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At least 739 records · Page 41

Advanced Manufacturing and Materials for Hydropower: Challenges and Opportunities

Hydropower is a well-established industry that has been largely contributing to the global generation of clean and renewable energy for more than a century. In the United States in 2021, it accounted for 30% of all renewable energy generation and 6.1% of the total energy portfolio. Hydropower technology and designs have been optimized throughout the years, but manufacturing of hydropower components still relies heavily on traditional methods and materials. Changes in global energy production systems and international supply chain issues are inspiring the manufacturing sector to reconsider their processes. Similarly, the hydropower industry is facing manufacturing challenges stemming from well-known maintenance issues, environmental impact mitigations, and changes in operations. These challenges, along with continued innovation in new hydropower and pumped storage development and modernization of the fleet, present an opportunity for advanced manufacturing and materials (AMM) to provide immense value to the hydropower industry. In support of the US Department of Energy’s (DOE’s) Water Power Technologies Office (WPTO), this report aims to characterize the current and emerging manufacturing-related challenges in US hydropower and to identify the high-impact opportunities in AMM that could address these challenges. The results highlighted in this report were collected through literature review, individual stakeholder interviews, and an in-person workshop organized at DOE’s Oak Ridge National Laboratory Manufacturing Demonstration Facility that brought together hydropower industry stakeholders, advanced manufacturing R&D, and the government.

13 HYDRO ENERGY↗

Direct Air Capture of CO 2 and Delivery to Photobioreactors for Algal Biofuel Production (Final Report)

A mobile DAC system was designed and constructed to pair with photobioreactors growing algae for biofuel production. The DAC system was designed as a versatile research system, rather than a compact production unit. The system was constructed and mounted on a mobile skid to facilitate transportation to the algae production site. Within the DAC system, CO 2 was captured using amine-loaded monoliths that allow for high CO 2 uptake with low pressure drop. The CO 2 is collected using a Global Thermostat patented temperature/vacuum swing adsorption (TVSA) process. Amine sorbents and process conditions were optimized to produce 10 to >20 g CO 2 .h-1. The stability of the amine sorbents was also studied, with sorbent modifications made to improve stability to degradation by oxidation. An Algenol-developed Spirulina strain (Arthrospira platensis AB2293) was selected as the production cyanobacterial strain. AB2293 cultured was inoculum for outdoor production following PBR installation by Algenol. The PBR system was composed of three independent PBRs, with each PBR composed of four hanging bags internally recirculated by a liquid turnover pump. The PBRs were operated outdoors in Atlanta, GA, and integrated with the DAC system. Algae were grown with similar productivity using DAC-CO 2 as algae grown using pure CO 2 obtained commercially (Airgas). Throughout the experimental duration, no discoloration was observed, and cellular morphology was consistent between the two experimental treatments. An LCA including lifecycle greenhouse gas emissions, full life cycle inventory of the Algenol system and the DAC system and integrated DAC+PBR system was developed. Lifecycle greenhouse gas emissions were calculated for capture of carbon dioxide using input from Global Thermostat and the National Renewable Energy Laboratory. Three scenarios for energy provision were evaluated: a natural gas combined heat and power system sized to meet the electricity requirement, a natural gas combined heat and power system sized to meet the process heat requirements, and a system without on-site power that procures the electricity from the grid. In all three cases, as expected, the major contributor to the emissions is the energy consumption associated with the desorption step of the DAC process. The LCA quantified the reduced potential energy and greenhouse gas emissions of heat and mass integration of DAC and Algenol compared to unintegrated DAC and Algenol systems. A life cycle assessment of the role of sorbent productivity and lifetime was also developed. The development of more robust, oxidation resistant DAC sorbents may enable small reductions in energy requirements and in lifecycle greenhouse gas emissions and other environmental impacts. NREL performed techno-economic analysis (TEA) to identify the integration scenario most likely to achieve a 15% cost reduction target versus the baseline. Heat and mass integration of DAC and the PBR is critical to minimizing the MFSP. The baseline case utilizes no heat and mass integration, and the DAC system provides 100% of the CO 2 required by the photobioreactors (20 tonnes/hr), operating for 12 hours/day capturing 40 tonnes CO 2 /operating hour. The minimum fuel selling price (MFSP) of ethanol calculated from the baseline case was $10.68/gal ethanol. This corresponds with a targeted MFSP of $9.07/gal ethanol (or 15% reduction). This target was achieved by integration Option 2a with the greatest cost reduction of 17.8% (or $8.78/gal) and integration Option 2b with a cost reduction of 16.4% (or $8.93/gal). Reductions in MFSP are attributed to two primary process considerations: (a) CO 2 storage at night reduces the capital expenses associated with DAC (i.e., increasing on-stream time); and (b) distributed DAC scenarios (DAC-PBR integration Options 2a and 2b) make use of boiler and DAC CHP flue gas CO 2 (free). Direct air capture on-stream time was one of the largest contributors to MFSP reduction.

09 BIOMASS FUELS↗

A Privacy-Aware Federated Learning Framework for Distributed Energy Resource Analytics in Constrained Environments

To be resilient against extreme weather events, the rural communities in Puerto Rico are leveraging distributed energy resources (DER). However, computing frameworks sup-porting the grid in critical decision-making are still largely centralized. Sensitive consumer data are transmitted over the Internet or cellular networks to a secondary or tertiary node. It guarantees better situational awareness at the cost of a wider attack surface, jeopardizing user privacy, as more DER come online. Cloud, Edge, and Fog computing all require data aggregation at some level. This paper introduces a privacy-aware federated learning framework that leverages the Fog model by pushing analytics all the way to the DER and load assets. These local models train on individual asset data and transmit only learned parameters (such as weights) over secure communications to a global decision-maker. By abstracting personally identifiable consumer data without impacting decision optimality, this framework better aligns with distributed power generation paradigm.

Sundararajan, Aditya↗

A photovoltaic catenary-tent array for the Martian surface

To provide electrical power during an exploration mission to Mars, a deployable tent-shaped structure with a flexible photovoltaic (PV) blanket is proposed. The array is designed with a self-deploying mechanism utilizing pressurized gas expansion. The structural design for the array uses a combination of cables, beams, and columns to support and deploy the PV blanket. Under the force of gravity, a cable carrying a uniform load will take the shape of a catenary curve. A catenary-tent collector is self shading which must be taken into account in the solar radiation calculation. The shape and the area of the shadow on the array was calculated and used in the determination of the global irradiance on the array. The PV blanket shape and structure dimensions were optimized to achieve a configuration which maximizes the specific power (W/kg). The optimization was performed for three types of PV blankets (silicon, gallium arsenide over germanium, and amorphous silicon) and two types of structural materials (carbon composite and arimid fiber composite). The results show that the catenary shape of the PV blanket corresponding to zero end angle at the base with respect to the horizontal results in the highest specific power. The tent angle is determined by optimizing the specific mass and the output power for maximum specific power. The combination of carbon fiber structural material and amorphous silicon blanket produces the highest specific power.

Colozza, Anthony J.↗

A photovoltaic catenary-tent array for the Martian surface

To provide electrical power during an exploration mission to Mars, a deployable tent-shaped structure with a flexible photovoltaic (PV) blanket is proposed. The array is designed with a self-deploying mechanism utilizing pressurized gas expansion. The structural design for the array uses a combination of cables, beams, and columns to support and deploy the PV blanket. Under the force of gravity a cable carrying a uniform load will take the shape of a catenary curve. A catenary-tent collector is self shadowing which must be taken into account in the solar radiation calculation. The shape and the area of the shadow on the array was calculated and used in the determination of the global radiation on the array. The PV blanket shape and structure dimension were optimized to achieve a configuration which maximizes the specific power (W/kg). The optimization was performed for four types of PV blankets (Si, GaAs/Ge, GaAs CLEFT, and amorphous Si) and four types of structure materials (Carbon composite, Aramid Fiber composite, Aluminum, and Magnesium). The results show that the catenary shape of the PV blanket, which produces the highest specific power, corresponds to zero end angle at the base with respect to the horizontal. The tent angle is determined by the combined effect of the array structure specific mass and the PV blanket output power. The combination of carbon composite structural material and GaAs CLEFT solar cells produce the highest specific power. The study was carried out for two sites on Mars corresponding to the Viking Lander locations. The designs were also compared for summer, winter, and yearly operation.

Crutchik, M.↗

Stereo imaging based particle velocimeter

Three dimensional coordinates of an object are determined from it's two dimensional images for a class of points on the object. Two dimensional images are first filtered by a Laplacian of Gaussian (LOG) filter in order to detect a set of feature points on the object. The feature points on the left and the right images are then matched using a Hopfield type optimization network. The performance index of the Hopfield network contains both local and global properties of the images. Parallel computing in stereo matching can be achieved by the proposed methodology.

Batur, Celal↗

Toward Comprehensive Uncertainty Predictions for Remote Imaging Spectroscopy

Remote imaging spectroscopy’s role in Earth science will grow in the coming decade as a series of globe-spanning spectroscopy missions launch from NASA, ESA, and other agencies. The nature of remote imaging spectroscopy will change, advancing from short regional studies to address global multi-year questions. The diversity of data will also grow with exposure to a wider range of biomes and atmospheric conditions. To execute these new investigations we must reconcile diverse observing conditions to derive consistent global maps. To this end, rig- orous uncertainty quantification and propagation enables an optimal synthesis of data accounting for observing conditions and data quality. Understanding data uncertainties is also important for principled hypothesis testing, information content assessment, and informed decision making by end users. We survey prior efforts in uncer- tainty quantification for imaging spectroscopy, and describe methods for validating the accuracy of uncertainty predictions. We conclude with a discussion of remaining challenges and promising avenues for future research.

Susiluoto, Jouni↗

Simulated Inherent Optical Properties of Aquatic Particles Using the Equivalent Algal Populations (EAP) Model

Paired measurements of phytoplankton absorption and backscatter, the inherent optical properties central to the interpretation of ocean colour remote sensing data, are notoriously rare. We present a dataset of Chlorophyll a (Chl a) -specific phytoplankton absorption, scatter and backscatter for 17 different phytoplankton groups, derived from first principles using measured in vivo pigment absorption and a well-validated semi-analytical coated sphere model which simulates the full suite of biophysically consistent phytoplankton optical properties. The optical properties of each simulated phytoplankton cell are integrated over an entire size distribution and are provided at high spectral resolution. The model code is additionally included to enable user access to the complete set of wavelength-dependent, angularly resolved volume scattering functions. This optically coherent dataset of hyperspectral optical properties for a set of globally significant phytoplankton groups has potential for use in algorithm development towards the optimal exploitation of the new age of hyperspectral satellite radiometry.

Equivalent Algal Populations↗

On-Orbit OCI Characterization Measurements from the first 6 Months of the PACE Mission

The Ocean Color Instrument (OCI) on NASA’s Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) mission has been providing data to the science community since April 2024. OCI is a hyperspectral imager, providing almost daily global coverage, at a spatial resolution of 1.2km. Its design specifications were optimized for ocean color and atmospheric applications, but terrestrial studies could benefit from its hyperspectral coverage as well. The ocean color requirements called for very high radiometric accuracy, which could benefit a wide variety of applications. This paper presents results from the first 6 months of on-orbit calibration and characterization measurements, including absolute calibration, spectral registration, temporal trending of radiometric sensitivity, signal to noise ratio, and linearity, with a focus on the commissioning results obtained in the first 2 months after launch.

calibration↗

On-Orbit OCI Characterization Measurements from the first 6 Months of the PACE Mission

The Ocean Color Instrument (OCI) on NASA’s Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) mission has been providing data to the science community since April 2024. OCI is a hyperspectral imager, providing almost daily global coverage, at a spatial resolution of 1.2km. Its design specifications were optimized for ocean color and atmospheric applications, but terrestrial studies could benefit from its hyperspectral coverage as well. The ocean color requirements called for very high radiometric accuracy, which could benefit a wide variety of applications. This paper presents results from the first 6 months of on-orbit calibration and characterization measurements, including absolute calibration, spectral registration, temporal trending of radiometric sensitivity, signal to noise ratio, and linearity, with a focus on the commissioning results obtained in the first 2 months after launch.

calibration↗

Reduced Order Models Generation for HTGRs Pebble Shuffling Procedure Optimization Studies

This report provides an initial study for producing reduced-order models (ROMs) of pebble-bed high temperature gas reactor (HTGR) models for the purposes of design optimization. As an initial study, this work is meant to be exploratory---identifying useful workflows and methods for ROM generation---and not meant to be a catch-all analysis of HTGR ROM generation and usage for optimization. This report summarizes three tasks performed in Fiscal Year 2022: 1) the creation of HTGR model, 2) the sensitivity analysis of model design parameters, and 3) an introduction to ROM generation techniques. The representative HTGR model created in this work is a multiphysics equilibrium-core using the BlueCRAB (comprehensive reactor analysis bundle) reactor analysis application, coupling four physical phenomena: neutronics, streamline depletion, porous flow thermal hydraulics, and pebble heat conduction. Part of the model creation was identifying some design parameters and quantities of interest that are relevant in an optimization analysis and adjustable in the model. The sensitivity analysis utilized a polynomial chaos expansion methodology to compute global sensitivity metrics. This analysis showed that thermal hydraulics parameters and quantities of interest had a relatively small impact on simulation results. Finally, the ROM generation work involved exploring three different ROM methodologies: polynomial regression, a Gaussian process, and artificial neural networks. Using a cross-validation technique to characterize ROM performance, the Gaussian process and single-layer artificial neural networks showed the most promising results. Overall, this study was insightful and the lessons learned will be invaluable for the eventual development of an HTGR design optimization workflow.

97 MATHEMATICS AND COMPUTING↗

Trends and limits of CO 2 capture in solid and liquid sorbents at standard conditions

Carbon capture and storage (CCS) plays a critical role in achieving climate change mitigation targets, offering a pathway to decarbonize power generation, industrial processes, and heat production while addressing atmospheric CO 2 removal. While CCS technologies are technically advanced, the widespread adoption of 100 % CO 2 capture capacities such as 1 mol of CO 2 /mol of material and 1 g CO 2 /g storage (targeted by the DARPA, Defense Sciences Office, USA Govt.) has raised questions about the feasibility of achieving higher capture capacities. In the context of limiting global warming to 1.5°C, reaching 100 % CO 2 capture capacity is increasingly necessary, with residual emissions requiring complementary carbon dioxide removal (CDR) technologies. This review exclusively focuses on the CO 2 capture capacities of various sorbents under standard conditions, using different evaluation metrics. This study explores the performance of solid and liquid sorbents under standard conditions, analyzing factors including surface area, pore structure, solvent type, and functionalization to identify materials optimized for industrial-scale CCS applications. Emerging sorbents, including ILs, MOFs, COFs, POPs, DES, RCC, hybrid materials, and reactive sorbents, offer significant potential for enhanced selectivity and energy-efficient regeneration. Through a systematic assessment of gravimetric, volumetric, and molar capacities, the study provides insights into material efficiencies and trade-offs, offering guidance on optimizing sorbent selection for specific applications. The research advances understanding of scalable CCS technologies, contributing to global efforts to achieve net-zero emissions and address the pressing challenge of climate change.

Absorption↗

On the energy landscape of symmetric quantum signal processing

Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given polynomial f , the parameters (called phase factors) can be obtained by solving an optimization problem. However, the cost function is non-convex, and has a very complex energy landscape with numerous global and local minima. It is therefore surprising that the solution can be robustly obtained in practice, starting from a fixed initial guess Φ 0 that contains no information of the input polynomial. To investigate this phenomenon, we first explicitly characterize all the global minima of the cost function. We then prove that one particular global minimum (called the maximal solution) belongs to a neighborhood of Φ 0 , on which the cost function is strongly convex under the condition ‖ f ‖ ∞ = O ( d − 1 ) with d = d e g ( f ) . Our result provides a partial explanation of the aforementioned success of optimization algorithms.

Wang, Jiasu↗

JWST Integrated Science Instrument Module Alignment Optimization Tool

During cryogenic vacuum testing of the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM), the global alignment of the ISIM with respect to the designed interface of the JWST optical telescope element (OTE) will be measured through a series of optical characterization tests. These tests will determine the locations and orientations of the JWST science instrument projected focal surfaces and entrance pupils with respect to their corresponding OTE optical interfaces. If any optical performance non-compliances are identified, the ISIM will be adjusted to improve its performance. In order to understand how to manipulate the ISIM's degrees of freedom properly and to prepare for the ISIM flight model testing, a series of optical-mechanical analyses have been completed to develop and identify the best approaches for bringing a non-compliant ISIM element into compliance. In order for JWST to meet its observatory-level optical requirements and ambitious science goals, the ISIM element has to meet approximately 150 separate optical requirements. Successfully achieving many of those optical requirements depends on the proper alignment of the ISIM element with respect to the OTE. To verify that the ISIM element will meet its optical requirements, a series of cryogenic vacuum tests will be conducted with an OTE Simulator (OSIM). An optical Ray Trace and Geometry Model tool was developed to help solve the multi-dimensional alignment problem. The tool allows the user to determine how best to adjust the alignment of the JWST ISIM with respect to the ideal telescope interfaces so that the approximately 150 ISIM optical performance requirements can be satisfied. This capability has not existed previously.

Bos, Brent↗

Characterizing the Roles of Biogeochemical Cycling and Ocean Circulation in Regulating Marine Copper Distributions

Copper (Cu) is a key micronutrient for marine phytoplankton. Its oceanic biogeochemical cycle has elicited considerable attention due to dissolved Cu exhibiting a unique linear profile with depth. Several processes have been proposed for explaining this behavior. Here, in this study, we characterize the relationships between the observed Cu, PO 4 3– , and Si on a global scale. We find that the depth profiles of Cu resemble those of Si more than of PO 4 3– in the global ocean. To understand their relationships, we couple the biogeochemical and internal circulation processes in a model, fitting optimal Cu:PO 4 3– uptake ratios and remineralization length-scales to replicate the marine Cu distributions. The modeling results suggest that Cu uptake needs in the Southern Ocean are substantially higher than those in other oceanic regions. In addition, our modeling results indicate a deep Cu remineralization in the global ocean. We offer an alternative mechanism that relies on biogeochemical cycling and internal circulation to produce the linear depth profiles of dissolved Cu. Our results suggest that diatoms are likely the major phytoplankton dominating oceanic Cu cycling.

54 ENVIRONMENTAL SCIENCES↗

Applications of wavelet-based compression to multidimensional Earth science data

A data compression algorithm involving vector quantization (VQ) and the discrete wavelet transform (DWT) is applied to two different types of multidimensional digital earth-science data. The algorithms (WVQ) is optimized for each particular application through an optimization procedure that assigns VQ parameters to the wavelet transform subbands subject to constraints on compression ratio and encoding complexity. Preliminary results of compressing global ocean model data generated on a Thinking Machines CM-200 supercomputer are presented. The WVQ scheme is used in both a predictive and nonpredictive mode. Parameters generated by the optimization algorithm are reported, as are signal-to-noise (SNR) measurements of actual quantized data. The problem of extrapolating hydrodynamic variables across the continental landmasses in order to compute the DWT on a rectangular grid is discussed. Results are also presented for compressing Landsat TM 7-band data using the WVQ scheme. The formulation of the optimization problem is presented along with SNR measurements of actual quantized data. Postprocessing applications are considered in which the seven spectral bands are clustered into 256 clusters using a k-means algorithm and analyzed using the Los Alamos multispectral data analysis program, SPECTRUM, both before and after being compressed using the WVQ program.

Bradley, Jonathan N.↗

Optimization of composite box-beam structures including effects of subcomponent interactions

Minimum mass designs are obtained for a simple box beam structure subject to bending, torque and combined bending/torque load cases. These designs are obtained subject to point strain and linear buckling constraints. The present work differs from previous efforts in that special attention is payed to including the effects of subcomponent panel interaction in the optimal design process. Two different approaches are used to impose the buckling constraints. When the global approach is used, buckling constraints are imposed on the global structure via a linear eigenvalue analysis. This approach allows the subcomponent panels to interact in a realistic manner. The results obtained using this approach are compared to results obtained using a traditional, less expensive approach, called the local approach. When the local approach is used, in-plane loads are extracted from the global model and used to impose buckling constraints on each subcomponent panel individually. In the global cases, it is found that there can be significant interaction between skin, spar, and rib design variables. This coupling is weak or nonexistent in the local designs. It is determined that weight savings of up to 7% may be obtained by using the global approach instead of the local approach to design these structures. Several of the designs obtained using the linear buckling analysis are subjected to a geometrically nonlinear analysis. For the designs which were subjected to bending loads, the innermost rib panel begins to collapse at less than half the intended design load and in a mode different from that predicted by linear analysis. The discrepancy between the predicted linear and nonlinear responses is attributed to the effects of the nonlinear rib crushing load, and the parameter which controls this rib collapse failure mode is shown to be the rib thickness. The rib collapse failure mode may be avoided by increasing the rib thickness above the value obtained from the (linear analysis based) optimizer. It is concluded that it would be necessary to include geometric nonlinearities in the design optimization process if the true optimum in this case were to be found.

Ragon, Scott A.↗

Knowledge Oriented Graph Unified Transformer (KOGUT) v0.1

KOGUT — Knowledge Oriented Graph Unified Transformer KOGUT implements the Relational Graph Transformer (RelGT) architecture for knowledge graph link prediction in biological domains, with a primary focus on microbial growth media prediction. While the original RelGT (arXiv:2505.10960) targets relational tables, time series, and multi-table databases, KOGUT adapts this architecture for heterogeneous biological knowledge graphs, providing first-in-class AI predictive models for microbial cultivation. Key Adaptations Beyond Original RelGT: - Knowledge Graph Focus: Applied to biological KGs with semantic node types (taxa, chemicals, media, phenotypes, environments) versus generic relational database tables, trained on the KG-Microbe knowledge graph (1.3M entities, 2.9M edges, 24 relation types). - Multimodal Node Encoding: Integrates node labels, categories, descriptions, and synonyms from KG metadata through learned embedding layers—adapting relational column features to graph node attributes with textual semantics. - Extended K-Hop Subgraph Strategy: Optimized neighborhood sampling (3-hop default, configurable up to 200 nodes) tuned for sparse biological networks, building on the original local-global attention framework with biological relation preservation. - Biolink Predicate Preservation: Type-specific transformations for 24 biological edge semantics (occurs_in, consumes, produces, has_phenotype, subclass_of) beyond standard relational foreign keys, enabling multi-relation link prediction. - Inductive Learning Support: Enables zero-shot predictions for novel taxa through feature-based embeddings (temperature, oxygen requirements, gram stain, cell shape), extending the original transductive relational benchmark scope to uncultured microorganisms. CheapSOTA Performance Optimizations (This Distribution): - VQ-EMA Centroid Attention: Vector quantization with exponential moving average for improved global context modeling (+5-10% MRR improvement). - HDF5 Precomputed Data Loading: One-time preprocessing of k-hop subgraphs to eliminate redundant graph traversals (2-5× training speedup). - Distributed Data Parallel Training: Multi-GPU support for scaling to larger knowledge graphs (tested on 4× NVIDIA A100 GPUs at NERSC Perlmutter). - Mixed Precision Training: Automatic mixed precision (AMP) for memory efficiency and faster training. Advantages Over Standard Knowledge Graph Embedding Models: Combines RelGT's proven multi-element tokenization (features, type, hop, structure) with graph-native biological representations, enabling interpretable link prediction across heterogeneous entities that standard embedding models (TransE, RotatE, ComplEx) and table-based transformers cannot directly model. Achieves near-perfect performance on microbial growth media prediction (MRR: 0.9966, Precision@1: 0.9932, Hit@10: 1.0000) while maintaining explainability through attention-based reasoning over biological pathways. Training Data: - KG-Microbe merged knowledge graph: 1,379,337 nodes, 2,960,472 edges - 24 biological relation types including taxonomic hierarchies, metabolic interactions, phenotype associations, and environmental relationships - Primary prediction task: Growth media suitability for microbial taxa (biolink:occurs_in, 50K edges) - Multi-relation capability: Predicts links for any of the 24 relation types, including chemical consumption/production, phenotype associations, and taxonomic classification Citation: Original RelGT Architecture: Dwivedi et al., "Relational Graph Transformer", arXiv:2505.10960, 2025 KOGUT Implementation: Knowledge Oriented Graph Unified Transformer for Microbial Growth Media Prediction Developed at Lawrence Berkeley National Laboratory (LBNL) Trained on NERSC Perlmutter supercomputer

Joachimiak, Marcin [Lawrence Berkeley National Lab↗