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DOE OSTI2026

MARVEL Reactor Fuel Performance Report

The Microreactor Applications Research Validation and EvaLuation (MARVEL) project is producing a high temperature liquid metal-cooled nuclear test bed at Idaho National Laboratory (INL) to ultimately improve the integration of microreactors to end-user applications. This ambitious effort seeks to design, authorize, construct, test, and operate the reactor within five years. In order to construct and operate the MARVEL reactor in a timely manner, the system will utilize materials and component designs which have already been used, qualified, or licensed from previous reactors. The MARVEL reactor will be located at the INL Transient Reactor Test (TREAT) facility in the north high-bay equipment pit and will use the existing 304 stainless steel-clad U-ZrH1.6 pin-type fuel system developed by General Atomics and purchased from TRIGA International. This fuel has been previously qualified under the United States Department of Energy’s (US DOE) Reduced Enrichment for Research and Test Reactors (RERTR) Program. Even though the regulator of the MARVEL reactor is the US DOE, the standards and overall approach recommended by the Nuclear Regulatory Commission is well-defined and utilized here. Following NUREG-1537 regulatory guidance, this report documents the authorization case for the MARVEL fuel system’s application to MARVEL and establishes stable and predictable fuel performance during the most thermophysically unfavorable conditions achievable in the MARVEL reactor. To that end, this report provides a comprehensive survey of the known thermophysical properties, performance, and quantitative relationships associated with the MARVEL reactor fuel element and uses this information to determine its mechanical integrity and risk of reaching unacceptable conditions during the most extreme accident scenarios predicted for the reactor using the most conservative assumptions available. The information contained herein is compiled from a combination of historical reports and peer reviewed scientific publication manuscripts. Known mechanisms under which the fuel is susceptible to failure are highlighted and compared to conditions that could exist in the MARVEL reactor during an unanticipated transient or accident scenario. The two scenarios considered for analysis in this report are (1) an unprotected loss of flow accident and (2) a hypothetical unprotected loss of coolant accident during the loss of flow accident. Preliminary 2D steady-state analyses herein indicate that both fuel-cladding chemical interactions and fuel-cladding mechanical interactions are negligible throughout the fuel’s operational cycle under both normal and high temperature accident scenario conditions. Although higher fidelity 3D time-dependent modeling and simulations are planned, the following may be concluded presently. The MARVEL fuel element maintains its geometric stability and structural integrity during the most extreme accident scenarios predicted for the MARVEL reactor. The hoop stress during the unprotected loss of flow accident reaches about -1.27 MPa; this negative stress indicates that it is compressive rather than tensile. The compressive stress is a result of the NaK pressure on the outside of the fuel element, caused by the restricted thermal expansion of the NaK coolant, exceeding the internal pressures generated inside of the fuel element. The hoop stress generated in the cladding during the unprotected loss of coolant accident reaches a maximum of about approximately 10 MPa, which is nearly an order of magnitude less than the predicted yield strength of the cladding under high-temperature accident scenario conditions. Calculations were compared with results from high performance computational simulations using BISON and are in very close agreement. A conservative MARVEL fuel meat peak temperature limit of 900 °C is recommended presently, which is about 180 °C higher than the peak fuel temperature predicted to occur during the most extreme accident. Based on the known properties and behavior of the MARVEL fuel element, the fuel successfully meets its design and safety requirements under normal and most extreme accident conditions with a large safety margin.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRSDate not supplied

Potential of a Plant Gas Exchange Mechanistic Model to Predict Plant Transpiration in Veggie on ISS

Plants are an essential part of long-duration space travel, as they enable food production and contribute to air revitalization through photosynthesis, and water recycling through transpiration. Understanding their growth mechanisms is essential to use them to sustain human life in space. In particular, gas exchange – e.g., CO2 absorption and water transpiration – are modified in microgravity because of the lack of buoyancy-driven convection, and in the long run, this could result in impaired plant growth. Water absorbed by the plants mainly depends on their size and on environmental conditions (air temperature, humidity and ventilation), but in microgravity watering plants is a delicate operation – too much water results in flooded roots and too little water leads in a few hours to wilted plants. This is regularly experienced in the Veggie system on ISS, which enables small-scale food production in microgravity since 2014. This presentation explores how a mechanistic model of plant gas exchange can help predict plant transpiration in Veggie and thus better predict daily watering. For each plant, inputs on canopy leaf area (acquired with daily photos), air temperature and relative humidity in the plant compartment, as well as airspeed at the top of its canopy enable accurate predictions of transpiration in microgravity. This brings a better understanding of water movement through the plant in microgravity in relation to ventilation and plant size and would result in easier management of plant watering in Veggie. Ultimately, this work could be applied to any space crop production in microgravity and be used for water management and yield predictions. This work was funded by NASA Space Biology through NASA postdoctoral program / USRA.

Lucie Poulet↗

NASA NTRSDate not supplied

Potential of a Plant Gas Exchange Mechanistic Model to Predict Plant Transpiration in Veggie on ISS

Lucie Poulet↗

NASA NTRS1982

Spectral estimates of intercepted solar radiation by corn and soybean canopies

Attention is given to the development of methods for combining spectral and meteorological data in crop yield models which are capable of providing accurate estimates of crop condition and yields throughout the growing season. The present investigation is concerned with initial tests of these concepts using spectral and agronomic data acquired in controlled experiments. The data were acquired at the Purdue University Agronomy Farm, 10 km northwest of West Lafayette, Indiana. Data were obtained throughout several growing seasons for corn and soybeans. Five methods or models for predicting yields were examined. On the basis of the obtained results, it is concluded that estimating intercepted solar radiation using spectral data is a viable approach for merging spectral and meteorological data in crop yield models.

Gallo, K. P.↗

NASA NTRS1957

Tensile Properties of Some Structural Sheet Materials Under Rapid-Heating Conditions

The results of the NACA tests to determine the tensile strength of some structural sheet materials heated to failure at temperature rates from 0.2 deg. F to 100 deg F per second under constant load conditions are reviewed . Yield and rupture stresses obtained under rapid-heating conditions are compared with the results of conventional elevated-temperature tensile tests. The relation between rapid-heating tests, short-time creep tests, and conventional creep tests is discussed . The application of a phenomenological theory for calculating rapid-heating curves is shown. Methods are given for predicting yield and rupture stresses and temperatures from master curves and temperature-rate parameters

Heimerl, George J.↗

NASA NTRS2015

Modelling Bambara Groundnut Yield in Southern Africa: Towards a Climate-Resilient Future

Current agriculture depends on a few major species grown as monocultures that are supported by global research underpinning current productivity. However, many hundreds of alternative crops have the potential to meet real world challenges by sustaining humanity, diversifying agricultural systems for food and nutritional security, and especially responding to climate change through their resilience to certain climate conditions. Bambara groundnut (Vigna subterranea (L.) Verdc.), an underutilised African legume, is an exemplar crop for climate resilience. Predicted yield performances of Bambara groundnut by AquaCrop (a crop−water productivity model) were evaluated for baseline (1980−2009) and mid-century climates (2040−2069) under 20 downscaled Global Climate Models (CMIP5-RCP8.5), as well as for climate sensitivities (AgMIPC3MP) across 3 locations in Southern Africa (Botswana, South Africa, Namibia). Different land - races of Bambara groundnut originating from various semi-arid African locations showed diverse yield performances with diverse sensitivities to climate. S19 originating from hot-dry conditions in Namibia has greater future yield potential compared to the Swaziland landrace Uniswa Red-UN across study sites. South Africa has the lowest yield under the current climate, indicating positive future yield trends. Namibia reported the highest baseline yield at optimum current temperatures, indicating less yield potential in future climates. Bambara groundnut shows positive yield potential at temperatures of up to ~31degC, with further warming pushing yields down. Thus, many regions in Southern Africa can utilize Bambara groundnut successfully in the coming decades. This modelling exercise supports decisions on genotypic suitability for present and future climates at specific locations.

farm crops↗

NASA NTRS1983

A theory of rotating stall of multistage axial compressors

A theoretical analysis was made of rotating stall in axial compressors of many stages, finding conditions for a permanent, straight-through traveling disturbance, with the steady compressor characteristic assumed known, and with simple lag processes ascribed to the flows in the inlet, blade passages, and exit regions. For weak disturbances, predicted stall propagation speeds agree well with experimental results. For a locally-parabolic compressor characteristic, an exact nonlinear solution is found and discussed. For deep stall, the stall-zone boundary is most abrupt at the trailing edge, as expected. When a complete characteristic having unstalling and reverse-flow features is adopted, limit cycles governed by a Lienard's equation are found. Analysis of these cycles yields predictions of recovery from rotating stall; a relaxation oscillation is found at some limiting flow coefficient, above which no solution exists. Recovery is apparently independent of lag processes in the blade passages, but instead depends on the lags originating in the inlet and exit flows, and also on the shape of the given characteristic diagram. Small external lags and tall diagrams favor early recovery. Implications for future research are discussed.

Moore, F. K.↗

DOE OSTI2025

Comparison of interlaminar damage modeling strategies for hybrid composite/aluminum laminates subjected to low-velocity impact

Low-velocity impact of hybrid metal-composite structures was investigated experimentally and computationally. Composite laminates consisting of 2D woven glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) were joined with a 6061-T6 aluminum plate using an epoxy adhesive. Two variations of the structure were studied; one consisting of all plies oriented at 0° and one consisting of all plies oriented at 45°. A drop tower was used to impact structures at a range of energies, including energies above and below the threshold at which the aluminum layer was perforated. Numerical simulations were implemented using Sierra/SM, an in-house transient dynamics finite element code developed at Sandia National Laboratories. A Hosford plasticity model was used to describe the response of the aluminum layer. A newly implemented orthotropic continuum damage mechanics (CDM) constitutive model was used to represent the composite laminate. This 3D-CDM model was compared to a cohesive zone model (2D-CDM/CZM) to investigate efficacy of aluminum perforation energy prediction, delamination prediction, and computational cost. Accuracy of each model was evaluated using the experimental results. Each showed good agreement with the tests for both the force and velocity histories, as well as the observed damage mechanisms. The 2D-CDM/CZM model was marginally more accurate in capturing both the composite and aluminum behavior — this model averaged error percentages of -11.2% and 10.8% for residual velocity and peak force, respectively. Meanwhile, the 3D-CDM model predictions yielded average error percentages of -35.5% (velocity) and 22.6% (force). However, the 3D-CDM model generally resulted in a decreased computational cost; the average run time was 14% shorter than the 2D-CDM/CZM model and 3x as many timesteps per hour were computed using the same computational resources. In conclusion, new experimental data on the impact and perforation resistance of metal-composite laminates is presented in addition to numerical predictions of the impact behavior.

Carbon fiber↗

NASA NTRS1992

Prediction of high frequency combustion instability in liquid propellant rocket engines

The present use of a numerical model developed for the prediction of high-frequency combustion stabilities in liquid propellant rocket engines focuses on (1) the overall behavior of nonlinear combustion instabilities (2) the effects of acoustic oscillations on the fuel-droplet vaporization and combustion process in stable and unstable engine operating conditions, oscillating flowfields, and liquid-fuel trajectories during combustion instability, and (3) the effects of such design parameters as inlet boundary conditions, initial spray conditions, and baffle length. The numerical model has yielded predictions of the tangential-mode combustion instability; baffle length and droplet size variations are noted to have significant effects on engine stability.

Kim, Y. M.↗

DOE OSTI2022

High Yield, Economical and Environmentally Benign Production of Rare Earth Elements from Coal Ash [Abstract]

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2025

Investigating Electron Conductivity Regimes in the Bacterial Cytochrome Wire OmcS

The anaerobic bacterium Geobacter sulfurreducens produces extracellular, electronically conductive cytochrome polymer wires that are conductive over micron length scales. Structure models from cryo-electron microscopy data show OmcS wires form a linear chain of hemes along the protein wire axis, which is proposed as the structural basis supporting their electronic properties. However, the mechanism by which this heme arrangement supports long-range electronic conduction remains unknown. Structure models from cryo-electron microscopy data show these wires form a linear chain of hemes along the protein wire axis, which is proposed as the structural basis supporting their electronic properties. Existing computational models using static heme redox potentials and coupling energies fail to explain experimental observations, predicting conductances 10,000 to 100,000 times lower than measured values. Here, we investigate how dynamic disorder affects site energies, interheme coupling, and long-range electronic conductivity within these cytochrome wires. We introduce an approach to extract charge carrier site information directly from Kohn–Sham density functional theory, without employing projector schemes, and show that site and coupling energies are highly sensitive to changes in interheme geometry and the surrounding electrostatic environment. Unlike models that incorporate dynamic disorder as a thermally averaged quantity, our quantum charge carrier model incorporates proxies for dynamic disorder through decoherence corrections, yielding predicted diffusion coefficient closer to what is expected from experiment and comparable with other organic-based electronic materials. Based on these simulations, we propose that the instantaneous fluctuations of the local electrostatic environment can transiently lift energy degeneracies and delocalize charge carriers. Furthermore, these studies reveal how incorporating dynamic fluctuations associated with the environment resolves the discrepancy between theory and experiment in microbial cytochrome wires and highlight design principles for bioinspired, heme-based conductive materials.

Bioinorganic chemistry↗

DOE OSTI2022

High Yield, Economical and Environmentally Benign Production of Rare Earth Elements from Coal Ash (Phase II Final Summary Report)

Fly ash stored in landfills and ponds across the United States is an attractive, abundant domestic resource for the cost-effective recovery of rare earth elements (REE) and other critical minerals (CM). Physical Sciences Inc. (PSI) and its team members, Winner Water Services (WWS) and University of Kentucky/Center for Applied Energy Research (UK/CAER) successfully executed a multiphase program that developed technologies and their implementation in a pilot plant. We demonstrated plant operations for cost-effective and environmentally-friendly production of rare earth element oxide (REO) concentrates, and the critical minerals scandium and aluminum (in the forms of salts or oxide products), from coal ash. We also constructed and demonstrated a research-scale (0.5 kg/day) micropilot facility to validate the key physical and chemical processing operations, predict yields, and troubleshoot process bottlenecks. The project team then designed, constructed and operated two decoupled pilot plants: (1) an operational pilot plant for physical separation processes with capacity of 0.4 metric tons per day (tpd), where we optimized processes to produce selected ash fractions as the feedstock for chemical processing and as valuable byproducts such as cenospheres, magnetic ash, and secondary fuel carbon, and (2) an operational pilot plant for chemical ash processing with a capacity of 0.5 tpd that developed optimized processes for the production of: (a) REO concentrates, (b) critical minerals (Sc, Al), and (c) beneficiated ash as a valuable byproduct suitable for cement applications. In Phase I, the project team (with Equinox Chemicals in place of WWS) developed and demonstrated the feasibility of the physical and chemical separation processes, developed the design of a pilot plant, and began the development of a preliminary techno-economic model. In the baseline (initial) Phase II program, the project team developed and demonstrated the above pilot scale plant, producing salable REE concentrates, including Y and Sc (REYSc), plus commercially viable byproducts, using environmentally safe and high-yield physical and chemical enrichment processes. The team successfully demonstrated chemical pilot design, construction, shakedown, and operations of the plant. We produced the Phase II deliverable REYSc concentrate ((50 g of >60 wt.% purity REYSc salts on elemental basis), generated the feed for the Phase II follow-on program, identified processing challenges for future optimizations, and refined the techno-economic model. In the Phase II follow-on program, the project team: (1) developed and demonstrated processes to increase the REE amount by 3X (content basis) and convert the Phase II REE salt mixture to an oxide mixture, (2) produced/delivered >38 g of REO mixture with >85 wt.% purity (elemental basis); (3) developed processes to recover critical minerals scandium and aluminum from intermediate streams; (4) produced/delivered > 1 g of scandium salt mixture with >85 wt. % purity (elemental basis); (5) produced/delivered > 100 g of aluminum oxide type material with >70% wt. purity (elemental basis); and (6) updated the techno-economic model from the baseline Phase II program to assess CAPEX and OPEX of a commercial operation. This program has developed extensive databases on process chemistry, unit operations, plant engineering, and techno-economics that will enable further scale-up toward commercial plant design. Specific future developments will be focused on achieving dramatic savings in energy, reagent usage, and operating costs. The combined results will contribute significantly for maturing the technologies of REE recovery from coal byproducts and promote the establishment of domestic REE and CM supply chains.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2021

Quantifying the propagation of parametric uncertainty on flux balance analysis

Flux balance analysis (FBA) and associated techniques operating on stoichiometric genome-scale metabolic models play a central role in quantifying metabolic flows and constraining feasible phenotypes. At the heart of these methods lie two important assumptions: (i) the biomass precursors and energy requirements neither change in response to growth conditions nor environmental/genetic perturbations, and (ii) metabolite production and consumption rates are equal at all times (i.e., steady-state). Despite the stringency of these two assumptions, FBA has been shown to be surprisingly robust at predicting cellular phenotypes. In this paper, we formally assess the impact of these two assumptions on FBA results by quantifying how uncertainty in biomass reaction coefficients, and departures from steady-state due to temporal fluctuations could propagate to FBA results. In the first case, conditional sampling of parameter space is required to re-weigh the biomass reaction so as the molecular weight remains equal to 1 g mmol –1 , and in the second case, metabolite (and elemental) pool conservation must be imposed under temporally varying conditions. Results confirm the importance of enforcing the aforementioned constraints and explain the robustness of FBA biomass yield predictions.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1995

Interactions of CO2, temperature and management practices: simulations with a modified version of CERES-Wheat

A new growth subroutine was developed for CERES-Wheat, a computer model of wheat (Triticum aestivum) growth and development. The new subroutine simulates canopy photosynthetic response to CO2 concentrations and light levels, and includes the effects of temperature on canopy light-use efficiency. Its performance was compared to the original CERES-Wheat V-2 10 in 30 different cases. Biomass and yield predictions of the two models were well correlated (correlation coefficient r > 0.95). As an application, summer growth of spring wheat was simulated at one site. Modeled crop responses to higher mean temperatures, different amounts of minimum and maximum warming, and doubled CO2 concentrations were compared to observations. The importance of irrigation and nitrogen fertilization in modulating the wheat crop climatic responses were also analyzed. Specifically, in agreement with observations, rainfed crops were found to be more sensitive to CO2 increases than irrigated ones. On the other hand, low nitrogen applications depressed the ability of the wheat crop to respond positively to CO2 increases. In general, the positive effects of high CO2 on grain yield were found to be almost completely counterbalanced by the negative effects of high temperatures. Depending on how temperature minima and maxima were increased, yield changes averaged across management practices ranged from -4% to 8%.

NASA Discipline Life Support Systems↗

DOE OSTI2026

Bayesian discovery of optimal reduced order models from mechanistic and experimental data: A case study of Pd penetration in TRISO fuels using BISON

TRistructural ISOtropic (TRISO) particles rely on a silicon carbide (SiC) layer as the primary structural material and barrier to metallic fission products (FPs) release. Accurate prediction of palladium (Pd) transport and penetration is therefore critical for qualifying TRISO fuels for advanced reactors. The empirical correlation for Pd penetration in BISON is derived from historical particle-fuel data, but cannot explain the large scatter in the experimental data that arises from varying experimental conditions. To aid fuel qualification, we previously developed a mechanistic reduced order model (ROM) using BISON that resolves these dependencies. Here, in this work we build on that mechanistic ROM and perform validation and quantify its uncertainty using Bayesian uncertainty quantification (UQ). calibration against a suite of in-pile and out-of-pile experiments spanning particle compositions, geometries, and operating conditions, and we benchmark it against the empirical correlation. Bayesian UQ identifies influential parameters, calibrates them to data, and yields predictive intervals. Results show that while the empirical correlation can be tuned to fit a single experiment type, it transfers poorly; the mechanistic ROM sustains accuracy with credible uncertainty across disparate conditions. This demonstrates a practical path—via Bayesian UQ applied to mechanistic ROMs—to leverage single-effect experiments for inferring in-reactor behavior and supporting TRISO fuel qualification.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2017

Predictive Modeling of Fast-Curing Thermosets in Nozzle-Based Extrusion

This work presents an approach to modeling the dynamic spreading and curing behavior of thermosets in nozzle-based extrusions. Thermosets cover a wide range of materials, some of which permit low-temperature processing with subsequent high-temperature and high-strength working properties. Extruding thermosets may overcome the limited working temperatures and strengths of conventional thermoplastic materials used in additive manufacturing. This project aims to produce technology for the fabrication of thermoset-based structures leveraging advances made in nozzle-based extrusion, such as fused deposition modeling (FDM), material jetting, and direct writing. Understanding the synergistic interactions between spreading and fast curing of extruded thermosetting materials will provide essential insights for applications that require accurate dimensional controls, such as additive manufacturing [1], [2] and centrifugal coating/forming [3]. Two types of thermally curing thermosets -- one being a soft silicone (Ecoflex 0050) and the other being a toughened epoxy (G/Flex) -- served as the test materials in this work to obtain models for cure kinetics and viscosity. The developed models align with extensive measurements made with differential scanning calorimetry (DSC) and rheology. DSC monitors the change in the heat of reaction, which reflects the rate and degree of cure at different crosslinking stages. Rheology measures the change in complex viscosity, shear moduli, yield stress, and other properties dictated by chemical composition. By combining DSC and rheological measurements, it is possible to establish a set of models profiling the cure kinetics and chemorheology without prior knowledge of chemical composition, which is usually necessary for sophisticated mechanistic modeling. In this work, we conducted both isothermal and dynamic measurements with both DSC and rheology. With the developed models, numerical simulations yielded predictions of diameter and height of droplets, along with width and height of extruded lines cured at varied temperatures. Experimental results carried out on a goniometric platform and a nozzle-based 3D printer showed agreement with the numerical simulations. Finally, this presentation will show how the models are adaptable to the planning of tool paths and designs in additive manufacturing.

Xie, Jingjin↗

DOE OSTI2021

Impact of duration and missing data on the long-term photovoltaic degradation rate estimation

Accurate quantification of photovoltaic (PV) system degradation rate (R D ) is essential for lifetime yield predictions. Although R D is a critical parameter, its estimation lacks a standardized methodology that can be applied on outdoor field data. The purpose of this paper is to investigate the impact of time period duration and missing data on R D by analyzing the performance of different techniques applied to synthetic PV system data at different linear R D patterns and known noise conditions. The analysis includes the application of different techniques to a 10-year synthetic dataset of a crystalline Silicon PV system, with emulated degradation levels and imputed missing data. Here, the analysis demonstrated that the accuracy of ordinary least squares (OLS), year-on-year (YOY), autoregressive integrated moving average (ARIMA) and robust principal component analysis (RPCA) techniques is affected by the evaluation duration with all techniques converging to lower R D deviations over the 10-year evaluation, apart from RPCA at high degradation levels. Moreover, the estimated R D is strongly affected by the amount of missing data. Filtering out the corrupted data yielded more accurate R D results for all techniques. It is proven that the application of a change-point detection stage is necessary and guidelines for accurate R D estimation are provided.

14 SOLAR ENERGY↗

DOE OSTI2020

Determination of the strong coupling constant $\alpha_{S}(m_\mathrm{Z})$ from measurements of inclusive W$^\pm$ and Z boson production cross sections in proton-proton collisions at $ \sqrt{\mathrm{s}} $ = 7 and 8 TeV

Twelve measurements of inclusive cross sections of W$^{±}$ and Z boson production, performed in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV, are compared with perturbative quantum chromodynamics calculations at next-to-next- to-leading order (NNLO) accuracy obtained with the CT14, HERAPDF2.0, MMHT14, and NNPDF3.0 parton distribution functions (PDFs). Data and theory agree well for all PDF sets, taking into account the experimental and theoretical uncertainties. A novel procedure is employed to extract the strong coupling constant at the Z pole mass from a detailed comparison of all the experimental fiducial cross sections to the corresponding NNLO theoretical predictions, yielding $ {\alpha}_{\mathrm{S}}\left({m}_{\mathrm{Z}}\right)={0.1163}_{-0.0031}^{+0.0024} $ (CT14), $ {0.1072}_{-0.0040}^{+0.0043} $ (HERAPDF2.0), 0.1186 ± 0.0025 (MMHT14), and 0.1147 ± 0.0023 (NNPDF3.0). Using the results obtained with the CT14 and MMHT14 PDFs, which yield the most robust and stable α$_{S}$(m$_{Z}$) extractions, a value $ {\alpha}_{\mathrm{S}}\left({m}_{\mathrm{Z}}\right)={0.1175}_{-0.0028}^{+0.0025} $ is determined.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗