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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 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Validation of Aquarius Measurements Using Radiative Transfer Models at L-Band

Aquarius/SAC-D was launched in June 2011 by NASA and CONAE (Argentine space agency). Aquarius includes three L-band (1.4 GHz) radiometers dedicated to measuring sea surface salinity. We report detailed comparisons of Aquarius measurements with radiative transfer model predictions. These comparisons were used as part ofthe initial assessment of Aquarius data. In particular, they were used successfully to estimate the radiometer calibration bias and stability. Further comparisons are being performed to assess the performance of models in the retrieval algorithm for correcting the effect of sources of geophysical "noise" (e.g. the galactic background, atmospheric attenuation and reflected signal from the Sun). Such corrections are critical in bringing the error in retrieved salinity down to the required 0.2 practical salinity unit (psu) on monthly global maps at 150 km by 150 km resolution. The forward models making up the Aquarius simulator have been very useful for preparatory studies in the years leading to Aquarius' launch. The simulator includes various components to compute effects ofthe following processes on the measured signal: 1) emission from Earth surfaces (ocean, land, ice), 2) atmospheric emission and absorption, 3) emission from the Sun, Moon and celestial Sky (directly through the antenna sidelobes or after reflection/scattering at the Earth surface), 4) Faraday rotation, and 5) convolution of the scene by the antenna gain patterns. Since the Aquarius radiometers tum-on in late July 2011, the simulator has been used to perform a first order validation of the data. This included checking the order of magnitude ofthe signal over ocean, land and ice surfaces, checking the relative amplitude of signal at different polarizations, and checking the variation with incidence angle. The comparisons were also used to assess calibration bias and monitor instruments calibration drift. The simulator is also being used in the salinity retrieval. For example, initial assessments of the salinity retrieved from Aquarius data showed degradation in accuracy at locations where glint from the galactic sky background was important. This was traced to an inaccurate correction for the Sky glint. We present comparisons of the simulator prediction to the Aquarius data in order to assess the performances of the models of various physical processes impacting the measurements, such as the effect of sea surface roughness, the impact of the celestial Sky and the Sun emission scattered at the rough ocean surface. We discuss what components of the simulator appear reliable and which ones need improvements. Improved knowledge on the radiative transfer models at L-band will not only lead to better salinity retrieved from Aquarius data, it will also allow be beneficial for SMOS or the upcoming SMAP mission.

Dinnat, E.↗
DOE OSTI2024

Highly Ordered Eutectic Mesostructures via Template‐Directed Solidification within Thermally Engineered Templates

Template-directed self-assembly of solidifying eutectics results in emergence of unique microstructures due to diffusion constraints and thermal gradients imposed by the template. Here, the importance of selecting the template material based on its conductivity to control heat transfer between the template and the solidifying eutectic, and thus the thermal gradients near the solidification front, is demonstrated. Simulations elucidate the relationship between the thermal properties of the eutectic and template and the resultant microstructure. The overarching finding is that templates with low thermal conductivities are generally advantageous for forming highly organized microstructures. When electrochemically porosified silicon pillars (thermal conductivity < 0.3 Wm −1 K −1 ) are used as the template into which an AgCl-KCl eutectic is solidified, 99% of the unit cells in the solidified structure exhibit the same pattern. In contrast, when higher thermal conductivity crystalline silicon pillars (≈100 Wm −1 K −1 ) are utilized, the expected pattern is only present in 50% of the unit cells. The thermally engineered template results in mesostructures with tunable optical properties and reflectances nearly identical to the simulated reflectances of perfect structures, indicating highly ordered patterns are formed over large areas. This work highlights the importance of controlling heat flows in template-directed self-assembly of eutectics.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Accurate determination of chemical abundances near a supermassive black hole

The metal abundances in galactic nuclei carry key information on the history of star formation and mass transfer in central regions of galaxies. X-ray fluorescence analysis is a unique tool to reliably measure the abundances of various elements via simple physics. Here we present a new observation of the active nucleus in the Circinus galaxy with the XRISM satellite at unprecedented X-ray energy resolution. The fluorescent iron Kα line profile modified by Compton scattering indicates that the material responsible for its emission is cold and metal rich and is located ≳0.024 pc from the supermassive black hole, consistent with the dusty torus region. The abundance pattern derived from comparing fluorescent line intensities of different metals shows subsolar ratios of argon- and calcium-to-iron and a supersolar ratio of nickel-to-iron. This abundance pattern is best produced by a combination in number fraction of 92$^{+2}_{–4}$% core-collapse supernovae from progenitor stars less massive than 20$^{+3}_{–2}$ M ⊙ and 8$^{+4}_{–2}$% type Ia supernovae. This suggests that gas feeding the supermassive black hole was enriched by recent core-collapse supernovae. Our findings imply that in metal-rich environments stars more massive than about 20 M ⊙ directly collapse into black holes or make faint supernovae without ejecting heavy metals into the space.

Astronomy and AstroPhysics↗
DOE OSTI2021

Absolute calibration of the Lyman-α measurement apparatus at DIII-D

The LLAMA (Lyman-Alpha Measurement Apparatus) diagnostic was recently installed on the DIII-D tokamak [Rosenthal et al., Rev. Sci. Instrum. (submitted) (2020)]. LLAMA is a pinhole camera system with a narrow band Bragg mirror, a bandpass interference filter, and an absolute extreme ultraviolet photodiode detector array, which measures the Ly-α brightness in the toroidal direction on the inboard, high field side (HFS) and outboard, low field side (LFS). This contribution presents a setup and a procedure for an absolute calibration near the Ly-α line at 121.6 nm. The LLAMA in-vacuum components are designed as a compact, transferable setup that can be mounted in an ex situ vacuum enclosure that is equipped with an absolutely calibrated Ly-α source. The spectral purity and stability of the Ly-α source are characterized using a vacuum ultraviolet spectrometer, while the Ly-α source brightness is measured by a NIST-calibrated photodiode. The non-uniform nature of the Ly-α source emission was overcome by performing a calibration procedure that scans the Ly-α source position and employs a numerical optimization to determine the emission pattern. Nominal and measured calibration factors are determined and compared, showing agreement within their uncertainties. A first conversion of the measured signal obtained from DIII-D indicates that the Ly-α brightness on the HFS and LFS is on the order of 1020 Ph sr-1 m-2 s-1. The established calibration setup and procedure will be regularly used to re-calibrate the LLAMA during DIII-D vents to monitor possible degradation of optical components and detectors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Electronic structure, magnetic properties, spin orientation, and doping effect in Mn 3 Si 2 Te 6

The layered material Mn 3 Si 2 Te 6 , with alternating stacking honeycomb and triangular layers, is attracting considerable attention due to its rich physical properties. Here, in this study, using density functional theory and classical Monte Carlo (MC) methods, we systematically study this system with the 3d 5 electronic configuration. Near the Fermi level, the states are mainly contributed by Te 5p orbitals hybridized with Mn 3d orbitals, resembling a charge-transfer system. Furthermore, the spin orientations of the ferrimagnetic (FiM) ground state display different conductive behaviors when along the ab plane or out-of-plane directions: insulating vs metallic states. The energy difference between the FiM [110] insulating and FiM [001] metallic phases is very small (~0.71 meV/Mn) . Changing the angle θ of spin orientation from in-plane to out-of-plane directions, the band gaps of this system are gradually reduced, leading to an insulator-metal transition, resulting in an enhanced electrical conductivity, related to the colossal angular magnetoresistance (MR) effect. Although the three main magnetic couplings were found to be antiferromagnetic, overall the ground state is FiM. In addition, we also constructed the magnetic phase diagram using the classical XY spin model studied with the MC method. Three magnetic phases were obtained, including antiferromagnetic order, noncollinear spin patterns, and FiM order. Moreover, we also investigated the Se and Ge doping into the Mn 3 Si 2 Te 6 system: the FiM state has the lowest energy among the magnetic candidates for both Se- and Ge-doped cases. The magnetic anisotropy energy (MAE) decreases in the Se-doped case because the Mn orbital moment is reduced as the doping x increases. Due to the small spin-orbit-coupling effect of Se, the insulator-metal transition caused by the spin orientation disappears in the Se-doped case, resulting in an insulating phase in the FiM [001] phase. This causes a reduced colossal angular MR. However, both the MAE and the band gap of the Ge-doped case do not change much with increasing doping x . Our results for Mn 3 Si 2 Te 6 could provide guidance to experimentalists and theorists working on this system or related materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Recognition of glycoside hydrolase 12 proteins by the immune receptor RXEG1 confers Fusarium head blight resistance in wheat

Summary Fusarium head blight (FHB), caused by Fusarium graminearum , is a devastating disease in wheat ( Triticum aestivum ) that results in substantial yield losses and mycotoxin contamination. Reliable genetic resources for FHB resistance in wheat are lacking. In this study, we characterized glycoside hydrolase 12 (GH12) family proteins secreted by F. graminearum . We established that two GH12 proteins, Fg05851 and Fg11037, have functionally redundant roles in F. graminearum colonization of wheat. Furthermore, we determined that the GH12 proteins Fg05851 and Fg11037 are recognized by the leucine‐rich‐repeat receptor‐like protein RXEG1 in the dicot Nicotiana benthamiana . Heterologous expression of RXEG1 conferred wheat responsiveness to Fg05851 and Fg11037, enhanced wheat resistance to F. graminearum and reduced levels of the mycotoxin deoxynivalenol in wheat grains in an Fg05851/Fg11037‐dependent manner. In the RXEG1 transgenic lines, genes related to pattern‐triggered plant immunity, salicylic acid, jasmonic acid, and anti‐oxidative homeostasis signalling pathways were upregulated during F. graminearum infection. However, the expression of these genes was not significantly changed during infection by the deletion mutant ΔFg05851/Fg11037 , suggesting that the recognition of Fg05851/Fg11037 by RXEG1 triggered plant resistance against FHB. Moreover, introducing RXEG1 into three other different wheat cultivars via crossing also conferred resistance to F. graminearum . Expression of RXEG1 did not have obvious deleterious effects on plant growth and development in wheat. Our study reveals that N. benthamiana RXEG1 remains effective when transferred into wheat, a monocot, which in turn suggests that engineering wheat with interfamily plant immune receptor transgenes is a viable strategy for increasing resistance to FHB.

Wang, Zongkuan↗
DOE OSTI2024

DAWN: Dashboard for Agricultural Water Use and Nutrient Management—A Predictive Decision Support System to Improve Crop Production in a Changing Climate

Abstract Climate change presents huge challenges to the already-complex decisions faced by U.S. agricultural producers, as seasonal weather patterns increasingly deviate from historical tendencies. Under USDA funding, a transdisciplinary team of researchers, extension experts, educators, and stakeholders is developing a climate decision support Dashboard for Agricultural Water use and Nutrient management (DAWN) to provide Corn Belt farmers with better predictive information. DAWN’s goal is to provide credible, usable information to support decisions by creating infrastructure to make subseasonal-to-seasonal forecasts accessible. DAWN uses an integrated approach to 1) engage stakeholders to coproduce a decision support and information delivery system; 2) build a coupled modeling system to represent and transfer holistic systems knowledge into effective tools; 3) produce reliable forecasts to help stakeholders optimize crop productivity and environmental quality; and 4) integrate research and extension into experiential, transdisciplinary education. This article presents DAWN’s framework for integrating climate–agriculture research, extension, and education to bridge science and service. We also present key challenges to the creation and delivery of decision support, specifically in infrastructure development, coproduction and trust building with stakeholders, product design, effective communication, and moving tools toward use.

Meteorology & Atmospheric Sciences↗
NASA NTRS1984

The distribution of reconnection geometry in flux transfer events using energetic ion, plasma and magnetic data

The distribution of energetic ion anisotropies in flux transfer events (FTEs) about the dayside magnetopause has been determined for ISEE 2 crossings of the boundary in 1977 and 1978. When the events are sorted according to the sign of the east-west component of the magnetic field in the magnetosphere, a clear correlation is observed on the northern morningside. When the field is eastward, particles flow antiparallel to the field, implying field line connection to the Northern Hemisphere; when the field is westward, the opposite is true. On the afternoonside, the particle anisotropies are correlated with latitude. Explanations for this pattern are discussed which involve FTE formation at low latitudes with subsequent motion at a velocity given by the vector superposition of the Alfven velocity from the release of magnetic tension and the magnetosheath bulk flow velocity. Evidence that the geomagnetic and not the geocentric solar magnetospheric equator is the source of FTEs is considered.

Daly, P. W.↗
NASA NTRS1985

Bidirectional Reflectance Modeling of Non-homogeneous Plant Canopies

The objective of this research is to develop a 3-dimensional radiative transfer model for predicting the bidirectional reflectance distribution function (BRDF) for heterogeneous vegetation canopies. The model (named BIGAR) considers the angular distribution of leaves, leaf area index, the location and size of individual subcanopies such as widely spaced rows or trees, spectral and directional properties of leaves, multiple scattering, solar position and sky condition, and characteristics of the soil. The model relates canopy biophysical attributes to down-looking radiation measurements for nadir and off-nadir viewing angles. Therefore, inversion of this model, which is difficult but practical should provide surface biophysical pattern; a fundamental goal of remote sensing. Such a model also will help to evaluate atmospheric limitations to satellite remote sensing by providing a good surface boundary condition for many different kinds of canopies. Furthermore, this model can relate estimates of nadir reflectance, which is approximated by most satellites, to hemispherical reflectance, which is necessary in the energy budget of vegetated surfaces.

Norman, J. M.↗
NASA NTRS2016

Observations and Simulations of the Na I D-1 Line profiles in an M-Class Solar Flare

We study the temporal evolution of the Na I D1 line profiles in the M3.9 flare SOL2014-06-11T21:03UT, using observations at high spectral resolution obtained with the Interferometric Bidimensional Spectrometer instrumentation the Dunn Solar Telescope combined with radiative hydrodynamic simulations. Our results show a significant increase in the intensities of the line core and wings during the flare. The analysis of the line profiles from the flare ribbons reveals that the Na I D1 line has a central reversal with excess emission in the blue wing (blue asymmetry).We combine RADYN and RH simulations to synthesize Na I D1 line profiles of the flaring atmosphere and find good agreement with the observations. Heating with a beam of electrons modifies the radiation field in the flaring atmosphere and excites electrons from the ground state 3s 2S to the first excited state 3p 2P, which in turn modifies the relative population of the two states. The change in temperature and the population density of the energy states make the sodium line profile revert from absorption into emission. Furthermore, the rapid changes in temperature break the pressure balance between the different layers of the lower atmosphere, generating upflow/downflow patterns. Analysis of the simulated spectra reveals that the asymmetries of the Na I D1 flare profile are produced by the velocity gradients in the lower solar atmosphere.

methods: numerical↗
DOE OSTI2025

Structure and Synthesizability of Iron–Sulfur Metal–Organic Frameworks

Sulfur-based metal–organic frameworks (MOFs) and coordination polymers (CPs) are an emerging class of hybrid materials that have received growing attention due to their magnetic, conductive, and catalytic properties with potential applications in electrocatalysis and energy storage. In this work, we report a high-throughput virtual screening protocol to predict the synthesizability of candidate metal–sulfur MOFs/CPs by computing the thermodynamically stable structures resulting from a particular combination of metal cluster, linker, cation, and synthetic conditions. Free energies are computed by using all-atom classical mechanical thermodynamic integration. Low-free-energy structures are refined using ab initio density functional theory, and pair distribution functions and powder X-ray diffraction patterns are calculated to complement and guide experimental structure determination. We validate the computational approach by retrospective predictions of the stable structure produced by experimental syntheses, and a subsequent screen predicts Fe 4 S 4 -BDT–TPP as a new thermodynamically stable one-dimensional (1D) CP comprising a redox-active Fe 4 S 4 cluster, a 1,4-benzenedithiolate (BDT) linker, and a tetraphenylphosphonium (TPP) countercation. Furthermore, this material is experimentally synthesized, and the 1D chain structure of the crystal is confirmed using microcrystal electron diffraction. The computational screening pipeline is generically transferable to neutral and ionic MOFs/CPs comprising arbitrary metal clusters, linkers, cations, and synthetic conditions, and we make it freely available as an open source tool to guide and accelerate the discovery and engineering of novel porous materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Ultrafast optical melting of trimer superstructure in layered 1T′-TaTe2

Abstract Quasi-two-dimensional transition-metal dichalcogenides are a key platform for exploring emergent nanoscale phenomena arising from complex interactions. Access to the underlying degrees-of-freedom on their natural time scales motivates the use of advanced ultrafast probes sensitive to self-organised atomic-scale patterns. Here, we report the ultrafast investigation of TaTe 2 , which exhibits unique charge and lattice trimer order characterised by a transition upon cooling from stripe-like chains into a (3 × 3) superstructure of trimer clusters. Utilising MeV-scale ultrafast electron diffraction, we capture the photo-induced TaTe 2 structural dynamics – exposing a rapid ≈ 1.4 ps melting of its low-temperature ordered state followed by recovery via thermalisation into a hot cluster superstructure. Density-functional calculations indicate that the initial quench is triggered by intra-trimer Ta charge transfer which destabilises the clusters, unlike melting of charge density waves in other TaX 2 compounds. Our work paves the way for further exploration and ultimately rapid optical and electronic manipulation of trimer superstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Deconvoluting thermomechanical effects in X-ray diffraction data using machine learning

X-ray diffraction is ideal for probing the sub-surface state during complex or rapid thermomechanical loading of crystalline materials. However, challenges arise as the size of diffraction volumes increases due to spatial broadening and because of the inability to deconvolute the effects of different lattice deformation mechanisms. Here, we present a novel approach that uses combinations of physics-based modeling and machine learning to deconvolve thermal and mechanical elastic strains for diffraction data analysis. The method builds on a previous effort to extract thermal strain distribution information from diffraction data. The new approach is applied to extract the evolution of the thermomechanical state during laser melting of an Inconel 625 wall specimen which produces significant residual stress upon cooling. A combination of heat transfer and fluid flow, elasto-plasticity and X-ray diffraction simulations is used to generate training data for machine-learning (Gaussian process regression, GPR) models that map diffracted intensity distributions to underlying thermomechanical strain fields. First-principles density functional theory is used to determine accurate temperature-dependent thermal expansion and elastic stiffness used for elasto-plasticity modeling. The trained GPR models are found to be capable of deconvoluting the effects of thermal and mechanical strains, in addition to providing information about underlying strain distributions, even from complex diffraction patterns with irregularly shaped peaks.

36 MATERIALS SCIENCE↗
NASA NTRS1991

Automated target recognition and tracking using an optical pattern recognition neural network

The on-going development of an automatic target recognition and tracking system at the Jet Propulsion Laboratory is presented. This system is an optical pattern recognition neural network (OPRNN) that is an integration of an innovative optical parallel processor and a feature extraction based neural net training algorithm. The parallel optical processor provides high speed and vast parallelism as well as full shift invariance. The neural network algorithm enables simultaneous discrimination of multiple noisy targets in spite of their scales, rotations, perspectives, and various deformations. This fully developed OPRNN system can be effectively utilized for the automated spacecraft recognition and tracking that will lead to success in the Automated Rendezvous and Capture (AR&C) of the unmanned Cargo Transfer Vehicle (CTV). One of the most powerful optical parallel processors for automatic target recognition is the multichannel correlator. With the inherent advantages of parallel processing capability and shift invariance, multiple objects can be simultaneously recognized and tracked using this multichannel correlator. This target tracking capability can be greatly enhanced by utilizing a powerful feature extraction based neural network training algorithm such as the neocognitron. The OPRNN, currently under investigation at JPL, is constructed with an optical multichannel correlator where holographic filters have been prepared using the neocognitron training algorithm. The computation speed of the neocognitron-type OPRNN is up to 10(exp 14) analog connections/sec that enabling the OPRNN to outperform its state-of-the-art electronics counterpart by at least two orders of magnitude.

Chao, Tien-Hsin↗
NASA NTRS2010

Global Variability of Mesoscale Convective System Anvil Structure from A-Train Satellite Data

Mesoscale convective systems (MCSs) in the tropics produce extensive anvil clouds, which significantly affect the transfer of radiation. This study develops an objective method to identify MCSs and their anvils by combining data from three A-train satellite instruments: Moderate Resolution Imaging Spectroradiometer (MODIS) for cloud-top size and coldness, Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) for rain area size and intensity, and CloudSat for horizontal and vertical dimensions of anvils. The authors distinguish three types of MCSs: small and large separated MCSs and connected MCSs. The latter are MCSs sharing a contiguous rain area. Mapping of the objectively identified MCSs shows patterns of MCSs that are consistent with previous studies of tropical convection, with separated MCSs dominant over Africa and the Amazon regions and connected MCSs favored over the warm pool of the Indian and west Pacific Oceans. By separating the anvil from the raining regions of MCSs, this study leads to quantitative global maps of anvil coverage. These maps are consistent with the MCS analysis, and they lay the foundation for estimating the global radiative effects of anvil clouds. CloudSat radar data show that the modal thickness of MCS anvils is about 4-5 km. Anvils are mostly confined to within 1.5-2 times the equivalent radii of the primary rain areas of the MCSs. Over the warm pool, they may extend out to about 5 times the rain area radii. The warm ocean MCSs tend to have thicker non-raining and lightly raining anvils near the edges

Yuan, Jian↗
NASA NTRS2010

Global Variability of Mesoscale Convective System

Mesoscale convective systems (MCSs) in the tropics produce extensive anvil clouds, which significantly affect the transfer of radiation. This study develops an objective method to identify MCSs and their anvils by combining data from three A-train satellite instruments: Moderate Resolution Imaging Spectroradiometer (MODIS) for cloud-top size and coldness, Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) for rain area size and intensity, and CloudSat for horizontal and vertical dimensions of anvils. The authors distinguish three types of MCSs: small and large separated MCSs and connected MCSs. The latter are MCSs sharing a contiguous rain area. Mapping of the objectively identified MCSs shows patterns of MCSs that are consistent with previous studies of tropical convection, with separated MCSs dominant over Africa and the Amazon regions and connected MCSs favored over the warm pool of the Indian and west Pacific Oceans. By separating the anvil from the raining regions of MCSs, this study leads to quantitative global maps of anvil coverage. These maps are consistent with the MCS analysis, and they lay the foundation for estimating the global radiative effects of anvil clouds. CloudSat radar data show that the modal thickness of MCS anvils is about 4--5 km. Anvils are mostly confined to within 1.5--2 times the equivalent radii of the primary rain areas of the MCSs. Over the warm pool, they may extend out to about 5 times the rain area radii. The warm ocean MCSs tend to have thicker non-raining and lightly raining anvils near the edges of their actively raining regions, indicating that anvils are generated in and spread out from the primary raining regions of the MCSs. Thicker anvils are nearly absent over continental regions.

Yuan, J.↗
DOE OSTI2023

Distributed out-of-memory NMF on CPU/GPU architectures

We propose an efficient distributed out-of-memory implementation of the non-negative matrix factorization (NMF) algorithm for heterogeneous high-performance-computing systems. The proposed implementation is based on prior work on NMFk, which can perform automatic model selection and extract latent variables and patterns from data. In this work, we extend NMFk by adding support for dense and sparse matrix operation on multi-node, multi-GPU systems. The resulting algorithm is optimized for out-of-memory problems where the memory required to factorize a given matrix is greater than the available GPU memory. Memory complexity is reduced by batching/tiling strategies, and sparse and dense matrix operations are significantly accelerated with GPU cores (or tensor cores when available). Input/output latency associated with batch copies between host and device is hidden using CUDA streams to overlap data transfers and compute asynchronously, and latency associated with collective communications (both intra-node and inter-node) is reduced using optimized NVIDIA Collective Communication Library (NCCL) based communicators. Benchmark results show significant improvement, from 32X to 76x speedup, with the new implementation using GPUs over the CPU-based NMFk. Good weak scaling was demonstrated on up to 4096 multi-GPU cluster nodes with approximately 25,000 GPUs when decomposing a dense 340 Terabyte-size matrix and an 11 Exabyte-size sparse matrix of density 10 -6 .

97 MATHEMATICS AND COMPUTING↗