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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 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

Encealdus Orbilander: A Flagship Mission Concept for Astrobiology

"Whether life exists beyond Earth remains a fundamental question driving our exploration of the Solar System. At Saturn’s moon Enceladus, plumes of oceanic material vented into space allow the investigation of the astrobiological potential of an ocean world, hinted at by Cassini, without the necessity of drilling through kilometers of ice crust. The Enceladus Orbilander is a flagship ($2.56B in fiscal year 2025 dollars) mission concept created for the 2023–2033 Planetary Science Decadal Survey. Orbilander takes full advantage of the opportunity provided by Enceladus’ plumes to search for signs of life. A single spacecraft both orbits and lands, capturing samples from four distinct reservoirs offered by the plumes. These samples, both particulate and vapor, are then analyzed by the Life Detection Suite (LDS), a set of five instruments conducting complementary and orthogonal biosignature-seeking measurements. To provide the context that specifically enhances interpretation of LDS measurements, geochemical and geophysical investigations are conducted both in orbit and on the surface. These reveal the physio-chemical state of the ocean and core as well as the processes involved in ejection of plume material and how these affect the ocean material analyzed by the LDS. The Orbilander can be delivered to the Saturn system via several launch vehicle and trajectory options, including a direct trajectory (7-year cruise), a ∆V-EGA trajectory (9-year cruise) and several options using an inner cruise with Venus and Earth flybys (10-year cruise). Upon Saturn Orbit Insertion, a 4-year moon tour pumps down the Orbilander’s orbit to intercept Enceladus. The most optimal arrival times balance the Jupiter flyby opportunities of the late 2030s and solar illumination at the Enceladus high southern latitudes where plume material is most abundant. This mission concept therefore targets project start in 2030. Upon Enceladus Orbit Insertion, the Orbilander begins a 1.5-year-long campaign of landing site reconnaissance, remote sensing science, and collecting sufficient plume sample to run all but one of the LDS measurements. After successful landing, the Orbilander spends 2 years on the surface conducting multiple LDS measurements with all five instruments on actively and passively collected plume material, as well as seismic investigations. The schedule laid out here is well-defined, but the mission also has operational and resource flexibility should additional reconnaissance be needed. As part of the design study, mission and development risks were identified and mitigation strategies proposed. Technologies key to achieving the life detection science objectives include instrumentation matured under programs like COLDTech and ICEE-2, such as aspects of the sampling system and microfluidic devices, as well as well-known techniques like high-resolution and separation-capable mass spectrometers. Autonomous onboard navigation is planned to maintain a halo orbit around Enceladus to enable passive sampling from orbit as well as reconnaissance measurements for use in site selection and landing. Terrain relative navigation is included to ensure safe landing, given that targeted areas may contain landing hazards. Continued development of radioisotope thermoelectric generator (RTG) technology and long-life batteries is essential for this long duration mission. The Enceladus Orbilander represents an optimal point in the trade space of science value versus cost, taking advantage of the extensive knowledge of Enceladus provided by Cassini, how well Enceladus lends itself to a search for life in material from its ocean, and the flexibility afforded by the innovative design developed by the APL team. By taking full advantage of Enceladus’ plumes both in orbit and on the surface, Orbilander represents a robust search for life with complementary and orthogonal biosignatures as well as contextual geophysical and geochemical measurements, determining not only whether Enceladus is inhabited (at levels up to 500,000× scarcer than in Earth’s oceans) but also why. "

Exobiology↗
DOE OSTI2026

Enabling Dynamic Probabilistic Risk Assessment of Physical Security Using EMRALD and MAAP (Presentation)

The optimization of physical security in nuclear power plants requires sophisticated methodologies that integrate operator actions and plant behavior through advanced simulation tools. Idaho National Laboratory has developed the Modeling and Analysis for Safety and Security using the Dynamic EMRALD Framework (MASS-DEF) methodology, an approach that integrates force-on-force simulations, dynamic probabilistic risk assessment, and thermal hydraulics modeling to enhance security planning while reducing costs. A reduced order model for thermal hydraulic simulations performed by the Modular Accident Analysis Program (MAAP) was developed to evaluate reactor core behavior during attack scenarios. MAAP simulations are computationally intensive and must be run in a secure environment, complicating analysis and validation. By pre-computed scenario outcomes for a small number of modified parameters, the reduced order model significantly decreases the computational cost and enables offsite review of the results.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Runtime power allocation approach for GAMESS hybrid CPU‐GPU implementation

Summary To improve power consumption of applications at the runtime, modern processors provide frequency scaling capabilities, which along with workload optimization, are also available on GPU accelerators. In this work, a runtime strategy is proposed to distribute a given power allocation among the host components and the GPU according to the current application performance and power usage, such that GPU execution is prioritized over CPU for power allocation to maximize application performance. Next, the strategy is tailored to an application, a quantum‐chemistry package GAMESS for ab initio electronic structure calculations. Specifically, GAMESS hybrid CPU–GPU implementation as provided in the Libcchem library is considered. Experiments, performed on a 28‐core node with a Kepler GPU, resulted in performance gains of up to 50% under the proposed strategy and the largest power allocation considered here as compared with the scenario when this allocation was equally distributed among the computing‐platform components.

Sundriyal, Vaibhav↗
DOE OSTI2020

GPU-Based Static Data-Flow Analysis for Fast and Scalable Android App Vetting

Many popular vetting tools for Android applications use static code analysis techniques. In particular, Interprocedural Data-Flow Graph (IDFG) construction is the computation at the core of Android static data-flow analysis and consumes most of the analysis time. Many analysis tools use a worklist algorithm, an iterative fixed-point approach, to construct the IDFG. In this paper, we observe that a straightforward GPU parallelization of the worklist algorithm leads to significant underutilization of the GPU resources. We identify four performance bottlenecks, namely, frequent dynamic memory allocations, high branch divergence, workload imbalance, and irregular memory access patterns. Accordingly, we propose GDroid, a GPU-based worklist algorithm implementation with multiple fine-grained optimizations tailored to common characteristics of Android applications. The optimizations considered are: matrix-based data structure, memory access-based node grouping, and worklist merging. Our experimental evaluation, performed on 1000 Android applications, shows that the proposed optimizations are beneficial to performance, and GDroid can achieve up to 128X speedups against a plain GPU implementation.

Android security↗
DOE OSTI2024

Control And Optimization Modular Modeling Application For Nuclear Deployment

The purpose of the COMMAND code is to provide a flexible, scalable tool for use in developing, integrating, and testing the technologies necessary for achieving autonomous operations of advanced nuclear reactors. The code enables users to efficiently implement custom simulations and experiments by combining key methods from different software modules. These modules are focused on: modeling and simulation tools, such as nuclear simulation tools used for high-fidelity modeling (e.g., Reactor Excursion and Leak Analysis Program [RELAP5-3D] and Monte Carlo N-Particle [MCNP]); machine learning and optimization tools (e.g., anomaly detection and data-driven modeling techniques); advanced control in its digital, high-performance, and supervisory control forms (e.g., proportional integral derivative (PID) control and model predictive control (MPC); and integration with hardware through industrial communication protocols. To ensure flexibility and scalability, COMMAND was designed to be both modular—the software “pieces” all inherit from generic building blocks and can be combined and connected to create complicated simulations—and high performing—designed for parallel processing, enabling simulations and experiments to take advantage of multi-core computers, servers, and nodes. The code is written in the Python programming language due to the language's popularity, active community, and open-source and cross-platform nature. Maintaining consistency with other simulation tools used within the nuclear energy community, users implement simulations and experiments through text input files, which define components, parameters, connections, etc., through lines of text. Given that COMMAND is written in Python, these input files are native Python scripts, and so use the standard Python structure and formatting. This also enables users to take advantage of Python's extensive package library to develop custom capabilities for their specific use cases.

Faber, Jacob [Idaho National Laboratory (INL), Ida↗
DOE OSTI2023

BayFlux: A Bayesian method to quantify metabolic Fluxes and their uncertainty at the genome scale

Metabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. 13 C Metabolic Flux Analysis ( 13 C MFA) is considered to be the gold standard for measuring metabolic fluxes. 13 C MFA typically works by leveraging extracellular exchange fluxes as well as data from 13 C labeling experiments to calculate the flux profile which best fit the data for a small, central carbon, metabolic model. However, the nonlinear nature of the 13 C MFA fitting procedure means that several flux profiles fit the experimental data within the experimental error, and traditional optimization methods offer only a partial or skewed picture, especially in “non-gaussian” situations where multiple very distinct flux regions fit the data equally well. Here, we present a method for flux space sampling through Bayesian inference (BayFlux), that identifies the full distribution of fluxes compatible with experimental data for a comprehensive genome-scale model. This Bayesian approach allows us to accurately quantify uncertainty in calculated fluxes. We also find that, surprisingly, the genome-scale model of metabolism produces narrower flux distributions (reduced uncertainty) than the small core metabolic models traditionally used in 13 C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from 13 C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P- 13 C MOMA and P- 13 C ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods by quantifying prediction uncertainty.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1988

Technology developments for a compound cycle engine

The Compound Cycle Engine (CCE) is a highly turbocharged, power compounded power plant which combines the light weight pressure rise capability of a gas turbine with the high efficiency of a diesel. When optimized for a rotorcraft, the CCE will reduce fuel burned for a typical 2 hour (plus 30 min reserve) mission by 30 to 40 percent when compared to a conventional advanced technology gas turbine. The CCE can provide a 50 percent increase in range-payload product on this mission. Results of recent activities in a program to establish the technology base for a CCE are presented. The objective of this program is to research and develop those critical technologies which are necessary for the demonstration of a multicylinder diesel core in the early 1990s. A major accomplishment was the initial screening and identification of a lubricant which has potential for meeting the material wear rate limits of the application. An in-situ wear measurement system also was developed to provide accurate, readily obtainable, real time measurements of ring and liner wear. Wear data, from early single cylinder engine tests, are presented to show correlation of the in-situ measurements and the system's utility in determining parametric wear trends. A plan to demonstrate a compound cycle engine by the mid 1990s is included.

Bobula, George A.↗
DOE OSTI2021

Revisiting Huffman Coding: Toward Extreme Performance on Modern GPU Architectures

Today's high-performance computing (HPC) applications are producing vast volumes of data, which are challenging to store and transfer efficiently during the execution, such that data compression is becoming a critical technique to mitigate the storage burden and data movement cost. Huffman coding is arguably the most efficient Entropy coding algorithm in information theory, such that it could be found as a fundamental step in many modern compression algorithms such as DEFLATE. On the other hand, today's HPC applications are more and more relying on the accelerators such as GPU on supercomputers, while Huffman encoding suffers from low throughput on GPUs, resulting in a significant bottleneck in the entire data processing. In this paper, we propose and implement an efficient Huffman encoding approach based on modern GPU architectures, which addresses two key challenges: (1) how to parallelize the entire Huffman encoding algorithm, including codebook construction, and (2) how to fully utilize the high memory-bandwidth feature of modern GPU architectures. The detailed contribution is fourfold. (1) We develop an efficient parallel codebook construction on GPUs that scales effectively with the number of input symbols. (2) We propose a novel reduction based encoding scheme that can efficiently merge the codewords on GPUs. (3) We optimize the overall GPU performance by leveraging the state-of-the-art CUDA APIs such as Cooperative Groups. (4) We evaluate our Huffman encoder thoroughly using six real-world application datasets on two advanced GPUs and compare with our implemented multithreaded Huffman encoder. Experiments show that our solution can improve the encoding throughput by up to 5.0× and 6.8× on NVIDIA RTX 5000 and V100, respectively, over the state-of-the-art GPU Huffman encoder, and by up to 3.3× over the multithread encoder on two 28-core Xeon Platinum 8280 CPUs.

Tian, Jiannan↗
DOE OSTI2018

Current Management of High-Risk Breast Lesions

Purpose of review: The purpose of this review is to describe recent updates in the management of high-risk breast lesions. We review the various high-risk breast lesions and evaluate the collective literature regarding the rates of upgrade to invasive cancer or ductal carcinoma in situ with excisional biopsy as well as the increased risk for future breast cancer development that a diagnosis of a high-risk breast lesion may portend. For those lesions associated with an increased risk of breast cancer, we discuss the appropriate surveillance regimens as well as risk reduction opportunities available to patients. Recent findings: Recent studies may suggest a role for close imaging observation in certain clinical settings when a benign intraductal papilloma or flat epithelial atypia is identified by core needle breast biopsy. Ongoing prospective clinical trials should reveal valuable data to help answer this question. Summary: Clinical management of high-risk breast lesions identified and determined to be concordant after image-guided core needle biopsy varies and prospective data are needed to better guide management decisions. High-risk breast lesions require close radiologic-pathologic correlation when diagnosed by image-guided breast core needle biopsy. Excisional biopsy can exclude a higher-grade lesion such as DCIS or invasive cancer; however, in certain cases, close observation with follow-up may be appropriate. Additionally, women who have certain high-risk lesions such as lobular carcinoma in situ, atypical ductal hyperplasia, or atypical lobular hyperplasia are at an increased risk for the future development of breast cancer and should undergo risk assessment and discussion of risk reduction measures. Ongoing and future prospective trials may provide data to better guide these management decisions and optimize patient care.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2025

Perovskite Catalysts for Pure-Water-Fed Anion-Exchange-Membrane Electrolyzer Anodes: Co-design of Electrically Conductive Nanoparticle Cores and Active Surfaces

Anion-exchange-membrane water electrolyzers (AEMWEs) are a possible low-capital-expense, efficient, and scalable hydrogen-production technology with inexpensive hardware, earth-abundant catalysts, and pure water. However, pure-water-fed AEMWEs remain at an early stage of development and suffer from inferior performance compared with proton-exchange-membrane water electrolyzers (PEMWEs). One challenge is to develop effective non-platinum-group-metal (non-PGM) anode catalysts and electrodes in pure-water-fed AEMWEs. We show how LaNiO3-based perovskite oxides can be tuned by cosubstitution on both A- and B-sites to simultaneously maintain high metallic electrical conductivity along with a degree of surface reconstruction to expose a stable Co-based active catalyst. The optimized perovskite, Sr0.1La0.9Co0.5Ni0.5O3, yielded pure-water AEMWEs operating at 1.97 V at 2.0 A cm-2 at 70 °C with a pure-water feed, thus illustrating the utility of the catalyst design principles.

Zhai, Tingting↗
DOE OSTI2020

A cautionary tale: Problems in the valence-CASSCF description of the ground state (X1Σ+) of BF

In the full optimized reaction space and valence-complete active space self-consistent field (vCAS) methods, a set of active orbitals is defined as the union of the valence orbitals on the atoms, all possible configurations involving the active orbitals are generated, and the orbitals and configuration coefficients are self-consistently optimized. Such wave functions have tremendous flexibility, which makes these methods incredibly powerful but can also lead to inconsistencies in the description of the electronic structure of molecules. In this paper, the problems that can arise in vCAS calculations are illustrated by calculations on the BH and BF molecules. BH is well described by the full vCAS wave function, which accounts for molecular dissociation and 2s–2p near-degeneracy in the boron atom. The same is not true for the full vCAS wave function for BF. There is mixing of core and active orbitals at short internuclear distances and swapping of core and active orbitals at large internuclear distances. In addition, the virtual 2π orbitals, which were included in the active space to account for the 2s–2p near degeneracy effect, are used instead to describe radial correlation of the electrons in the F2pπ-like pairs. Although the above changes lead to lower vCAS energies, they lead to higher vCAS+1+2 energies as well as irregularities and/or discontinuities in the potential energy curves. All of the above problems can be addressed by using the spin-coupled generalized valence bond-inspired vCAS wave function for BF, which includes only a subset of the atomic valence orbitals in the active space.

Xu, Lu T. (ORCID:0000000182064902)↗
DOE OSTI2021

Scaling pair count to next galaxy surveys

ABSTRACT Counting pairs of galaxies or stars according to their distance is at the core of real-space correlation analyses performed in astrophysics and cosmology. Upcoming galaxy surveys (LSST, Euclid) will measure properties of billions of galaxies challenging our ability to perform such counting in a minute-scale time relevant for the usage of simulations. The problem is only limited by efficient access to the data, hence belongs to the big data category. We use the popular Apache Spark framework to address it and design an efficient high-throughput algorithm to deal with hundreds of millions to billions of input data. To optimize it, we revisit the question of non-hierarchical sphere pixelization based on cube symmetries and develop a new one dubbed the ‘Similar Radius Sphere Pixelization’ (SARSPix) with very close to square pixels. It provides the most adapted indexing over the sphere for all distance-related computations. Using LSST-like fast simulations, we compute autocorrelation functions on tomographic bins containing between a hundred million to one billion data points. In each case, we achieve the construction of a standard pair-distance histogram in about 2 min, using a simple algorithm that is shown to scale, over a moderate number of nodes (16–64). This illustrates the potential of this new techniques in the field of astronomy where data access is becoming the main bottleneck. They can be easily adapted to other use-cases as nearest-neighbours search, catalogue cross-match or cluster finding. The software is publicly available from https://github.com/astrolabsoftware/SparkCorr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Grid Operator Analytics and Assessment Tools for Inverter- Based Resources Dominated Grid (GOAAT-IBR) Project Update

This presentation provides an update on the OPTIMA GOAAT project, with emphasis on the cloud-native data platform developed in-house to ingest, manage, and operationalize high-resolution power system data. Since our last NASPI presentation, accessible via OSTI ID #2671437, the project team advanced the design and deployment of a scalable architecture capable of handling both synchronized and non-synchronized streams, including PMU, point-on-wave (POW), COMTRADE, and SCADA data. These materials review the project status, recent progress, and key lessons learned. The core of the presentation examines the architecture and engineering of our cloud-native ingestion and data management platform. We then explain how pipelines were designed to collect, normalize, time-align, store, and serve heterogeneous data at scale. We will discuss design choices such as data models, streaming versus batch ingestion, storage tiers, and interoperability with analytics applications. Practical experiences with cloud-native technologies were shared during the event, including benefits, limitations, and integration challenges in a utility environment, along with methods used to improve performance, reduce latency, and optimize resource usage. The presentation also showcases user interface designs and visualization tools that convert raw measurements and analytics results into intuitive, actionable insights for operators and engineers. During the presentation examples were provided demonstrating how visualization, event views, and summarized analytics enhance situational awareness and support operational decision-making. These use cases illustrate how a well-designed data infrastructure can bridge the gap between high-volume measurements and practical grid operations.

Aminifar, Farrokh↗
NASA NTRS1978

A re-entrant groove hydrogen heat pipe

This paper extends the development of reentrant groove technology to hydrogen heat pipes. Parametric analyses are presented which optimize the theoretical design while considering the limitations of state-of-the-art extrusion technology. Acceptable production-type runs of extruded lengths (over 300 m) could only be achieved at the expense of a wider nominal groove opening than specified (0.33 mm vs. 0.20 mm). However, dimensional variations of other critical dimensions were within 0.05 mm, which exceeded expectations. The 6063-T6 aluminum extrusion is 14.6 mm OD with a wall thickness of 1.66 mm and contains 20 axial grooves which surround a central 9.3-mm-diam vapor core. Each axial groove is 0.775-mm-diam with a 0.33 mm opening. An excess vapor reservoir is provided at the evaporator to minimize the pressure containment hazard during ambient storage. Details of the instrumentation and helium-cooled test installation are also presented.

Alario, J.↗
NASA NTRS1993

The Design of Mechanically Compatible Fasteners for Human Mandible Reconstruction

Mechanically compatible fasteners for use with thin or weakened bone sections in the human mandible are being developed to help reduce large strain discontinuities across the bone/implant interface. Materials being considered for these fasteners are a polyetherertherketone (PEEK) resin with continuous quartz or carbon fiber for the screw. The screws were designed to have a shear strength equivalent to that of compact/trabecular bone and to be used with a conventional nut, nut plate, or an expandable shank/blind nut made of a ceramic filled polymer. Physical and finite element models of the mandible were developed in order to help select the best material fastener design. The models replicate the softer inner core of trabecular bone and the hard outer shell of compact bone. The inner core of the physical model consisted of an expanding foam and the hard outer shell consisted of ceramic particles in an epoxy matrix. This model has some of the cutting and drilling attributes of bone and may be appropriate as an educational tool for surgeons and medical students. The finite element model was exercised to establish boundary conditions consistent with the stress profiles associated with mandible bite forces and muscle loads. Work is continuing to compare stress/strain profiles of a reconstructed mandible with the results from the finite element model. When optimized, these design and fastening techniques may be applicable, not only to other skeletal structures, but to any composite structure.

Roberts, Jack C.↗
DOE OSTI2020

Nonfused Nonfullerene Acceptors with an A–D–A'–D–A Framework and a Benzothiadiazole Core for High-Performance Organic Solar Cells

Nonfullerene acceptors (NFAs) have contributed significantly to the progress of organic solar cells (OSCs). However, most NFAs feature a large fused-ring backbone, which usually requires a tedious multiple-step synthesis, and are not applicable to commercial applications. An alternative strategy is to develop nonfused NFAs, which possess synthetic simplicity and facile tunability in optoelectronic properties and solid-state microstructures. In this work, we report two nonfused NFAs, BTCIC and BTCIC-4Cl, based on an A-D-A'-D-A architecture, which possess the same electron-deficient benzothiadiazole central core but different electron-withdrawing terminal groups. The optical properties, energy levels, and molecular crystallinities were finely tuned by changing the terminal groups. Moreover, a decent power conversion efficiency of 9.3 and 10.5% has been achieved by BTCIC and BTCIC-4Cl, respectively, by blending them with an appropriate polymer donor. These results demonstrate the potential of A-D-A'-D-A type nonfused NFAs for high-performance OSCs. Further development of nonfused NFAs will be very fruitful by employing appropriate building blocks and via side-chain optimizations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Optimized Quantum Phase Estimation for Simulating Electronic States in Various Energy Regimes

While quantum algorithms for simulation exhibit better asymptotic scaling than their classical counterparts, they currently cannot be implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical simulations of these quantum algorithms. In particular, the quantum phase estimation (QPE) algorithm is among several approaches that have attracted much attention in recent years for its genuine quantum character. However, it is memory-intensive to simulate and intractable for moderate system sizes. Herein, this paper discusses the performance and applicability of QPESIM, a new simulation of the QPE algorithm designed to take advantage of modest computational resources. In particular, we demonstrate the versatility of QPESIM in simulating various electronic states by examining the ground and core-level states of H 2 O. For these states, we also discuss the effect of the active-space size on the quality of the calculated energies. For the high-energy core-level states, we demonstrate that new QPE simulations for active spaces defined by 15 active orbitals significantly reduce the errors in core-level excitation energies compared to earlier QPE simulations using smaller active spaces.

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

Adiabatic quantum linear regression

Abstract A major challenge in machine learning is the computational expense of training these models. Model training can be viewed as a form of optimization used to fit a machine learning model to a set of data, which can take up significant amount of time on classical computers. Adiabatic quantum computers have been shown to excel at solving optimization problems, and therefore, we believe, present a promising alternative to improve machine learning training times. In this paper, we present an adiabatic quantum computing approach for training a linear regression model. In order to do this, we formulate the regression problem as a quadratic unconstrained binary optimization (QUBO) problem. We analyze our quantum approach theoretically, test it on the D-Wave adiabatic quantum computer and compare its performance to a classical approach that uses the Scikit-learn library in Python. Our analysis shows that the quantum approach attains up to $${2.8 \times }$$ 2.8 × speedup over the classical approach on larger datasets, and performs at par with the classical approach on the regression error metric. The quantum approach used the D-Wave 2000Q adiabatic quantum computer, whereas the classical approach used a desktop workstation with an 8-core Intel i9 processor. As such, the results obtained in this work must be interpreted within the context of the specific hardware and software implementations of these machines.

97 MATHEMATICS AND COMPUTING↗