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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantifying the impact of precision errors on quantum approximate optimization algorithms

The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical algorithm that seeks to achieve approximate solutions to optimization problems by iteratively alternating between intervals of controlled quantum evolution. Here, we examine the effect of analog precision errors on QAOA performance from the perspective of both algorithmic training and performance guarantees. Leveraging cumulant expansions, we recast the faulty QAOA as a control problem in which precision errors are expressed as multiplicative control noise and derive bounds on the performance of QAOA. We show using both analytical techniques and numerical simulations that fixed precision implementations of QAOA circuits are subject to an exponential degradation in performance dependent upon the number of optimal QAOA layers and magnitude of the precision error. Despite this significant reduction, we show that it is possible to mitigate precision errors in QAOA via digitization of the variational parameters at the cost of increasing circuit depth.

quantum algorithms↗
NASA NTRS1990

Dynamic Characteristics of Space Station Freedom Mars and Lunar Evolution Reference Configurations

One concept for a manned mission to Mars uses an evolutionary version of Space Station Freedom (SSF) as a transportation node. The station is modified by the addition of dual keels, an upper and lower boom, additional laboratory and habitation modules, increased power and an assembly platform. With these modifications the station is called the Mars Evolution Reference Configuration (MERC). The mass of the station is 65 percent greater than the mass of SSF and its moments of inertia through the mass center are greater by approximately a factor of four. Over a period of months, several flights from Earth to low-Earth-orbit carry the components of a manned Mars piloted vehicle (MPV) to the MERC where the vehicle is constructed on the assembly platform. After each flight the station is reboosted to an appropriate altitude, such that the orbit decay due to atmospheric drag forces lowers the spacecraft to the proper altitude at the appropriate time for rendezvous with the next assembly flight. When the assembly process is completed, the MPV, which has a mass of approximately 200,000 lbm, is situated on the evolutionary station. The mass increase of the MERC with MPV system over SSF is 112 percent and the moments of inertia about axes through the mass center increase by up to a factor of 12. When the MPV is assembled, inspected and verified, the mission is ready to proceed and the MPV is moved from the station to a staging area and mated with fueled trans-Mars injection stages for the flight to Mars. This presentation describes a finite element model of the MERC formulated to investigate the expected low frequency modes and its variation with the addition of a large payload. A basic reboost procedure using near-continuous firing of reaction control system jets is proposed with off-modulation of the jets used to control flight attitude. The reboost procedure is described with the closed-loop attitude control dictating jet on/off cycling based on feedback signals which contain both the rigid body rotation information and the elastic rotations local to the attitude sensor. The presentation contains a description of the dynamic response at critical points of the station during the reboost and concludes with results of a brief study of the dynamic characteristics of a Lunar transportation node configuration.

Ayers, J. Kirk↗
NASA NTRS1993

Controls-structures integrated design optimization with shape variations

The shape design variables have been introduced into the set of design variables of the Controls-Structure Integrated (CSI) Design of space-structures. The importance of the shape variations in improving the design (obtained with only control and sizing variables) has been aptly illustrated. Two different types of design variables that describe the shape variations of the structure have been introduced. In the first case, the nodal coordinates have been considered as design variables. This has the inherent difficulty of having too many design variables. This not only is time consuming but also memory intensive and may not yield a manufacturable shape to the structure. The second approach has been introduced to overcome this difficulty. The structure is allowed to vary in a particular pre defined pattern. The coefficients of these patterns are considered as the shape design variables. The eigenvalue and eigenvector sensitivity equations with respect to these coefficient design variables have been developed and are used to approximate the eigenvalues and eigenvectors in a perturbed design.

Koganti, Gopichand↗
NASA NTRS1948

Preliminary Results of an Investigation by the Wing-Flow Method of the Longitudinal Stability Characteristics of a 1/50-Scale Semispan Model of the McDonnell XP-88 Airplane

This paper presents the results of measurements of longitudinal stability of a 1/50-scale model of the XP-88 airplane by the wing-flow method. Lift, rolling-moment, hinge-moment, and pitching-moment characteristics as well as the downwash at the tail were measured over a Mach number range from approximately 0.5 to 1.05 at Reynolds numbers below 1,000,000. No measurements of drag were obtained. No abrupt changes due to Mach number were noted in any of the parameters measured. The data indicated that the wing was subject to early tip stalling; that the tail effectiveness decreased gradually with increasing Mach number up to M = 0.9, but increased again at higher Mach numbers; that the variation of downwash with angle of attack did not change appreciably with Mach number except between 0.95 and 1.0 where d(epsilon)/d(alpha), decreased from 0.46 to 0.32; that at zero lift with a stabilizer setting of -1.5 deg there was a gradually increasing nosing-up tendency with increasing Mach number; and that the control-fixed stability in maneuvers at constant speed gradually increased with increasing Mach number.

Crane, Harold L.↗
DOE OSTI2025

Influence of simple terrain on the spatial variability of a low-level jet and wind farm performance in the AWAKEN field campaign

In wind energy research, scientific challenges are often associated with complex terrain sites, where orography, vegetation, and buildings disrupt flow uniformity. However, even sites characterized as simple terrain can exhibit significant spatial variability in wind speed, particularly during stable boundary layers (SBLs) and low-level jets (LLJs). This study investigates these terrain interactions using both simulations and observations from the American WAKe ExperimeNt (AWAKEN). We employ a multiscale Weather Research and Forecasting (WRF) model simulation, integrating mesoscale forcing in the coarse domains and representing three rows of turbines from the King Plains wind farm as generalized actuator disks (GAD) in the large-eddy simulation (LES) domains. During a nocturnal LLJ event on 3 April 2023, the downstream, wake-affected turbine rows outperformed the upstream, unwaked row by 25 %–51 %. This counterintuitive result arises from terrain-induced streamwise variations in hub-height wind speed of approximately 4 m s −1 over 5 km – equivalent to ∼50 % of the upstream reference speed. This enhancement outweighs the wake-induced reduction in mean wind speed (∼12 %) and global blockage effects reported in the literature (∼1 %–3.4 %). The multiscale simulations capture the intra-farm spatial variability in power performance observed in SCADA data. Terrain-induced vertical displacement of the LLJ, coupled with large wind shear below the jet maximum, drives the substantial streamwise acceleration within the wind farm. These findings underscore the importance of accounting for spatial variability related to terrain, even in simple landscapes, particularly during LLJ conditions. Incorporating such effects into reduced-order modeling frameworks for wind farm design and control could significantly enhance their effectiveness.

17 WIND ENERGY↗
NASA NTRS1997

Applying Space Technology to Enhance Control of an Artificial Arm

At the present time, myoelectric prostheses perform only one function of the hand: open and close with the thumb, index and middle finger coming together to grasp various shaped objects. To better understand the limitations of the current single-function prostheses and the needs of the individuals who use them, The Institute for Rehabilitation and Research (TIRR), sponsored by the National Institutes of Health (August 1992 - November 1994), surveyed approximately 2500 individuals with upper limb loss. When asked to identify specific features of their current electric prosthesis that needed improvement, the survey respondents overwhelmingly identified the lack of wrist and finger movement as well as poor control capability. Simply building a mechanism with individual finger and wrist motion is not enough. Individuals with upper limb loss tend to reject prostheses that require continuous visual monitoring and concentration to control. Robotics researchers at NASA's Johnson Space Center (JSC) and Rice University have made substantial progress in myoelectric teleoperation. A myoelectric teleoperation system translates signals generated by an able-bodied robot operator's muscles during hand motions into commands that drive a robot's hand through identical motions. Farry's early work in myoelectric teleoperation used variations over time in the myoelectric spectrum as inputs to neural networks to discriminate grasp types and thumb motions. The resulting schemes yielded up to 93% correct classification on thumb motions. More recently, Fernandez achieved 100% correct non-realtime classification of thumb abduction, extension, and flexion on the same myoelectric data. Fernandez used genetic programming to develop functions that discriminate between thumb motions using myoelectric signal parameters. Genetic programming (GP) is an evolutionary programming method where the computer can modify the discriminating functions' form to improve its performance, not just adjust numerical coefficients or weights. Although the function development may require much computational time and many training cases, the resulting discrimination functions can run in realtime on modest computers. These results suggest that myoelectric signals might be a feasible teleoperation medium, allowing an operator to use his or her own hand and arm as a master to intuitively control an anthropomorphic robot in a remote location such as outer space.

Atkins, Diane↗
NASA NTRS2020

Analyzing Changes in the Complexity of Climate in the Last Four Decades Using MERRA-2 Radiation Data

The energy balance of the Earth is controlled by the shortwave and longwave radiation emitted to space. Changes in the thermodynamic state of the system over time afect climate and are noticeable when viewing the system as a whole. In this paper, we study the changes in the complexity of climate in the last four decades using data from the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2). First, we study the complexity of the shortwave and longwave radiation felds independently using Approximate Entropy and Sample Entropy, observing that the rate of complexity change is faster for shortwave radiation. Then, we study the causality of those changes using Transfer Entropy to capture the non-linear dynamics of climate, showing that the changes are mainly driven by the variations in shortwave radiation. The observed behavior of climatic complexity could be explained by the changes in cloud amount, and we research that possibility by investigating its evolution from a complexity perspective using data from the International Satellite Cloud Climatology Project (ISCCP).

Delgado-Bonal, Alfonso↗
NASA NTRS1980

Polarization and position measurements of Type III bursts

The positional and polarization characteristics of Type III bursts in the range 24-220 MHz as measured by the Culgoora radioheliograph, spectrograph and spectropolarimeter are reported. The study includes 997 bursts which are of two classes: fundamental-harmonic (F-H) pairs and 'structureless' bursts with no visible F-H structure, and concentrates on the polarization of the bursts and the variation of polarization from centre to limb. The observed centre-to-limb decrease in polarization approximately follows a cosine law. This decrease is not as predicted by simple theory but is consistent with other observations which imply that open field lines from an active region diverge strongly. The observed o-mode polarization of harmonic radiation implies that the wave vectors of Langmuir waves are always parallel, within about 20 deg, to the magnetic field, while the constancy of H polarization with frequency implies that the ratio of gyromagnetic to plasma frequency, the Alfven speed and the plasma beta are constant with height on the open field lines above an active region. Finally, it is inferred that some factor, in addition to the magnetic field strength, controls the polarization of F radiation.

Suzuki, S.↗
NASA NTRS2014

Calculation of Operations Efficiency Factors for Mars Surface Missions

For planning of Mars surface missions, to be operated on a sol-by-sol basis by a team on Earth (where a "sol" is a Martian day), activities are described in terms of "sol types" that are strung together to build a surface mission scenario. Some sol types require ground decisions based on a previous sol's results to feed into the activity planning ("ground in the loop"), while others do not. Due to the differences in duration between Earth days and Mars sols, for a given Mars local solar time, the corresponding Earth time "walks" relative to the corresponding times on the prior sol/day. In particular, even if a communication window has a fixed Mars local solar time, the Earth time for that window will be approximately 40 minutes later each succeeding day. Further complexity is added for non-Mars synchronous communication relay assets, and when there are multiple control centers in different Earth time zones. The solution is the development of "ops efficiency factors" that reflect the efficiency of a given operations configuration (how many and location of control centers, types of communication windows, synchronous or non-synchronous nature of relay assets, sol types, more-or-less sustainable operations schedule choices) against a theoretical "optimal" operations configuration for the mission being studied. These factors are then incorporated into scenario models in order to determine the surface duration (and therefore minimum spacecraft surface lifetime) required to fulfill scenario objectives. The resulting model is used to perform "what-if" analyses for variations in scenario objectives. The ops efficiency factor is the ratio of the figure of merit for a given operations factor to the figure of merit for the theoretical optimal configuration. The current implementation is a pair of models in Excel. The first represents a ground operations schedule for 500 sols in each operations configuration for the mission being studied (500 sols was chosen as being a long enough time to capture variations in relay asset interactions, Earth/Mars time phasing, and seasonal variations in holidays). This model is used to estimate the ops efficiency factor for each operations configuration. The second model in a separate Excel spreadsheet is a scenario model, which uses the sol types to rack up the total number of "scenario sols" for that scenario (in other words, the ideal number of sols it would take to perform the scenario objectives). Then, the number of sols requiring ground in the loop is calculated based on the soil types contained in the given scenario. Next, the scenario contains a description of what sequence of operations configurations is used, for how many days each, and this is used with the corresponding ops efficiency factors for each configuration to calculate the "ops duration" corresponding to that scenario. Finally, a margin is applied to determine the minimum surface lifetime required for that scenario. Typically, this level of analysis has not been performed until much later in the mission, and has not been able to influence mission design. Further, the notion of moving to sustainable operations during Prime Mission - and the effect that that move would have on surface mission productivity and mission objective choices - has not been encountered until the most recent rover missions (MSL and Mars 2018).

Layback, Sharon L.↗
DOE OSTI2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Osmotic control of the spacing of parallel shear cracks in shale growing subcritically in geologic past

The geological genesis of natural cracks in sedimentary rocks such as shale is a problem that needs to be understood to improve the technology of hydraulic fracturing as well as deep sequestration of harmful fluids. Why are the vertical natural cracks roughly parallel and equidistant, and why is the spacing roughly 10 cm rather than 1 cm or 100 cm? Fracture mechanics of critical cracks cannot answer this question. Neither can the material heterogeneity. The growth of critical parallel cracks is impossible because the relative crack face displacements would immediately localize into one crack, leading to an earthquake. The cracks must have formed, on the tectonic time scale, by a slow growth of subcritical shear cracks governed by the Charles-Evans law. The idea advanced here is that what controls the crack spacing is the balance between the reduction, due to shear dilatancy, of the concentration of ions such as Na + and Cl - in each fracture process zone (PFZ), which decelerates the cracks, and the restoration of ion concentration by diffusion of ions from the space between the cracks into the FPZ. This diffusion of water is driven mainly by the osmotic pressure gradient, which offsets the deceleration and depends strongly on the crack spacing. A simple analytical solution of the steady state is rendered possible by approximating the ion concentration profiles between adjacent cracks by parabolic arcs. Applying this theory to Woodford shale yields the approximate crack spacing of 10 cm, which is realistic. Furthermore, the stability of unlimited parallel mode II frictional crack growth is proven by examining the second variation of the free energy. Water concentration drop in the FPZ due to shear dilatancy and its restoration by water diffusion from the inter-crack space have similar effect, although probably much weaker.

42 ENGINEERING↗
NASA NTRS1983

Atmospheric temperatures near the tropical tropopause Temporal variations, zonal asymmetry and implications for stratospheric water vapor

Analysis of temperature measurements obtained over an eight-year period in the vicinity of the low-latitude tropopause confirms the existence of longitude regions which are consistently colder by approximately 2-3 K than elsewhere in the tropics. These temperature differences, however, are confined to a layer of thickness 3-5 km centered on the tropopause. The lowest monthly mean temperatures observed at the colder stations yield saturation mixing ratios that are consistent with the range of measured stratospheric water vapor. Examination of the daily variations in temperature at a given station reveals a more complex pattern than indicated by the monthly averages. On many days temperatures at the colder longitudes correspond to water vapor abundances that are less than observed in the stratosphere despite the favorable comparison of the monthly means. The results point to the need for a series of water vapor soundings at selected longitudes and times in order to define the extent to which the tropical tropopause controls the stratospheric water vapor abundance.

Frederick, J. E.↗
NASA NTRS1987

Boundary-layer and wake measurements on a swept, circulation-control wing

Wind tunnel measurements of boundary layer and wake velocity profiles and surface static pressure distributions are presented for a swept, circulation control wing. The model is an aspect ratio four semispan wing mounted on the tunnel side wall as a sweep angle of 45 deg. A full span, tangetial, rearward blowing, circulation control slot is located ahead of the trailing edge on the upper surface. Flow surveys were obtained at mid-semispan at freestream Mach numbers of 0.425 and 0.70. Boundary layer profiles measured on the forward portions of the wing are approximately streamwise and two dimensional. The flow in the vicinity of the jet exit and in the near wake is highly three dimensional. The jet flow near the slot on the Coanda surface is directed normal to the slot. Near wake surveys show large outboard flows at the center of the wake. At Mach 0.425 and a 5 deg angle of attack, a range of jet blowing rates was found for which an abrupt transition from incipient separation to attached flow occurs in the boundary layer upstream of the slot. The variation in the lower surface separation location with blowing rate was determined from the boundary layer measurements at Mach 0.425.

Spaid, Frank W.↗
NASA NTRS2019

A Physical Model of Moulin Formation and Evolution

Nearly all proglacial water discharge from the present-day Greenland Ice Sheet is routed englacially via moulins. Identification of these moulins in high-resolution imagery is a frequent topic of study, but the processes controlling how and where moulins form, including on past ice sheets for which remote-sensing data are not available, remain poorly understood. Because moulins may reasonably compose approximately 10-15% of the englacial-subglacial hydrologic system, the evolution and shape of moulins can alter the timing of meltwater inputs to the bed. This evolution can impact both the form of the subglacial hydrologic system and the structure of associated geomorphological structures. Here, we develop a physical model of moulin formation and evolution to constrain the role of englacial processes in controlling the form and structure of the subglacial hydrologic system. Ice deformation within and around a moulin is both viscous and elastic, with the rate of turbulent and heat dissipation from water circulation in the moulin controlling both moulin wall melting and warming of the surrounding ice. We find moulin geometry is responsive to changes in these parameters over hours to days, indicating that diurnal and multi-day variations in surface melt can substantially alter the geometry of a moulin and the pressure-discharge relationship at the bed of the ice sheet. These results should be considered carefully when determining surface water inputs for subglacial hydrologic models. In the future, a parameter space study of these results will be combined with an analytic model to create a predictive, stochastic model of moulin and crevasse locations. This future model will be applicable to constraining the potential for surface-to-bed connections in regions where the exact ice-sheet surface morphology is not known, including ice sheets under future warming atmospheric conditions, and paleo ice sheets, where moulins created modern landforms.

Andrews, Lauren C.↗
NASA NTRS2003

MAP Propulsion System Thermal Design

The propulsion system of the Microwave Anisotropy Probe (MAP) had stringent requirements that made the thermal design unique. To meet instrument stability requirements the system had to be designed to keep temperatures of all components within acceptable limits without heater cycling. Although the spacecraft remains at a fixed 22 sun angle at L2, the variations in solar constant, property degradation, and bus voltage range all significantly affect the temperature. Large portions of the fuel lines are external to the structure and all components are mounted to non-conductive composite structure. These two facts made the sensitivity to the MLI effective emissivity and bus temperature very high. Approximately two years prior to launch the propulsion system was redesigned to meet MAP requirements. The new design utilized hardware that was already installed in order to meet schedule constraints. The spacecraft design and the thermal requirements were changed to compensate for inadequacies of the existing hardware. The propulsion system consists of fuel lines, fill and drain lines/valve, eight thrusters, a HXCM, and a propulsion tank. A voltage regulator was added to keep critical components within limits. Software was developed to control the operational heaters. Trim resistors were put in series with each operational heater circuits and the tank survival heater. A highly sophisticated test program, which included real time model correlation, was developed to determine trim resistors sizes. These trim resistors were installed during a chamber break and verified during thermal balance testing.

Mosier, Carol L.↗
NASA NTRS2013

File Specification for GEOS-5 FP (Forward Processing)

The GEOS-5 FP Atmospheric Data Assimilation System (GEOS-5 ADAS) uses an analysis developed jointly with NOAA's National Centers for Environmental Prediction (NCEP), which allows the Global Modeling and Assimilation Office (GMAO) to take advantage of the developments at NCEP and the Joint Center for Satellite Data Assimilation (JCSDA). The GEOS-5 AGCM uses the finite-volume dynamics (Lin, 2004) integrated with various physics packages (e.g, Bacmeister et al., 2006), under the Earth System Modeling Framework (ESMF) including the Catchment Land Surface Model (CLSM) (e.g., Koster et al., 2000). The GSI analysis is a three-dimensional variational (3DVar) analysis applied in grid-point space to facilitate the implementation of anisotropic, inhomogeneous covariances (e.g., Wu et al., 2002; Derber et al., 2003). The GSI implementation for GEOS-5 FP incorporates a set of recursive filters that produce approximately Gaussian smoothing kernels and isotropic correlation functions. The GEOS-5 ADAS is documented in Rienecker et al. (2008). More recent updates to the model are presented in Molod et al. (2011). The GEOS-5 system actively assimilates roughly 2 × 10(exp 6) observations for each analysis, including about 7.5 × 10(exp 5) AIRS radiance data. The input stream is roughly twice this volume, but because of the large volume, the data are thinned commensurate with the analysis grid to reduce the computational burden. Data are also rejected from the analysis through quality control procedures designed to detect, for example, the presence of cloud. To minimize the spurious periodic perturbations of the analysis, GEOS-5 FP uses the Incremental Analysis Update (IAU) technique developed by Bloom et al. (1996). More details of this procedure are given in Appendix A. The assimilation is performed at a horizontal resolution of 0.3125-degree longitude by 0.25- degree latitude and at 72 levels, extending to 0.01 hPa. All products are generated at the native resolution of the horizontal grid. The majority of data products are time-averaged, but four instantaneous products are also available. Hourly data intervals are used for two-dimensional products, while 3-hourly intervals are used for three-dimensional products. These may be on the model's native 72-layer vertical grid or at 42 pressure surfaces extending to 0.1 hPa. This document describes the gridded output files produced by the GMAO near real-time operational FP, using the most recent version of the GEOS-5 assimilation system. Additional details about variables listed in this file specification can be found in a separate document, the GEOS-5 File Specification Variable Definition Glossary. Documentation about the current access methods for products described in this document can be found on the GMAO products page: http://gmao.gsfc.nasa.gov/products/.

GSI↗
NASA NTRS1987

Boundary-layer and wake measurements on a swept, circulation-control wing

Wind-tunnel measurements of boundary-layer and wake velocity profiles and surface static pressure distributions are presented for a swept, circulation-control wing. The model is an aspect-ratio-four semispan wing mounted on the tunnel side wall at a sweep angle of 45 deg. A full-span, tangential, rearward blowing, circulation-control slot is located ahead of the trailing edge on the upper surface. Flow surveys were obtained at mid-semispan at freestream Mach numbers of 0.425 and 0.70. Boundary-layer profiles measured on the forward portions of the wing are approximately streamwise and two dimensional. The flow in the vicinity of the jet exit and in the near wake is highly three dimensional. The jet flow near the slot on the Coanda surface is directed normal to the slot. Near-wake surveys show large outboard flows at the center of the wake. At Mach 0.425 and a 5-deg angle of attack, a range of jet-blowing rates was found for which an abrupt transition from incipient separation to attached flow occurs in the boundary layer upstream of the slot. The variation in the lower-surface separation location with blowing rate was determined from boundary-layer measurements at Mach 0.425.

Spaid, Frank W.↗
NASA NTRS1993

Variational Trajectory Optimization Tool Set: Technical description and user's manual

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.

Bless, Robert R.↗