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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Silicon Carbide Multilayer Piping for High Temperature sCO 2 Brayton Cycle

Efficiencies of greater than 50% in supercritical carbon dioxide (sCO 2 ) Brayton power cycle systems can be achieved only at turbine inlet temperatures of above 700°C. In support of the push to higher temperatures, a finite element model was developed by Materials Research & Design, Inc. (MR&D) with support from Ceramic Tubular Products, LLC. (CTP) to guide the refinement of CTP’s high temperature ceramic multilayer piping. The multilayer technology combines the advantages of a monolithic silicon carbide (SiC) tube and a SiOC f /SiOC ceramic matrix composite (CMC), the result of which is a material with high-temperature strength and stability, high mechanical and thermal shock resistance, and high corrosion resistance. In addition to fabricating test specimens to refine the finite element model, long-duration, high temperature CO 2 exposure tests were performed by Sandia National Laboratories (SNL) on two varieties of inner monolithic SiC.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Interface Problem Formulation Improvements with Application to Nuclear Fuel Performance Analysis

The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation Program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. This report documents new developments and robustness improvements in mechanical and thermal (gap heat transfer) contact formulations. The improvements range from the migration of industrial level (“assessment”) nuclear fuel model setups to the usage of mortar formulations, the addition of frictional contact to one-dimensional layered representations of fuel and cladding components, and the addition of the Petrov-Galerkin approach to dual mortar, which improves performance on curved, relatively coarse meshes. In addition, the Lagrange-multiplier enforcement of mechanical mortar contact constraints has been extended to two additional types of enforcement: penalty and augmented Lagrange-Uzawa. We show that the latter approach yields the same interface results as dual mortar in the Multiphysics Object-Oriented Simulation Environment, with the advantage of not worsening the condition number of the system matrix—thereby enabling the use of some general implementations of iterative preconditioners, at the expense of additional system evaluations (i.e., augmentations).

42 ENGINEERING↗
DOE OSTI2023

Testing shell-model interactions at high excitation energy and low spin: Nuclear resonance fluorescence in Ge 74

With their complex low-spin structure, the germanium isotopes have accrued a large number of experimental data which challenge nuclear models. The structure of the 74 Ge isotope is investigated here with nuclear resonance fluorescence as part of an extensive campaign of experimental tests of the shell model in the germanium isotopic chain using a number of complementary techniques. Levels were excited with 3.10 – 5.44 MeV photon beams provided by the High Intensity Gamma-Ray Source at TUNL. Many new levels were identified and their spins, parities, branching ratios, and associated scattering cross section values were determined. Large-scale shell-model calculations, which include jj44b and JUN45 effective interactions developed to describe nuclei in this mass region, predict the new data satisfactorily. Herein this study extends the validation of these two interactions, which are candidates for computation of matrix elements to be used in the interpretation of neutrinoless double-β decay experiments in 76 Ge, into the low-spin, high excitation energy domain.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Neutron Irradiation Induced Changes in Isotopic Abundance of 6Li and 3D Nanoscale Distribution of Tritium in LiAlO2 Pellets Analyzed by Atom Probe Tomography

Tritium, a radioactive isotope of hydrogen is produced by neutron irradiation of 6Li enriched LiAlO2 pellets in Tritium producing burnable absorber rods (TPBARs). Three-dimensional nanoscale mapping of Tritium in irradiated pellets is critical to understand its spatial variation and its association with various microstructural features in the pellets. Spatially resolved analysis of 6Li isotopic enrichment in such ceramic pellets before and after irradiation can provide insights to heterogeneities in Li isotopic distribution. However, Li being a light isotope, its spatially resolved compositional or isotopic analysis is a challenging task to most analytical methods. Here we used atom probe tomography, to evaluate the Li isotopic enrichment in both the LiAlO¬2 matrix and the Li deficient secondary phase LiAl5O8 before irradiation. These results were then compared with 6Li isotopic ratio measured by APT analysis of neutron irradiated pellets to clearly demonstrate the unique capability of APT to quantitatively analyze the isotopic enrichment of 6Li as well as for other light elements present in these materials. Evidence for heterogenous nanoscale distribution of 3H and O3H within irradiated pellet microstructure is also provided, which is attributed to 3H trapping in irradiation induced vacancy clusters or voids within the LiAlO2 matrix. The characterization results given here, now prove the feasibility for using APT for analyzing nanoscale spatially resolved isotopic enrichment of Li as well as other light elements such as Tritium in TPBARs. This work also paves way to adopt APT for analyzing light elements such as Li and tritium in materials used for nuclear fusion reactor applications, geochemistry, astrophysics as well as for energy storage applications.

Devaraj, Arun↗
DOE OSTI2020

Multivariate Curve Resolution (MCR) using Principal Components Inputs and Rigorous Equality and Inequality Constraints

This MATLAB pseudocode perform multivariate curve resolution (MCR) using PCA scores & loadings of data as inputs. It employs rigorous least squares equality and inequality constraints for all elements in the solution factor matrices. It also can be used to perform nonnegative matrix factorization. SAND2020-12650 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

Van Benthem, Mark↗
DOE OSTI2023

Measurements and computational analysis of the natural decay of 176 Lu

Background: Mainly because of its long half-life and despite its scientific relevance, spectroscopic measurements of 176 Lu forbidden β decays are very limited and lack formulation of shape factors. A direct precise measurement of its Q value is also presently unreported. In addition, the description of forbidden decays provides interesting challenges for nuclear theory. The comparison of precise experimental results with theoretical calculations for these decays can help to test underlying models and can aid the interpretation of data from other experiments. Purpose: Perform the first precision measurements of 176 Lu β-decay spectra and attempt the observation of its electron capture decays, as well as perform the first precision direct measurement of the 176 Lu β-decay Q value. Compare the shape of the precisely determined experimental β spectra to theoretical calculations, and compare the end point energy to that obtained from an independent Q value measurement. Method: Here, the 176 Lu β-decay spectra measurements and the search for electron capture decays were performed with an experimental setup that employed lutetium-containing scintillator crystals and a NaI(Tl) spectrometer for coincidence counting. The β decay Q value was determined via high-precision Penning trap mass spectrometry (PTMS) with the LEBIT facility at the National Superconducting Cyclotron Laboratory. The β-spectrum calculations were performed within the Fermi theory formalism with nuclear structure effects calculated using a shell model approach. Results: Both β transitions of 176 Lu were experimentally observed and corresponding shape factors formulated in their entire energy ranges. The search for electron capture decay branches led to an experimental upper limit of 6.3×10 –6 relative to its β decays. The 176 Lu β-decay and electron capture Q values were measured using PTMS to be 1193.0(6) and 108.9(8) keV, respectively. This enabled precise β end point energies of 596.2(6) and 195.3(6) keV to be determined for the primary and secondary β decays, respectively. The conserved vector current hypothesis was applied to calculate the relativistic vector matrix elements. The β-spectrum shape was shown to significantly depend on the Coulomb displacement energy and on the value of the axial vector coupling constant gA, which was extracted according to different assumptions. Conclusion: The implemented self-scintillation method has provided unmatched observations of 176 Lu, independently validated by the first direct measurements of its β-decay Q value by Penning trap mass spectrometry. Theoretical study of the main β transition led to the extraction of very different effective gA and log10f values, showing that a high-precision description of this transition would require a realistic nuclear structure with nucleus deformation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Energy Exascale Computational Fluid Dynamics Simulations With the Spectral Element Method

Development and application of the open-source GPU-based fluid-thermal simulation code, NekRS, are described. Time advancement is based on an efficient kth-order accurate timesplit formulation coupled with scalable iterative solvers. Spatial discretization is based on the high-order spectral element method (SEM), which affords the use of fast, low-memory, matrix-free operator evaluation. Further, recent developments include support for nonconforming meshes using overset grids and for GPU-based Lagrangian particle tracking. Results of large-eddy simulations of atmospheric boundary layers for wind-energy applications as well as extensive nuclear energy applications are presented.

42 ENGINEERING↗
DOE OSTI2021

Determination of oxidation rates and volatile oxidation products for HTGR graphite matrix material exposed to steam atmospheres

High-temperature gas-cooled reactors (HTGRs) in operation use tristructural isotropic (TRISO) particles embedded in graphite and carbonized resin matrix to form the fuel element. This graphite matrix material serves as a supportive structural element, heat transfer medium, and neutron moderator. In HTGR designs, fuel compacts are exposed to helium coolant, which facilitates high outlet temperatures (750°C 2 O, 800°C 2 , and H 2 , are quantified in varied oxidant atmospheres using a coupled thermogravimetric analyzer and mass spectrometer. Furthermore, oxidation rates reported here for varied steam (H 2 O [g]) atmospheres are predominantly linear and comparable with literature values in the range of tested temperatures (800–1200°C). Changes in dominant matrix oxidation products from primarily CO to a mixture of CO, CO 2 , and H 2 were observed at higher temperatures (≥1000°C) and steam atmospheres (≥5 kPa pH 2 O). Kinetic data indicates that there was no shift in oxidation regime with chemical oxidation occurring at all temperatures and H2O (g) atmospheres tested. These data provide insight into the oxidation behavior of graphite matrix material and will inform future testing conditions, notably mixed atmospheric conditions, of HTGR fuel elements.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Lattice calculation of short-range contributions to neutrinoless double-beta decay 𝜋 − → 𝜋 + ⁢𝑒⁢𝑒 at physical pion mass

Neutrinoless double-beta (0⁢𝜈⁢𝛽⁢𝛽) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the 𝜋 − → 𝜋 + ⁢𝑒⁢𝑒 process contribute at leading order in the 0⁢𝜈⁢𝛽⁢𝛽 decay channel 𝑛⁢𝑛 → 𝑝⁢𝑝⁢𝑒⁢𝑒 through pion exchange between nucleons. However, current lattice calculations show notable discrepancies in predicting these short-range contributions. To address this issue, we perform a lattice QCD calculation of the 𝜋 − → 𝜋 + ⁢𝑒⁢𝑒 matrix elements using domain wall fermion ensembles at the physical pion mass generated by the RBC/UKQCD Collaboration. To mitigate contamination from around-the-world effects, we develop a new method to reconstruct and subtract them directly from lattice data. We then perform nonperturbative renormalization in the regularization-independent symmetric momentum-subtraction scheme (RI/SMOM), using the (𝛾 𝜇 , 𝛾 𝜇 ) and ($\not{𝑞}$, $\not{𝑞}$) projectors. Compared with previous studies, this work reduces the uncertainties in the matrix elements and provides an independent cross-check that helps to reconcile the discrepancies among previous lattice calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Single-Particle Isotopic Analysis Using the Liquid Sampling-Atmospheric Pressure Glow Discharge Microplasma Coupled to an Orbitrap Mass Spectrometer

Isotope ratio (IR) determinations on individual particles can provide valuable information relative to the sample, including processing and dating, which could be valuable to geological and nuclear material analysis communities. In comparison to “bulk” measurements, in which all particle information is lost and homogenized within a sample, “particle” measurements allow for fingerprinting and can provide unique insights related to the sample’s nano- and micro- compositions. Furthermore, the complex nature of particles, with potential isobaric interferences from either the matrix or other elements within the same particle, poses a significant analytical challenge for conventional mass spectrometry platforms employed for elemental analysis due to their limited mass resolution. Presented here is the first demonstration of an ultrahigh resolution method for single particle (SP) isotopic analysis using the liquid sampling-atmospheric pressure glow discharge (LS-APGD) microplasma ionization source coupled to an Orbitrap mass spectrometer and FTMS Booster X2T acquisition/processing system. For proof of concept, well-characterized CeO 2 microparticles with a nominal diameter of 1.0 μm were analyzed at a mass resolution of ∼330,000. Important instrumental parameters were optimized to enable the detection of single particles. The 142 Ce/ 140 Ce ratio of individual particles and the population average were determined and compared to an SP inductively coupled plasma time-of-flight mass spectrometry (ICP-TOF-MS) analysis. The isotopic accuracy and precision were determined by two methods and found to be in good agreement with the SP-ICP-TOF-MS method, with the linear regression slope method providing a more accurate ratio, showing a ∼1.4% relative difference from the ratio determined from a particle digest. The encouraging performance of the method was further supported by a determined detection limit of 2.9 fg ( 142 Ce). The developed method is anticipated to overcome many of the challenges posed by isobaric interferences encountered in conventional mass spectrometry techniques when analyzing real-world samples for particle isotopic composition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

FLAG review 2024

We review lattice results related to pion, kaon, 𝐷-meson, 𝐵-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor 𝑓+⁡(0) arising in the semileptonic 𝐾 → 𝜋 transition at zero momentum transfer, as well as the decay-constant ratio 𝑓 𝐾 ⁡/𝑓 𝜋 and its consequences for the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements 𝑉 𝑢⁢𝑠 and 𝑉 𝑢⁢𝑑 . We review the determination of the 𝐵 𝐾 parameter of neutral kaon mixing as well as the additional four 𝐵 parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for 𝑚 𝑐 and 𝑚 𝑏 as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant 𝛼 𝑠 . We review the determinations of nucleon charges from the matrix elements of both isovector and flavor-diagonal axial, scalar and tensor local quark bilinears, and momentum fraction, helicity moment and the transversity moment from one-link quark bilinears. We also review determinations of scale-setting quantities. Finally, in this review we have added a new section on the general definition of the low-energy limit of the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

EDA R-Matrix Evaluations Report on n+ 9 Be, n+ 16 O [Slides]

This presentation discusses new developments in light-element R-matrix evaluation and recent light-element work. The presentation also reviewed R-matrix theory, EDAf90 code implementation, including interface EDAf90 with NJOY, ENDFtk, EXFOR/CSISRS, and a new evaluation for n+ 9 Be. The presentation concludes by stating that further development is needed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Phenomenological R -Matrix parameterization of direct, doorway, and compound nuclear reactions [Abstract]

Although formal expressions for scattering matrix accounting for direct, doorway, and compound nuclear (CN) resonant reactions have been derived several decades ago in both the transition ( T -)matrix formalism and the reactance ( K -)matrix formalism, the absence of corresponding expressions in phenomenological R -matrix formalism has limited the application of the latter to CN resonant reactions only. We remove this limitation by parameterizing direct, doorway, and CN resonant reactions in a phenomenological R -matrix scattering matrix, and provide a parameterization for a corresponding Reich-Moore approximation of eliminated capture channels. Direct reactions induce (previously neglected) mixing among the incoming or outgoing R -matrix channel wave functions, parameterized by real and orthonormal channel-rotation matrix, M , whereby the original scattering matrix U is transformed into M T UM . Any real and orthonormal matrix, M , can be equivalently expressed as e η , where η is a real and skew-symmetric 2 rotation-generating matrix that subsequently yields a more intuitive parameterization of eliminated direct capture reactions in Reich-Moore approximation. A phenomenological R -matrix parameterization of doorway reactions is inferred by equating the expression for reactance ( K -)matrix, given in terms of Brune’s alternative R -matrix parameterization, to a corresponding expression derived using Feshbach’s projection operator formalism. Assuming that all doorway states, just like CN states, are confined within spheres defined by R -matrix channel radii, a new R -matrix-like term induced by doorway states is gleaned, wherein each doorway state is parameterized by its energy, width, and the strength of its coupling to each CN state. Since a Reich-Moore approximation for retained-channel scattering matrix ought to approximate the effect of eliminated capture channels taking place via direct, doorway, or CN reactions, each of the three kinds of reactions contributing to the capture entails a corresponding Reich-Moore parameterization in a first-order approximation: direct contribution is parameterized by introducing finite diagonal elements of a retained-channel rotation-generating matrix, doorway contribution is parameterized by doorway capture widths, while CN contribution is parameterized by conventional Reich-Moore capture widths. We will present evidence of direct and doorway reactions observed in recent measurements of resolved resonance cross sections at the Gaerttner LINAC Center at Rensselaer Polytechnic Institute, and will outline a path for implementing this new R -matrix parameterization into the SAMMY nuclear data evaluation code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

237 Np Mössbauer Isomer Shifts: A Lesson About the Balance of Static and Dynamic Electron Correlation in Heavy Element Complexes

A large set of neptunium compounds with different oxidation states (III to VII) was assembled to study the Mössbauer isomer shift by wave function calculations and better understand covalency in f-elements complexes. The contact density approach was used to calculate the isomer shift using complete active space self-consistent field (CASSCF) multiconfiguration wave functions, as well as matrix product states [from Density Matrix Renormalization Group (DMRG) algorithms] for large active spaces. Dynamic correlation effects for the isomer shifts were treated via CASPT2 energy derivatives with respect to the nuclear radius. The CASSCF calculations appear to produce different orbital overlocalization errors for low and high Np oxidation states. For compounds with low Np oxidation numbers, the errors can be attributed to the overlocalization of the 5f orbitals. For the compounds with high Np oxidation numbers, the main errors arise from an overlocalization of ligand orbitals and concomitant to weak donation bonding. Attempts to mitigate the overlocalization errors with large active spaces using DMRG were only partially successful, showing that explicit treatment of dynamic correlation is necessary for accurate predictions of Mössbauer isomer shifts. The CASPT2 calculations perform very satisfactorily. For a subset of Np compounds, both static and dynamic correlation effects were substantial. Furthermore, a rational active space selection based on orbital entanglement diagrams proved beneficial for determining the optimal reference wave function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Designing Nuclear Fuels with a Multi-Principal Element Alloying Approach

Previous research has shown that multi-principal element alloys (MPEAs) using chromium, molybdenum, niobium, tantalum, titanium, vanadium, and zirconium can form stable body-centered-cubic (BCC) structures across a large temperature region (25°C to 1000°C). This is the same crystal structure as γ-uranium (U), which has shown desirable thermal and irradiation behavior in previous alloy fuel research. It is hypothesized then that the MPEA alloying approach can be used to produce a stable BCC uranium-bearing alloy and to retain its stability throughout anticipated operating regimes of power-producing reactors. Candidate elements were assessed using Monte Carlo N-Particle (MCNP) analysis to determine uranium densities necessary to make the alloy an economically viable fuel compared to conventional fuel forms. Following neutronic considerations, materials property databases and empirical predictors were used to determine the compositions with a high potential to form a BCC solid solution alloy. The final four alloys were MoNbTaU 2 , MoNbTiU 2 , NbTaTiU 2 , and NbTaVU 2 , which were cast using arc melting of raw elemental foils and chunks. Characterization of the fabricated alloys included scanning electron microscopy, X-ray diffraction, energy dispersive X-ray spectroscopy, and transmission electron microscopy. The results showed a two-phase system with a U-rich matrix phase surrounding the refractory precipitates. The U phase was found to contain varying concentrations of the alloying elements and was a BCC γ-U phase. These results warrant further research to identify ideal compositions for use as an advanced alloy fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Power counting to saturation

We present a description of saturation in small 𝑥 deep inelastic scattering from power counting in a top-down effective theory derived from quantum chromodynamics (QCD). A factorization formula isolates the universal physics of the nucleus at leading power in 𝑥. The onset of saturation is then understood as a breakdown in the expansion in an emergent power counting parameter, which is defined by the matrix element of a gauge invariant operator. We identify a new radiation mode, which enables us to extend previous literature by distinguishing the appearance of the saturation scale from the transition to nonlinear evolution.

Astronomy & Astrophysics↗
DOE OSTI2020

FLAG Review 2019: Flavour Lattice Averaging Group (FLAG)

Abstract We review lattice results related to pion, kaon, D -meson, B -meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $$f_+(0)$$ f + ( 0 ) arising in the semileptonic $$K \rightarrow \pi $$ K → π transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_\pi $$ f K / f π and its consequences for the CKM matrix elements $$V_{us}$$ V us and $$V_{ud}$$ V ud . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$SU(2)_L\times SU(2)_R$$ S U ( 2 ) L × S U ( 2 ) R and $$SU(3)_L\times SU(3)_R$$ S U ( 3 ) L × S U ( 3 ) R Chiral Perturbation Theory. We review the determination of the $$B_K$$ B K parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $$m_c$$ m c and $$m_b$$ m b as well as those for D - and B -meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $$\alpha _s$$ α s . Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

FLAG Review 2021

Abstract We review lattice results related to pion, kaon, D -meson, B -meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $$f_+(0)$$ f + ( 0 ) arising in the semileptonic $$K \rightarrow \pi $$ K → π transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_\pi $$ f K / f π and its consequences for the CKM matrix elements $$V_{us}$$ V us and $$V_{ud}$$ V ud . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$SU(2)_L\times SU(2)_R$$ S U ( 2 ) L × S U ( 2 ) R and $$SU(3)_L\times SU(3)_R$$ S U ( 3 ) L × S U ( 3 ) R Chiral Perturbation Theory. We review the determination of the $$B_K$$ B K parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $$m_c$$ m c and $$m_b$$ m b as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $$\alpha _s$$ α s . We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗