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NASA NTRS1991

On the Power of Abstract Interpretation

Increasingly sophisticated applications of static analysis place increased burden on the reliability of the analysis techniques. Often, the failure of the analysis technique to detect some information my mean that the time or space complexity of the generated code would be altered. Thus, it is important to precisely characterize the power of static analysis techniques. We follow the approach of Selur et. al. who studied the power of strictness analysis techniques. Their result can be summarized by saying 'strictness analysis is perfect up to variations in constants.' In other words, strictness analysis is as good as it could be, short of actually distinguishing between concrete values. We use this approach to characterize a broad class of analysis techniques based on abstract interpretation including, but not limited to, strictness analysis. For the first-order case, we consider abstract interpretations where the abstract domain for data values is totally ordered. This condition is satisfied by Mycroft's strictness analysis that of Sekar et. al. and Wadler's analysis of list-strictness. For such abstract interpretations, we show that the analysis is complete in the sense that, short of actually distinguishing between concrete values with the same abstraction, it gives the best possible information. We further generalize these results to typed lambda calculus with pairs and higher-order functions. Note that products and function spaces over totally ordered domains are not totally ordered. In fact, the notion of completeness used in the first-order case fails if product domains or function spaces are added. We formulate a weaker notion of completeness based on observability of values. Two values (including pairs and functions) are considered indistinguishable if their observable components are indistinguishable. We show that abstract interpretation of typed lambda calculus programs is complete up to this notion of indistinguishability. We use denotationally-oriented arguments instead of the detailed operational arguments used by Selur et. al.. Hence, our proofs are much simpler. They should be useful for further future improvements.

Reddy, Uday S.↗

NASA NTRS1986

A new sunspot umbral model and its variation with the solar cycle

Semiempirical model atmospheres are presented for the darkest parts of large sunspot umbrae, regions have called umbral cores. The approach is based on general-purpose computational procedures that are applicable to different types of stellar atmospheres. It is shown that recent umbral intensity measurements of the spectral energy distribution may be accounted for by an umbral core atmospheric model that varies with time during the solar cycle; the observed center-limb variation can be accounted for by the properties of the model. Three umbral core models are presented, corresponding to the early, middle, and late phases of the solar cycle. These three models also may be regarded as having the properties of dark, average, and bright umbral cores respectively. The effects of atomic, opacity, and abundance data uncertainties on the model calculations are briefly discussed. For comparison, a new reference model for the average quiet solar photosphere is given.

Maltby, P.↗

NASA NTRS1971

Mapping soil types from multispectral scanner data.

Multispectral remote sensing and computer-implemented pattern recognition techniques were used for automatic ?mapping' of soil types. This approach involves subjective selection of a set of reference samples from a gray-level display of spectral variations which was generated by a computer. Each resolution element is then classified using a maximum likelihood ratio. Output is a computer printout on which the researcher assigns a different symbol to each class. Four soil test areas in Indiana were experimentally examined using this approach, and partially successful results were obtained.

Kristof, S. J.↗

NASA NTRS1999

How Does the Global-Scale Atmosphere Circulation Produce Clouds?

Although clouds are produced by "micro-scale" processes, these processes operate as a response to global-scale atmospheric motions to produce the complex geographic distribution of clouds on Earth. One way to attack this larger-scale problem is to combine global-scale satellite observations of cloud property variations with global-scale determinations of the atmospheric circulation. Such a global data analysis can be used to describe the mean characteristics of clouds and their variations for comparison with global circulation models, to identify systematic relations among observed cloud properties and atmospheric motions, or to estimate, directly, the derivative relations of the processes at work using statistical life-cycle-composites of cloud system evolution. Another approach is to find what characteristics of the global atmospheric circulation are revealed in observed global-scale cloud variations. For the first time this type of analysis is possible with the advent of global, satellite-based cloud (ISCCP), precipitation (microwave-based), and water vapor (merged infrared and microwave) datasets, together with global wind datasets (ECMWF and NCEP re-analyses), all of which resolve features at least down to the upper end of the mesoscale and cover more than a decade. We report on some preliminary attempts to identify quantitative relationships between atmospheric motions and cloud properties that are relevant to cloud processes. Three examples are given: (1) cloud variations at the smallest scales and what they reveal about the nature of small-scale turbulence in the atmospheric boundary layer, (2) cloud variations at "moderate" weather-scales and what they reveal about meteorological storm systems, and (3) cloud variations at the largest scales and what they indicate about interannual variations of climate.

Rossow, William B.↗

NASA NTRS1972

Discrete rotor noise.

Description of a single unified theory to account generally for the discrete radiation from the whole family of heavily loaded axial flow rotors, including helicopter rotors, propellers, and compressors. The approach used is to analyze, in a Fourier way, the periodic blade loading variation (azimuth profile) into blade loading harmonics (BLH) and then sum the total radiation from each BLH. The basic differences between high and low solidity rotor spectrums are considered, emphasizing the difference between subsonic and supersonic rotor noise. The special effect of helicopter blade slap and compressor rotor-stator interaction is discussed, and measured rotor spectrums have been included to help illustrate the theory.

Wright, S. E.↗

NASA NTRS1976

Observations of Jupiter's radio emission at 327 MHz and 1410 MHz during the Pioneer 11 fly-by

During the 1974 fly-by of Jupiter by the Pioneer 11 spacecraft, radio observations were carried out daily at 327 and 1410 MHz for a period of 60 days centered on December 3, 1974, the day of closest approach to Jupiter. The 1410-MHz data reveal two significant short-term variations in the Jovian radio emission; the largest one is probably present also at 327 MHz although Faraday rotation in earth's ionosphere could have affected the data. The two radio bursts appear to be correlated with two long-duration electron bursts observed in the energy ranges from 2 to 7 and 6 to 30 MeV.

Kundu, M. R.↗

NASA NTRS1979

Effect of Mach number and Reynolds number on a normal shock-wave/turbulent boundary-layer interaction

Experimental values of wall pressure and skin friction have been obtained for Mach numbers from 1.32 to 1.48 and for Reynolds numbers from 8.5 x 10 to the 6th to 225 x 10 to the 6th. Increasing the Mach number reduces the wall shear and promotes incipient separation. Reynolds number variations have little effect except at the lowest value where the flow abruptly approaches separation. Comparisons are made with solutions to the time-dependent, Reynolds-averaged, Navier-Stokes equations incorporating a two-equation, Wilcox-Rubesin turbulence model. The computations are in agreement with the experimental results. Additional numerical results indicated that the wind-tunnel walls constrained the flow and suppressed the formation of a separation bubble at the shock wave.

Mateer, G. G.↗

NASA NTRS1981

Control system development for an organic Ranking cycle engine

An organic Rankine cycle engine is used as part of a solar thermal power conversion assembly (PCA). The PCA, including a direct-heated cavity receiver and a shaft-mounted alternator, is mounted at the focal point of a parabolic dish concentrator. The engine controls are required to maintain approximately constant values of turbine inlet temperature and shaft speed, despite variation in the concentrated solar power input to the receiver. The controls design approach, system models, and initial stability and performance analysis results are presented herein.

Bergthold, F. M., Jr.↗

NASA NTRS1985

Periodic orbits of the general three-body problem for the sun-Jupiter-Saturn system

Two families of symmetric periodic orbits of the planar, general, three-body problem are presented. The masses of the three bodies include ratios equal to the sun-Jupiter-Saturn system and the periods of the orbits of Jupiter and Saturn are in a 2:5 resonance. The (linear) stability of the orbits are studied in relation to eccentricity and mass variations. The generation of the two families of periodic orbits follows a systematic approach and employs (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to the elliptic restricted problem and from the circular and elliptic problems to the general problem through bifurcation phenomena relating the three dynamical systems. The approach also provides insight into the evolutionary process of periodic orbits continued from the restricted problems to the general problem.

Kwok, J. H.↗

NASA NTRS1987

Loran-C monitoring

The Loran-C monitor developed by Ohio University will collect Loran signal data for storage on magnetic tape. Stationed at the Ohio University Airport, Athens, Ohio, the monitor will provide valuable information concerning the daily and seasonal variation of the Loran-C signals for use in non-precision approach studies. With the aid of a second monitor, located in Gallion, Ohio, it can be determined if the errors found at a particular geographic location correlate with those found at another location. This will give some indication as to how far apart monitors can be positioned to obtain accurate non-precision approach data for various airports.

Edwards, Jamie↗

NASA NTRS1989

Three-dimensional simulation of underexpanded plumes using upwind algorithms

Different numerical techniques have been examined for simulating the underexpanded plumes in supersonic flows. The results revealed that the monotone differentiable limiter is superior to the TVD (total variation diminishing) minmod limiter when the MUSCL (monotonic upstream schemes for conservation laws) approach is used for Roe's upwind scheme. Roe's upwind scheme is found to be superior to the central difference scheme not only for capturing shock waves, but also for capturing shear flows.

Obayashi, Shigeru↗

NASA NTRS1990

A proposed Kalman filter algorithm for estimation of unmeasured output variables for an F100 turbofan engine

To develop advanced control systems for optimizing aircraft engine performance, unmeasurable output variables must be estimated. The estimation has to be done in an uncertain environment and be adaptable to varying degrees of modeling errors and other variations in engine behavior over its operational life cycle. This paper presents an approach to estimate unmeasured output variables by explicitly modeling the effects of off-nominal engine behavior as biases on the measurable output variables. A state variable model accommodating off-nominal behavior is developed for the engine, and Kalman filter concepts are used to estimate the required variables. Results are presented from nonlinear engine simulation studies as well as the application of the estimation algorithm on actual flight data. The formulation presented has a wide range of application since it is not restricted or tailored to the particular application described in the paper.

Alag, Gurbux S.↗

NASA NTRS1990

Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets

Numerical methods have been used successfully in atomic Dirac-Hartree-Fock (DHF) calculations for many years. Some DHF calculations using numerical methods have been done on diatomic molecules, but while these serve a useful purpose for calibration, the computational effort in extending this approach to polyatomic molecules is prohibitive. An alternative more in line with traditional quantum chemistry is to use an analytical basis set expansion of the wave function. This approach fell into disrepute in the early 1980's due to problems with variational collapse and intruder states, but has recently been put on firm theoretical foundations. In particular, the problems of variational collapse are well understood, and prescriptions for avoiding the most serious failures have been developed. Consequently, it is now possible to develop reliable molecular programs using basis set methods. This paper describes such a program and reports results of test calculations to demonstrate the convergence and stability of the method.

Dyall, Kenneth G.↗

NASA NTRS1990

A proposed Kalman filter algorithm for estimation of unmeasured output variables for an F100 turbofan engine

To develop advanced control systems for optimizing aircraft engine performance, unmeasurable output variables must be estimated. The estimation has to be done in an uncertain environment and be adaptable to varying degrees of modeling errors and other variations in engine behavior over its operational life cycle. This paper represented an approach to estimate unmeasured output variables by explicitly modeling the effects of off-nominal engine behavior as biases on the measurable output variables. A state variable model accommodating off-nominal behavior is developed for the engine, and Kalman filter concepts are used to estimate the required variables. Results are presented from nonlinear engine simulation studies as well as the application of the estimation algorithm on actual flight data. The formulation presented has a wide range of application since it is not restricted or tailored to the particular application described.

Alag, Gurbux S.↗

NASA NTRS1990

Synthesis: Intertwining product and process

Synthesis is a proposed systematic process for rapidly creating different members of a program family. Family members are described by variations in their requirements. Requirements variations are mapped to variations on a standard design to generate production quality code and documentation. The approach is made feasible by using principles underlying design for change. Synthesis incorporates ideas from rapid prototyping, application generators, and domain analysis. The goals of Synthesis and the Synthesis process are discussed. The technology needed and the feasibility of the approach are also briefly discussed. The status of current efforts to implement Synthesis methodologies is presented.

Weiss, David M.↗

NASA NTRS1992

Free-edge effects in laminates under extension, bending and twisting. II - Sublaminate/layer modeling and analysis

The stress-function-based variational method of Yin (1991) is extended and modified into a combined layer/sublaminate approach applicable to a laminated strip composed of a large number of differently orientated, anisotropic elastic plies. Lekhnitskii's (1963) stress functions are introduced into two interior layers adjacent to a particular interface. The remaining layers are grouped into an upper sublaminate and a lower sublaminate. The stress functions are expanded in truncated power series of the thickness coordinate, and the differential equations governing the coefficient functions are derived by using the complementary virtual work principle. The layer/sublaminate approach limits the dimension of the eigenvalue problem to a fixed number irrespective of the number of layers in the sublaminate, so that reasonably accurate solutions of the interlaminar stresses can be computed with extreme ease. For symmetric, four-layer, angle-ply and cross-ply laminates, a comparison of the previous analysis results based on the pure layer model and new results based on two different layer/sublaminate models indicates reasonable over-all agreement in the interlaminar stresses and superior agreement in the total peeling and shearing force.

Yin, Wan-Lee↗

NASA NTRS1991

Measurement of subresolution terrain displacements using SPOT panchromatic imagery

It is shown that satellite-derived imagery can be used to measure subresolution horizontal terrain displacements associated with present-day earthquakes, sand dune migration, glacial motion, coastal sediment transport, and pre-eruptive volcanic processes. This use of these data allows the detection of change and the determination of rates of many environmental processes worldwide. The premise of the method is that areally extensive, subresolution spatial differences in ground patterns between images acquired at different times can be accurately measured to high precision and can be distinguished from systematic image differences, such as those due to sensing-system attitude variations. Thus far, a preliminary algorithm has been tested that shows that the approach is reasonable.

Crippen, Robert E.↗

NASA NTRS1994

The constant current loop: A new paradigm for resistance signal conditioning

A practical single constant current loop circuit for the signal conditioning of variable-resistance transducers has been synthesized, analyzed, and demonstrated. The strain gage and the resistance temperature detector are examples of variable-resistance sensors. Lead wires connect variable-resistance sensors to remotely located signal-conditioning hardware. The presence of lead wires in the conventional Wheatstone bridge signal-conditioning circuit introduces undesired effects that reduce the quality of the data from the remote sensors. A practical approach is presented for suppressing essentially all lead wire resistance effects while indicating only the change in resistance value. Theoretical predictions supported by laboratory testing confirm the following features of the approach: (1) dc response; (2) the electrical output is unaffected by extremely large variation in the resistance of any or all lead wires; (3) the electrical output remains zero for no change in gage resistance; (4) the electrical output is inherently linear with respect to gage resistance change; (5) the sensitivity is double that of a Wheatstone bridge circuit; and (6) the same excitation wires can serve multiple independent gages. An adaptation of current loop circuit is presented that simultaneously provides an output signal voltage directly proportional to transducer resistance change and provides temperature information that is unaffected by transducer and lead wire resistance variations. These innovations are the subject of NASA patent applications.

Anderson, Karl F.↗