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At least 469 records · Page 26

Technical Learning and Integration of Interns in Advanced Protection Lab Space: Enhancements to Testbed and Experiments to Improve Workflows for Producing Datasets

This report presents a successful technical learning integration of student interns in the Advanced Protection Laboratory space, located in the Grid Research Integration and Deployment Center (GRID-C) at the Department of Energy’s (DOE’s) Oak Ridge National Laboratory (ORNL). The Advanced Protection Laboratory was created for the primary goal of supporting DOE’s research projects and technical staff at ORNL. As a secondary goal, the space was used for collaborating with ORNL’s intern programs, providing support to the lab’s mentors and student interns. In 2024, three student interns spent a summer in the Advanced Protection lab space and were involved in the DarkNet Distributed Ledger Technology (DLT) project. The students had a great opportunity to gain hands-on experience with communication and protective relay equipment focused on information technology, data analytics, and cybersecurity. Experiences in the lab space with real equipment and software integration offer education and professional development for students, which is especially important because of a need in the energy industry to recruit highly skilled power and communication engineers.

42 ENGINEERING↗

Understanding Biases in Sample Preparation Techniques for Coupled Scanning Electron Microscopy and MAMA PuO 2 Morphological Analysis

In this project, the scanning electron microscopy (SEM) sampling method used during the statistical design study (SDS) was investigated to determine if any sampling biases were present in the analyzed data. Using standard particle size distribution powders from the National Institute of Standards and Technology (NIST 1984 standard reference material) with the origin wet dispersion method, it was determined that a bias to smaller particles was present. This was supported by theoretical calculations using Stokes’ law to determine the settling rate of spherical particles of roughly the same size and mass as those found in the SDS. Based on the theoretical calculations, it was determined that the settling rate for each of the 76 powder sets in the SDS could be unique based on specific particle shape and mass distributions, making a universal correction factor/formula not applicable. Therefore, priority shifted to developing an improved wet dispersion method that significantly reduced the particle settling rate for all particle size and shapes. This was achieved by replacing the original solvent (isopropyl alcohol) with a heavy liquid (lithium heteropolytungstates), which dramatically slowed the settling rate and allowed for the capture of a suitable homogeneous aliquot. SEM imaging and Morphological Analysis for Material Attribution (MAMA) software analysis were conducted on the NIST standard, and the SEM/MAMA data were compared to data captured by a dynamic image analysis particle size analyzer. The resulting data confirmed that the new wet dispersion method does indeed deliver an improved representative aliquot to the SEM stub. For instance, in the NIST certificate, the average particle size is ~17.1 µm ± 2.2 µm with a normal distribution. The initial wet dispersion method resulted in a drastically reduced average particle size of 6.1 µm in addition to a non-representative heavy bi-modal distribution whereas the improved LST wet dispersion method resulting in an average particle size that was much closer to the NIST certificate (12.7 µm) with a similar normal distribution. Although the improved method was still short of the NIST certificate average, atomic force microscopy analysis determined that the resulting ~20-25% reduction in size was due to particles sinking into the carbon sticky tape used for SEM imaging. It is believed that that this bias can be calibrated in a much more predicable manner than the original settling rate bias. In addition, the matching normal distribution curves between the NIST certificate and the heavy liquid method indicate a much-improved representative aliquot has been sampled and imaged. A surrogate CeO 2 powder was used to reflect PuO 2 more accurately and to aid in implementing radiological controls and shielding. The resulting data sets from the SEM/MAMA method and the particle size analyzer give almost identical average particle sizes and particle distribution statistics. Future work will re-analyze several select runs from the SDS to determine if morphological signatures can be found with the improved sampling method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

ANALYSIS TOOLS FOR SIZING AND PLACEMENT OF ENERGY STORAGE IN GRID APPLICATIONS

The purpose of this report was to review pertinent literature and studies to identify current state-of-the-art models and analytical tools that optimize the siting, sizing, and economic value of energy storage in a smart grid infrastructure. In recent decades, research and development has significantly improved the cost and reliability of energy storage systems. However, a relatively small percentage of that work has focused on engineering tools for integrating energy storage into existing or future electric grids. This literature review revealed that only a small number of software tools exist, and that those tools only partially address the needs for placement, sizing, and overall control strategies of stationary energy storage within a smart grid infrastructure. None of the tools comprehensively captures the benefits of energy storage, which would reveal all of the potential values. None of the tools or models provides optimization features that identify optimal placement and sizing options within a transmission or distribution system context. This review identifies a need for tool development to fill the gap in the grid analytics and provides some recommendations of guiding principles for advancing the analytical capabilities needed for the engineering and grid planning communities.

energy storage↗

An Open Source Extensible Smart Energy Framework

Aggregated distributed energy resources are the subject of much interest in the energy industry and are expected to play an important role in meeting our future energy needs by changing how we use, distribute and generate electricity. This energy future includes an increased amount of energy from renewable resources, load management techniques to improve resiliency and reliability, and distributed energy storage and generation capabilities that can be managed to meet the needs of the grid as well as individual customers. These energy assets are commonly referred to as Distributed Energy Resources (DER). DERs rely on a means to communicate information between an energy provider and multitudes of devices. Today DER control systems are typically vendor-specific, using custom hardware and software solutions. As a result, customers are locked into communication transport protocols, applications, tools, and data formats. Today’s systems are often difficult to extend to meet new application requirements, resulting in stranded assets when business requirements or energy management models evolve. By partnering with industry advisors and researchers, an implementation DER research platform was developed called the Smart Energy Framework (SEF). The hypothesis of this research was that an open source Internet of Things (IoT) framework could play a role in creating a commodity-based eco-system for DER assets that would reduce costs and provide interoperable products. SEF is based on the AllJoynTM IoT open source framework. The demonstration system incorporated DER assets, specifically batteries and smart water heaters. To verify the behavior of the distributed system, models of water heaters and batteries were also developed. An IoT interface for communicating between the assets and a control server was defined. This interface supports a series of “events” and telemetry reporting, similar to those defined by current smart grid communication standards. The results of this effort demonstrated the feasibility and application potential of using IoT frameworks for the creation of commodity-based DER systems. All of the identified commodity-based system requirements were met by the AllJoyn framework. By having commodity solutions, small vendors can enter the market and the cost of implementation for all parties is reduced. Utilities and aggregators can choose from multiple interoperable products reducing the risk of stranded assets. Based on this research it is recommended that interfaces based on existing smart grid communication protocol standards be created for these emerging IoT frameworks. These interfaces should be standardized as part of the IoT framework allowing for interoperability testing and certification. Similarly, IoT frameworks are introducing application level security. This type of security is needed for protecting application and platforms and will be important moving forward. Recommendations are that along with DER-based data model interfaces, platform and application security requirements also be prescribed when IoT devices support DER applications.

25 ENERGY STORAGE↗

Autonomous Microgrid Restoration Using Grid-Forming Inverters and Smart Circuit Breakers: Preprint

The proliferation of distributed inverter-based resources (IBRs) raises the questions if these IBRs can be used to blackstart microgrids and distribution feeders after major outages. In this paper, we propose and evaluate an autonomous microgrid restoration concept using grid-forming (GFM) IBRs and smart circuit creakers (SCBs). The concept is first explored in simulation platform and then a hardware testbed containing actual GFM inverters is developed to demonstrate these functionalities. A combination of dispatchable virtual oscillator control (dVOC) and droop-based control schemes have been designed for GFM inverter controls in the software simulations and hardware testbed. Subsequently, operation of SCBs using two distinct principles have been demonstrated that can restore or connect portions of the network.

grid reconfiguration↗

Phasor Domain Steady-State Modeling and Design of the DC–DC Modular Multilevel Converter

The DC-DC Modular Multilevel Converter (MMC), which originated from the AC-DC MMC, is an attractive converter topology for interconnection of medium-/high-voltage DC grids. This paper presents design considerations for the DC-DC MMC to achieve high efficiency and reduced component sizes. A steady-state mathematical model of the DC-DC MMC in the phasor-domain is developed. Based on the developed model, a design approach is proposed to size the components and to select the operating frequency of the converter to satisfy a set of design constraints while achieving high efficiency. The design approach includes sizing of the arm inductor, Sub-Module (SM) capacitor, and phase filtering inductor along with the selection of AC operating frequency of the converter. The accuracy of the developed model and the effectiveness of the design approach are validated based on the simulation studies in the PSCAD/EMTDC software environment. The analysis and developments of this paper can be used as a guideline for design of the DC-DC MMC.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Next-Generation Optimization under Uncertainty: Structure-Oriented Algorithms

With the advent of the smart grid, renewable technologies, and carbon emission programs, a key concern is the coordination of national infrastructures such as the electricity, natural gas, and water supply network systems. Anticipating and mitigating uncertainty of weather, demands, and contingencies in a more integrated environment is necessary to maximize resource efficiency and prevent cascading failures that can ultimately lead to catastrophic shortages of supplies. This project developed scalable algorithms for stochastic optimization capable of addressing extreme-scale problems (motivated by challenges in the design and operation of national infrastructures). Specifically, the project developed a new family of algorithms to solve continuous stochastic problems to local and global optimality as well as algorithms to solve mixed-integer convex and nonconvex stochastic programs. We developed supporting local and global convergence theory for these algorithms and implemented the algorithms in open-source software packages that can leverage high-performance computing architectures.

24 POWER TRANSMISSION AND DISTRIBUTION↗

MPC4CLR (Model-Predictive-Control-for-Critical-Load-Restoration-in-Power-Distribution-Systems) [SWR-22-24]

Model predictive control (MPC) is a system or process control technique for making decisions under uncertainty via rolling look-ahead optimizations at each control step where only the current step decisions are applied, and the rest are discarded. In this work, we developed an MPC for a critical load restoration (CLR) in power distribution systems to recover system service (electricity delivery) following an extreme event-triggered substation outage. The method considers the problem of controlling distributed energy resources (DERs) of the distribution system with the objective of achieving maximum load pick up while satisfying distribution network flow and voltage constraints. A linearized optimal power flow (OPF) model is employed to represent the physics of the network. The problem formulation is augmented with a ramping (up) reserve product for the DERs to ensure improved and upward monotonic load restoration as time evolves. Simulation analysis and performance tests are performed using a modified IEEE 13-bus test feeder integrated with wind, solar, microturbine, and energy storage battery. The software is developed using various software packages in Julia and Python. The MPC model is implemented using the JuMP optimization language in Julia while the data analytics including renewable generation and load demand forecasts, running the MPC simulation and visualizations is performed in Python.

Eseye, Abinet Tesfaye↗

Decentralized Signal Processing and Distributed Control of Collaborative Autonomous Networks (17-ERD-101 LDRD Final Report)

Intelligent autonomous sensor networks, often comprised of large numbers of sensors, must be capable of jointly exploiting data collected at each agent in the network, and using that data to optimize their future actions towards multiple mission objectives. Centralized signal processing and optimization solutions process all data and determine all future actions at a single agent, and the resulting information and commands are disseminated back to the network. The communications bandwidth this requires and the single point of failure the central agent represents often make these solutions untenable for national security applications. In this project, several fundamental algorithms for solving both the decentralized signal processing and network optimization were developed, as well as simulation software to validate the results of these algorithms at scale. Specifically, novel algorithms for Bayesian decentralized estimation and decentralized detection and optimization based on the alternating direction method of multipliers (ADMM) were developed for autonomous sensor networks and published in the literature. The first large scale simulation of autonomous sensor networks (1000 agents) was conducted on this project, validating the performance of the developed algorithms. These algorithms and simulation tools are critical components of any decentralized autonomous network and have current and future national security applications, including distributed sensor networks for detection, estimation, and tracking problems, and large decentralized cyber-physical infrastructure such as the power grid.

42 ENGINEERING↗

High spatial resolution mapping of deposition layers on plasma facing materials by laser ablation microprobe time-of-flight mass spectroscopy

A laser ablation microprobe time-of-flight mass spectroscopy (LAM-TOF-MS) system with high spatial resolution, ∼20 nm in depth and ∼500 μm or better on the surface, is developed to analyze the composition distributions of deposition layers on the first wall materials or first mirrors in tokamak. The LAM-TOF-MS system consists of a laser ablation microprobe combined with a TOF-MS and a data acquisition system based on a LabVIEW program software package. Laser induced ablation combined with TOF-MS is an attractive method to analyze the depth profile of deposited layer with successive laser shots, therefore, it can provide information for composition reconstruction of the plasma wall interaction process. In this work, we demonstrate that the LAM-TOF-MS system is capable of characterizing the depth profile as well as mapping 2D composition of deposited film on the molybdenum first mirror retrieved from HL-2A tokamak, with particular emphasis on some of the species produced during the ablation process. The presented LAM-TOF-MS system provides not only the 3D characterization of deposition but also the removal efficiency of species of concern.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Recovery Act: A Measurement -- Management Technology for Improving Energy Efficiency in Data Centers and Telecommunication Facilities (Final Technical Report)

Data center (DC) electricity use is increasing at an annual rate of over 20% and presents a concern for the Information Technology (IT) industry, governments, and the society. A large fraction of the energy use is consumed by the compressor cooling to maintain the recommended operating conditions for IT equipment. The most common way to improve the DC efficiency is achieved by optimally provisioning the cooling power to match the global heat dissipation in the DC. However, at a more granular level, the large range of heat densities of today's IT equipment makes the task of provisioning cooling power optimized to the level of individual computer room air conditioning (CRAC) units much more challenging. Distributed sensing within a DC enables the development of new strategies to improve energy efficiency, such as hot spot elimination through targeted cooling, matching power consumption at rack level with workload schedule, and minimizing power losses. The scope of Measurement and Management Technologies (MMT) is to develop a software tool and the underlying sensing technology to provide critical decision support and control for DC and telecommunication facilities (TF) operations. A key aspect of MMT technology is integration of modeling tools to understand how changes in one operational parameter affect the overall DC response. It is demonstrated that reduced ordered models for DC can generate, in less than 2 seconds computational time, a three dimensional thermal model in a 50 kft 2 DC. This rapid modeling enables real time visualization of the DC conditions and enables "0what if" scenarios simulations to characterize response to "disturbances". One such example is thermal zone modeling that matches the cooling power to the heat generated at a local level by identifying DC zones cooled by a specific CRAC. Turning off a CRAC unit can be simulated to understand how the other CRAC utilization changes and how server temperature responds. Several new sensing technologies were added to the existing MMT platform: (1) air contamination (corrosion) sensors, (2) power monitoring, and (3) a wireless environmental sensing network. All three technologies are built on cost effective sensing solutions that increase the density of sensing points and enable high resolution mapping of DCs. The wireless sensing solution enables Air Conditioning Unit (ACU) control while the corrosion sensor enables air side economization and can quantify the risk of IT equipment failure due to air contamination. Validation data for six test sites demonstrate that leveraging MMT energy efficiency solutions combined with industry best practices results in an average of 20% reduction in cooling energy, without major infrastructure upgrades. As an illustration of the unique MMT capabilities, a data center infrastructure efficiency (DCIE) of 87% (industry best operation) was achieved. The technology is commercialized through IBM System and Technology Lab Services that offers MMT as a solution to improve DC energy efficiency. Estimation indicates that deploying MMT in existing DCs can results in an 8 billion kWh savings and projection indicates that constant adoption of MMT can results in obtainable savings of 44 billion kWh in 2035. Negotiations are under way with business partners to commercialize/license the ACU control technology and the new sensor solutions (corrosion and power sensing) to enable third party vendors and developers to leverage the energy efficiency solutions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

BEopt-CA (Ex) -- A Tool for Optimal Integration of EE/DR/ES+PV in Existing California Homes. Cooperative Research and Development Final Report, CRADA Number CRD-11-429

Opportunities for combining energy efficiency, demand response, and energy storage with PV are often missed, because the required knowledge and expertise for these different technologies exist in separate organizations or individuals. Furthermore, there is a lack of quantitative tools to optimize energy efficiency, demand response and energy storage with PV, especially for existing buildings. Our goal is to develop a modeling tool, BEopt-CA (Ex), with capabilities to facilitate identification and implementation of a balanced integration of energy efficiency (EE), demand response (DR), and energy storage (ES) with photovoltaics (PV) within the residential retrofit market. To achieve this goal, we will adapt and extend an existing tool -- BEopt -- that is designed to identify optimal combinations of efficiency and PV in new home designs. In addition, we will develop multifamily residential modeling capabilities for use in California, to facilitate integration of distributed solar power into the grid in order to maximize its value to California ratepayers. The project is follow-on research that leverages previous California Solar Initiative RD&D investment in the BEopt software. BEopt facilitates finding the least cost combination of energy efficiency and renewables to support integrated DSM (iDSM) and Zero Net Energy (ZNE) in California residential buildings. However, BEopt is currently focused on modeling single-family houses and does not include satisfactory capabilities for modeling multifamily homes. The project brings BEopt's existing modeling and optimization capabilities to multifamily buildings, including duplexes, triplexes, townhouses, flats, and low-rise apartment buildings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Michel Electron Selection with SPINE for DUNE Far Detector Simulation

Michel electrons are a valuable input for particle detector calibration due to their consistent kinetic energy distribution. This report details the evaluation of a Michel electron identification method's application to simulated data from the DUNE (Deep Underground Neutrino Experiment) far detector. This method, which relies on the neural network-based particle classification software SPINE (Scalable Particle Imaging with Neural Embeddings), was developed and calibrated using simulated data for the SBND (Short-Baseline Neutrino Detector) experiment before being applied to simulated DUNE data from a 1x2x6 subset of far detector modules.

Wilson, Dante [Colorado State U.]↗

Self-assessed performance improves statistical fusion of image labels

Purpose: Expert manual labeling is the gold standard for image segmentation, but this process is difficult, time-consuming, and prone to inter-individual differences. While fully automated methods have successfully targeted many anatomies, automated methods have not yet been developed for numerous essential structures (e.g., the internal structure of the spinal cord as seen on magnetic resonance imaging). Collaborative labeling is a new paradigm that offers a robust alternative that may realize both the throughput of automation and the guidance of experts. Yet, distributing manual labeling expertise across individuals and sites introduces potential human factors concerns (e.g., training, software usability) and statistical considerations (e.g., fusion of information, assessment of confidence, bias) that must be further explored. During the labeling process, it is simple to ask raters to self-assess the confidence of their labels, but this is rarely done and has not been previously quantitatively studied. Herein, the authors explore the utility of self-assessment in relation to automated assessment of rater performance in the context of statistical fusion. Methods: The authors conducted a study of 66 volumes manually labeled by 75 minimally trained human raters recruited from the university undergraduate population. Raters were given 15 min of training during which they were shown examples of correct segmentation, and the online segmentation tool was demonstrated. The volumes were labeled 2D slice-wise, and the slices were unordered. A self-assessed quality metric was produced by raters for each slice by marking a confidence bar superimposed on the slice. Volumes produced by both voting and statistical fusion algorithms were compared against a set of expert segmentations of the same volumes. Results: Labels for 8825 distinct slices were obtained. Simple majority voting resulted in statistically poorer performance than voting weighted by self-assessed performance. Statistical fusion resulted in statistically indistinguishable performance from self-assessed weighted voting. The authors developed a new theoretical basis for using self-assessed performance in the framework of statistical fusion and demonstrated that the combined sources of information (both statistical assessment and self-assessment) yielded statistically significant improvement over the methods considered separately. Conclusions: The authors present the first systematic characterization of self-assessed performance in manual labeling. The authors demonstrate that self-assessment and statistical fusion yield similar, but complementary, benefits for label fusion. Finally, the authors present a new theoretical basis for combining self-assessments with statistical label fusion.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Power & Water Facility and Infrastructure Planning: CRADA Final Report

Los Alamos National Laboratory (LANL) has developed software and expertise for planning power grids and for examining the human resource issues for a nuclear power program. These programs, and other LANL software innovations, can offer an efficient manner in which to assist the power and water generation industries in both developed and undeveloped countries.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Southwest Wind Power R&D Test Site Development at the National Wind Technology Center (CRADA CRD-12-00472 Final Report)

Southwest Windpower, Inc. (SWWP) has been designing and distributing small wind turbines for more than 22 years and is the recognized global leader in the design, manufacturing and distribution of small wind systems (400-3000 watts). The company has been a pioneer in the development of wind technology and has built and shipped more than 170,000 wind turbines to over 120 countries worldwide. Headquartered in Flagstaff AZ, SWWP has sales representatives in over 88 countries. Applications for SWWP systems include residential homes, commercial properties, micro grids, remote cabins, telecom transmitters, offshore platforms, water pumping and sailboats. In addition, U.S. Department of Defense uses SWWP’s products in Forward Operating Bases (FOB’s), USGS uses them for remote monitoring of glacier movements and the CIA uses them to provide power seismic monitoring. Today, SWWP plans development of new technologies to address distributed energy market needs and become even more aggressive in international markets. This strategy includes extensive Research, Development, Demonstration & Deployment (RDD&D) activities to improve existing production line into more simple, reliable, and cost-effective wind turbine systems. Important part of such activities is the field testing of the new systems, which should provide: (i) validation of the reliable operation of hardware and software; (ii) validation of numerical models of the system and its components; (iii) field comparison of various control and optimization strategies; (iv) customized reliability testing; (v) customized monitoring and analysis testing; and (vi) IEC certification testing (vii) filed demonstration of system performance and reliability. Such field testing facility should encompass multiple towers and appropriate data acquisition systems. SWWP is exploring to move part of the engineering department to Colorado, and execute its RDD&D strategies in this new location. Partnership with NREL will provide great insights into SWWP’s RDD&D processes and more efficient commercialization by utilizing NWTC as the field testing site, and working close with NREL personnel. NWTC is ideally suited to strain the design. NREL is very experienced with customized and IEC testing. During this project, Southwest Windpower aims to improve the value proposition of distributed renewable energy, and make it a competitive choice in the energy markets. As of today, more then 170,000 small wind turbines, manufactured in the U.S., are installed in more then 180 countries. With the improved value proposition, Southwest Windpower wants to create and address new market needs, substantially increase its sales domestically and internationally, which should have positive impact on the creation of American jobs, competitiveness of U.S. economy, export or U.S. products, and the use of renewable energy.

17 WIND ENERGY↗

MILK : a Python scripting interface to MAUD for automation of Rietveld analysis

Modern diffraction experiments ( e.g. in situ parametric studies) present scientists with many diffraction patterns to analyze. Interactive analyses via graphical user interfaces tend to slow down obtaining quantitative results such as lattice parameters and phase fractions. Furthermore, Rietveld refinement strategies ( i.e. the parameter turn-on-off sequences) tend to be instrument specific or even specific to a given dataset, such that selection of strategies can become a bottleneck for efficient data analysis. Managing multi-histogram datasets such as from multi-bank neutron diffractometers or caked 2D synchrotron data presents additional challenges due to the large number of histogram-specific parameters. To overcome these challenges in the Rietveld software Material Analysis Using Diffraction ( MAUD ), the MAUD Interface Language Kit ( MILK ) is developed along with an updated text batch interface for MAUD . The open-source software MILK is computer-platform independent and is packaged as a Python library that interfaces with MAUD . Using MILK , model selection ( e.g. various texture or peak-broadening models), Rietveld parameter manipulation and distributed parallel batch computing can be performed through a high-level Python interface. A high-level interface enables analysis workflows to be easily programmed, shared and applied to large datasets, and external tools to be integrated with MAUD . Through modification to the MAUD batch interface, plot and data exports have been improved. The resulting hierarchical folders from Rietveld refinements with MILK are compatible with Cinema: Debye–Scherrer , a tool for visualizing and inspecting the results of multi-parameter analyses of large quantities of diffraction data. In this manuscript, the combined Python scripting and visualization capability of MILK is demonstrated with a quantitative texture and phase analysis of data collected at the HIPPO neutron diffractometer.

97 MATHEMATICS AND COMPUTING↗

Center for Computing Research Highlights

Sandia has a legacy of leadership in the advancement of high performance computing (HPC) at extreme scales. First-of-a-kind scalable distributed-memory parallel platforms such as the Intel Paragon, ASCI Red (the world’s first teraflops computer), and Red Storm (co-developed with Cray) helped form the basis for one of the most successful supercomputer product lines ever: the Cray XT series. Sandia also has pioneered system software elements—including lightweight operating systems, the Portals network programming interface, advanced interconnection network designs, and scalable I/O— that are critical to achieving scalability on large computing systems.

97 MATHEMATICS AND COMPUTING↗