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NASA NTRS2004

Computationally-Efficient Minimum-Time Aircraft Routes in the Presence of Winds

A computationally efficient algorithm for minimizing the flight time of an aircraft in a variable wind field has been invented. The algorithm, referred to as Neighboring Optimal Wind Routing (NOWR), is based upon neighboring-optimal-control (NOC) concepts and achieves minimum-time paths by adjusting aircraft heading according to wind conditions at an arbitrary number of wind measurement points along the flight route. The NOWR algorithm may either be used in a fast-time mode to compute minimum- time routes prior to flight, or may be used in a feedback mode to adjust aircraft heading in real-time. By traveling minimum-time routes instead of direct great-circle (direct) routes, flights across the United States can save an average of about 7 minutes, and as much as one hour of flight time during periods of strong jet-stream winds. The neighboring optimal routes computed via the NOWR technique have been shown to be within 1.5 percent of the absolute minimum-time routes for flights across the continental United States. On a typical 450-MHz Sun Ultra workstation, the NOWR algorithm produces complete minimum-time routes in less than 40 milliseconds. This corresponds to a rate of 25 optimal routes per second. The closest comparable optimization technique runs approximately 10 times slower. Airlines currently use various trial-and-error search techniques to determine which of a set of commonly traveled routes will minimize flight time. These algorithms are too computationally expensive for use in real-time systems, or in systems where many optimal routes need to be computed in a short amount of time. Instead of operating in real-time, airlines will typically plan a trajectory several hours in advance using wind forecasts. If winds change significantly from forecasts, the resulting flights will no longer be minimum-time. The need for a computationally efficient wind-optimal routing algorithm is even greater in the case of new air-traffic-control automation concepts. For air-traffic-control automation, thousands of wind-optimal routes may need to be computed and checked for conflicts in just a few minutes. These factors motivated the need for a more efficient wind-optimal routing algorithm.

Jardin, Matthew R.↗

NASA NTRS2014

Centrifugally Stiffened Rotor: Eternal Flight as the Solution for 'X': NIAC Phase I Final Report

Flight has always captured man's imagination. This is evidenced by the great variety of aerial vehicles that exist today. Everything from fixed-wing to rotorcraft; satellites to spaceships;mono-wing to quadrotor. However, despite the wide variety of flying vehicles, not one of them has attained eternal flight. Accomplishing this feat is one of the great challenges still facing the aviation community. Motivation Achieving eternal flight opens the doors to atmospheric satellites. Existing satellites have a great number of capabilities that enrich our lives; however,their distance from the surface of the earth precludes certain types of transmission capabilities. Once eternal flight is achieved, that vehicle can serve the same role as ordinary satellites, but its close proximity will allow for real time two way communications,like wireless broadband internet. And with active controls, atmospheric satellites would not be constrained to geosynchronous orbits, like our existing satellite technology. Many projects are under way to achieve this goal;however, most of these research efforts follow the same design methodology, and have exhausted the limits of this particular design. This concept introduces a completely new aerial vehicle structure,which uses the best features of fixed-wing and rotorcraft designs. Combining the best features of different classes of aircraft, expands the capabilities beyond what either one can achieve on its own.

Atmospheric Satellites↗

NASA NTRS2022

Alignment of Optical Backscatter Measurements from the EXPORTS Northeast Pacific Field Deployment

Backscattering of light is commonly measured by ocean observing systems, including ships and autonomous platforms, and is used as a proxy for the concentration of water column constituents such as phytoplankton and particulate carbon. Multiple on-going projects involve large numbers of independent measurements of backscatter, as well as other biologically relevant parameters, to understand how biology is changing in time and space throughout the global ocean. Rarely are there sufficient measurements to test how well these instruments are inter-calibrated in real-world deployment conditions. This paper develops a procedure to align multiple independently calibrated backscatter instruments to each other using nearby profiling casts and applies this method to nine instruments deployed during a recent field campaign in the North Pacific during August–September of 2018. This process revealed several incorrect calibrations; post-alignment, all nine instruments aligned extremely well with each other. We also tested an alignment to a deep-water reference and found that this method is generally sufficient but has significant limitations; this procedure lacks the ability to correct instruments measuring only shallow profiles and can only account for additive offsets, not multiplicative changes. These findings highlight the utility of process studies involving several independent measurements of similar parameters in the same area.

North Pacific↗

DOE OSTI2022

BENCH-SCALE DEVELOPMENT OF A TRANSFORMATIVE MEMBRANE PROCESS FOR PRE-COMBUSTION CO 2 CAPTURE

This final technical report describes work conducted by Membrane Technology and Research, Inc. (MTR) for the Department of Energy, National Energy Technology Laboratory (DOE NETL) on development of the second generation (Gen-2) Proteus™ membrane modules and a pre-combustion membrane process for carbon dioxide (CO 2 ) capture from an Integrated Gasification Combined Cycle (IGCC) plant for power generation (award number DE-FE0031632). The work was conducted from October 1, 2018 through March 30, 2022. The overall goal of this project was to bring a Gen-2 version of the H2-selective Proteus membrane to bench-scale module (component) testing with real syngas. MTR was assisted in this project by Susteon, a technology development company with extensive experience in gasification processes, and the University of North Dakota Energy & Environmental Research Center (EERC), who provided the host site for the slipstream field testing. This report details the work conducted to optimize the Gen-2 Proteus membrane and develop modules capable of operation at 200°C; demonstrate membrane module performance processing coal-derived syngas during a field test at EERC; and optimize integration of a dual-membrane process into an IGCC with carbon capture. Work for this project included membrane optimization and scale-up, module component screening and fabrication of high-temperature lab- and bench-scale modules, design and fabrication of a bench-scale field test membrane skid, operation of the field test skid processing coal-derived syngas at EERC, and a detailed techno-economic analysis (TEA) of the MTR dual-membrane process for IGCC power plant pre-combustion CO 2 capture. This project validated recent membrane technology advancements, mitigates risk in future scale-up activities, and moved the membrane pre-combustion capture technology from TRL-4 to TRL-5. Key results for each major task are discussed in the report.

10 SYNTHETIC FUELS↗

NASA NTRS2000

Aircraft Conflict Analysis and Real-Time Conflict Probing Using Probabilistic Trajectory Modeling

Methods for maintaining separation between aircraft in the current airspace system have been built from a foundation of structured routes and evolved procedures. However, as the airspace becomes more congested and the chance of failures or operational error become more problematic, automated conflict alerting systems have been proposed to help provide decision support and to serve as traffic monitoring aids. The problem of conflict detection and resolution has been tackled from a number of different ways, but in this thesis, it is recast as a problem of prediction in the presence of uncertainties. Much of the focus is concentrated on the errors and uncertainties from the working trajectory model used to estimate future aircraft positions. The more accurate the prediction, the more likely an ideal (no false alarms, no missed detections) alerting system can be designed. Additional insights into the problem were brought forth by a review of current operational and developmental approaches found in the literature. An iterative, trial and error approach to threshold design was identified. When examined from a probabilistic perspective, the threshold parameters were found to be a surrogate to probabilistic performance measures. To overcome the limitations in the current iterative design method, a new direct approach is presented where the performance measures are directly computed and used to perform the alerting decisions. The methodology is shown to handle complex encounter situations (3-D, multi-aircraft, multi-intent, with uncertainties) with relative ease. Utilizing a Monte Carlo approach, a method was devised to perform the probabilistic computations in near realtime. Not only does this greatly increase the method's potential as an analytical tool, but it also opens up the possibility for use as a real-time conflict alerting probe. A prototype alerting logic was developed and has been utilized in several NASA Ames Research Center experimental studies.

Yang, Lee C.↗

NASA NTRS2010

Charge-Spot Model for Electrostatic Forces in Simulation of Fine Particulates

The charge-spot technique for modeling the static electric forces acting between charged fine particles entails treating electric charges on individual particles as small sets of discrete point charges, located near their surfaces. This is in contrast to existing models, which assume a single charge per particle. The charge-spot technique more accurately describes the forces, torques, and moments that act on triboelectrically charged particles, especially image-charge forces acting near conducting surfaces. The discrete element method (DEM) simulation uses a truncation range to limit the number of near-neighbor charge spots via a shifted and truncated potential Coulomb interaction. The model can be readily adapted to account for induced dipoles in uncharged particles (and thus dielectrophoretic forces) by allowing two charge spots of opposite signs to be created in response to an external electric field. To account for virtual overlap during contacts, the model can be set to automatically scale down the effective charge in proportion to the amount of virtual overlap of the charge spots. This can be accomplished by mimicking the behavior of two real overlapping spherical charge clouds, or with other approximate forms. The charge-spot method much more closely resembles real non-uniform surface charge distributions that result from tribocharging than simpler approaches, which just assign a single total charge to a particle. With the charge-spot model, a single particle may have a zero net charge, but still have both positive and negative charge spots, which could produce substantial forces on the particle when it is close to other charges, when it is in an external electric field, or when near a conducting surface. Since the charge-spot model can contain any number of charges per particle, can be used with only one or two charge spots per particle for simulating charging from solar wind bombardment, or with several charge spots for simulating triboelectric charging. Adhesive image-charge forces acting on charged particles touching conducting surfaces can be up to 50 times stronger if the charge is located in discrete spots on the particle surface instead of being distributed uniformly over the surface of the particle, as is assumed by most other models. Besides being useful in modeling particulates in space and distant objects, this modeling technique is useful for electrophotography (used in copiers) and in simulating the effects of static charge in the pulmonary delivery of fine dry powders.

Walton, Otis R.↗

DOE OSTI2020

Gauges, loops, and polynomials for partition functions of graphical models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is #P-hard that is of an exponential complexity with respect to the number of variables. Here, aimed at approximating the partition function, we consider multi-graph models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge function technique from Chertkov and Chernyak with the technique developed in Anari and Oveis Gharan 2017 arXiv:1702.02937; Gurvits 2011 arXiv:1106.2844; Straszak and Vishnoi 2017 55th Annual Allerton Conf. on Communication, Control, and Computing, based on the recent progress in the field of real stable polynomials. We show that the Gauge function, representing a single-out term in a finite sum expression for the partition function which achieves extremum at the so-called belief-propagation gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, Gauge function can be used to recover the partition function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists of the application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in multi-graph models on decreasing in size (number of edges) graphs with the same partition function as in the original multi-graph model. Even though the complexity of computing factors in the sequence of the derived multi-graph models and respective Gauge functions grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the partition function.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Strym: A Python Package for Real-time CAN Data Logging, Analysis and Visualization to Work with USB-CAN Interface

In this report, we describe a data analysis tool developed for decoding and analyzing vehicle data obtained from a passenger vehicle’s onboard controller area network (CAN) bus. The tool developed in this paper provides a timeseries framework to perform domain-specific analysis at scale when interpreting data from a vehicle or a collection of vehicles in light of how to design intelligent vehicle applications. The tool, called Strym, exploits the CAN bus mechanism of modern vehicles to capture data using commercially available CAN-to-USB hardware Comma.ai Panda devices, managed through open-source software Libpanda. Strym permits the decoding of vendor-specific CAN messages in a vehicle-agnostic manner. Through this, a researcher can characterize data throughput, assess data quality, and perform analyses. Such analyses are useful in a number of research such as studying human driving behavior in mixed-autonomy, new driver models, rare-event detection, traffic flow estimation, and custom control of vehicles.

Performance evaluation, Smart cities, Intelligent ↗

DOE OSTI2026

Integrating Flow Imaging Analysis and Single-Particle ICP-TOFMS for Comprehensive Micro- and Nanoplastic Characterization

Flow imaging analysis (FIA), provides composition-agnostic morphological characterization. These measurements of particle size and shape are valuable to mass-based analysis, such as single particle inductively coupled plasma time-of-flight mass spectrometry (sp-ICP-TOFMS), which provides quantitative data on elements within particles. Using these two methods together enables informed use of geometric assumptions required by sp-ICP-TOFMS, as particle mass is typically converted to a particle diameter using assumed-spherical geometry. To validate this concept, parallel measurements to determine particle diameters were performed by FIA and sp-ICP-TOFMS on four particle suspensions: 300 nm polystyrene Eu-doped nanoparticles, 1 μm Fe-rich beads, 3 μm four element calibration polystyrene beads and 5 μm polystyrene beads. The Fe-particles obtained the highest percent difference from the manufacturer’s nominal diameter, as the mean diameter obtained by FIA was overestimated by 21% and sp-ICP-TOFMS underestimated the mean diameter by 20.7%. Two types of particles were selected to test the effect of varying the particle number concentrations (PNC) on sizing accuracy, and both methods accurately sized each particle population at the PNC expected. Single particle analysis of carbon has continued to be a popular research topic, with direct applications to environmental pollutants in terms of nano- and micro- plastics. Real-world plastic particles were studied, and FIA’s measured circularity values demonstrated that the particles deviated from spherical geometries, therefore sp-ICP-TOFMS data should be interpreted as mass-based rather than size-based. Combining these techniques enables improved interpretation of particle populations and evaluation of particle sizes.

Szakas, Sarah [ORNL] (ORCID:0000000241332197)↗

DOE OSTI2025

FLAMES─Fast, Low-Storage, Accurate, and Memory-Efficient Adaptive Sampling─Approach to Resolve Spatially Dependent Dynamics of Molecular Liquids

Many critical phenomena in soft matter occur at large length scales, necessitating the resolution of their structure and dynamics at low wavenumbers. However, resolving wavenumber-dependent dynamics computationally via molecular dynamics simulations presents significant challenges, as these phenomena span several orders of magnitude in both time and length scales, resulting in high computational costs and memory demands. Here, this work highlights the computational and memory challenges associated with analyzing molecular trajectories in reciprocal space and demonstrates a method to address them. We introduce FLAMESFast, Low-storage, Accurate, and Memory-Efficient adaptive Sampling, which is a direct method for calculation of structure factors, allowing us to select only the required number of wavevectors for binning. We also use wavenumber-dependent time steps to extract dynamics. Our FLAMES approach effectively mitigates computational and memory/storage bottlenecks. We demonstrate the method using simulations of a model system, liquid octane, at various temperatures. Comparisons with experimental data and real space computation show that the FLAMES technique achieves high accuracy in resolving temperature- and spatially dependent dynamics while being significantly more computationally efficient and requiring less memory and storage than methods based on a uniform wavevector grid and fixed temporal spacing.

Chen, Guang [Argonne National Laboratory (ANL), Ar↗

DOE OSTI2025

𝜂 and 𝜂′ Production in 𝐽/𝜓 Radiative Decays from Quantum Chromodynamics

We present a first principles calculation within quantum chromodynamics (QCD) of the radiative decays of the 𝐽/𝜓 into the light pseudoscalar mesons 𝜂 and 𝜂′. Within a lattice computation we obtain the transition form factors as a function of photon virtuality from the timelike region, accessible experimentally via the “Dalitz” decay 𝐽/𝜓 →𝑒 + ⁢𝑒 − ⁢𝜂 (′) , through to the real photon point corresponding to 𝐽/𝜓 →𝛾⁢𝜂 (′) . This is the first calculation in lattice QCD with two (heavier than physical) degenerate flavors of light quark and a heavier strange quark, in which the 𝜂′ appears as the first excited state with pseudoscalar isoscalar quantum numbers. We access it reliably by using variationally optimized operators , the use of which also improves the purity of the 𝐽/𝜓 and 𝜂 signals, reducing systematic uncertainties. High quality results at a large number of kinematic points are obtained in a typically noisy disconnected process by using a novel correlator averaging procedure. Our results show the expected enhanced production of the 𝜂′ over the 𝜂 in this process, and suggest that the demonstrated lattice technology is suitable for future calculations considering processes in which light meson resonances are produced.

form factors↗

DOE OSTI2025

HighDimMixedModels.jl: Robust high-dimensional mixed-effects models across omics data

High-dimensional mixed-effects models are an increasingly important form of regression in which the number of covariates rivals or exceeds the number of samples, which are collected in groups or clusters. The penalized likelihood approach to fitting these models relies on a coordinate descent algorithm that lacks guarantees of convergence to a global optimum. Here, we empirically study the behavior of this algorithm on simulated and real examples of three types of data that are common in modern biology: transcriptome, genome-wide association, and microbiome data. Our simulations provide new insights into the algorithm’s behavior in these settings, and, comparing the performance of two popular penalties, we demonstrate that the smoothly clipped absolute deviation (SCAD) penalty consistently outperforms the least absolute shrinkage and selection operator (LASSO) penalty in terms of both variable selection and estimation accuracy across omics data. To empower researchers in biology and other fields to fit models with the SCAD penalty, we implement the algorithm in a Julia package, HighDimMixedModels.jl .

Gorstein, Evan↗

DOE OSTI2021

GT Flex: A Coordinated Multi-Building Pilot Study

Buildings are a significant and untapped resource for providing utility electric grid services. Recent studies have estimated that buildings could reduce the peak demand on the electric grid in the U.S. by almost 25% through effective combinations of energy efficiency (EE) measures and load flexibility strategies (Langevin et al. 2021). The U.S. Department of Energy (DOE) has established a goal to triple energy efficiency and demand flexibility in both residential and commercial sections by 2030 compared to 2020 levels (Satchwell et al. 2021). Such findings place buildings alongside electric vehicles, photovoltaics, electric batteries, and other distributed energy resources (DERs) as primary technologies needed for supporting high renewable energy generation grids. Coordinating and optimizing multiple buildings and other DERs is more beneficial and valuable when compared with individual buildings and DERs operating as siloed resources, uncoordinated with others (Olgyay et al. 2020). A pilot study at the Georgia Institute of Technology (GIT) was conducted to evaluate value propositions of a multi-building scale project seeking carbon reduction, energy efficiency and grid-interactive capabilities, by demonstrating the means by which stakeholders can determine the technical and financial merits of grid-interactivity and energy efficiency technologies coordinated across multiple assets. The study focused on analyzing technical feasibility of deploying thermal load flexibility strategies at the multi-building scale, coordinated to not exceed existing infrastructure constraints at the pilot site. Results show that campus can provide 3-3.5 MW of potential load shed over a 4-hour event window through coordinated dispatch of thermal cooling load flexibility without exceeding existing infrastructure capacities. Under future high renewable scenarios, this thermal flexibility resource is also valuable when coordinated to reduce curtailment of intermittent renewables. Economic analyses were performed to effectively communicate various value propositions of grid-interactive and efficient building (GEB) thermal flexibility strategies. Load flexibility presents a financial value proposition to the campus today. By conducting rationalized, coordinated dispatch in response to real time price (RTP) fluctuations, the campus can benefit materially from daily price arbitrage. The RTP signal acts as an aggregating mechanism between the utility and customer to call on demand flexibility resources, with a large portion of the benefit deriving from a relatively small number of days. Realizing and maximizing this benefit with thermal load flexibility requires careful attention to the timing of pricing signals and parameterization of dispatch to overcome efficiency penalties. Grid value and signals are expected to evolve over time, and thermal load flexibility shows potential to adapt dispatch logic to support intermittent renewable generation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

SPARC-X: Quantum simulations at extreme scale - reactive dynamics from first principles

We have developed the massively parallel electronic structure code SPARC-X: a computational framework for performing Kohn-Sham Density Functional Theory (DFT) calculations that can scale linearly with the number of atoms in the system, while being able to leverage petascale and emerging exascale parallel computers to study chemical phenomena at unprecedented length and time scales. SPARC-X exploits a recent breakthrough in electronic structure methodologies: systematically improvable, strictly local, orthonormal, discontinuous real-space bases that efficiently and systematically capture the local chemistry of the system. With further adaptation using new machine-learning techniques and the use of the massively parallel Spectral Quadrature (SQ) electronic structure method, the algorithmic complexity and prefactor associated with DFT calculations involving semilocal as well as hybrid functionals are dramatically reduced. Using petascale computational resources, SPARC-X enables quantum mechanical simulations at length and time scales previously accessible only by empirical approaches, e.g., 1,000,000 atoms for a few picoseconds using semilocal functionals or 1,000 atoms for a few picoseconds using hybrid functionals. Using exascale resources, the sizes and times targeted are two orders of magnitude larger. Such a capability has applications in a wide variety of chemical sciences, including reactive interfaces where large length- and/or long time-scales are needed and traditional force fields fail. This is particularly important in dynamic catalysis, where bond breaking and formation must be understood in detail. We developed, tested, and employed the SPARC-X framework to understand the photocatalytic properties of TiO 2 nanoparticles, revealing finite size effects that cannot be captured with standard model systems or functionals. This integrated development and application strategy ensures that SPARC-X remains a robust, efficient, and scalable software package for quantum simulations on current petascale and emerging exascale computing resources.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1973

Basic failure mechanisms in advanced composites

The fundamental failure mechanisms which result from the interaction of thermal cycling and mechanical loading of carbon-epoxy composites were studied. This work was confined to epoxy resin uniderictionally reinforced with HTS carbon fibers, and consists of first identifying local fiber, matrix and interface failure mechanisms using the model composite specimen containing a small number of fibers so that optical techniques can be used for characterization. After the local fracture process has been established for both mechanical loading and thermal cycling, engineering composite properties and gross fracture modes are then examined to determine how the local events contribute to real composite performance. Flexural strength in high fiber content specimens shows an increase in strength with increased thermal cycling. Similar behavior is noted for 25 v/o material up to 200 cycles; however, there is a drastic reduction after 200 cycles indicating a major loss of integrity probably through the accumulation of local cleavage cracks in the tensile region.

Mazzio, V. F.↗

NASA NTRS1985

Unsteady flow in a supersonic cascade with two in-passage shocks

A model for a supersonic blade row with two in-passage shock waves is developed. It accounts for three-dimensional effects in real flows by using an altered blade shape in a two-dimensional cascade. There is enough flexibility in the choice of blade shape to accommodate a desired entrance angle, exit angle, boundary-layer thickness and stage pressure ratio at a given entrance Mach number. The model divides the mean flow into regions of uniform or one-dimensional flow in which the solutions for the unsteady flow may be formed successively. The analysis makes use of previous solutions for unsteady flow in cascades and over an oscillation wedge. Six flow conditions are chosen in the range of parameters for which the two-shock model is valid for studies of flutter in torsion and bending. It is found, in keeping with previous results from a single-shock model, that in each case there is increasing instability with decreasing frequency.

Braun, W. H.↗

NASA NTRS1993

Transient liquid-crystal technique used to produce high-resolution convective heat-transfer-coefficient maps

In this transient technique the preheated isothermal model wall simulates the classic one-dimensional, semi-infinite wall heat transfer conduction problem. By knowing the temperature of the air flowing through the model, the initial temperature of the model wall, and the surface cooling rate measured at any location with time (using the fast-response liquid-crystal patterns recorded on video tape), the heat transfer coefficient can be calculated for the color isothermal pattern produced. Although the test was run transiently, the heat transfer coefficients are for the steady-state case. The upstream thermal boundary condition was considered to be isothermal. This transient liquid-crystal heat-transfer technique was used in a transient air tunnel in which a square-inlet, 3-to-1 exit transition duct was placed. The duct was preheated prior to allowing room temperature air to be suddenly drawn through it. The resulting isothermal contours on the duct surfaces were revealed using a surface coating of thermochromic liquid crystals that display distinctive colors at particular temperatures. A video record was made of the temperature and time data for all points on the duct surfaces during each test. The duct surfaces were uniformly heated using two heating systems: the first was an automatic temperature-controlled heater blanket completely surrounding the test duct like an oven, and the second was an internal hot-air loop through the inside of the test duct. The hot-air loop path was confined inside the test duct by insulated heat dams located at the inlet and exit ends of the test duct. A recirculating fan moved hot air into the duct inlet, through the duct, out of the duct exit, through the oven, and back to the duct inlet. The temperature nonuniformity of the test duct model wall was held very small. Test results are reported for two inlet Reynolds numbers of 200,000 and 1,150,000 (based on the square-inlet hydraulic diameter) and two free-stream turbulence intensities of about 1 percent, which is typical of wind tunnels, and up to 20 percent (using a grid), which is typical of real engine conditions.

Hippensteele, Steven A.↗

NASA NTRS1994

A Fortran-90 Based Multiprecision System

The author has developed a new version of his Fortran multiprecision computation system that is based on the Fortran-90 language. With this new approach, a translator program is not required - translation of Fortran code for multiprecision is accomplished by merely utilizing advanced features of Fortran-90, such as derived data types and operator extensions. This approach results in more reliable translation and also permits programmers of multiprecision applications to utilize the full power of the Fortran-90 language. Three multiprecision datatypes are supported in this system: multiprecision integer. real and complex. All the usual Fortran conventions for mixed mode operations are supported, and many of the Fortran intrinsics, such as SIN, EXP and MOD, are supported with multiprecision arguments. This paper also briefly describes an interesting application of this software, wherein new number-theoretic identities have been discovered by means of multiprecision computations.

Bailey, David H.↗