solar data across the United States and globally. While the NSRDB employs a physical model for computing global horizontal irradiance (GHI), its current method for estimating cloudy-sky direct normal irradiance (DNI) relies on surface observations and empirical models. Recently, a novel physics-based approach, the Fast All-Sky Radiation Model for Solar applications with DNI (FARMS-DNI), was developed to enhance the DNI forecasting. FARMS-DNI incorporates both direct and scattered solar radiation within the circumsolar region, resulting in improved day-ahead DNI predictions when integrated into the Weather Research and Forecasting model with Solar extensions (WRF-Solar). This study integrates FARMS-DNI into the NSRDB algorithm to generate high-resolution DNI data from satellite resources. Our findings reveal that FARMS-DNI effectively mitigates the substantial DNI overestimation present in the conventional NSRDB across surface sites, particularly in conditions categorized as cloudy overcast. Consequently, this innovative model substantially enhances the overall accuracy of the NSRDB.

DNI↗
DOE OSTI2026

Ultrafast vertical photoconductive intrinsic diamond switch with high current (17.1 A at 1 kV)

Here, this Letter reports on a vertical, bulk-conducting photoconductive semiconductor switch (PCSS) fabricated on an intrinsic Type IIa single-crystal diamond substrate. Under near-bandgap excitation at 225 nm with a 20 μ J pulse, a strong photocurrent response of 17.1 A at 1 kV DC bias magnitude is obtained by (i) tuning the optical trigger wavelength to the “matched-absorption” window (224–235 nm) near the band edge, where the optical penetration depth becomes comparable to the 500 μ m substrate thickness, and (ii) choosing the bias polarity ensuring electron-dominant conduction, given that electrons have a higher mobility than holes in diamond. The PCSS has an area-normalized responsivity of 54.2 mA W −1 cm −2 and an effective on-resistance of 8.48 Ω, with a fast 90%–10% transient fall time of 25 ns, attributed to carrier sweep-out. These results support vertical, bulk-conducting intrinsic diamond PCSS as a promising platform for high-power optical switching and provide new insight into intrinsic photoconductivity in diamond.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Evidence of Completion of Milestone 3: Experimental Testbed

Construction and deployment of the experimental testbed encountered scheduling delays, and completion was subsequently further delayed by curtailment of LANL operations due to the COVID-19 pandemic. Between March and October, LANL was in a state of “Limited Operations” such that only certain “mission-critical” work was performed with approximately 25% on-site staffing. In spite of this, much of the lab space preparation was executed and the five initial model house” units were constructed and installed during this period. Still, the pace of construction was impacted by difficulty in coordinating personnel and minimizing contact between workers. Currently, LANL is in the mode of “Normal Operations with Maximum Telework,” which continues to limit the availability of on-site personnel. Nevertheless, Milestone 3 is now complete. This document describes the experiment as it is deployed and provides status for each task for this milestone.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2026

PowerModelsGAT-AI: Physics-Informed Graph Attention for Multi-System Power Flow With Continual Learning

Solving the alternating current power flow equations in real time is essential for secure grid operation, yet classical Newton–Raphson solvers can be slow under stressed conditions. Existing graph neural networks for power flow are typically trained on a single system and often degrade on different systems. We present PowerModelsGAT-AI, a physics-informed graph attention network that predicts bus voltages and generator injections. The model uses bus-type-aware masking to handle different bus types and balances multiple loss terms, including a power-mismatch penalty, using learned weights. We evaluate the model on 14 benchmark systems (4 to 6,470 buses) and train a unified model on 13 of these under contingency conditions with up to two branch outages, achieving an average normalized mean absolute error of 0.89% for voltage magnitudes and R 2 >0.99 for voltage angles. We also show continual learning: when adapting a base model to a new 1,354-bus system, standard fine-tuning causes severe forgetting with error increases exceeding 1000% on base systems, while our experience replay and elastic weight consolidation strategy keeps error increases below 2% and in some cases improves base-system performance. Interpretability analysis shows that learned attention weights correlate with physical branch parameters (susceptance: r=0.38 ; thermal limits: r=0.22 ), and feature importance analysis supports that the model captures established power flow relationships.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

MegaWatt Mayhem: Grid Operator Challenges Center Loads

This report provides a summary of the challenges faced by United States electricity grid operators in accommodating and anticipating the rapid deployment of large loads, particularly data centers, based on academic literature and industry working groups. The report highlights the unique requirements and operational characteristics of data centers, which differ significantly from traditional industrial loads. Key issues addressed utility planning considerations, with emphasis on the implications for grid operators, impacts to normal operations for grid operators, reliability considerations during periods of grid stress, and resilience considerations for the changing operational paradigms based on data centers. Real-world examples are used to highlight these challenges and the changes that grid operators must address. The findings underscore the necessity for coordinated efforts and innovative solutions from both grid operators and regulatory bodies to ensure the stable integration of large loads into the grid. This report is the first in a series that will explore the challenges of data center deployments based on several key power system perspectives.

24 - POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Tightest Mixed-Integer Programming Formulations for Quadratic SCUC Optimization

In this project, we developed new, tighter Mixed-Integer Programming (MIP) formulations for the combined Alternating Current (AC) Security-Constrained Unit Commitment (SCUC) and Security-Constrained Optimal Power Flow (SCOPF). The work addresses a critical challenge in power system operations: efficiently determining which generation units to commit and how to optimally dispatch them while maintaining network reliability constraints for both normal and contingency scenarios. Our efforts: 1. Advance the Understanding of SCUC/SCOPF Modeling: By introducing tighter MIP formulations and leveraging cutting-edge optimization tools (Julia/JuMP, PowerModels.jl), this project has pushed forward the state of the art in efficient power systems scheduling. 2. Enhance Technical and Economic Feasibility: The methods developed provide more accurate and potentially faster solutions to large-scale, realistic scheduling and dispatch problems in electric power systems, which can translate into improved reliability and potentially lower costs for grid operations. 3. Benefit to the Public: Greater efficiency in power system operations leads to cost savings for utilities and end-users. Improved reliability and integration of advanced modeling approaches can facilitate the adoption of clean energy resources and better accommodate uncertainties in renewable generation. Because this technology could impact bulk power markets and reliability, these innovations have far-reaching public benefits in terms of cost savings, reliability, and sustainability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Optimal Control Strategy With Efficiency and Reliability Improvement for Offshore DC Microgrids

Offshore microgrids, due to their remote location and lack of external energy support, face significant challenges in wide-range load operation and maintenance. Consequently, efficiency and reliability are critical concerns for converters in offshore dc microgrids. This article presents an optimal control strategy aimed at enhancing both efficiency and reliability. A normalized nonlinear relationship between power loss and thermal stress of a paralleled converter is first established. Based on this, a dual-objective optimization function with an active weight function as well as a system overall performance index is established. The active weight function dynamically adjusts the control priority based on converter efficiency and switching device thermal stress. Then, the optimal power-sharing strategy is derived by the Lagrange multiplier method with the proposed optimal function. Additionally, to accommodate a wide load range, an optimal selection strategy for operating converter combinations is proposed, requiring only low-bandwidth communication. Experiment verification is given to validate the effectiveness of the proposed control strategy. The experiment results demonstrate that the proposed control strategy can improve the overall performance of offshore microgrids by optimizing efficiency and reliability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Three-dimensional imaging of pion using lattice QCD: generalized parton distributions

In this work, we report a lattice calculation of x-dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer −t. The calculations are based on an N f = 2 + 1 gauge ensemble of highly improved staggered quarks with Wilson-Clover valence fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD matrix elements for both symmetric and asymmetric momenta transfers with similar values and show the equivalence of both frames. Then, focusing on the asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD matrix elements obtained from the lattice calculations. After the Fourier transforms, the quasi-GPDs are then matched to the light-cone GPDs within the framework of large momentum effective theory with improved matching, including the next-to-next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. We also present the 3-dimensional image of the pion in impact-parameter space through the Fourier transform of the momentum transfer −t.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗