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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 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Computational discovery of ultra-strong, stable, and lightweight refractory multi-principal element alloys. Part I: design principles and rapid down-selection

Abstract Refractory metal-based multi-principal element alloys (MPEAs) are compelling materials for high-temperature (1000–2000 K) structural applications. However, only a minuscule fraction of their vast and heterogeneous compositional design space has been explored, leaving many potentially interesting alloys undiscovered. In this two-part work, a large region of the 11-element Al-Cr-Fe-Hf-Mo-Nb-Ta-Ti-V-W-Zr design space is computationally explored to identify refractory MPEAs with simultaneously high yield strength or specific yield strength and body-centered cubic (BCC) solid solution stability. In Part I , two case studies illuminate key factors and considerations in the yield strength versus phase stability tradeoff, provide guidelines for narrowing the expansive design space, and identify many candidates predicted to be stronger than refractory MPEAs reported to date, with BCC phase stability. Our findings indicate that medium entropy ternary alloys can outperform alloys with more elements and highlight the importance of exploring regions away from the equiatomic center of composition space.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Sparse expansions of multicomponent oxide configuration energy using coherency and redundancy

We report that compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict sampling requirements necessary to obtain minimal coherence measurements for compressed sensing to guarantee accurate estimation of model parameters are difficult and in some cases impossible to satisfy due to the inability of physical systems to access certain configurations. Nevertheless, the dependence of energy on atomic configuration can still be adequately learned without these strict requirements by using compressed sensing by way of coherent measurements using redundant function sets known as frames. We develop a particular frame constructed from the union of all occupancy-based cluster expansion basis sets. We illustrate how using this highly redundant frame yields sparse expansions of the configuration energy of complex oxide materials that are competitive and often surpass the prediction accuracy and sparsity of models obtained from standard cluster expansions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

First Experiments and Radiographs on the MegaJOuLe Neutron Imaging Radiography (MJOLNIR) Dense Plasma Focus

We report a dense plasma focus (DPF) is a relatively compact coaxial plasma gun, which completes its discharge as a Z-pinch. These devices are designed to operate at a variety of scales to produce short (<100 ns) pulses of ions, X-rays, and/or neutrons. LLNL recently constructed and brought into operation a new device, the MegaJOuLe Neutron Imaging Radiography (MJOLNIR) DPF, which is designed for radiography and high-yield operations. This device has been commissioned and has achieved neutron yields of up to 3.8E11 neutrons/pulse at 2.5-MA peak current while operating at up to 1 MJ of stored energy in its original pulsed power configuration. MJOLNIR is equipped with a wide range of diagnostics, including nuclear activation detectors, neutron time-of-flight (nToF) detectors, a fast-framing camera, optical light gates, and a time-gated neutron and X-ray imager. LLNL also runs unique particle-in-cell (PIC) simulations of DPF discharges in the Chicago code and has gained significant insight into the various physical factors that influence neutron yield. MJOLNIR is one of the first DPFs whose design and continual upgrades are heavily influenced by model predictions. In this article, we describe insights from modeling, device operation, and recent results. Comparisons between modeling predictions and measurements, as well as X-ray and neutron images are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Tensile Property and Lifetime Prediction for Low-Temperature Aged Uranium-Niobium Alloys

Thermal aging models and lifetime predictions for uranium-niobium (U-Nb) alloys were created using an approach similar to those previously employed. Lifetime estimates for generic U-6Nb components were thus updated; the reported value being 800 years. This update represents a small change in lifetime vs. that of the 2012 assessment (540 years). This lifetime estimate emerged from consideration of several model fits specific to the aging datasets and properties chosen. Aging was quantified using quasi-static tensile properties measured on specimens artificially aged for up to 10 years. The major change relative to the most recent 2012 LANL assessment was that a more comprehensive body of U-Nb literature data was mined, in addition to being augmented by the latest LANL and UK AWE data. The tensile data compilation was published separately (LANL report LA-14493, December 2016). Recognizing the chemical banding of industrially produced U-6Nb, models were developed for the mid-range (6 wt.%) and extrema (4 and 8 wt.%) compositions. Lifetime estimates were calculated for all three alloy classes (4, 6, 8 wt.% nominal) and two measures of total tensile elongation (TE) to failure, namely TE-ext. — extensometer method, and TE-NCD — normalized crosshead displacement method. The conservative assumption was made that whichever composition (4, 6, or 8 wt.% Nb) and property (TE-ext or TE-NCD) was the first to cross the ductility failure threshold would limit the lifetime of the entire component. Tensile strength properties did not figure into the lifetime predictions, but could be useful as age-sensitive diagnostics and were also modeled. Of these, only first yield strength is expected to show a change at 40°C aging vs. time = 0 over the ~100-year timespan of engineering interest. Second yield strength evolves more slowly, and ultimate tensile strength slower still. Among all the models, the apparent activation energies for aging were mostly in the narrow 29– 37 kcal/mol range, which is close to that for diffusion of Nb in gamma-uranium. This agreement may be coincidental. The data from recent long-term aging studies substantially improved the model fit quality and robustness of the lifetimes. Appendices document sensitivity studies of the model fits and lifetimes with respect to using more limited datasets. These results highlight the limitations of relying solely on data from scattered literature studies and smaller datasets more generally.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions

Many materials of interest to Sandia transition from fluid to solid or have regions of both phases coexisting simultaneously. Currently there are, unfortunately, no material models that can accurately predict this material response. This is relevant to applications that "birth stress" related to geoscience, nuclear safety, manufacturing, energy production and bioscience. Accurately capturing solidification and residual stress enables fully predictive simulations of the evolving front shape or final product. Accurately resolving flow of proppants or blood could reduce environmental impact or lead to better treatments for heart attacks, thrombosis, or aneurism. We will address a science question in this proposal: When does residual stress develop during the critical transition from liquid to solid and how does it affect material deformation? Our hypothesis is that these early phases of stress development are critical to predictive simulation of material performance, net shape, and aging. In this project, we use advanced constitutive models with yield stress to represent both fluid and solid behavior simultaneously. The report provides an abbreviated description of the results from our LDRD "Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions," since we have written four papers that document the work in detail and which we reference. We give highlights of the work and describe the gravitationally driven flow visualization experiment on a model yield stress fluid, Carbopol, at various concentrations and flow rates. We were able to collapse the data on a single master curve by showing it was self-similar. We also describe the Carbopol rheology and the constitutive equations of interest including the Bingham-Carreau-Yasuda model, the Saramito model, and the HB-Saramito model including parameter estimation for the shear and oscillatory rheology. We present several computational models including the 3D moving mesh simulations of both the Saramito models and Bingham-Carreau-Yasuda (BCY) model. We also show results from the BCY model using a 3D level set method and two different ways of handling reduced order Hele-Shaw modeling for generalized Newtonian fluids. We present some first ever two-dimensional results for the modified Jeffries Kamani-Donley-Rogers constitutive equation developed during this project. We include some recent results with a successful Saramito-level set coupling that allows us to tackle problems with complex geometries like mold filling in a thin gap with an obstacle, without the need for remeshing or remapping. We report on some experiments for curing systems where fluorescent particles are used to track material flow. These experiments were carried out in an oven on Sylgard 184 as a model polymerizing system. We conclude the report with a summary of accomplishments and some thoughts on follow-on work.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Synthesis of Hf 0.75 Ta 0.25 B 2 for self-coating TPS

Ultra-high temperature ceramic materials (UHTCs) are important for designing high-performance aerospace vehicles that can withstand repeated exposures to high temperatures. UHTCs mixed with silicides often have well-controlled oxidation due to the formation of protective silicates, which create a regenerative outer protective layer. Borides are known to have high melting points, high hardness and reasonably good oxidation resistance. In this study, Hf 0.75 Ta 0.25 B 2 (HTB) is proposed as a potential alternative to YSZ protective coatings and ZrB 2- SiC composites via the formation of Hf 6 Ta 2 O 17 (HTO) passivation layer. The objective of this paper is to explore the parameter space of HTB synthesis via borocarbothermal (BCTR). Effects on particle size, phase purity, and residual oxygen content were analyzed with parameters of atmosphere composition, reactant grain sizes, and differing reaction pathways. The BCTR of HfO 2 and Ta 2 O 5 were analyzed to predict HTB behavior. It was shown that both one-step and two-step reaction routes can yield HTB, but two-step yields a purer product. Nano B 4 C produced finer HTB and facilitated reaction completion. Using a reducing atmosphere also enhanced reaction completion

36 MATERIALS SCIENCE↗
DOE OSTI2020

Predictive Model of Charge Mobilities in Organic Semiconductor Small Molecules with Force-Matched Potentials

Charge mobility of crystalline organic semiconductors (OSC) is limited by local dynamic disorder. Recently, the charge mobility for several high mobility OSCs, including TIPS-pentacene, were accurately predicted from a density functional theory (DFT) simulation constrained by the crystal structure and the inelastic neutron scattering spectrum, which provide direct measures of the structure and the dynamic disorder in the length scale and energy range of interest. However, the computational expense required for calculating all of the atomic and molecular forces is prohibitive. In this work, we demonstrate the use of density functional tight binding (DFTB), a semiempirical quantum mechanical method that is 2 to 3 orders of magnitude more efficient than DFT. We show that force matching a many-body interaction potential to DFT derived forces yields highly accurate DFTB models capable of reproducing the low-frequency intricacies of experimental inelastic neutron scattering (INS) spectra and accurately predicting charge mobility. We subsequently predicted charge mobilities from our DFTB model of a number of previously unstudied structural analogues to TIPS-pentacene using dynamic disorder from DFTB and transient localization theory. The approach we establish here could provide a truly rapid simulation pathway for accurate materials properties prediction, in our vision applied to new OSCs with tailored properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Smart culture medium optimization for recombinant protein production: Experimental, modeling, and AI/ML-driven strategies

Recombinant protein production (RPP) is central to biotechnology, where recombinant proteins are used as either end products or catalysts in the synthesis of chemicals, fuels, and materials. Among the major cost drivers, culture medium plays a pivotal role in determining protein yield and quality. This review presents a comprehensive perspective on the critical stages of “smart” culture medium optimization: planning, screening, modeling, optimization, and validation. In the planning stage, we examine the nutritional and energetic roles of medium components, including carbon, nitrogen, amino acids, salts, and trace metals, and their impacts on culture parameters such as pH, oxidative state, and osmolality. We highlight the variability in trace metal content due to water sources, culture vessels, and raw materials, which can substantially influence RPP. The screening stage covers Design of Experiments (DoE) approaches, assessing their theoretical basis, implementation, and limitations. For modeling, we describe methods that integrate experimental data to develop predictive models for smart medium formulation. Model-based optimization strategies can then be employed to select optimal media compositions for a given application. The validation stage aims to evaluate model predictions and provide feedback for model training and refinement. Finally, we survey mechanistic and artificial intelligence/machine learning (AI/ML)-driven models as integrated, transformational tools for predictive modeling of bioprocess conditions, nutrient availability, cellular metabolism, and protein quality, with the goal of optimizing culture media to enhance protein yields while reducing costs and environmental impact. We conclude by addressing the challenges of translating laboratory-scale medium optimization to industrial-scale settings and exploring future AI/ML-driven approaches that may overcome current bottlenecks and accelerate medium design for RPP. Overall, this review provides a unified framework for advancing smart medium design in RPP.

Artificial Intelligence/Machine Learning (AI/ML)↗
DOE OSTI2022

Integration of physiologically relevant photosynthetic energy flows into whole genome models of light‐driven metabolism

SUMMARY Characterizing photosynthetic productivity is necessary to understand the ecological contributions and biotechnology potential of plants, algae, and cyanobacteria. Light capture efficiency and photophysiology have long been characterized by measurements of chlorophyll fluorescence dynamics. However, these investigations typically do not consider the metabolic network downstream of light harvesting. By contrast, genome‐scale metabolic models capture species‐specific metabolic capabilities but have yet to incorporate the rapid regulation of the light harvesting apparatus. Here, we combine chlorophyll fluorescence parameters defining photosynthetic and non‐photosynthetic yield of absorbed light energy with a metabolic model of the pennate diatom Phaeodactylum tricornutum. This integration increases the model predictive accuracy regarding growth rate, intracellular oxygen production and consumption, and metabolic pathway usage. Through the quantification of excess electron transport, we uncover the sequential activation of non‐radiative energy dissipation processes, cross‐compartment electron shuttling, and non‐photochemical quenching as the rapid photoacclimation strategy in P. tricornutum. Interestingly, the photon absorption thresholds that trigger the transition between these mechanisms were consistent at low and high incident photon fluxes. We use this understanding to explore engineering strategies for rerouting cellular resources and excess light energy towards bioproducts in silico . Overall, we present a methodology for incorporating a common, informative data type into computational models of light‐driven metabolism and show its utilization within the design–build–test–learn cycle for engineering of photosynthetic organisms.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Predicting stress response and improved protein overproduction in Bacillus subtilis

Abstract Bacillus subtilis is a well-characterized microorganism and a model for the study of Gram-positive bacteria. The bacterium can produce proteins at high densities and yields, which has made it valuable for industrial bioproduction. Like other cell factories, metabolic modeling of B. subtilis has discovered ways to optimize its metabolism toward various applications. The first genome-scale metabolic model (M-model) of B. subtilis was published more than a decade ago and has been applied extensively to understand metabolism, to predict growth phenotypes, and served as a template to reconstruct models for other Gram-positive bacteria. However, M-models are ill-suited to simulate the production and secretion of proteins as well as their proteomic response to stress. Thus, a new generation of metabolic models, known as metabolism and gene expression models (ME-models), has been initiated. Here, we describe the reconstruction and validation of a ME model of B. subtilis , i JT964-ME. This model achieved higher performance scores on the prediction of gene essentiality as compared to the M-model. We successfully validated the model by integrating physiological and omics data associated with gene expression responses to ethanol and salt stress. The model further identified the mechanism by which tryptophan synthesis is upregulated under ethanol stress. Further, we employed i JT964-ME to predict amylase production rates under two different growth conditions. We analyzed these flux distributions and identified key metabolic pathways that permitted the increase in amylase production. Models like i JT964-ME enable the study of proteomic response to stress and the illustrate the potential for optimizing protein production in bacteria.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

The economic value of photovoltaic performance loss mitigation in electricity spot markets

Photovoltaic (PV) performance is affected by reversible and irreversible losses. These can typically be mitigated through responsive and proactive operations and maintenance (O&M) activities. However, to generate profit, the cost of O&M must be lower than the value of the recovered electricity. This value depends both on the amount of recovered energy and on the electricity prices, which can vary significantly over time in spot markets. The present work investigates the impact of the electricity price variability on the PV profitability and on the related O&M activities in Italy, Portugal, and Spain. Here, it is found that the PV revenues varied by 1.6 × to 1.8 × within the investigated countries in the last 5 years. Moreover, forecasts predict higher average prices in the current decade compared to the previous one. These will increase the future PV revenues by up to 60% by 2030 compared to their 2015–2020 mean values. These higher revenues will make more funds available for better maintenance and for higher quality components, potentially leading to even higher energy yield and profits. Linearly growing or constant price assumptions cannot fully reproduce these expected price trends. Furthermore, significant price fluctuations can lead to unexpected scenarios and alter the predictions.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

The H•/H– Redox Couple and Absolute Hydration Energy of H–

A supermolecule-continuum approach with water clusters up to n = 16 H2O molecules has been used to predict the absolute hydration free energies at 298 K ($\Delta$G hyd ) of both hydrogen (H•) and hydride (H - ) to be 4.6 and -78 ± 2 kcal/mol, respectively. These values are combined with a high accuracy prediction of the gas phase electron affinity ($\Delta$G gas,298K = -16.9 kcal/mol) to determine the aqueous electron affinity of H• of 99.5 ± 2 kcal/mol, which yields a reduction potential for H• vs SHE of -0.03 ± 0.15 V. This value is in agreement within 0.2 V with most estimates obtained using a wide variety of approaches. The results of this study can be used to improve the absolute hydricity scale in water which provides additional insights into how a putative hydride interacts with solvent, but do not change the ability to predict the relative reactivity of two species using relative hydricity scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Enhanced Feedstock Characterization and Modeling to Facilitate Optimal Preprocessing and Deconstruction of Corn Stover (Final Report)

This project addresses the challenge of processing corn stover by fractionating this biomass feedstock to both streamline processing and generate new potential co-products. Additionally, the project developed new field-deployable analytical tools that can be coupled with empirical models that were used to predict feedstock properties and processing performance. The overall scope of this project was: (1) identify conditions for optimal corn stover fractionation using a two- stage physical fractionation, (2) assess how physical fractionation impacts properties, partitioning of biomass, and response to processing, (3) further adapt, develop, and validate several advanced characterization tools for assessing biomass properties that can be linked to processing behavior, and (4) develop and validate predictive models based on measurements that can be performed “in the field” or “at the biorefinery gate” to predict feedstock processing behavior (preprocessing and deconstruction). The first objective employed pre-separation processing (size reduction) which was next subjected to enhanced separations to yield fractions enriched or depleted in select compositional components or properties. For the second objective, fractions were screened for their response to post-separation processing (pretreatment and enzymatic hydrolysis). Detailed characterization profiles were developed and dynamic image analysis to assess distribution of particle size and morphology. For the final objective, we utilized these tools to develop empirical models to assess the relative abundance of tissue type in order to assess fractionation efficacy and to predict fraction performance during pretreatment and enzymatic hydrolysis.

09 BIOMASS FUELS↗
DOE OSTI2020

Generalized and Mechanistic PV Module Performance Prediction From Computer Vision and Machine Learning on Electroluminescence Images

Electroluminescence (EL) imaging of photovoltiac (PV) modules offers high-speed, high-resolution information about device performance, affording opportunities for greater insight and efficiency in module characterization across manufacturing, research and development, and power plant operations and management. Predicting module electrical properties from EL image features is a critical step toward these applications. In this article, we demonstrate quantification of both generalized and performance mechanism-specific EL image features, using pixel intensity-based and machine learning classification algorithms. From EL image features, we build predictive models for PV module power and series resistance, using time-series current-voltage (I-V) and EL data obtained stepwise on five brands of modules spanning three Si cell types through two accelerated exposures: damp heat (DH) (85°C/85% RH) and thermal cycling (TC) (IEC 61215). Overall, 195 pairs of EL images and I-V characteristics were analyzed, yielding 11700 individual PV cell images. A convolutional neural network was built to classify cells by the severity of busbar corrosion with high accuracy (95%). Generalized power predictive models estimated the maximum power of PV modules from EL images with high confidence and an adjusted-R 2 of 0.88, across all module brands and cell types in extended DH and TC exposures. Mechanistic degradation prediction was demonstrated by quantification of busbar corrosion in EL images of three module brands in DH, and subsequent modeling of series resistance using these mechanism-specific EL image features. For modules exhibiting busbar corrosion, we demonstrated series resistance predictive models with adjusted-R 2 of up to 0.73.

14 SOLAR ENERGY↗
DOE OSTI2022

Prediction of curing kinetics of resorcinol‐added resole phenolic resins using differential scanning calorimetry for the fabrication of carbon/carbon composites

Phenolic resins are commonly used as carbon precursors for the fabrication of carbon/carbon composites due to their high carbon yield and aromatic nature. To decrease curing times, acid catalysts are generally used, but the addition of resorcinol was found to have a similar effect while being incorporated into the resin matrix with no contamination or corrosion issues. In this work, the curing kinetics of pure, 10, 20, and 30 wt% resorcinol-added phenolic resins were investigated through differential scanning calorimetry. Heating rates of 0.5, 1, 2.5, and 5°C min -1 were used with several curing models to predict isothermal curing. Averaged mean absolute error (MAE) for the isoconversional mathematical approaches namely Kissinger–Akahira–Sunose (MAE = 12.9 min), Flynn–Wall–Ozawa (15.8 min), and Vyazovkin (14 min) show that these methods provide the best predictions, attributed to their adoption of an activation energy that depends on the extent of cure (E a (α)). The Kissinger method (MAE = 36 min), which depends only on peak temperature with a constant activation energy assumption, and the data noise sensitive Friedman model (MAE = 1144.7 min) provide the least accurate results. Thermogravimetric analysis revealed that resorcinol decreases the curing times by up to 71% without lowering carbon yield.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Kinetic-ballooning-bifurcation in tokamak pedestals across shaping and aspect-ratio

We use a new gyrokinetic threshold model to predict a bifurcation in tokamak pedestal width-height scalings that depends strongly on plasma shaping and aspect-ratio. The bifurcation arises from the first and second stability properties of kinetic-ballooning-modes that yields wide and narrow pedestal branches, expanding the space of accessible pedestal widths and heights. The wide branch offers potential for edge-localized-mode-free pedestals with high core pressure. For negative triangularity, low-aspect-ratio configurations are predicted to give steeper pedestals than conventional-aspect-ratio. Both wide and narrow branches have been attained in tokamak experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Rational Design of Superconducting Metal Hydrides via Chemical Pressure Tuning**

Abstract The high critical superconducting temperatures ( T c s) of metal hydride phases with clathrate‐like hydrogen networks have generated great interest. Herein, we employ the Density Functional Theory‐Chemical Pressure (DFT‐CP) method to explain why certain electropositive elements adopt these structure types, whereas others distort the hydrogenic lattice, thereby decreasing the T c . The progressive opening of the H 24 polyhedra in MH 6 phases is shown to arise from internal pressures exerted by large metal atoms, some of which may favor an even higher hydrogen content that loosens the metal atom coordination environments. The stability of the LaH 10 and LaBH 8 phases is tied to stuffing of their shared hydrogen network with either additional hydrogen or boron atoms. The predictive capabilities of DFT‐CP are finally applied to the Y−X−H system to identify possible ternary additions yielding a superconducting phase stable to low pressures.

Hilleke, Katerina P.↗
DOE OSTI2025

Measurement of the inclusive $\textrm{t}\overline{\textrm{t}}$ cross section in final states with at least one lepton and additional jets with 302 pb −1 of pp collisions at $\sqrt{\textrm{s}}$ = 5.02 TeV

A measurement of the top quark pair ($ \textrm{t}\overline{\textrm{t}} $) production cross section in proton-proton collisions at a centre-of-mass energy of 5.02 TeV is presented. The data were collected at the LHC in autumn 2017, in dedicated runs with low-energy and low-intensity conditions with respect to the default configuration, and correspond to an integrated luminosity of 302 pb$^{−1}$. The measurement is performed using events with one electron or muon, and multiple jets, at least one of them being identified as originating from a b quark (b tagged). Events are classified based on the number of all reconstructed jets and of b-tagged jets. Multivariate analysis techniques are used to enhance the separation between the signal and backgrounds. The measured cross section is $ 62.5\pm 1.6{\left(\textrm{stat}\right)}_{-2.5}^{+2.6}\left(\textrm{syst}\right)\pm 1.2\left(\textrm{lumi}\right) $ pb. A combination with the result in the dilepton channel based on the same data set yields a value of 62.3 ± 1.5 (stat) ± 2.4 (syst) ± 1.2 (lumi) pb, to be compared with the standard model prediction of $ {69.5}_{-3.7}^{+3.5} $ pb at next-to-next-to-leading order in perturbative quantum chromodynamics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗