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At least 1,243 records · Page 69

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NASA NTRS1992

Control design based on a linear state function observer

An approach to the design of low-order controllers for large scale systems is proposed. The method is derived from the theory of linear state function observers. First, the realization of a state feedback control law is interpreted as the observation of a linear function of the state vector. The linear state function to be reconstructed is the given control law. Then, based on the derivation for linear state function observers, the observer design is formulated as a parameter optimization problem. The optimization objective is to generate a matrix that is close to the given feedback gain matrix. Based on that matrix, the form of the observer and a new control law can be determined. A four-disk system and a lightly damped beam are presented as examples to demonstrate the applicability and efficacy of the proposed method.

Su, Tzu-Jeng↗

NASA NTRS1993

Streamwise computation of three-dimensional flows using two stream functions

An approach to compute 3D flows using two stream functions is presented. The independent variables used are chi, a spatial coordinate, and xi and eta, values of stream functions along two sets of suitably chosen intersecting stream surfaces. The dependent variables used are the streamwise velocity, and two functions that describe the stream surfaces. Since the value of a stream function is constant along the solid boundaries, this choice of variables makes it easy to satisfy the boundary conditions. To illustrate the approach, computations of incompressible potential flow through a circular-to-rectangular transition duct are also presented.

Greywall, M. S.↗

NASA NTRS1993

A function approximation approach to anomaly detection in propulsion system test data

Ground test data from propulsion systems such as the Space Shuttle Main Engine (SSME) can be automatically screened for anomalies by a neural network. The neural network screens data after being trained with nominal data only. Given the values of 14 measurements reflecting external influences on the SSME at a given time, the neural network predicts the expected nominal value of a desired engine parameter at that time. We compared the ability of three different function-approximation techniques to perform this nominal value prediction: a novel neural network architecture based on Gaussian bar basis functions, a conventional back propagation neural network, and linear regression. These three techniques were tested with real data from six SSME ground tests containing two anomalies. The basis function network trained more rapidly than back propagation. It yielded nominal predictions with, a tight enough confidence interval to distinguish anomalous deviations from the nominal fluctuations in an engine parameter. Since the function-approximation approach requires nominal training data only, it is capable of detecting unknown classes of anomalies for which training data is not available.

Whitehead, Bruce A.↗

NASA NTRS1993

Efficient and accurate computation of the incomplete Airy functions

The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high-frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals with such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. In this paper a convergent series solution for the incomplete Airy functions is derived. Asymptotic expansions involving several terms are also developed and serve as large argument approximations. The combination of the series solution with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data.

Constantinides, E. D.↗

NASA NTRS1993

Luminosity functions and color-magnitude diagrams for three OB associations in the Large Magellanic Cloud

Using the point spread function photometry program DAOPHOT, we have used UBV CCD photometry to construct color-magnitude diagrams and luminosity functions for three OB associations in the Large Magellanic Cloud. The region LH 76 appears to be completely coeval; the region LH 13 shows some evidence for noncoevality which will need to be checked with spectra of the stars in question. The region LH 105, which lies on the southern edge of 30 Doradus, shows significant contamination by an underlying older population, possibly from previous star forming events. The luminosity functions, which serve as the first step toward determining the initial mass function in these regions, are calculated.

Degioia-Eastwood, K.↗

NASA NTRS1994

On the Gibbs phenomenon 4: Recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function

We continue our investigation of overcoming Gibbs phenomenon, i.e., to obtain exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. We show that if we are given the first N Gegenbauer expansion coefficients, based on the Gegenbauer polynomials C(sub k)(sup mu)(x) with the weight function (1 - x(exp 2))(exp mu - 1/2) for any constant mu is greater than or equal to 0, of an L(sub 1) function f(x), we can construct an exponentially convergent approximation to the point values of f(x) in any subinterval in which the function is analytic. The proof covers the cases of Chebyshev or Legendre partial sums, which are most common in applications.

Gottlieb, David↗

NASA NTRS1995

Aerodynamic parameter estimation via Fourier modulating function techniques

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

Pearson, A. E.↗

NASA NTRS1995

The luminosity function of quasars

We propose a new evolutionary model for the optical luminosity function of quasars. Our analytical model is derived from fits to the empirical luminosity function estimated by Hartwick and Schade and Warren, Hewett, and Osmer on the basis of more than 1200 quasars over the range of redshifts 0 approximately less than z approximately less than 4.5. We find that the evolution of quasars over this entire redshift range can be well fitted by a Gaussian distribution, while the shape of the luminosity function can be well fitted by either a double power law or an exponential L(exp 1/4) law. The predicted number counts of quasars, as a function of either apparent magnitude or redshift, are fully consistent with the observed ones. Our model indicates that the evolution of quasars reaches its maximum at z approximately = 2.8 and declines at higher redshifts. An extrapolation of the evolution to z approximately greater than 4.5 implies that quasars may have started their cosmic fireworks at z(sub f) approximately = 5.2-5.5. Forthcoming surveys of quasars at these redshifts will be critical to constrain the epoch of quasar formation. All the results we derived are based on observed quasars and are therefore subject to the bias of obscuration by dust in damped Ly alpha systems. Future surveys of these absorption systems at z approximately greater than 3 will also be important if the formation epoch of quasars is to be known unambiguously.

Pei, Yichuan C.↗

NASA NTRS1995

Constraints on the gamma-ray burst luminosity function from Pioneer Venus Orbiter and BATSE observations

We examine the width of the gamma ray burst luminosity function through the distribution of Gamma Ray Burst (GRB) peak fluxes as detected by the Pioneer Venus Orbiter (PVO) and the Burst and Transient Source Experiment (BATSE). The strength of the analysis is greatly enhanced by using a merged catalog of peak fluxes from both instruments with good cross-calibration of their sensitivities. The range of peak fluxes is increased by approximately a factor of 20 relative to the BATSE catalog. Thus, more sensitive investigations of the log N - log P distribution are possible. We place constraints on the width of the luminosity function of gamma-ray bursts brighter than the BATSE completeness limit by comparing the intensity distribution in the merged catalog with those produced by a variety of spatial density and luminosity functions. For the models examined, 90% of the detectable bursts have peak luminosities within a range of 10, indicating that the peak luminosities of gamma-ray bursts span a markedly less wide range of values than many other of their measurable properties. We also discuss for which slopes of a power-law luminosity function the observed width is at the upper end of the constrained range. This is essential in determining the power-law slopes for which luminosity-duration correlations could be important.

Ulmer, Andrew↗

NASA NTRS1994

The luminosity function of the CfA Redshift Survey

We use the CfA Reshift Survey of galaxies with m(sub z) less than or equal to 15.5 to calculate the galaxy luminosity function over the range -13 less than or equal to M(sub z) less than or equal to -22. The sample includes 9063 galaxies distributed over 2.1 sr. For galaxies with velocities cz greater or equal to 2500 km per sec, where the effects of peculiar velocities are small, the luminosity function is well represented by a Schechter function with parameters phi(sub star) = 0.04 +/- 0.01 per cu Mpc, M(sub star) = -18.8 +/- 0.3, and alpha = -1.0 +/- 0.2. When we include all galaxies with cz greater or equal to 500 km per sec, the number of galaxies in the range -16 less than or equal to M(sub z) less than or equal to -13 exceeds the extrapolation of the Schechter function by a factor of 3.1 +/- 0.5. This faint-end excess is not caused by the local peculiar velocity field but may be partially explained by small scale errors in the Zwicky magnitudes. Even with a scale error as large as 0.2 mag per mag, which is unlikely, the excess is still a factor of 1.8 +/- 0.3. If real, this excess affects the interpretation of deep counts of field galaxies.

Marzke, R. O.↗

NASA NTRS1996

New Interpretation of the Wigner Function

I define a two-sided or forward-backward propagator for the pseudo-diffusion equation of the 'squeezed' Q function. This propagator leads to squeezing in one of the phase-space variables and anti-squeezing in the other. By noting that the Q function is related to the Wigner function by a special case of the above propagator, I am led to a new interpretation of the Wigner function.

Daboul, Jamil↗

NASA NTRS1996

Q (Alpha) Function and Squeezing Effect

The relation of squeezing and Q(alpha) function is discussed in this paper. By means of Q function, the squeezing of field with gaussian Q(alpha) function or negative P(a)function is also discussed in detail.

Yunjie, Xia↗

NASA NTRS1996

Downlink Probability Density Functions for EOS-McMurdo Sound

The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.

Christopher, P.↗

NASA NTRS1993

Effects of Local Compression on Peroneal Nerve Function in Humans

A new apparatus was developed to compress the anterior compartment selectively and reproducibly in humans. Thirty-five normal volunteers were studied to determine short-term thresholds of local tissue pressure that produce significant neuromuscular dysfunction. Local tissue fluid pressure adjacent to the deep peroneal nerve was elevated by the compression apparatus and continuously monitored for 2-3 h by the slit catheter technique. Elevation of tissue fluid pressure to within 35-40 mm Hg of diastolic blood pressure (approx. 40 mm Hg of in situ pressure in our subjects) elicited a consistent progression of neuromuscular deterioration including, in order, (a) gradual loss of sensation, as assessed by Semmes-Weinstein monofilaments, (b) subjective complaints, (c) reduced nerve conduction velocity, (d) decreased action potential amplitude of the extensor digitorum brevis muscle, and (e) motor weakness of muscles within the anterior compartment. Generally, higher intracompartment at pressures caused more rapid deterioration of neuromuscular function. In two subjects, when in situ compression levels were 0 and 30 mm Hg, normal neuromuscular function was maintained for 3 h. Threshold pressures for significant dysfunction were not always the same for each functional parameter studied, and the magnitudes of each functional deficit did not always correlate with compression level. This variable tolerance to elevated pressure emphasizes the need to monitor clinical signs and symptoms carefully in the diagnosis of compartment syndromes. The nature of the present studies was short term; longer term compression of myoneural tissues may result in dysfunction at lower pressure thresholds.

Hargens, Alan R.↗

NASA NTRS1997

An NPARC Turbulence Module with Wall Functions

The turbulence module recently developed for the NPARC code has been extended to include wall functions. The Van Driest transformation is used so that the wall functions can be applied to both incompressible and compressible flows. The module is equipped with three two-equation K-epsilon turbulence models: Chien, Shih-Lumley and CMOTR models. Details of the wall functions as well as their numerical implementation are reported. It is shown that the inappropriate artificial viscosity in the near-wall region has a big influence on the solution of the wall function approach. A simple way to eliminate this influence is proposed, which gives satisfactory results during the code validation. The module can be easily linked to the NPARC code for practical applications.

Zhu, J.↗

NASA NTRS1995

Modified Interior Distance Functions (Theory and Methods)

In this paper we introduced and developed the theory of Modified Interior Distance Functions (MIDF's). The MIDF is a Classical Lagrangian (CL) for a constrained optimization problem which is equivalent to the initial one and can be obtained from the latter by monotone transformation both the objective function and constraints. In contrast to the Interior Distance Functions (IDF's), which played a fundamental role in Interior Point Methods (IPM's), the MIDF's are defined on an extended feasible set and along with center, have two extra tools, which control the computational process: the barrier parameter and the vector of Lagrange multipliers. The extra tools allow to attach to the MEDF's very important properties of Augmented Lagrangeans. One can consider the MIDFs as Interior Augmented Lagrangeans. It makes MIDF's similar in spirit to Modified Barrier Functions (MBF's), although there is a fundamental difference between them both in theory and methods. Based on MIDF's theory, Modified Center Methods (MCM's) have been developed and analyzed. The MCM's find an unconstrained minimizer in primal space and update the Lagrange multipliers, while both the center and the barrier parameter can be fixed or updated at each step. The MCM's convergence was investigated, and their rate of convergence was estimated. The extension of the feasible set and the special role of the Lagrange multipliers allow to develop MCM's, which produce, in case of nondegenerate constrained optimization, a primal and dual sequences that converge to the primal-dual solutions with linear rate, even when both the center and the barrier parameter are fixed. Moreover, every Lagrange multipliers update shrinks the distance to the primal dual solution by a factor 0 less than gamma less than 1 which can be made as small as one wants by choosing a fixed interior point as a 'center' and a fixed but large enough barrier parameter. The numericai realization of MCM leads to the Newton MCM (NMCM). The approximation for the primal minimizer one finds by Newton Method followed by the Lagrange multipliers update. Due to the MCM convergence, when both the center and the barrier parameter are fixed, the condition of the MDF Hessism and the neighborhood of the primal ninimizer where Newton method is 'well' defined remains stable. It contributes to both the complexity and the numerical stability of the NMCM.

Polyak, Roman A.↗

NASA NTRS1997

Atomic, Molecular, and Optical Physics: Optical Excitation Function of H(1s-2p) Produced by electron Impact from Threshold to 1.8 keV

The optical excitation function of prompt Lyman-Alpha radiation, produced by electron impact on atomic hydrogen, has been measured over the extended energy range from threshold to 1.8 keV. Measurements were obtained in a crossed-beams experiment using both magnetically confined and electrostatically focused electrons in collision with atomic hydrogen produced by an intense discharge source. A vacuum-ultraviolet mono- chromator system was used to measure the emitted Lyman-Alpha radiation. The absolute H(1s-2p) electron impact excitation cross section was obtained from the experimental optical excitation function by normalizing to the accepted optical oscillator strength, with corrections for polarization and cascade. Statistical and known systematic uncertainties in our data range from +/- 4% near threshold to +/- 2% at 1.8 keV. Multistate coupling affecting the shape of the excitation function up to 1 keV impact energy is apparent in both the present experimental data and present theoretical results obtained with convergent close- coupling (CCC) theory. This shape function effect leads to an uncertainty in absolute cross sections at the 10% level in the analysis of the experimental data. The derived optimized absolute cross sections are within 7% of the CCC calculations over the 14 eV-1.8 keV range. The present CCC calculations converge on the Bethe- Fano profile for H(1s-2p) excitation at high energy. For this reason agreement with the CCC values to within 3% is achieved in a nonoptimal normalization of the experimental data to the Bethe-Fano profile. The fundamental H(1s-2p) electron impact cross section is thereby determined to an unprecedented accuracy over the 14 eV - 1.8 keV energy range.

James, G. K.↗

NASA NTRS1997

Ion Sources and Acceleration Mechanisms Inferred from Local Distribution Functions

This study investigates the sources of the ions up the complex and nonisotropic H(+) velocity distribution functions observed by the Geotail spacecraft on May 23, 1995, in the near-Earth magnetotail region and recently reported by Frank et al. [1996]. A distribution function observed by Geotail at -10 R(sub E) downtail is used as input for the large scale kinetic (LSK) technique to follow the trajectories of approximately 90,000 H(+) ions backward in time. Time-dependent magnetic and electric fields are taken from a global magnetohydrodynamic (MHD) simulation of the magnetosphere and its interactions with appropriate solar wind and IMF conditions. The ion population described by the Geotail distribution function was found to consist of a mixture of particles originating from three distinct sources: the ionosphere, the low latitude boundary layer (LLBL), and the high latitude plasma mantle. Ionospheric particles had direct access along field lines to Geotail, and LLBL ions convected adiabatically to the Geotail location. Plasma mantle ions, on the other hand, exhibited two distinct types of behavior. Most near-Earth mantle ions reached Geotail on adiabatic orbits, while distant mantle ions interacted with the current sheet tailward of Geotail and had mostly nonadiabatic orbits. Ions from the ionosphere, the LLBL, and the near-Earth mantle were directly responsible for the well-separated, low energy structures easily discernible in the observed and modeled distribution functions. Distant mantle ions formed the higher energy portion of the Geotail distribution. Thus, we have been successful in extracting useful information about particle sources, their relative contribution to the measured distribution and the acceleration processes that affected particle transport during this time.

Ashour-Abdalla, M.↗