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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Dissecting protein tyrosine phosphatase signaling by engineered chemogenetic control of its activity

Protein tyrosine phosphatases (PTPases) are critical mediators of dynamic cell signaling. A tool capable of identifying transient signaling events downstream of PTPases is essential to understand phosphatase function on a physiological time scale. We report a broadly applicable protein engineering method for allosteric regulation of PTPases. This method enables dissection of transient events and reconstruction of individual signaling pathways. Implementation of this approach for Shp2 phosphatase revealed parallel MAPK and ROCK II dependent pathways downstream of Shp2, mediating transient cell spreading and migration. Furthermore, we show that the N-SH2 domain of Shp2 regulates MAPK-independent, ROCK II-dependent cell migration. Engineered targeting of Shp2 activity to different protein complexes revealed that Shp2-FAK signaling induces cell spreading whereas Shp2-Gab1 or Shp2-Gab2 mediates cell migration. We identified specific transient morphodynamic processes induced by Shp2 and determined the role of individual signaling pathways downstream of Shp2 in regulating these events. Broad application of this approach is demonstrated by regulating PTP1B and PTP-PEST phosphatases.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Muon-induced fission as a probe of the underlying dynamics in nuclear fission

Muon-induced fission could be utilized as a probe to study the underlying dynamics of nuclear fission. Here, the probability of muon attachment to the light asymmetric fission fragment is sensitive to fission dynamics, such as the timescale and friction of the fission event, charge asymmetry, and possibly the shape of the fission fragments. We focus on muonic atoms that are formed with actinide nuclei. A relativistic approach is employed, solving the Dirac equation for the muonic wave function in the presence of a time-dependent electromagnetic field generated by the fissioning nucleus. Computations are carried out on a three-dimensional Cartesian lattice with no symmetry assumptions. The results show a strong dependence of the attachment probability on the fission charge asymmetry and a more modest dependence on friction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Emergence of pseudoresonance in high-intensity resonant inelastic x-ray scattering

We report resonant inelastic x-ray scattering (RIXS) spectra of neon atoms interacting with intense x-ray pulses generated using an x-ray free-electron laser (XFEL). We find that an unexpected peak emerges near the 𝐾⁢𝛼 line of Ne, which does not coincide with any physical resonances of neon ions. We perform theoretical calculations based on a quantum-state-resolved rate-equation approach with x-ray-induced processes including possible resonant excitations. Our dynamics simulations demonstrate that a sequence of multiple resonant photoabsorption events are involved and the interplay of those multiple resonances in combination with the relatively large spectral bandwidth of XFEL radiation leads to the emergent resonance-like structure at a position where no resonances exist. Our finding offers critical guidance for future applications of high-intensity RIXS at XFEL facilities.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Nonlinear dynamics, avalanches, and noise for driven Wigner crystals

Here we consider the driven dynamics of Wigner crystals interacting with random disorder. Using numerical simulations, we find a rich variety of transport phenomena as a function of charge density, drive, and pinning strength. For weak pinning, the system forms a defect-free crystal that depins elastically. When the pinning is stronger, a pinned glass phase appears that depins into a filamentary flow state, transitions at higher drives into a disordered flow phase, and finally forms a moving smectic. Within the filamentary flow phase, the conduction curves can show switching dynamics as well as negative differential conductivity in which switching events cause some flow channels to be blocked. The velocity noise in the filamentary flow regime exhibits narrow band characteristics due to the one-dimensional nature of the motion, while the moving smectic has narrow band velocity noise with a washboard frequency. In the disordered flow state, the noise power reaches a peak value and the noise has a 1/$\mathcal{f}$ character. Our transport results are consistent with recent experimental transport studies in systems where Wigner crystal states are believed to be occurring. Below the conduction threshold, we find that avalanches with a power-law size distribution appear when there are sudden local rearrangements of charges from one pinned configuration to another.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Detectability of standing accretion shock instabilities activity in supernova neutrino signals

We introduce a novel methodology for establishing the presence of standing accretion shock instabilities (SASI) in the dynamics of a core collapse supernova from the observed neutrino event rate at water- or ice- based neutrino detectors. The methodology uses a likelihood ratio in the frequency domain as a test- statistics; it is also employed to assess the potential to estimate the frequency and the amplitude of the SASI modulations of the neutrino signal. The parameter estimation errors are consistent with the minimum possible errors as evaluated from the inverse of the Fisher information matrix, and close to the theoretical minimum for the SASI amplitude. Using results from a core-collapse simulation of a 15 solar-mass star by Kuroda et al. [Astrophys. J. 851, 62 (2017).] as a test bed for the method, we find that SASI can be identified with high confidence for a distance to the supernova of up to ~6 kpc for IceCube and up to ~3 kpc for a 0.4 Mt mass water Cherenkov detector. This methodology will aid the investigation of a future galactic supernova.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Save or spend? Diverging water‐use strategies of grasses and encroaching clonal shrubs

Abstract Shrub encroachment is one of the primary threats to mesic grasslands around the world. This dramatic shift in plant cover has the potential to alter ecosystem‐scale water budgets and responses to novel rainfall regimes. Understanding divergent water‐use strategies among encroaching shrubs and the grasses they replace is critical for predicting shifts in ecosystem‐scale water dynamics as a result of shrub encroachment, particularly if drought events become more frequent and/or severe in the future. In this study, we assessed how water‐use traits of a rapidly encroaching clonal shrub (Cornus drummondii) and a dominant C 4 grass (Andropogon gerardii) impact responses to changes in water availability in tallgrass prairie. We assessed intra‐annual change in depth of water uptake, turgor loss point and stomatal regulation in each species. Sampling took place at Konza Prairie Biological Station (northeastern KS, USA) during the 2021 and 2022 growing seasons. Cornus drummondiishifted from shallow to deep soil water sources across the 2021 and 2022 growing seasons. This plasticity in depth of water uptake facilitated a ‘wasteful’ water‐use strategy inC. drummondii, where stomatal conductance and transpiration rates continued to increase even when no further gain in photosynthetic rate occurred.A. gerardiiphotosynthetic rates and stomatal conductance were more variable through time and were more responsive to changes in leaf water potential thanC. drummondii. However, intra‐annual adjustment of turgor loss point was more pronounced inC. drummondii(Δπ TLP = −0.48 MPa ± 0.15 SD) than inA. gerardii(Δπ TLP = −0.29 MPa ± 0.19 SD). Synthesis. These results suggest thatC. drummondiiis highly resilient to changes in water availability in surface soils and will likely remain unaffected by future droughts unless they are severe enough to reduce the availability of deep soil water. Given that clonal shrubs are key invaders of grasslands world‐wide, increased leaf‐level water loss is expected to accelerate ecosystem‐level drying as clonal shrub encroachment proceeds in mesic grasslands.

Environmental Sciences & Ecology↗
DOE OSTI2020

Learning reference governor for cycle-to-cycle combustion control with misfire avoidance in spark-ignition engines at high exhaust gas recirculation–diluted conditions

Cycle-to-cycle feedback control is employed to achieve optimal combustion phasing while maintaining high levels of exhaust gas recirculation by adjusting the spark advance and the exhaust gas recirculation valve position. The control development is based on a control-oriented model that captures the effects of throttle position, exhaust gas recirculation valve position, and spark timing on the combustion phasing. Under the assumption that in-cylinder pressure information is available, an adaptive extended Kalman filter approach is used to estimate the exhaust gas recirculation rate into the intake manifold based on combustion phasing measurements. The estimation algorithm is adaptive since the cycle-to-cycle combustion variability (output covariance) is not known a priori and changes with operating conditions. A linear quadratic regulator controller is designed to maintain optimal combustion phasing while maximizing exhaust gas recirculation levels during load transients coming from throttle tip-in and tip-out commands from the driver. During throttle tip-outs, however, a combination of a high exhaust gas recirculation rate and an overly advanced spark, product of the dynamic response of the system, generates a sequence of misfire events. In this work, an explicit reference governor is used as an add-on scheme to the closed-loop system in order to avoid the violation of the misfire limit. The reference governor is enhanced with model-free learning which enables it to avoid misfires after a learning phase. Experimental results are reported which illustrate the potential of the proposed control strategy for achieving an optimal combustion process during highly diluted conditions for improving fuel efficiency.

42 ENGINEERING↗
DOE OSTI2025

Ensemble Simulation Techniques and Fast Randomized Algorithms

The major goals of the project were to develop and analyze new ensemble simulation techniques, including trajectory stratification and preconditioned MCMC techniques, as well as develop fast numerical linear algebra techniques closely related to ensemble simulation ideas. The trajectory stratification techniques involve simulating in parallel short trajectory fragments of a Markov process confined to a specific region of space‐time and then patching together the statistics gathered to assemble estimates of very general dynamical properties. We have also developed this approach for rare event simulation and extended the techniques to applications requiring a more general framework (such as electronic structure calculations). The preconditioned MCMC techniques involve simulating multiple Markov chains in parallel and then using information from the ensemble to speed the mixing of each individual chain. The fast randomized linear algebra methods are motivated by the diffusion Monte Carlo technique, but are applicable to finding the dominant eigenvalue of (almost) general matrices. For most non‐negative matrices, the schemes result in an error (compared to the power method) that is constant in the dimension of the problem. For more general matrices, we see a very clear sublinear cost trend in computational tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Geophysical and Environmental Monitoring Data, Lower Watershed, Teller Road Mile Marker 27, Seward Peninsula, Alaska, 2017-2019

This data set contains geophysical and environmental monitoring data acquired between September 2017 and 2019 at the lower Teller watershed, Seward Peninsula, Alaska. Geophysical data comprises processed resistivity data, acquired daily between Spring and Fall of 2018 and 2019, and a baseline measurement of Fall 2017. The environmental monitoring data comprises depth resolved, distributed soil moisture and soil temperature data. These measurements were obtained used Decagon 5TE sensors placed at 0.1 m, 0.2 m , 0.3 m, and 0.4 m depth. In addition, temperature data at 0.5 m, 1.0 m, and 1.5 m were acquired using Hobo temperature sensors. Data were collected to improve our understanding of the hydrological response of discontinuous permafrost systems, in particular focusing on multi-annual dynamics and short term disturbances, such as snowmelt or precipitation events. The electrical resistivity tomography (ERT) monitoring data are included as processed resistivity models, with model cells x dimension equal to the distance along the profile, and model z dimension being elevation. The start and end point of the transect are (UTM Zone 3N): E 454881.66 m, N 7178949.45 m, and E 454772.60, N 7178885.81. Locations of the soil moisture and temperature sensors are provided in the data package. This dataset is discussed in detail in the Uhlemann, S. et al 2021 paper listed in the references. This dataset includes one *.pdf user guide and 315 *.csv data files included within four zipped files.The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research.The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska.Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Cyclic dynamics of misfires and partial burns in a dilute spark-ignition engine

Here, this study investigates the cyclic dynamics of cumulative heat release data past the edge of stability in a dilute spark-ignition engine. Emphasis is placed on analyzing the cyclic dynamics near the dilute limit where partial burns and misfires are frequent. These events are often followed by a higher-energy cycle due to the feed-forward mechanism present in the residual gases. These patterns are deterministic and increase the coefficient of variation to undesirable levels. Symbol sequence analysis was used to investigate the cyclic dynamics of these low–high patterns. The heat release was partitioned on an energy basis to give physical meaning to each partition and each sequence created when analyzing the symbol sequence results. This partitioning method provided insight into the differences in the dynamics when operating in the misfire or partial burn regime. These differences could impact the control method used.

42 ENGINEERING↗
DOE OSTI2022

IM3/HyperFACETS Thermodynamic Global Warming (TGW) Simulation Datasets

Publication For a thorough description of the methods, see the peer-reviewed paper: Jones, A.D., Rastogi, D., Vahmani, P. et al. Continental United States climate projections based on thermodynamic modification of historical weather. Sci Data 10, 664 (2023). https://doi.org/10.1038/s41597-023-02485-5 Overview The IM3 / HyperFACETS climate simulations provide 40-year historical (1980-2019) as well as four 80-year future simulations (2020-2099) over the U.S. The future simulations are split into near (2020-2059) and far future (2060-2099) segments. The future scenarios span a range of plausible changes in future climate (both Global Circulation Model (GCM) and Representative Concentration Pathways/Shared Socioeconomic Pathway (RCP/SSP) dimensions). The simulations provide climate variables with high spatiotemporal resolution (25 hourly variables and 207 3-hourly variables at 12 km2). The datasets are generated using dynamical downscaling with the WRF (Weather Research and Forecasting) model (version 4.2.1) and therefore preserve physical consistency across variables. WRF is a state-of-the-art, fully compressible, non-hydrostatic, mesoscale numerical weather prediction model. WRF is coupled with an urban canopy model (UCM), which resolves urban surfaces. The future scenarios were developed using a thermodynamic global warming approach where past events are replayed under a range of future warming conditions. These scenarios therefore provide a perspective on potential increases in extreme event intensity, geographic scope, and duration, with previously non-extreme conditions potentially crossing new thresholds to be considered extreme by today's standards. This approach is not intended to estimate future changes in extreme event frequency that might result from changes in large-scale atmospheric dynamics. This dataset has NOT been bias corrected. A bias corrected version of selected variables is under development and will be released here when available. Scenarios Files Data for each scenario is provided in weekly NetCDF files. 25 variables are available at hourly resolution, and 207 variables are available at three-hourly resolution. Spatial resolution is 12km and spans the conterminous United States (CONUS), including some areas of Canada and Mexico, resulting in a grid of 424 by 299 cells. The spatial projection is a Lambert Conformal Conic with the following proj-string: "+proj=lcc +lat_0=40.0000076293945 +lon_0=-97 +lat_1=30 +lat_2=45 +x_0=0 +y_0=0 +R=6370000 +units=m +no_defs". The available scenarios and simulation periods are listed below: historical | 1980 - 2019 rcp45cooler | 2020 - 2059 rcp45cooler | 2060 - 2099 rcp45hotter | 2020 - 2059 rcp45hotter | 2060 - 2099 rcp85cooler | 2020 - 2059 rcp85cooler | 2060 - 2099 rcp85hotter | 2020 - 2059 rcp85hotter | 2060 - 2099 * The first year (1979, 2019, and 2059) of data within each scenario represents a model warmup period and should not be used. These are located in the `spinup_files` directory. Historical year 2020 is considered an extra year of data beyond the simulation period and can be found in the `additional_files` directory. For information on specific variables and a more in-depth discussion of methodology, please refer to the data landing page at https://tgw-data.msdlive.org. Delta Warming Files The global and CONUS warming deltas for each scenario are provided in degrees Celsius annually and monthly. Restart Files Yearly restart files are provided for each scenario which can be used to restart the WRF model at a particular point in time. Spinup Files The first year of data within each simulation period represents a model warmup period and should not be used. The files are provided here for the sake of reproducibility. Additional Files Additional years of data are provided as an extension of the historic simulation.

Jones, Andrew D.↗
DOE OSTI2023

Off-policy deep reinforcement learning with automatic entropy adjustment for adaptive online grid emergency control

Electric overloading conditions and contingencies put modern power systems at risk of voltage collapse and blackouts. Load shedding is crucial to maintain voltage stability for grid emergency control. However, the rule- or model-based schemes rely on accurate dynamic system models and face considerable challenges in adapting to various operating conditions and uncertain event occurrences. Here, to address these issues, this paper proposes a novel deep reinforcement learning (DRL)-based voltage stability control algorithm with automatic entropy adjustment (AEA) for grid emergency control. Various dynamic network components for complex system operations are modeled to construct the DRL environment. An off-policy soft actor-critic architecture is developed to maximize the expected reward and policy entropy simultaneously. The AEA mechanism is proposed to facilitate the policy maximum entropy procedure, and the proposed method can automatically provide effective discrete and continuous actions against various fault scenarios. Our approach accomplishes high sampling efficiency, scalability, and auto-adaptivity of the control policies under high uncertainties. Comparative studies with the existing DRL-based control methods in IEEE benchmarks indicate salient performance improvement of the proposed method for dynamic system emergency control.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Investigating the Causes and Impacts of Convective Aggregation in a High Resolution Atmospheric GCM

Abstract A ∼50 km resolution atmospheric general circulation model (GCM) is used to investigate the impact of radiative interactions on spatial organization of convection, the model's mean state, and extreme precipitation events in the presence of realistic boundary conditions. Mechanism‐denial experiments are performed in which synoptic‐scale feedbacks between radiation and dynamics are suppressed by overwriting the model‐generated atmospheric radiative cooling rates with its monthly varying climatological values. When synoptic‐scale radiative interactions are disabled, the annual mean circulation and precipitation remain almost unchanged, however tropical convection becomes less aggregated, with an increase in cloud fraction and relative humidity in the free troposphere but a decrease in both variables in the boundary layer. Changes in cloud fraction and relative humidity in the boundary layer exhibit more sensitivity to the presence of radiative interactions than variations in the degree of aggregation. The less aggregated state is associated with a decrease in the frequency of extreme precipitation events, coincident with a decrease in the dynamical contribution to the magnitude of extreme precipitation. At regional scales, the spatial contrast in radiative cooling between dry and moist regions diminishes when radiative interactions are suppressed, reducing the upgradient transport of energy, degree of aggregation, and frequency of extreme precipitation events. However, the mean width of the tropical rain belt remains almost unaffected when radiative interactions are disabled. These results offer insights into how radiation‐circulation coupling affects the spatial organization of convection, distributions of clouds and humidity, and weather extremes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Parameter Reduction of Composite Load Model Using Active Subspace Method

Over the past decades, the increasing penetration of distributed energy resources (DERs) has dramatically changed the power load composition in the distribution networks. The traditional static and dynamic load models can hardly capture the dynamic behavior of modern loads especially for fault-induced delayed voltage recovery (FIDVR) events. Thus, a more comprehensive composite load model with combination of static load, different types of induction motors, single-phase A/C motor, electronic load and DERs has been proposed by Western Electricity Coordinating Council (WECC). However, due to the large number of parameters and model complexity, the WECC composite load model (WECC CMLD) raises new challenges to power system studies. To overcome these challenges, in this paper, a cutting-edge parameter reduction (PR) approach for WECC CMLD based on active subspace method (ASM) is proposed. Firstly, the WECC CMLD is parameterized in a discrete-time manner for the application of the proposed method. Then, parameter sensitivities are calculated by discovering the active subspace, which is a lower-dimensional linear subspace of the parameter space of WECC CMLD in which the dynamic response is most sensitive. The interdependency among parameters can be taken into consideration by our approach. Finally, the numerical experiments validate the effectiveness and advantages of the proposed approach for WECC CMLD model.

active subspace↗
DOE OSTI2021

Event-modeled Risk Assessment Using Linked Diagrams

Event Modeling Risk Assessment using Linked Diagrams (EMRALD) is a software tool developed at INL for researching the capabilities of dynamic PRA (Probabilistic Risk Assessment). In order to promote the effective use of dynamic PRA by the general community, EMRALD focuses on the following key aspects: Simplifying the modeling process by providing a structure that corresponds to traditional PRA modeling methods Providing a user interface (UI) that makes it easy for the user to model and visualize complex interactions Allowing the user to couple with other analysis applications such as physics based simulations. This includes one-way communication for most applications and two-way loose coupling for customizable applications Providing the sequence and timing of events that lead to the specified outcomes when calculating results Traditional aspects of components with basic events, fault trees, and event trees are all captured in a dynamic framework of state diagrams, which are displayed.

Prescott, SteveR↗
DOE OSTI2025

Evaluating ecosystem water use efficiency and recovery dynamics during flash droughts: insights from observations and model simulations

Flash droughts (FD), rapidly emerging in a warming future, disrupt ecosystems, agriculture, and water security. Ecosystem water use efficiency (WUE), the ratio of gross primary production (GPP) to actual evapotranspiration (AET), balances carbon assimilation and water loss. FD rapidly disrupts this balance, making WUE critical for assessing plant stress and recovery. Here, this study investigates the dynamics of landscape-scale WUE, and the components of GPP and AET under FD utilizing both observed data from the Missouri Ozark AmeriFlux site (US-MOz) and version 2 of the U.S. Department of Energy’s Earth, Energy, Exascale System Model (E3SM) Land Model (ELMv2). Observations and simulations reveal GPP as dominant for WUE during earlier FD events (2005, 2007, 2012), shifting to AET in recent events (2014, 2018). This agreement indicates that the ELM can capture the shifting dynamics of GPP and AET in regulating WUE under FD conditions. However, the ELM systematically underestimates both GPP and AET and does so in a manner that does not preserve their ratio. As a result, WUE is also underestimated, suggesting that GPP is more strongly underestimated than AET. Furthermore, the ELM also underestimates the speed of GPP recovery, producing an artificially prolonged GPP recovery time following FD events. Observed environmental drivers such as vapor pressure deficit (VPD), soil moisture (SM), and predawn leaf water potential (PLWP) effectively predict WUE, but ELM primarily highlights SM, underestimating VPD’s role. This study demonstrates that relying solely on soil moisture fails to capture the rapid hydraulic recovery observed in PLWP, underscoring the necessity of integrating plant hydraulics into land surface models to improve flash drought predictability.

Evapotranspiration↗
DOE OSTI2022

Detecting hidden transient events in noisy nonlinear time-series

The information impulse function (IIF), running Variance, and local Hölder Exponent are three conceptually different time-series evaluation techniques. These techniques examine time-series for local changes in information content, statistical variation, and point-wise smoothness, respectively. Using simulated data emulating a randomly excited nonlinear dynamical system, this study interrogates the utility of each method to correctly differentiate a transient event from the background while simultaneously locating it in time. Computational experiments are designed and conducted to evaluate the efficacy of each technique by varying pulse size, time location, and noise level in time-series. Our findings reveal that, in most cases, the first instance of a transient event is more easily observed with the information-based approach of IIF than with the Variance and local Hölder Exponent methods. While our study highlights the unique strengths of each technique, the results suggest that very robust and reliable event detection for nonlinear systems producing noisy time-series data can be obtained by incorporating the IIF into the analysis.

42 ENGINEERING↗
DOE OSTI2020

Probing nuclear effects with neutrino-induced charged-current neutral pion production

We study neutrino-induced charged-current (CC) $\pi^0$ production on carbon nuclei using events with fully imaged final-state proton-$\pi^0$ systems. Novel use of final-state correlations based on transverse kinematic imbalance enable the first measurements of the struck nucleon's Fermi motion, of the intranuclear momentum transfer (IMT) dynamics, and of the final-state hadronic momentum configuration in neutrino pion production. Event distributions are presented for i) the momenta of neutrino-struck neutrons below the Fermi surface, ii) the direction of missing transverse momentum characterizing the strength of IMT, and iii) proton-pion momentum imbalance with respect to the lepton scattering plane. The observed Fermi motion and IMT strength are compared to the previous MINERvA measurement of neutrino CC quasielastic-like production. The measured shapes and absolute rates of these distributions, as well as the cross-section asymmetries show tensions with predictions from current neutrino generator models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗