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DOE OSTI2024

A Novel Dew Point Meter: Application to the Measurement of the Sulfuric Acid Dew Point for Combustion Flue Gas

Accurate knowledge of acid dew point is essential for industrial and applied combustion applications. Sulfur in the fuel or raw materials is converted to sulfur dioxide (SO2) during combustion, and a portion of the SO2 is oxidized to sulfur trioxide (SO3). The SO3 will react to form H2SO4 vapor when in the presence of water vapor. Even with just trace levels of H2SO4 vapor in the gas phase (1-10 ppm), the dew point can reach 100°C and higher. To avoid acid condensation and the resulting corrosion on heat recovery equipment, plant engineers must ensure that surface temperatures are above the acid dew point, but this decreases the efficiency of thermal energy recovery. Thus, there is a trade-off between minimizing equipment corrosion and maximizing thermal energy recovery, and the acid dew point is a key parameter for this optimization. Commercially available acid dew point meters use electric conductivity sensors. These sensors are known to greatly underestimate the dew point due to their low sensitivity. In addition, no validation testing has been reported for these units and they are often expensive. In this work, we analyze the theory of the sulfuric acid condensation and develop a novel dew point meter based on this analysis. The meter consists of a novel optical instrument that is designed to monitor the slightest appearance of condensation on a hydrophobic window surface as the surface temperature of the window is slowly decreased. In this way, an accurate measurement of the dew point is obtained under a wide range of concentrations. The basis of the instrument is that a collimated beam from a diode laser will generate forward scattered light when the beam encounters surface condensate, and a sophisticated array detector is used to sensitively monitor the onset of light scattering. The measurement procedures are established to rapidly find the acid dew point, while minimizing error. Further, to calibrate the dew point meter we developed a calibration system based on a liquid bubbler that can generate a stable gas flow with a known sulfuric acid dew point. Test results show that the dew point meter can accurately measure acid dew point over a wide range. For H2SO4 vapor concentrations as low as 6 ppm the acid dew point is measured with an error of only ~1°C. To demonstrate the versatility of this instrument, the dew point meter was adapted for use with a high-pressure flow cell to allow for measurements of the dew point of flue gas from pressurized oxy-fuel combustion in a 100 kWth pressurized reactor.

Cheng, Mao↗

DOE OSTI2020

Constraining the Twomey effect from satellite observations: issues and perspectives

Abstract. The Twomey effect describes the radiative forcing associated with a change in cloud albedo due to an increase in anthropogenic aerosol emissions. It is driven by the perturbation in cloud droplet number concentration (ΔNd, ant) in liquid-water clouds and is currently understood to exert a cooling effect on climate. The Twomey effect is the key driver in the effective radiative forcing due to aerosol–cloud interactions, but rapid adjustments also contribute. These adjustments are essentially the responses of cloud fraction and liquid water path to ΔNd, ant and thus scale approximately with it. While the fundamental physics of the influence of added aerosol particles on the droplet concentration (Nd) is well described by established theory at the particle scale (micrometres), how this relationship is expressed at the large-scale (hundreds of kilometres) perturbation, ΔNd, ant, remains uncertain. The discrepancy between process understanding at particle scale and insufficient quantification at the climate-relevant large scale is caused by co-variability of aerosol particles and updraught velocity and by droplet sink processes. These operate at scales on the order of tens of metres at which only localised observations are available and at which no approach yet exists to quantify the anthropogenic perturbation. Different atmospheric models suggest diverse magnitudes of the Twomey effect even when applying the same anthropogenic aerosol emission perturbation. Thus, observational data are needed to quantify and constrain the Twomey effect. At the global scale, this means satellite data. There are four key uncertainties in determining ΔNd, ant, namely the quantification of (i) the cloud-active aerosol – the cloud condensation nuclei (CCN) concentrations at or above cloud base, (ii) Nd, (iii) the statistical approach for inferring the sensitivity of Nd to aerosol particles from the satellite data and (iv) uncertainty in the anthropogenic perturbation to CCN concentrations, which is not easily accessible from observational data. This review discusses deficiencies of current approaches for the different aspects of the problem and proposes several ways forward: in terms of CCN, retrievals of optical quantities such as aerosol optical depth suffer from a lack of vertical resolution, size and hygroscopicity information, non-direct relation to the concentration of aerosols, difficulty to quantify it within or below clouds, and the problem of insufficient sensitivity at low concentrations, in addition to retrieval errors. A future path forward can include utilising co-located polarimeter and lidar instruments, ideally including high-spectral-resolution lidar capability at two wavelengths to maximise vertically resolved size distribution information content. In terms of Nd, a key problem is the lack of operational retrievals of this quantity and the inaccuracy of the retrieval especially in broken-cloud regimes. As for the Nd-to-CCN sensitivity, key issues are the updraught distributions and the role of Nd sink processes, for which empirical assessments for specific cloud regimes are currently the best solutions. These considerations point to the conclusion that past studies using existing approaches have likely underestimated the true sensitivity and, thus, the radiative forcing due to the Twomey effect.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2020

Constraining the Twomey effect from satellite observations: Issues and perspectives

The Twomey effect describes the radiative forcing associated with a change in cloud albedo due to an increase in anthropogenic aerosol emissions. It is driven by the perturbation in cloud droplet number concentration (ΔNd,ant) in liquid-water clouds and is currently understood to exert a cooling effect on climate. The Twomey effect is the key driver in the effective radiative forcing due to aerosol–cloud interactions which also comprises rapid adjustments. These adjustments are essentially the responses of cloud fraction and liquid water path to ΔNd,ant and thus scale approximately with it. While the fundamental physics of the influence of added aerosol particles on the droplet concentration (Nd) is well described by established theory at the particle scale (micrometres), how this relationship is expressed at the large scale (hundreds of kilometres) ΔNd,ant remains uncertain. The discrepancy between process understanding at particle scale and insufficient quantification at the climate-relevant large scale is caused by co-variability of aerosol particles and vertical wind and by droplet sink processes. These operate at scales on the order of 10s of metres at which only localized observations are available and at which no approach exists yet to quantify the anthropogenic perturbation. Different atmospheric models suggest diverse magnitudes of the Twomey effect even when applying the same anthropogenic aerosol emission perturbation. Thus, observational data are needed to quantify and constrain the Twomey effect. At the global scale, this means satellite data. There are three key uncertainties in determining ΔNd,ant, namely the quantification (i) of the cloud-active aerosol – the cloud condensation nuclei concentrations (CCN) at or above cloud base –, (ii) of Nd, as well as (iii) the statistical approach for inferring the sensitivity of Nd to aerosol particles from the satellite data. A fourth uncertainty, the anthropogenic perturbation to CCN concentrations, is also not easily accessible from observational data. This review discusses deficiencies of current approaches for the different aspects of the problem and proposes several ways forward: In terms of CCN, retrievals of optical quantities such as aerosol optical depth suffer from a lack of vertical resolution, size and hygroscopicity information, the non-direct relation to the concentration of aerosols, the impossibility to quantify it within or below clouds, and the problem of insufficient sensitivity at low concentrations, in addition to retrieval errors. A future path forward can include utilizing colocated polarimeter and lidar instruments, ideally including high spectral resolution lidar capability at two wavelengths to maximize vertically resolved size distribution information content. In terms of Nd, a key problem is the lack of operational retrievals of this quantity, and the inaccuracy of the retrieval especially in broken-cloud regimes. As for the Nd – to – CCN sensitivity, key issues are the updraught distributions and the role of Nd sink processes, for which empirical assessments for specific cloud regimes are currently the best solutions. These considerations point to the conclusion that past studies using existing approaches have likely underestimated the true sensitivity and, thus, the radiative forcing due to the Twomey effect.

Twomey effect↗

DOE OSTI2020

Fast Dynamic Aperture Optimization with Reversal Integration

A fast method for dynamic aperture (DA) optimization of storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symme- try, a numerical forward integration di ers from its reversal. For chaotic trajectories, cumulative round-o errors are scaled, which results in an exponential growth in the di erence. The exponential e ect, intrinsically associated with the Lyapunov exponent, is a generic indicator of chaos because it represents the sensitivity of chaotic motion to an initial condition. A chaos indicator of the charged particle motion is then obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. \backward integrations." The indicator was con rmed to be ob- servable through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. The DA of the National Synchrotron Light Source II storage ring, and another test di raction-limited light source ring, were optimized using this method for the purpose of demonstration.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Yesterday’s extremes, today’s new normal: flood risk in the Kathmandu Valley, Nepal

Unplanned urban growth has left many cities increasingly vulnerable to extreme rainfall events, particularly in regions with inadequate drainage infrastructures and development encroaching on natural floodplains. Here, in this perspective paper, we examine the September 2024 floods that struck Central Nepal, triggered by a persistent low-pressure system and enhanced by converging moisture flows from the Arabian Sea and the Bay of Bengal which led to widespread catastrophic damage. In the Kathmandu Valley, floodwaters expanded to more than 2.5 times the bankfull water extent, causing significant damage to housing, transportation network, and critical infrastructure, displacing thousands of residents, and severely disrupting urban services. This event highlights the urgent need for improved flood management strategies that integrate both structural and non-structural measures into the infrastructure development. While early warning systems provided critical lead time, challenges remain in reducing forecasting uncertainties and improving communication across government agencies and with local communities. A forward-looking approach is essential, including probabilistic flood forecasting systems, sustainable floodplain management, risk-sensitive land use planning, climate- and disaster- resilient infrastructure development, and the integration of nature-based solutions like urban green and blue spaces to mitigate flood impacts. By involving local communities in planning and preparedness efforts, particularly through citizen science initiatives, and engagement with underserved and disadvantaged communities, Nepal can better adapt to the growing risks posed by extreme rainfall and urban flooding and enhance long-term disaster resilience in rapidly urbanizing areas like Kathmandu Valley.

Kathmandu Valley↗

DOE OSTI2026

First Measurement of Sub-GeV nu_mu Charged-Current Coherent Pion Production on Argon in MicroBooNE

Coherent pion production, characterized by a neutrino interacting with an entire nucleus without breaking it apart, results in a forward-going muon, pion, and a low-momentum recoil nucleus. This process provides a sensitive probe of neutrino-nucleus interactions and offers a potential standard candle for neutrino-flux normalization in neutrino-oscillation experiments. We present the first measurement of the flux-averaged charged-current coherent pion production cross section on argon nucleus using the MicroBooNE liquid argon time projection chamber. The analysis employs particle identification together with a data-driven background parameterization to isolate the coherent signal. This measurement uses the full MicroBooNE dataset collected from the Fermilab Booster Neutrino Beam, corresponding to an exposure of 1.26E10^21 protons on target and an average neutrino energy of approximately 0.8 GeV. The result provides the first constraint on charged-current coherent pion production on argon nucleus at sub-GeV energies and supplies important input for improving neutrino interaction modeling in current and future experiments such as DUNE.

Hussain, Adil [Kansas State U.] (ORCID:00000001621↗

NASA NTRS1978

An analysis of the gust-induced overspeed trends of helicopter rotors

Equations for analyzing the potential gust-induced overspeed tendency of helicopter rotors are presented. A parametric analysis was also carried out to illustrate the sensitivity of rotor angular acceleration to changes in rotor lift, propulsive force, tip speed, and forward velocity.

Jenkins, J. L., Jr.↗

NASA NTRS1982

Development of a helicopter rotor/propulsion system dynamics analysis

A time-domain analysis of coupled engine/drive train/rotor dynamics of a twin-engine, single main rotor helicopter model has been performed. The analysis incorporates an existing helicopter model with nonlinear simulations of a helicopter turboshaft engine and its fuel controller. System dynamic behavior is studied using the resulting simulation which included representations for the two engines and their fuel controllers, drive system, main rotor, tail rotor, and aircraft rigid body motions. Time histories of engine and rotor RPM response to pilot control inputs are studied for a baseline rotor and propulsion system model. Sensitivity of rotor RPM droop to fuel controller gain changes and collective input feed-forward gain changes are studied. Torque-load-sharing between the two engines is investigated by making changes in the fuel controller feedback paths. A linear engine model is derived from the nonlinear engine simulation and used in the coupled system analysis. This four-state linear engine model is then reduced to a three-state model. The effect of this simplification on coupled system behavior is shown.

Warmbrodt, W.↗

NASA NTRS2003

"Smoke": Characterization Of Smoke Particulate For Spacecraft Fire Detection

The "Smoke" experiment is a flight definition investigation that seeks to increase our understanding of spacecraft fire detection through measurements of particulate size distributions of preignition smokes from typical spacecraft materials. Owing to the catastrophic risk posed by even a very small fire in a spacecraft, the design goal for spacecraft fire detection is to detect the fire as quickly as possible, preferably in the preignition phase before a real flaming fire has developed. Consequently the target smoke for detection is typically not soot (typical of established hydrocarbon fires) but instead, pyrolysis products, and recondensed polymer particles. At the same time, false alarms are extremely costly as the crew and the ground team must respond quickly to every alarm. The U.S. Space Shuttle (STS: Space Transportation System) and the International Space Station (ISS) both use smoke detection as the primary means of fire detection. These two systems were designed in the absence of any data concerning low-gravity smoke particle (and background dust) size distributions. The STS system uses an ionization detector coupled with a sampling pump and the ISS system is a forward light scattering detector operating in the near IR. These two systems have significantly different sensitivities with the ionization detector being most sensitive (on a mass concentration basis) to smaller particulate and the light scattering detector being most sensitive to particulate that is larger than 1 micron. Since any smoke detection system has inherent size sensitivity characteristics, proper design of future smoke detection systems will require an understanding of the background and alarm particle size distributions that can be expected in a space environment.

Urban, David L.↗

NASA NTRS2018

Realistic Covariance Generation for the GPM Spacecraft

We present several different methods for generating realistic predictive covariance, including Monte-Carlo simulations and more direct linear methods which require the addition of process noise. The Monte-Carlo simulation starts with an epoch uncertainty sample basis and propagates each trial to a time of interest in the future. The variance-covariance of the state elements as well as other higher order sample statistics can be readily computed from the propagated sample. While this method preserves the nonlinear effects on the propagated uncertainty, it is computationally intensive as a statistically significant sample size must be considered in the propagation process. Moreover, if the epoch covariance is optimistic, this can result in an underestimation of the prediction error. Another method is to propagate a state sensitivity matrix simultaneously with the satellite state, which allows the epoch covariances to be propagated forward in a linear fashion. This method does not preserve the non-linearity of the satellite state uncertainty but is much less computationally intensive. The propagated state covariance is the scaled to represent the realistic level of GPM state uncertainty via a "e-tuning process." The tuning process generates an inflation factor based on the observed error statistics of the predictive satellite trajectories when compared to the definitive ones. Difference tuning strategies are considered and compared via Goodness-of-Fit method testing for the Gaussian properties of the scaled covariance.

prediction error↗

NASA NTRS1992

Automatic differentiation of advanced CFD codes for multidisciplinary design

Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown that sensitivity derivatives can be obtained accurately and efficiently using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier-Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that by using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3-D CFD code in a relatively short time, e.g., O(man-week) not O(man-year).

Bischof, C.↗

DOE OSTI2024

Bayesian Framework for Bioburden Density Estimation in Planetary Protection

To comply with the international planetary protection policy set forth by the Committee on Space Research and NASA Agency level requirements, spacecraft destined to biologically sensitive planetary bodies have to minimize terrestrial biological contamination. Analysis, testing and inspection are the standard forward verification activities that are used to demonstrate compliance with the biological contamination requirements. For testing of spacecraft surface areas, a swab or wipe sample is collected from surfaces prior to last access and subsequently processed in the lab using NASA Approved Planetary Protection Methods for Culture Based Assays. Raw data resulting from this assay is then statistically treated employing a mathematical paradigm stemming from the 1970’s Viking Lander Project to generate the bioburden density and total microbial bioburden present. This standard approach arbitrarily accounts for error and provides an upper conservative bound as it reports the maximum number of spores estimated to be present on flight hardware surfaces. A bioburden density estimate factors in the following variables: the observed bioburden count, representative volume processed, sampling efficiencies. Notably, to account for error in the approach, a 0 observed count is arbitrarily changed to a count of 1 for each hardware grouping. The data generated by spacecraft bioburden verification campaigns in the past have resulted in <80% of wipes and <90% of swabs containing a bioburden count of 0. As such, having a robust and well documented statistical approach for dealing with the probability of low incident rates is necessary to be able to estimate spacecraft bioburden. Being able to statistically describe the bioburden distribution and associated confidence level is a gamechanger for the development of bioburden allocations during mission design and will allow for tighter management of risk throughout spacecraft build. Thus, Empirical Bayes statistical approach was evaluated to estimate the microbial bioburden on spacecraft to mitigate the aforementioned mathematical concerns and provide a probabilistic bioburden distribution of the flight hardware surface. For application of this approach to performing bioburden calculations, a range of non-informative prior assumptions on hardware surfaces are explored for Bayesian analyses while informative priors using posterior distributions from prior assays are utilized for Empirical Bayes analyses. Several non-informative priors are currently under investigation to assess fitness including use of these priors to serve as a foundation to build off of NASA specification values or a basis of risk to account for unknowns during the integration and testing process. Informative priors under consideration are generated using sampled bioburden values from hardware originating within like processing environments (e.g. vendor cleaning process or similar assembly process), temporal spacecraft status events as a prediction for hardware cleanliness of future samples, and heritage system bioburden actuals to predict allocation for subsequent missions. Informative priors and probabilistic bioburden distributions are then validated using data sets from the Mars Exploration Rover, Mars Science Laboratory, and InSight missions. Using Empirical Bayes approach to generate a probabilistic bioburden distribution as demonstrated through mission use cases provides a valid approach for use in the end-to-end requirements verification process.

97 - MATHEMATICS AND COMPUTING↗

NASA NTRS2011

TPSAS-NF1676L-12839-DND

Hyper-spectral remote sensors, such as Atmospheric Infrared Sounder (AIRS) and Infrared Atmospheric Sounding Interferometer (IASI), provides top of atmospheric radiances with high information content on atmospheric and surface properties. In order to analyze these data in real time, fast, and accurate forward and inverse models are needed. We will describe a method of simultaneously retrieving atmospheric temperature, moisture, cloud, and surface properties using all available spectral channels without sacrificing computational speed. The method has been successfully applied to AIRS, IASI, and NAST-I data. By applying the same method to the current and future hyperspectral sounders, the derived products will have less errors due to biases introduced by different retrieval methods. We have compared the retrieved products to radiosondes, aircraft measurements and other validation dataset. Simulations have done to quantify retrieval errors associated with the retrievals. The essence of the method is to convert channel radiance spectra into super-channels by an Empirical Orthogonal Function (EOF) transformation. A Principal Component-based Radiative Transfer Model (PCRTM) developed at NASA Langley Research Center is used to calculate both the super-channel magnitudes and derivatives with respect to atmospheric profiles and other properties. The inversion algorithm is based on a non-linear Levenberg-Marquardt method with climatology covariance matrices and a priori information as constraints. One advantage of this approach is that it uses all information content from the hyper-spectral data so that the retrieval is less sensitive to instrument noise and eliminates the need for selecting a subset of the channels. The PCRTM forward model has also been used to performance end-to-end sensor performance simulations of the Climate Absolute Radiance and Refractivity Observatory (CLARREO).

Xu Liu↗

DOE OSTI2020

Forward Modeling the Orbits of Companions to Pulsating Stars from Their Light Travel Time Variations

Mutual gravitation between a pulsating star and an orbital companion leads to a time-dependent variation in path length for starlight traveling to Earth. These variations can be used for coherently pulsating stars, such as the δ Scuti variables, to constrain the masses and orbits of their companions. Observing these variations for δ Scuti stars has previously relied on subdividing the light curve and measuring the average pulsation phase in equally sized subdivisions, which leads to undersampling near periapsis. We introduce a new approach that simultaneously forward models each sample in the light curve and show that this method improves upon current sensitivity limits—especially in the case of highly eccentric and short-period binaries. We find that this approach is sensitive enough to observe Jupiter mass planets around δ Scuti stars under ideal conditions, and use gravity-mode pulsations in the subdwarf B star KIC 7668647 to detect its companion without radial velocity data. We further provide robust detection limits as a function of the signal-to-noise ratio of the pulsation mode and determine that the minimum detectable light travel time amplitude for a typical Kepler δ Scuti is around 2 s. This new method significantly enhances the application of light travel time variations to detecting short-period binaries with pulsating components, and pulsating A-type exoplanet host stars, especially as a tool for eliminating false positives.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2015

A Comparison of Three Algorithms for Orion Drogue Parachute Release

The Orion Multi-Purpose Crew Vehicle is susceptible to ipping apex forward between drogue parachute release and main parachute in ation. A smart drogue release algorithm is required to select a drogue release condition that will not result in an apex forward main parachute deployment. The baseline algorithm is simple and elegant, but does not perform as well as desired in drogue failure cases. A simple modi cation to the baseline algorithm can improve performance, but can also sometimes fail to identify a good release condition. A new algorithm employing simpli ed rotational dynamics and a numeric predictor to minimize a rotational energy metric is proposed. A Monte Carlo analysis of a drogue failure scenario is used to compare the performance of the algorithms. The numeric predictor prevents more of the cases from ipping apex forward, and also results in an improvement in the capsule attitude at main bag extraction. The sensitivity of the numeric predictor to aerodynamic dispersions, errors in the navigated state, and execution rate is investigated, showing little degradation in performance.

Matz, Daniel A.↗

DOE OSTI2020

Predicting Biological Cleanliness: An Empirical Bayes Approach for Spacecraft Bioburden Accounting

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Recoil imaging for dark matter, neutrinos, and physics beyond the Standard Model

Recoil imaging entails the detection of spatially resolved ionization tracks generated by particle interactions. This is a highly sought-after capability in many classes of detector, with broad applications across particle and astroparticle physics. However, at low energies, where ionization signatures are small in size, recoil imaging only seems to be a practical goal for micro-pattern gas detectors. This white paper outlines the physics case for recoil imaging, and puts forward a decadal plan to advance towards the directional detection of low-energy recoils with sensitivity and resolution close to fundamental performance limits. The science case covered includes: the discovery of dark matter into the neutrino fog, directional detection of sub-MeV solar neutrinos, the precision study of coherent-elastic neutrino-nucleus scattering, the detection of solar axions, the measurement of the Migdal effect, X-ray polarimetry, and several other applied physics goals. We also outline the R&D programs necessary to test concepts that are crucial to advance detector performance towards their fundamental limit: single primary electron sensitivity with full 3D spatial resolution at the $\sim$100 micron-scale. These advancements include: the use of negative ion drift, electron counting with high-definition electronic readout, time projection chambers with optical readout, and the possibility for nuclear recoil tracking in high-density gases such as argon. We also discuss the readout and electronics systems needed to scale-up such detectors to the ton-scale and beyond.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Measurement of the weak mixing angle at 13 TeV with the CMS detector

This document summarizes work in experimental high-energy physics completed as part of the author’s doctoral studies. The central piece of this thesis is the precision measurement of the effective weak mixing angle at the CMS detector. The effective weak mixing angle is a key parameter in the standard model of particle physics and is sensitive to radiative corrections from beyond standard model physics. The measurement is made by using the forward backwards asymmetry of Drell-Yan dilepton pairs. The data is from proton proton collisions at √s =13 TeV collected in Run 2 of the LHC from 2016-2018. The measurement uses dimuon and dielectron pairs and includes a special class of forward electrons developed for this measurement that do not rely on the tracking subdetector. Using the CT18Z parton distribution function set the weak mixing angle was determined to be [equation did not render] The largest contribution to the uncertainty comes from the parton distribution functions.

Taus, Rhys [Rochester U.]↗