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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Synergistic Density Functional Theory and Molecular Dynamics Approach to Elucidate PNIPAM–Water Interaction Mechanisms

This study employs Density Functional Theory (DFT) and Molecular Dynamics (MD) simulations to investigate interactions between water molecules and Poly(N-isopropylacrylamide) (PNIPAM). DFT reveals preferential water binding sites, with enhanced binding energy observed in the linker zone. Quantum Theory of Atoms in Molecules (QTAIM) and electron localization function (ELF) analyses highlight the roles of hydrogen bonding and steric hindrance. MD simulations unveil temperature-dependent hydration dynamics, with structural transitions marked by changes in the radius of gyration (Rg) and the radial distribution function (RDF), aligning with DFT findings. Our work goes beyond prior studies by combining a DFT, QTAIM and MD simulations approach across different PNIPAM monomer-to-30mer structures. It introduces a systematic quantification of pseudo-saturation thresholds and explores water clustering dynamics with structural specificity, which have not been previously reported in the literature. These novel insights establish a more complete molecular-level picture of PNIPAM hydration behavior and temperature responsiveness, emphasizing the importance of amide hydrogen and carbonyl oxygen sites in hydrogen bonding, which weakens above the lower critical solution temperature (LCST), resulting in increased hydrophobicity and paving the way for understanding water sorption mechanisms, offering guidance for future applications such as dehumidification and atmospheric water harvesting.

08 HYDROGEN↗
DOE OSTI2023

Investigation of Nanoparticle Degradation in Hydrogen Fuel Cell Systems through Automated Electron Microscopy

Proton exchange membrane fuel cells (PEMFC) are promising devices for the deployment of hydrogen-powered heavy-duty vehicles, providing a higher efficiency for similar driving range and fueling time than the existing ones. However, PEMFCs still encounter durability challenges mainly due to catalyst degradation in the cathode. Mitigating these performance losses requires a better understanding of the degradation mechanisms under heavy-duty accelerated stress tests (ASTs) [1]. Scanning transmission electron microscopy (STEM) combined with energy dispersive X-ray spectroscopy (EDS) are key tools for the analysis of Pt and PtCo nanoparticle size, spatial distribution and composition [2]. Electron tomography is also used to determine the rate and type of degradation of catalyst nanoparticles as a function of their position on the carbon support. In this work, automated data acquisition software, paired with a custom Python code, have been used to study the effect of different accelerated stress tests (ASTs) on nanoparticle coarsening [2]. Figure 1 shows high-angle annular dark-field (HAADF)-STEM images and EDS maps comparing the cathodes of membrane electrode assemblies (MEAs) following an electrocatalyst AST performed under H2/N2 with that of the heavy-duty AST performed under H2/air. We will discuss how AST conditions affect considerably the spatial distribution of the nanoparticles across the electrode between the membrane and microporous layer. Although the median particle size increased more in the MEA aged under the heavy-duty AST, as determined using a high-throughput image analysis, the quantitative EDS measurements demonstrate that the electrocatalyst AST resulted in more Pt and Co dissolution from the cathode, which is another important indicator of electrocatalyst degradation. We will further present the impact of the relative humidity (% RH) on the degradation mechanisms demonstrated using the same approach. Electron tomography has been used to distinguish the Pt nanoparticles residing on the carbon support surface (exterior) from those within the pore structure (interior) in order to determine the relative stability of interior and exterior nanoparticles. As shown in Figure 2, we will compare the Pt catalyst particle size at the beginning of test (BOT) and end of test (EOT), and discuss the importance of automating the electron tomography workflow, i.e. acquisition, reconstruction, and visualization, to increase sampling and determine the standard deviation of these measurement. The outlook for utilizing low-dose cryo-tomography for limiting damage to the catalyst, support, and especially proton-conducting ionomer will also be discussed [3].

Amichi, Lynda↗
DOE OSTI2022

A deep potential model with long-range electrostatic interactions

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the DP long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples: the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Background optimization of powder electron diffraction for implementation of the e-PDF technique and study of the local structure of iron oxide nanocrystals

The local structural characterization of iron oxide nanoparticles is explored using a total scattering analysis method known as pair distribution function (PDF) (also known as reduced density function) analysis. The PDF profiles are derived from background-corrected powder electron diffraction patterns (the e-PDF technique). Due to the strong Coulombic interaction between the electron beam and the sample, electron diffraction generally leads to multiple scattering, causing redistribution of intensities towards higher scattering angles and an increased background in the diffraction profile. In addition to this, the electron–specimen interaction gives rise to an undesirable inelastic scattering signal that contributes primarily to the background. The present work demonstrates the efficacy of a pre-treatment of the underlying complex background function, which is a combination of both incoherent multiple and inelastic scatterings that cannot be identical for different electron beam energies. Therefore, two different background subtraction approaches are proposed for the electron diffraction patterns acquired at 80 kV and 300 kV beam energies. From the least-square refinement (small-box modelling), both approaches are found to be very promising, leading to a successful implementation of the e-PDF technique to study the local structure of the considered nanomaterial.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Estimating Electron Temperature and Density Using Van Allen Probe Data: Typical Behavior of Energetic Electrons in the Inner Magnetosphere

Abstract The Earth's inner magnetosphere contains multiple electron populations influenced by different factors. The cold electrons of the plasmasphere, warm plasma that contributes to the ring current, and the relativistic plasma of the radiation belts often seem to behave independently. Using omni‐directional flux and energy measurements from the HOPE and Magnetic Electron Ion Spectrometer instruments aboard the Van Allen Probes, we provide a detailed density and temperature description of the inner magnetosphere, offering a comprehensive statistical analysis of the entire Van Allen Probe era. While number density and temperature data at geosynchronous orbit are available, this study focuses on the warm plasma in the inner magnetosphere . Values of density and temperature are extracted by fitting energy and phase space density to obtain the distribution function. The fitted distributions are related to the zeroth and second moments to estimate the number density and temperature. Analysis has indicated that a two Maxwellian fit is sufficient over a wide range of and that there are two independent plasma populations. The more energetic population has a median number density of approximately and a temperature of around 130 keV, with a temperature peak observed between L * = 4 and L * = 4.5. This population is relatively uniform in magnetic local time (MLT). In contrast, the less energetic warm electron population has a median number density of about and a temperature of 7.4 keV. Strong statistical trends in density and temperature across both L * and MLT are presented, along with potential sources driving these variations.

58 GEOSCIENCES↗
DOE OSTI2020

Electron temperature of the solar wind

Significance The problem of solar wind heating is one of the long-standing fundamental problems of space plasma physics. We propose that the electron component of the solar wind plasma is heated by electrons streaming from the hot solar corona and slowly losing their energy due to weak Coulomb collisions. Our first-principle kinetic derivation predicts the scaling of the solar wind electron temperature with the heliocentric distance, which is in good agreement with observations. Our theory reveals the role of the non-Maxwellian electron distribution function in the heating mechanism, and it may be valuable for interpreting the results of in situ satellite measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Role of matrix elements in the time-resolved photoemission signal

Time- and angle-resolved photoemission spectroscopy (TR-ARPES) provides access to the ultrafast evolution of electrons andmany-body interactions in solid-state systems. However, themomentum- and energy-resolved transient photoemission intensitymay not be unambiguously described by the intrinsic relaxation dynamics of photoexcited electrons alone.The interpretation of the time-dependent photoemission signal can be affected by the transient evolution of the electronic distribution, and both the one-electron removal spectral function aswell as the photoemissionmatrix elements. Here we investigate the topological insulator Bi 1.1 Sb 0.9 Te 2 S to demonstrate, bymeans of a detailed probe-polarization dependent study, the transient contribution ofmatrix elements toTR-ARPES.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Multifrequency Analysis of Favored Models for the Messier 87* Accretion Flow

Abstract The polarized images of the supermassive black hole Messier 87* (M87*) produced by the Event Horizon Telescope (EHT) provide a direct view of the near-horizon emission from a black hole accretion and jet system. The EHT theoretical analysis of the polarized M87* images compared thousands of snapshots from numerical models with a variety of spins, magnetization states, viewing inclinations, and electron energy distributions, and found a small subset consistent with the observed image. In this article, we examine two models favored by EHT analyses: a magnetically arrested disk with moderate retrograde spin and a magnetically arrested disk with high prograde spin. Both have electron distribution functions that lead to strong depolarization by cold electrons. We ray trace five snapshots from each model at 22, 43, 86, 230, 345, and 690 GHz to forecast future very long baseline interferometry (VLBI) observations and examine limitations in numerical models. We find that even at low frequencies where optical and Faraday rotation depths are large, approximately rotationally symmetric polarization persists, suggesting that shallow depths dominate the polarization signal. However, morphology and spectra suggest that the assumed thermal electron distribution is not adequate to describe emission from the jet. We find 86 GHz images show a ringlike shape determined by a combination of plasma and spacetime imprints, smaller in diameter than recent results from the Global mm-VLBI Array. We find that the photon ring becomes more apparent with increasing frequency, and is more apparent in the retrograde model, leading to large differences between models in asymmetry and polarization structure.

Astronomy & Astrophysics↗
DOE OSTI2023

In Situ Visualization of the Pinning Effect of Planar Defects on Li Ion Insertion

Longevity of Li ion batteries strongly depends on the interaction of transporting Li ions in electrode crystals with defects. However, detailed interactions between the Li ion flux and structural defects in the host crystal remain obscure due to the transient nature of such interactions. Here, by in situ transmission electron microscopy and density function theory calculations, we reveal how the diffusion pathways and transport kinetics of a Li ion can be affected by planar defects in a tungsten trioxide lattice. We uncover that changes in charge distribution and lattice spacing along the planar defects disrupt the continuity of ion conduction channels and dramatically increase the energy barrier of Li diffusion, thus, arresting Li ions at the defect sites and twisting the lithiation front. In conclusion, the atomic-scale understanding holds critical implications for rational interface design in solid-state batteries and solid oxide fuel cells.

25 ENERGY STORAGE↗
DOE OSTI2023

Self-organization of photoionized plasmas via kinetic instabilities

Abstract Self-organization in an unmagnetized collisionless plasma (in this paper) refers to formation of transient coherent structures such as collective oscillations (electrostatic waves) or magnetic fields resulting from so-called kinetic effects in the plasma. This topical review provides a comprehensive analysis of the self-organization of strong-field photoionized, non-equilibrium plasmas through kinetic instabilities. The authors propose and demonstrate a novel experimental platform that enables the formation of dense plasmas with known highly anisotropic and non-thermal electron velocity distribution functions on a timescale on the order of an inverse electron plasma frequency. We then show that such plasmas are highly susceptible to a hierarchy of kinetic instabilities, including two-stream, current filamentation and Weibel, that convert a fraction of the electron kinetic energy into electric and/or magnetic energy stored in self-organized structures. The electrostatic waves so produced are measured using a collective light (Thomson) scattering technique with femtosecond resolution as the kinetic instabilities aided by collisions eventually thermalize the plasma electrons. In addition, we describe a novel experimental technique that has made it possible to map the temporal evolution of the wavenumber spectrum of the thermal Weibel instability with picosecond resolution, which leads to the formation of quasi-static coherent magnetic fields with different topologies in photoionized plasmas. Finally, the paper summarizes the important results and discusses future directions on this topic.

Zhang, Chaojie (ORCID:0000000180353014)↗
DOE OSTI2026

Machine Learning Vacancy Formation Energy in Nickel-Based Superalloys

Thermal vacancies play a critical role in high-temperature Ni-based superalloys and influence various properties such as creep resistance, oxidation, etc. This study systematically investigates the impact of commonly used transition metals (Cr, Co, Fe), refractory metals (Nb, Ta, Mo, W) and other elements (Al, Cu, Ti, Mn) on the thermodynamic stability of 36 binary, 20 ternary, 11 quaternary, 9 quinary, and 3 senary FCC Ni-based alloys covering various elemental combinations. Density functional theory-based studies on Ni-X binary alloys show that higher concentrations of Cr, Nb, Ta, Al, and Ti introduce significant lattice distortions and broaden the distribution of vacancy formation energies (standard deviation up to 0.15 eV). These elements partially donate electrons, reducing their self-consistent chemical potentials relative to single-element reference values and lowering vacancy formation energies, while Co, Fe, Mo, and W show lower charge localization. These trends extend from 3-6 element alloys, where Cr, Nb, and Ta-rich compositions have low-energy states (~0.5 eV) that increase vacancy concentrations. Finally, graph neural network models are developed to screen over 5000 virtual alloys. Eleven leading compositions are identified with mean vacancy formation energy higher than 1.75 eV and vacancy concentration ~2 orders of magnitude lower than pure Ni at 1000 K. These results provide valuable guidelines to achieve controlled defect engineering in structural alloys.

DFT↗
DOE OSTI2022

Automating Component-Level Stress Measurements for Inverter Reliability Estimation

In the near future, grid operators are expected to regularly use advanced distributed energy resource (DER) functions, defined in IEEE 1547-2018, to perform a range of grid-support operations. Many of these functions adjust the active and reactive power of the device through commanded or autonomous operating modes which induce new stresses on the power electronics components. In this work, an experimental and theoretical framework is introduced which couples laboratory-measured component stress with advanced inverter functionality and derives a reduction in useful lifetime based on an applicable reliability model. Multiple DER devices were instrumented to calculate the additional component stress under multiple reactive power setpoints to estimate associated DER lifetime reductions. A clear increase in switch loss was demonstrated as a function of irradiance level and power factor. This is replicated in the system-level efficiency measurements, although magnitudes were different—suggesting other loss mechanisms exist. Using an approximate Arrhenius thermal model for the switches, the experimental data indicate a lifetime reduction of 1.5% when operating the inverter at 0.85 PF—compared to unity PF—assuming the DER failure mechanism thermally driven within the H-bridge. If other failure mechanisms are discovered for a set of power electronics devices, this testing and calculation framework can easily be tailored to those failure mechanisms.

Flicker, Jack (ORCID:0000000212232154)↗
DOE OSTI2021

Understanding the Adsorption of Rare-Earth Elements in Oligo-Grafted Mesoporous Carbon

Rare-earth elements (REEs) are 17 elements of the periodic table primarily consisting of lanthanides. In modern society, the usage of REEs is ubiquitous in almost all modern gadgets and therefore efficient recovery and separation of REEs are of high importance. Selective adsorption and chelation of REEs in solid sorbents is a unique and sustainable process for their recovery. In this work, single-stranded oligos with 100 units of thymine were grafted onto carboxylated mesoporous carbon to synthesize a sorbent with phosphorus and oxygen functionalities. Additionally, the sorbent was characterized by X-ray photoelectron spectroscopy, Fourier-transform infrared spectroscopy, and scanning electron microscopy-energy-dispersive X-ray spectroscopy. Three different REEs with varying atomic radii and densities, Lu, Dy, and La, were adsorbed onto the carbon from aqueous solutions. It was observed that the adsorbed amounts increased with the increase in the atomic radius or decrease in the atomic density. Calculation of the distribution coefficients for all the equilibrium adsorption amounts suggested that adsorption is more effective in the lower concentration region. The L 3 -edge X-ray absorption near-edge structure confirmed a 3+ oxidation state of REEs in the adsorbed phase. Extended X-ray absorption fine structure (EXAFS) confirmed the binding of REEs with oxygen functionalities in the adsorbed phase. The radial distribution functions calculated from the EXAFS data suggest a longer RE–O distance for La compared to those for Lu and Dy. The coordination numbers and Debye–Waller factors have typical values of about 8–9 atoms and 0.01–0.02 Å 2 , respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Atomic structure of an FeCrMoCBY metallic glass revealed by high energy x-ray diffraction

Amorphous bulk metallic glasses with the composition Fe 48 Cr 15 Mo 14 C 15 B 6 Y 2 have been of interest due to their special mechanical and electronic properties, including corrosion resistance, high yield-strength, large elasticity, catalytic performance, and soft ferromagnetism. Here, we apply a reverse Monte Carlo technique to unravel the atomic structure of these glasses. The pair-distribution functions for various atomic pairs are computed based on the high-energy x-ray diffraction data we have taken from an amorphous sample. Monte Carlo cycles are used to move the atomic positions until the model reproduces the experimental pair-distribution function. The resulting fitted model is consistent with our ab initio simulations of the metallic glass. Our study contributes to the understanding of functional properties of Fe-based bulk metallic glasses driven by disorder effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Enhancing perovskite electrocatalysis through synergistic functionalization of B-site cation for efficient water splitting

The family of perovskite oxides is a promising class of catalysts for diverse energy conversion processes including water splitting. In this work, a facile two-step manipulation (in-situ exsolution and post-sulfurization) strategy was proposed and applied to LaCo 0.2 Fe 0.8 O 3 (LCF) perovskite parent, through which, the electronic state, spatial immersion and intrinsic activity of B-site cobalt (Co) were stepwise tuned at nanoscale proximity accordingly (i.e., lattice Co ions segregated Co 0 → embedded CoS 2 ). Impressively, the as-prepared catalyst (S-LCF) obtains an emergent oxygen deficient microstructure seamlessly pinned with uniformly distributed CoS 2 nanoparticles (NPs), which demonstrates enhanced performance toward both oxygen evolution reaction (OER) and hydrogen evolution reaction (HER), and shows good stability in overall water splitting. The density functional theory (DFT) calculations illustrate the optimized metal-oxygen covalency and hydrogen adsorption Gibbs free energy (Δ G H *) on S-LCF, which further buttresses the prominence of our B-site cation engineering tactics.

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

Nanoconfinement of Molecular Magnesium Borohydride Captured in a Bipyridine-Functionalized Metal-Organic Framework

The lower limit of metal hydride nanoconfinement is demonstrated through the coordination of a molecular hydride species to binding sites inside the pores of a metal-organic framework (MOF). Magnesium borohydride, which has a high hydrogen capacity, is incorporated into the pores of UiO-67bpy (Zr6O4(OH)4(bpydc)6 with bpydc2- = 2,2'-bipyridine-5,5'- dicarboxylate) by solvent impregnation. The MOF retained its long-range order, and transmission electron microscopy and elemental mapping confirmed the retention of the crystal morphology and revealed a homogeneous distribution of the hydride within the MOF host. Notably, the B-, N-, and Mg-edge XAS data confirm the coordination of Mg(II) to the N atoms of the chelating bipyridine groups. In situ 11B MAS NMR studies helped elucidate the reaction mechanism and revealed that complete hydrogen release from Mg(BH4)2 occurs as low as 200 °C. Sieverts and thermogravimetric measurements indicate an increase in the rate of hydrogen release, with the onset of hydrogen desorption as low as 120 °C, which is approximately 150 °C lower than that of the bulk material. Furthermore, density functional theory calculations support the improved dehydrogenation properties and confirm the drastically lower activation energy for B-H bond dissociation.

Nanoconfinement, Metal Hydrides, Metal-Organic Fra↗
DOE OSTI2020

Bayesian inference of nuclear symmetry energy from measured and imagined neutron skin thickness in Sn 116 , 118 , 120 , 122 , 124 , 130 , 132 , Pb 208 , and Ca 48

The neutron skin thickness Δr np in heavy nuclei has been known as one of the most sensitive terrestrial probes of the nuclear symmetry energy E sym (ρ) around $\frac{2}{3}$ of the saturation density ρ 0 of nuclear matter. Existing neutron skin data mostly from hadronic observables suffer from large uncertainties and their extraction from experiments are often strongly model dependent. While waiting eagerly for the promised model-independent and high-precision neutron skin data for 208 Pb and 48 Ca from the parity-violating electron scattering experiments (PREX-II and CREX at JLab as well as MREX at MESA), within the Bayesian statistical framework using the Skyrme-Hartree-Fock model we infer the posterior probability distribution functions (PDFs) of the slope parameter L of the nuclear symmetry energy at ρ 0 from imagined Δr np ( 208 Pb)=0.15, 0.20, and 0.30 fm with a 1σ error bar of 0.02, 0.04, and 0.06 fm, respectively, as well as Δr np ( 48 Ca)=0.12, 0.15, and 0.25 fm, with different 1σ error bar of 0.01 and 0.02 fm, respectively. The results are compared with the PDFs of L inferred using the same approach from the available Δr np data for 116, 118, 120, 122, 124, 130, 132 Sn from hadronic probes. They are also compared with results from a recent Bayesian analysis of the radius and tidal deformability data of canonical neutron stars from GW170817 and NICER. The neutron skin data for Sn isotopes gives L = 45.5 $^{+ 26.5}_{-21.6}$ MeV surrounding its mean value or L = 53 . 4 $^{+ 18.6}_{ -29.5}$ MeV surrounding its maximum a posteriori value, respectively, with the latter smaller than but consistent with the L = 66 $^{+ 12}_{-20}$ MeV from the neutron star data within their 68% confidence intervals. We found that Δr np = 0.17 –0.18 fm in 208 Pb with an error bar of about 0.02 fm leads to a PDF of L compatible with that from analyzing the Sn data. To provide additionally useful information on L extracted from the Δr np of Sn isotopes, the experimental error bar of Δr np in 208 Pb should be at least smaller than 0.06 fm aimed by some current experiments. In addition, the Δr np ( 48 Ca) needs to be larger than 0.15 fm but smaller than 0.25 fm to be compatible with the Sn and/or neutron star results. To further improve our current knowledge about L and distinguish its PDFs in the examples considered, even higher precisions leading to significantly less than ±20 MeV error bars for L at 68% confidence level are necessary.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Precision QCD, Hadronic Structure & Forward QCD, Heavy Ions: Report of Energy Frontier Topical Groups 5, 6, 7 submitted to Snowmass 2021

This report was prepared on behalf of three Energy Frontier Topical Groups of the Snowmass 2021 Community Planning Exercise. It summarizes the status and implications of studies of strong interactions in high-energy experiments and QCD theory. We emphasize the rich landscape and broad impact of these studies in the decade ahead. Hadronic interactions play a central role in the high-luminosity Large Hadron Collider (LHC) physics program, and strong synergies exist between the (HL-)LHC and planned or proposed experiments at the U.S. Electron-Ion Collider, CERN forward physics experiments, high-intensity facilities, and future TeV-range lepton and hadron colliders. Prospects for precision determinations of the strong coupling and a variety of nonperturbative distribution and fragmentation functions are examined. We also review the potential of envisioned tests of new dynamical regimes of QCD in high-energy and high-density scattering processes with nucleon, ion, and photon initial states. The important role of the high-energy heavy-ion program in studies of nuclear structure and the nuclear medium, and its connections with QCD involving nucleons are summarized. We address ongoing and future theoretical advancements in multi-loop QCD computations, lattice QCD, jet substructure, and event generators. Cross-cutting connections between experimental measurements, theoretical predictions, large-scale data analysis, and high-performance computing are emphasized.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗