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NASA NTRS2004

Chandra Observations of the X-ray Environs of SN 1998bw/GRB 980425

We report X-ray studies of the environs of SN 1998bw and GRB 980425 using the Chandra X-Ray Observatory 1281 days after the gamma-ray burst (GRB). Eight X-ray point sources were localized, three and five each in the original error boxes, S1 and S2, assigned for variable X-ray counteparts to the GRB by BeppoSAX. The sum of the discrete X-ray sources plus continuous emission in S2 observed by Chandra on day 1281 is within a factor of 1.5 of the maximum and the upper limits seen by BeppoSAX. We conclude that S2 is the sum of several variable sources that have not disappeared and therefore is not associated with the GRB. Within S1, clear evidence is seen for a decline of approximately a factor of 12 between day 200 and day 1281. One of the sources in S 1, S 1 a, is coincident with the well-determined radio location of SN 1998bw and is certainly the remnant of that explosion. The nature of the other sources is also discussed. Combining our observation of the supernova with others of the GRB afterglow, a smooth X-ray light curve, spanning approx. 1400 days, is obtained by assuming that the burst and supernova were coincident at 35.6 Mpc. When this X-ray light curve is compared with those of the X-ray af "erglows" of ordinary GRBs, X-ray flashes, and ordinary supernovae, evidence emerges for at least two classes of light curves, perhaps bounding a continuum. By 3-10 yr, all these phenomena seem to converge on a common X-ray luminosity, possibly indicative of the supernova underlying them all. This convergence strengthens the conclusion that SN 1998 bw aid GRB 980425 took place in the same object.One possible explanation for the two classes is that a (nearly) standard GRB was observed at different angles, in which case X-ray afterglows with intermediate luminosities should eventually be discovered. Finally, we comment on the contribution of GRB afterglows to the ultraluminous X-ray source population.

Kouveliotou, C.↗

NASA NTRS2004

Chandra Observations of the X-ray Environs of SN 1998 bw/GRB 980425

We report X-ray studies of the environs of SN 1998bw and GRB 980425 using the Chandra X-Ray Observatory 1281 days after the GRB. Eight X-ray point sources were localized, three and five each in the original error boxes--S1 and S2--assigned for variable X-ray counterparts to the GRB by BeppoSAX. The sum of the discrete X-ray sources plus continuous emission in S2 observed by CXO on day 1281 is within a factor of 1.5 of the maximum and the upper limits seen by BeppoSAX. We conclude that S2 is the sum of several variable sources that have not disappeared, and therefore is not associated with the GRB. Within S1, clear evidence is seen for a decline of approximately a factor of 12 between day 200 and day 1281. One of the sources in S1, S1a, is coincident with the well-determined radio location of SN 1998bw, and is certainly the remnant of that explosion. The nature of the other sources is also discussed. Combining our observation of the supernova with others of the GRB afterglow, a smooth X-ray light curve, spanning (approx) 1300 days, is obtained by assuming the burst and supernova were coincident at 35. 6 Mpc. When this X-ray light curve is compared with those of the X-ray 'afterglows' of ordinary GRBs, X-ray Flashes, and ordinary supernovae, evidence emerges for at least two classes of lightcurves, perhaps bounding a continuum.

X-RAY SOURCES↗

NASA NTRS2006

Compressing Image Data While Limiting the Effects of Data Losses

ICER is computer software that can perform both lossless and lossy compression and decompression of gray-scale-image data using discrete wavelet transforms. Designed for primary use in transmitting scientific image data from distant spacecraft to Earth, ICER incorporates an error-containment scheme that limits the adverse effects of loss of data and is well suited to the data packets transmitted by deep-space probes. The error-containment scheme includes utilization of the algorithm described in "Partitioning a Gridded Rectangle Into Smaller Rectangles " (NPO-30479), NASA Tech Briefs, Vol. 28, No. 7 (July 2004), page 56. ICER has performed well in onboard compression of thousands of images transmitted from the Mars Exploration Rovers.

Kiely, Aaron↗

NASA NTRS1986

Landsat D Thematic Mapper image dimensionality reduction and geometric correction accuracy

To characterize and quantify the performance of the Landsat thematic mapper (TM), techniques for dimensionality reduction by linear transformation have been studied and evaluated and the accuracy of the correction of geometric errors in TM images analyzed. Theoretical evaluations and comparisons for existing methods for the design of linear transformation for dimensionality reduction are presented. These methods include the discrete Karhunen Loeve (KL) expansion, Multiple Discriminant Analysis (MDA), Thematic Mapper (TM)-Tasseled Cap Linear Transformation and Singular Value Decomposition (SVD). A unified approach to these design problems is presented in which each method involves optimizing an objective function with respect to the linear transformation matrix. From these studies, four modified methods are proposed. They are referred to as the Space Variant Linear Transformation, the KL Transform-MDA hybrid method, and the First and Second Version of the Weighted MDA method. The modifications involve the assignment of weights to classes to achieve improvements in the class conditional probability of error for classes with high weights. Experimental evaluations of the existing and proposed methods have been performed using the six reflective bands of the TM data. It is shown that in terms of probability of classification error and the percentage of the cumulative eigenvalues, the six reflective bands of the TM data require only a three dimensional feature space. It is shown experimentally as well that for the proposed methods, the classes with high weights have improvements in class conditional probability of error estimates as expected.

Ford, G. E.↗

NASA NTRS1998

To Err is Normable: The Computation of Frequency-Domain Error Bounds from Time-Domain Data

This paper exploits the relationships among the time-domain and frequency-domain system norms to derive information useful for modeling and control design, given only the system step response data. A discussion of system and signal norms is included. The proposed procedures involve only simple numerical operations, such as the discrete approximation of derivatives and integrals, and the calculation of matrix singular values. The resulting frequency-domain and Hankel-operator norm approximations may be used to evaluate the accuracy of a given model, and to determine model corrections to decrease the modeling errors.

Hartley, Tom T.↗

NASA NTRS1999

Crack Turning and Arrest Mechanisms for Integral Structure

In the course of several years of research efforts to predict crack turning and flapping in aircraft fuselage structures and other problems related to crack turning, the 2nd order maximum tangential stress theory has been identified as the theory most capable of predicting the observed test results. This theory requires knowledge of a material specific characteristic length, and also a computation of the stress intensity factors and the T-stress, or second order term in the asymptotic stress field in the vicinity of the crack tip. A characteristic length, r(sub c), is proposed for ductile materials pertaining to the onset of plastic instability, as opposed to the void spacing theories espoused by previous investigators. For the plane stress case, an approximate estimate of r(sub c), is obtained from the asymptotic field for strain hardening materials given by Hutchinson, Rice and Rosengren (HRR). A previous study using of high order finite element methods to calculate T-stresses by contour integrals resulted in extremely high accuracy values obtained for selected test specimen geometries, and a theoretical error estimation parameter was defined. In the present study, it is shown that a large portion of the error in finite element computations of both K and T are systematic, and can be corrected after the initial solution if the finite element implementation utilizes a similar crack tip discretization scheme for all problems. This scheme is applied for two-dimensional problems to a both a p-version finite element code, showing that sufficiently accurate values of both K(sub I) and T can be obtained with fairly low order elements if correction is used. T-stress correction coefficients are also developed for the singular crack tip rosette utilized in the adaptive mesh finite element code FRANC2D, and shown to reduce the error in the computed T-stress significantly. Stress intensity factor correction was not attempted for FRANC2D because it employs a highly accurate quarter-point scheme to obtain stress intensity factors.

Pettit, Richard↗

NASA NTRS1978

Prediction, evaluation, and specification of flying qualities by means of step target tracking

A new approach to flying qualities specification and evaluation is presented which coordinates current research in the areas of pilot ratings, pilot-aircraft modeling techniques, and simulation and flight test procedures. A time-domain pilot model is described which can model discontinuous and nonlinear pilot behavior in conjunction with completely general time-varying nonlinear aircraft models to simulate discrete maneuvers. This pilot-aircraft model is applied to an existing set of in-flight simulation data, and calculates tracking error and time-on-target statistics for step target tracking that directly relate to the reported pilot comments and ratings. Predicted step target tracking data for eighteen F-5E flight conditions are presented, and the use of the method for control system design is demonstrated using the YF-17.

Onstott, E. D.↗

NASA NTRS1987

Coupling finite element and spectral methods: First results

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

Bernardi, Christine↗

NASA NTRS1987

A numerical method for the solution of three dimensional, incompressible, viscous flows over slender bodies

A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.

Rosenfeld, Moshe↗

NASA NTRS1988

The discrete correlation function: A new method for analyzing unevenly sampled variability data

A method of measuring correlation functions without interpolating in the temporal domain, the discrete correlation function, is introduced. It provides an assumption-free representation of the correlation measured in the data, and allows meaningful error estimates. This method does not produce spurious correlations at zero lag due to correlated errors. It is shown that physical interpretation of active galactic nuclei cross-correlation functions requires knowledge of the input function's fluctuation power spectrum, involves model-dependence in the form of symmetry assumptions, and must take into account intrinsic scale bias. This technique was used to find a correlation in published IUE data for NGC 4151, which indicates that the broad C IV feature emanates from a shell 15 to 75 light-days in radius, assuming spherical symmetry.

Edelson, R. A.↗

NASA NTRS1990

Data-Acquisition Board For IBM PS/2 Computer

Circuit board containing microprocessors designed to control acquisition of data by IBM PS/2 computer. Plugged into one of 16-bit slots on mother board of computer. Controls transfer of data from as many as 48 discrete channels to Micro Channel Interface. With expansion of software, board recognizes and filters specified kinds of signal patterns, possibly to detect errors.

Hoang, Phuong-Dung T.↗

NASA NTRS1990

Coupling finite element and spectral methods - First results

Bernardi, Christine↗

NASA NTRS1991

Sinc-Galerkin estimation of diffusivity in parabolic problems

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

Smith, Ralph C.↗

NASA NTRS1994

Parallel, adaptive finite element methods for conservation laws

We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.

Biswas, Rupak↗

NASA NTRS1994

Smoothing DCT Compression Artifacts

Image compression based on quantizing the image in the discrete cosine transform (DCT) domain can generate blocky artifacts in the output image. It is possible to reduce these artifacts and RMS error by adjusting measures of block edginess and image roughness, while restricting the DCT coefficient values to values that would have been quantized to those of the compressed image. We also introduce a DCT coefficient amplitude adjustment that reduces RMS error.

Ahumada, A. J., Jr.↗

NASA NTRS2003

GOME Total Ozone and Calibration Error Derived Usign Version 8 TOMS Algorithm

The Global Ozone Monitoring Experiment (GOME) is a hyper-spectral satellite instrument measuring the ultraviolet backscatter at relatively high spectral resolution. GOME radiances have been slit averaged to emulate measurements of the Total Ozone Mapping Spectrometer (TOMS) made at discrete wavelengths and processed using the new TOMS Version 8 Ozone Algorithm. Compared to Differential Optical Absorption Spectroscopy (DOAS) techniques based on local structure in the Huggins Bands, the TOMS uses differential absorption between a pair of wavelengths including the local stiucture as well as the background continuum. This makes the TOMS Algorithm more sensitive to ozone, but it also makes the algorithm more sensitive to instrument calibration errors. While calibration adjustments are not needed for the fitting techniques like the DOAS employed in GOME algorithms, some adjustment is necessary when applying the TOMS Algorithm to GOME. Using spectral discrimination at near ultraviolet wavelength channels unabsorbed by ozone, the GOME wavelength dependent calibration drift is estimated and then checked using pair justification. In addition, the day one calibration offset is estimated based on the residuals of the Version 8 TOMS Algorithm. The estimated drift in the 2b detector of GOME is small through the first four years and then increases rapidly to +5% in normalized radiance at 331 nm relative to 385 nm by mid 2000. The lb detector appears to be quite well behaved throughout this time period.

Gleason, J.↗

NASA NTRS1978

Synthesis of finite settling time discrete systems

A new finite settling time (FST) control law is presented. The performance and the flexibility of this dual-rate, sampled-data law as applied to the class of error driven, feedback control systems are demonstrated. A hybrid analog/digital simulation is performed in order to illustrate the practical aspects of this type of finite settling time design.

Gatlin, J. A.↗

NASA NTRS1996

Uncertainty Modeling for Structural Control Analysis and Synthesis

The development of an accurate model of uncertainties for the control of structures that undergo a change in operational environment, based solely on modeling and experimentation in the original environment is studied. The application used throughout this work is the development of an on-orbit uncertainty model based on ground modeling and experimentation. A ground based uncertainty model consisting of mean errors and bounds on critical structural parameters is developed. The uncertainty model is created using multiple data sets to observe all relevant uncertainties in the system. The Discrete Extended Kalman Filter is used as an identification/parameter estimation method for each data set, in addition to providing a covariance matrix which aids in the development of the uncertainty model. Once ground based modal uncertainties have been developed, they are localized to specific degrees of freedom in the form of mass and stiffness uncertainties. Two techniques are presented: a matrix method which develops the mass and stiffness uncertainties in a mathematical manner; and a sensitivity method which assumes a form for the mass and stiffness uncertainties in macroelements and scaling factors. This form allows the derivation of mass and stiffness uncertainties in a more physical manner. The mass and stiffness uncertainties of the ground based system are then mapped onto the on-orbit system, and projected to create an analogous on-orbit uncertainty model in the form of mean errors and bounds on critical parameters. The Middeck Active Control Experiment is introduced as experimental verification for the localization and projection methods developed. In addition, closed loop results from on-orbit operations of the experiment verify the use of the uncertainty model for control analysis and synthesis in space.

Campbell, Mark E.↗