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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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531 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Unveiling field-transverse spin anisotropy in the spin liquid candidate α-RuCl3 via spin Hall magnetoresistance

α-RuCl3 has emerged as a possible candidate for a quantum spin liquid (QSL) that promises exotic quasiparticles relevant for fault-tolerant quantum computation. Here, we report spin-sensitive transport measurements using a proximal spin Hall metal, platinum (Pt), to probe magnetic moments in the insulator α-RuCl3. We observe spin Hall magnetoresistance (SMR), where both the transverse and longitudinal resistivities exhibit angular oscillations between the in-plane magnetic field and the current, driven by the interplay between the spin Hall effect in Pt and local magnetic moments in α-RuCl3. These oscillations occur from 1.5 to 18 T, covering the zigzag antiferromagnetic, putative QSL, and supposedly partially field-polarized phases. The phase of the SMR oscillations suggests that the local moments, whether static or fluctuating, develop spin anisotropy with a quantization axis in-plane and largely transverse to the magnetic field across all fields from 1.5 to 18 T. Temperature dependence indicates that the spin anisotropy operates at an energy scale similar to that of the reported QSL signatures in α-RuCl3.

Idzuchi, Hiroshi [Tohoku University, Japan]↗
DOE OSTI2024

Cation valency in water-in-salt electrolytes alters the short- and long-range structure of the electrical double layer

Highly concentrated aqueous electrolytes (termed water-in-salt electrolytes, WiSEs) at solid-liquid interfaces are ubiquitous in myriad applications including biological signaling, electrosynthesis, and energy storage. This interface, known as the electrical double layer (EDL), has a different structure in WiSEs than in dilute electrolytes. Here, we investigate how divalent salts [zinc bis(trifluoromethylsulfonyl)imide, Zn(TFSI) 2 ], as well as mixtures of mono- and divalent salts [lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) mixed with Zn(TFSI) 2 ], affect the short- and long-range structure of the EDL under confinement using a multimodal combination of scattering, spectroscopy, and surface forces measurements. Raman spectroscopy of bulk electrolytes suggests that the cation is closely associated with the anion regardless of valency. Wide-angle X-ray scattering reveals that all bulk electrolytes form ion clusters; however, the clusters are suppressed with increasing concentration of the divalent ion. To probe the EDL under confinement, we use a Surface Forces Apparatus and demonstrate that the thickness of the adsorbed layer of ions at the interface grows with increasing divalent ion concentration. Multiple interfacial layers form following this adlayer; their thicknesses appear dependent on anion size, rather than cation. Importantly, all electrolytes exhibit very long electrostatic decay lengths that are insensitive to valency. It is likely that in the WiSE regime, electrostatic screening is mediated by the formation of ion clusters rather than individual well-solvated ions. This work contributes to understanding the structure and charge-neutralization mechanism in this class of electrolytes and the interfacial behavior of mixed-electrolyte systems encountered in electrochemistry and biology.

Science & Technology - Other Topics↗
DOE OSTI2024

Mechanochemically responsive polymer enables shockwave visualization

Abstract Understanding the physical and chemical response of materials to impulsive deformation is crucial for applications ranging from soft robotic locomotion to space exploration to seismology. However, investigating material properties at extreme strain rates remains challenging due to temporal and spatial resolution limitations. Combining high-strain-rate testing with mechanochemistry encodes the molecular-level deformation within the material itself, thus enabling the direct quantification of the material response. Here, we demonstrate a mechanophore-functionalized block copolymer that self-reports energy dissipation mechanisms, such as bond rupture and acoustic wave dissipation, in response to high-strain-rate impacts. A microprojectile accelerated towards the polymer permanently deforms the material at a shallow depth. At intersonic velocities, the polymer reports significant subsurface energy absorption due to shockwave attenuation, a mechanism traditionally considered negligible compared to plasticity and not well explored in polymers. The acoustic wave velocity of the material is directly recovered from the mechanochemically-activated subsurface volume recorded in the material, which is validated by simulations, theory, and acoustic measurements. This integration of mechanochemistry with microballistic testing enables characterization of high-strain-rate mechanical properties and elucidates important insights applicable to nanomaterials, particle-reinforced composites, and biocompatible polymers.

Science & Technology - Other Topics↗
DOE OSTI2024

Making Plasticized Polymer Electrolytes Stable Against Sodium Metal for High‐Energy Solid‐State Sodium Batteries

Solid polymer electrolytes based on plastic crystals are promising for solid-state sodium metal (Na 0 ) batteries, yet their practicality has been hindered by the notorious Na 0 -electrolyte interface instability issue, the underlying cause of which remains poorly understood. Here, in this study, by leveraging a model plasticized polymer electrolyte based on conventional succinonitrile plastic crystals, we uncover its failure origin in Na 0 batteries is associated with the formation of a thick and non-uniform solid electrolyte interphase (SEI) and whiskery Na 0 nucleation/growth. Furthermore, we design a new additive-embedded plasticized polymer electrolyte to manipulate the Na 0 deposition and SEI formulation. For the first time, we demonstrate that introducing fluoroethylene carbonate (FEC) additive into the succinonitrile-plasticized polymer electrolyte can effectively protect Na 0 against interfacial corrosion by facilitating the growth of dome-like Na 0 with thin, amorphous, and fluorine-rich SEIs, thus enabling significantly improved performances of Na//Na symmetric cells (1,800 h at 0.5 mA cm −2 ) and Na//Na 3 V 2 (PO 4 ) 3 full cells (93.0 % capacity retention after 1,200 cycles at 1 C rate in coin cells and 93.1 % capacity retention after 250 cycles at C/3 in pouch cells at room temperature). Our work provides valuable insights into the interfacial failure of plasticized polymer electrolytes and offers a promising solution to resolving the interfacial instability issue.

25 ENERGY STORAGE↗
DOE OSTI2026

Microstructure-dependent particulate populations in ODS steels revealed by single-particle ICP-TOF-MS

In this work, we evaluated the ability of single-particle inductively coupled plasma time-of-flight mass spectrometry (SP-ICP-TOF-MS) to characterize particulates generated from 300 series stainless steels and oxide dispersion–strengthened (ODS) steels. Particulates were produced using two different rotary tools (cutting disk and grinding bit) to assess the influence of particle generation on effluent particulates. Across all materials and preparation techniques, SP-ICP-TOF-MS detected a substantial population of particles containing the expected constituent elements, with average compositions closely matching the nominal alloy values. A secondary population of Y-bearing particles was evident in ODS steels; their formation is strongly favored in particulates generated using the grinding bit. Specifically, in PM2000, Y-bearing particles were predominantly colocated with Al, whereas in 14YWT, Y-bearing particles were less frequently Fe-free but showed stronger colocation with Ti. These trends are consistent with the known microstructural differences between Y–Al–O oxide particles in PM2000 and finer Y–Ti–O nanoclusters in 14YWT. Together, these results demonstrate that SP-ICP-TOF-MS can resolve distinct particulate populations in complex, multicomponent steels at the femtogram mass scale, enabling particle-resolved insight into microstructure-driven phase separation and preparation-dependent particle generation.

Brubaker, Zach E. [Oak Ridge National Laboratory (↗
DOE OSTI2025

Active Fluids Form System-Spanning Filamentary Networks

Recent experimental realizations of liquid-liquid phase separation of active liquid crystals have offered an insight into the interaction between phase separation, ubiquitous in soft matter and biology, and chaotic active flows. Here, in this Letter, we use continuum theory to examine phase separation of an active liquid crystal and a passive fluid and report two new results. First, we provide an analytical derivation of the activity-induced suppression of the phase boundary of the coexistence region—a result first reported in simulations and experiments. We show that the shift in the critical point is a result of the balance between self-stirring active flows and phase-separating diffusive fluxes. Second, we show that this same balance is responsible for dramatically changing the morphology of the phase separated state, resulting in the emergence of a new mixed active phase consisting of a dynamical filamentous active network that invades the entire system area, trapping droplets of passive material. This structure exists even for very low volume fractions of active material. Our work provides an important step towards the goal of understanding how to use activity as a new handle for sculpting interfaces.

active nematics↗
DOE OSTI2026

Nanoscale Observation and Control of Quasiparticle Induced Magnetic Noise in a Superconducting Resonator

Superconducting circuits are arguably taking a leading role in driving the ongoing quantum technological revolution. A detailed knowledge of the microscopic fluctuating electromagnetic properties plays an important role in advancing the circuitry design, testing, and material integration of cutting-edge superconducting quantum electronics. Here, in this work, we report scanning nitrogen-vacancy (NV) quantum sensing of local magnetic noise environment of an on-chip superconducting resonator. We find that quasiparticle-induced fluctuating magnetic fields can drive NV spin relaxation, which shows a peak value around the superconducting transition point of niobium at the thermal equilibrium state. External microwave driving at the resonator mode frequency significantly increases the quasiparticle density, leading to enhancement of magnetic noise. We further perform optically detected magnetic resonance measurements to demonstrate quasiparticle magnetic noise mediated off-resonant dipole coupling between the NV center and niobium resonator. Our Letter reports experimental observation of the Hebel-Slichter peak signature by an external sensor outside of a superconductor. The presented study also highlights the advantages of quantum sensors in investigating miniaturized superconducting devices, providing insights into their future performance improvements.

Li, Senlei [Georgia Institute of Technology]↗
DOE OSTI2026

Requirements Description of VARPOW

This report presents the modeling and simulation capabilities of Argonne National Laboratory’s VARPOW code that is used in present reactor analysis activities. These capabilities will then be used to establish the set of VARPOW verification tasks necessary to verify VARPOW for usage on commercial projects. A similar approach was taken for the PERSENT, REBUS and DIF3D software packages.

Ramey, Kyle [Argonne National Laboratory (ANL), Ar↗
DOE OSTI2026

Interfacial Adhesion Mechanism of Anionic Polyelectrolyte Brushes Induced by Oppositely Charged Macromolecular Counterions

Abstract Polyelectrolyte brushes are widely used as model systems for investigating electrostatic interactions at soft interfaces and to achieve exceptional lubrication properties. Previous studies have primarily focused on their behavior in the presence of multivalent counterions, which induce brush collapse, ionic crosslinking, and pronounced changes in interfacial structures. However, interactions between polyelectrolyte brushes and oppositely charged macromolecular counterions, such as polycations, remain poorly understood. Here, we prepare well-defined polystyrene sulfonate (PSS) brushes fabricated via surface-initiated grafting and employ surface forces apparatus measurements to investigate their interactions with oppositely charged polycations. In contrast to multivalent ions, polycations do not induce noticeable brush collapse, but instead generate significant adhesion between symmetric PSS brush layers. This adhesion increases with both contact time and applied load, eventually reaching a steady plateau, indicating that the interaction is governed not simply by electrostatic screening but by the gradual formation of polycation-mediated bridging under confinement. Furthermore, the introduction of monovalent Na+ ions disrupts the adhesive interaction even at very low concentrations, suggesting that the bridging function of the adsorbed polycation is highly sensitive to competitive ionic screening. In comparison, measurements with trivalent counterions reveal the expected brush collapse behavior but minimal dependence of adhesion on contact time, highlighting a clear mechanistic distinction from the polymeric counterion case. Collectively, these results demonstrate that molecular size, configurational restriction, and confinement-induced rearrangement, rather than charge valency alone, govern the interaction behavior of macromolecular counterions at brush interfaces. This work provides new insight into the molecular origins of adhesion and the regulation of interfacial interactions in charged polymer brush systems.

Park, Jinwoo [Argonne National Laboratory , , , ,;↗
DOE OSTI2026

Observations of Offshore Low‐Level Jets Off the U.S. East Coast Reveal Systematic Biases in ERA5 and HRRR

Low-level jets (LLJs)—wind speed maxima typically occurring a few hundred meters above the surface—are common off the U.S. East Coast and influence many atmospheric processes with societal importance, including cloud formation, aviation safety, and search-and-rescue. However, their vertical structure and frequency remain poorly quantified due to limited offshore observations. This study presents new scanning Doppler LiDAR and infrared spectroradiometer data from the 2024 summer deployment of an offshore barge during the Wind Forecast Improvement Project 3. These coupled wind and temperature profiles provide unprecedented resolution to assess LLJ behavior and model performance. LLJs occurred in over 21% of observed profiles, with a weak diurnal preference for nighttime and early morning hours and maximum winds typically near 300 m. Both ERA5 and High-Resolution Rapid Refresh analysis underestimate jet wind speeds and misrepresent the boundary layer thermal structure. These results highlight persistent model biases and the critical need for high-resolution offshore observations.

17 WIND ENERGY↗
DOE OSTI2025

Grain boundary segregation and chemical ordering in CoCrFeMnNi multi-principal element alloy

Owing to their far-from-dilute compositions, multi-principal element alloys (MPEAs) can exhibit unique combinations of engineering properties. As nearly all MPEAs are polycrystalline aggregates, it is necessary to understand the interactions of various elemental species with grain boundaries (GBs). This is of particular importance in extreme environments, such as radiation and elevated temperatures, where such interactions have implications on the properties of MPEAs. Herein, we employ atomistic simulations to generate a series of [001] asymmetric tilt GBs in a model CoCrFeMnNi MPEA and quantify solute interactions and segregation to these boundaries. We employ the Warren-Cowley order parameters to investigate the interplay between GB segregation and chemical short-range order (SRO). At temperatures above 800 K, simulation results reveal the segregation of Cr and Mn to CoCrFeMnNi GBs and show weak dependence of boundary solute excess on GB geometry, at least for the boundaries explored in this work. At temperatures in the range of 673–800 K, formation of domains rich in Cr is observed at GBs in agreement with experimental observations. Quantitative analysis shows that solute excess of various alloying elements decreases rapidly with the increase in temperature in the range of 1000–1200 K. Furthermore, we show that GB regions exhibit SRO characteristics that are distinct from the bulk crystals, leading to spatial variations in SRO. In broad terms, our study highlights the need to account for GB interactions with alloying elements when designing advanced MPEAs with novel chemistries.

Wang, Yitao [Lehigh University, Bethlehem, PA (Uni↗
DOE OSTI2024

Resonant Metasurfaces with Van Der Waals Hyperbolic Nanoantennas and Extreme Light Confinement

This work reports on a metasurface based on optical nanoantennas made of van der Waals material hexagonal boron nitride. The optical nanoantenna made of hyperbolic material was shown to support strong localized resonant modes stemming from the propagating high-k waves in the hyperbolic material. An analytical approach was used to determine the mode profile and type of cuboid nanoantenna resonances. An electric quadrupolar mode was demonstrated to be associated with a resonant magnetic response of the nanoantenna, which resembles the induction of resonant magnetic modes in high-refractive-index nanoantennas. The analytical model accurately predicts the modes of cuboid nanoantennas due to the strong boundary reflections of the high-k waves, a capability that does not extend to plasmonic or high-refractive-index nanoantennas, where the imperfect reflection and leakage of the mode from the cavity complicate the analysis. In the reported metasurface, excitations of the multipolar resonant modes are accompanied by directional scattering and a decrease in the metasurface reflectance to zero, which is manifested as the resonant Kerker effect. Van der Waals nanoantennas are envisioned to support localized resonances and can become an important functional element of metasurfaces and transdimensional photonic components. By designing efficient subwavelength scatterers with high-quality-factor resonances, this work demonstrates that this type of nanoantenna made of naturally occurring hyperbolic material is a viable substitute for plasmonic and all-dielectric nanoantennas in developing ultra-compact photonic components.

Chemistry↗
DOE OSTI2026

Powering Large Loads: Solutions Across Transmission, Utility, and Facility Scales

This report synthesizes current strategies for accommodating large load growth through a review of publicly available technical literature and media insights around the United States (U.S.). Solutions are organized across three implementation scales (transmission, utility, and facility) and categorized according to common implementation pathways (including structural expansion, operations and efficiency, upgrades, and planning and policy).

Valdez, Raquel Lynn [Sandia National Laboratories ↗
DOE OSTI2024

Determining Stellar Elemental Abundances from DESI Spectra with the Data-driven Payne

Abstract Stellar abundances for a large number of stars provide key information for the study of Galactic formation history. Large spectroscopic surveys such as the Dark Energy Spectroscopic Instrument (DESI) and LAMOST take median-to-low-resolution (R≲ 5000) spectra in the full optical wavelength range for millions of stars. However, the line-blending effect in these spectra causes great challenges for elemental abundance determination. Here we employDD-Payne, a data-driven method regularized by differential spectra from stellar physical models, to the DESI early data release spectra for stellar abundance determination. Our implementation delivers 15 labels, including effective temperatureT eff , surface gravity log g , microturbulence velocityv mic , and the abundances for 12 individual elements, namely C, N, O, Mg, Al, Si, Ca, Ti, Cr, Mn, Fe, and Ni. Given a spectral signal-to-noise ratio of 100 per pixel, the internal precisions of the label estimates are about 20 K forT eff , 0.05 dex for log g , and 0.05 dex for most elemental abundances. These results agree with the theoretical limits from the Crámer–Rao bound calculation within a factor of 2. The majority of the accreted halo stars contributed by the Gaia–Enceladus–Sausage are discernible from the disk and in situ halo populations in the resultant [Mg/Fe]–[Fe/H] and [Al/Fe]–[Fe/H] abundance spaces. We also provide distance and orbital parameters for the sample stars, which spread over a distance out to ∼100 kpc. The DESI sample has a significantly higher fraction of distant (or metal-poor) stars than the other existing spectroscopic surveys, making it a powerful data set for studying the Galactic outskirts. The catalog is publicly available.

Astronomy & Astrophysics↗
DOE OSTI2026

HTGR Multiphysics Application Drivers FY26 Updates

This report summarizes FY26 progress under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program's high-temperature gas-cooled reactor (HTGR) application driver work, covering a wide range of activities such as code validation and multi-physics code assessment. 1) A detailed SAM model of the High-Temperature Engineering Test Reactor (HTTR) was developed using a unique-block grouping approach, with an extended parallel thermal network method to capture block-to-block conduction and radiation heat transfer, and applied to steady-state simulations of the HTTR 30~MW and 9~MW cases. 2) In another activity, SAM's newly implemented multi-component gas flow model was validated against the Natural convection Shutdown heat removal Test Facility (NSTF) argon ingress experiment, correctly capturing the density-driven suppression and thermal recovery of natural circulation observed when argon is introduced into the air-cooled Reactor Cavity Cooling System (RCCS) loop. 3) For the OECD/NEA High Temperature Test Facility (HTTF) benchmark, we co-led the international benchmark activities as well as the OECD/NEA final benchmark report to be released at the end of this year. 4) Finally, the coupled Griffin-SAM modeling capability for pebble-bed HTGRs was advanced by verifying the Griffin neutronics solution against Serpent Monte Carlo for a realistic non-uniform temperature distribution, resolving several deficiencies in the SAM-to-Griffin temperature transfer scheme, and enabling distinct fuel kernel, moderator, and coolant temperatures for cross section feedback. These new features were demonstrated in a PBR load-following transient.

Lee, Alvin↗
DOE OSTI2026

NanoPSD: A software for automatic detection of Nano-Particle Shape Distribution in electron microscopy images

Accurate quantification of the size and morphology of nanoparticles from electron microscopy (EM) images is essential to understand growth mechanisms, surface reactivity, and functional behavior in nanoscale materials. Manual analysis remains slow, subjective, and difficult to reproduce in large datasets. We introduce NanoPSD (Nano-Particle Shape Distribution), an open-source and fully automated framework for quantitative particle detection and morphology analysis from EM images. NanoPSD integrates adaptive contrast enhancement, polarity-agnostic scale-bar detection, Optical Character Recognition (OCR)-based calibration, and classical segmentation via Otsu thresholding with morphological refinement. Particle contours are used to extract geometric descriptors, including equivalent circular diameter, aspect ratio, circularity, and solidity, enabling automated classification into spherical, rod-like, and aggregate morphologies. The framework supports both single-image and batch processing, generating publication-quality visualizations, LaTeX-ready tables, and structured comma-separated values (CSV) datasets. As a demonstration, we applied NanoPSD to plasma-synthesized nanoparticle samples diagnosed via transmission electron microscopy (TEM). The code produced statistically robust size and morphology distributions spanning a few to tens of nanometers with minimal user supervision. The pipeline demonstrates high reproducibility and scalability, processing large image collections with consistent calibration and output formatting. Its modular design enables seamless integration of future deep-learning-based segmentation models, providing a pathway toward intelligent, data-driven electron microscopy analysis.

36 MATERIALS SCIENCE↗
DOE OSTI1975

Nuclear Safety [Vol. 16, No. 1, January-February 1975]

Nuclear Safety covers significant developments in the field of nuclear safety. The scope is limited to topics relevant to the analysis and control of hazards associated with nuclear energy, operations involving fissionable materials, and the products of nuclear fission and their effects on the environment. Primary emphasis is on safety in reactor design, construction, and operation; however, safety considerations in regard to the entire fuel cycle, including fuel fabrication, spent-fuel processing, nuclear waste disposal, handling of radioisotopes, and environmental effects of these operations, are also treated. Table of Contents for this issue follows. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 1 AEC Working Paper on Population Density Around Nuclear Power-Plant Sites Adapted by J. Ft. Buchanan, 8 Water-Reactor Safety-Research Information Meeting by Wm. B. Cottrell, D. O. Hobson, and G. D. Whitman; ACCIDENT ANALYSIS: 29 Burnout in Boiling Heat Transfer. Part I: Pool-Boiling Systems by A. E. Bergles; PLANT SAFETY FEATURES: 43 Radionuclide Behavior During Normal Operation of Liquid-Metal-Cooled Fast Breeder Reactors. Part 1: Production by C. A. Erdman and A. B. Reynolds; CONSEQUENCES OF EFFLUENT RELEASE: 60 The Control, Monitoring, and Reporting of Radioactivity in Effluents. Part 1: AEC-Owned Facilities by M. B. Biles and F. E. Coffman, 71 The Control, Monitoring, and Reporting of Radioactivity in Effluents. Part 2: AEC-Licensed Facilities by L. B. Higginbotham and J. T. Collins; OPERATING EXPERIENCES: 76 Incident at the Lucens Reactor by J. M. Miller, 79 IAEA Symposium on Experience from Operating and Fueling of Nuclear Power Reactors by William A. Pryor, 87 Recent Occurrences at Nuclear Reactors and Their Causes Compiled by William R. Casto, 98 Summary of Operating U. S. Power Reactors as of Nov. 1. 1974, 101 Selected Safety-Related Occurrences Reported in September and October 1974 Compiled by William R. Casto; CURRENT EVENTS: 104 General Administrative Activities Compiled by Wm. B. Cottrell, 110 Action on Power-Reactor Projects Undergoing Regulatory Review or Consideration Compiled by Wm. B. Cottrell, 119 Action on Nonreactor Projects Undergoing Regulatory Review or Consideration Compiled by Wm. B. Cottrell, 121 Proposed Rule Changes as of Oct. 31, 1974; MISCELLANY: 97 ASTM—Euratom Symposium on Radiation Dosimetry: Developments and Standardization (Announcement), 118 Workshops on In-Pile Filter Testing (Announcement), 119 IAEA Symposium on Radiological Impacts from Releases from Nuclear Facilities into Aquatic Environments (Announcement).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Multi-sensor Observations of a High-velocity Fireball over the South Atlantic on 2026 April 1

A high-velocity fireball was detected over the South Atlantic (41.9°S, 54.7°W) on 2026 April 1 at 02:13:14 UTC by U.S. Government (USG) sensors, with peak brightness at 90.5 km altitude. The event was well-observed from geostationary orbit by two civilian lightning imagers with near-orthogonal geometry, the Geostationary Operational Environmental Satellite-East Geostationary Lightning Mapper (GLM) and the Exploitation of Meteorological Satellites Meteosat Third Generation Imager 1 Lightning Imager, and it produced low-frequency acoustic signatures. The GLM measured a total radiated energy of 2.4 × 10 10 J, corresponding to a calculated impact energy of 0.086 kt TNT equivalent. Stereoscopic triangulation of the imager tracks yields an independent pre-atmospheric velocity of ~57 km s −1 , some 18% below the USG-reported value. Because orbital provenance is acutely sensitive to the entry velocity, whose reported uncertainty could be substantial, this discrepancy is notable. We document the multi-sensor record and identify the analysis required to assess provenance, which a subsequent study will present.

Silber, Elizabeth Allaryce [Sandia National Lab. (↗