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NASA NTRS1993

An algorithm for solving the perturbed gas dynamic equations

The present application of a compact, higher-order central-difference approximation to the linearized Euler equations illustrates the multimodal character of these equations by means of computations for acoustic, vortical, and entropy waves. Such dissipationless central-difference methods are shown to propagate waves exhibiting excellent phase and amplitude resolution on the basis of relatively large time-steps; they can be applied to wave problems governed by systems of first-order partial differential equations.

Davis, Sanford↗

NASA NTRS1995

The distribution of early- and late-type galaxies in the Coma cluster

The spatial distribution and the morohology-density relation of Coma cluster galaxies are studied using a new homogeneous photmetric sample of 450 galaxies down to B = 16.0 mag with quantitative morphology classification. The sample covers a wide area (10 deg X 10 deg), extending well beyond the Coma cluster. Morphological classifications into early- (E+SO) and late-(S) type galaxies are made by an automated algorithm using simple photometric parameters, with which the misclassification rate is expected to be approximately 10% with respect to early and late types given in the Third Reference Catalogue of Bright Galaxies. The flattened distribution of Coma cluster galaxies, as noted in previous studies, is most conspicuously seen if the early-type galaxies are selected. Early-type galaxies are distributed in a thick filament extended from the NE to the WSW direction that delineates a part of large-scale structure. Spiral galaxies show a distribution with a modest density gradient toward the cluster center; at least bright spiral galaxies are present close to the center of the Coma cluster. We also examine the morphology-density relation for the Coma cluster including its surrounding regions.

Doi, M.↗

NASA NTRS1995

The analysis of control trajectories using symbolic and database computing

This final report comprises the formal semi-annual status reports for this grant for the periods June 30-December 31, 1993, January 1-June 30, 1994, and June 1-December 31, 1994. The research supported by this grant is broadly concerned with the symbolic computation, mixed numeric-symbolic computation, and database computation of trajectories of dynamical systems, especially control systems. A review of work during the report period covers: trajectories and approximating series, the Cayley algebra of trees, actions of differential operators, geometrically stable integration algorithms, hybrid systems, trajectory stores, PTool, and other activities. A list of publications written during the report period is attached.

Grossman, Robert↗

NASA NTRS1999

Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms

This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.

Kurdila, Andrew J.↗

NASA NTRS1994

Long-Slit Spectra of Mars in the Thermal Infrared

We have obtained long-slit spectra of Mars in the 7-14 micrometer regime. Our two integrations, taken 1993 March 2, are spaced about 2 hours apart and are centered at longitudes of roughly 210 and 240 degrees. The data cover the Elysium Planitia and volcanic regions, the classical dark albedo regions of Cerburus and central and eastern Hesperia, and the classical bright albedo region Utopia Planitia. We have deconvolved the point spread function from the images using a maximum entropy reconstruction algorithm; the resulting spatial resolution of the images is better than 1". Mars occupies approximately 9" of the slit, and we have detected variations in the spectral emission from different areas of the planet. We are in the process of interpreting these spectral variations in terms of the temperature and composition of the surface and the transmission of the Martian atmospheric dust and gases.

Rowland, C. M.↗

NASA NTRS2003

Combined Radiometer-Radar Microphysical Profile Estimations with Emphasis on High Frequency Brightness Temperature Observations

Information about the vertical microphysical cloud structure is useful in many modeling and predictive practices. Radiometers and radars are used to observe hydrometeor properties. This paper describes an iterative retrieval algorithm that combines the use of airborne active and wideband (10 to 340 GHz) passive observations to estimate the vertical content and particle size distributions of liquid and frozen hydrometeors. The physically-based retrieval algorithm relies on the high frequencies (greater than 89 GHz) to provide details on the frozen hydrometeors. Neglecting the high frequencies yielded acceptable estimates of the liquid profiles, but the ice profiles were poorly retrieved. Airborne radar and radiometer observations from the third Convection and Moisture EXperiment (CAMEX-3) were used in the retrieval algorithm as constraints. Nadir profiles were estimated for a minute each of flight time (approximately 12.5 km along track) from an anvil, convection, and quasi- stratiform rain. The complex structure of the frozen hydrometeors required the most iterations for convergence for the anvil cloud type. The wideband observations were found to more than double the estimated frozen hydrometeor content as compared to retrievals using only 90-GHz and below. The convective and quasi-stratiform quickly reached convergence (minimized difference between observations and calculations using the estimated profiles). A qualitative validation using coincident in situ CAMEX-3 observations shows that the retrieved particle size distributions are well corroborated with independent measurements.

Gail Skofronick-Jackson↗

NASA NTRS2002

The Estimation Theory Framework of Data Assimilation

Lecture 1. The Estimation Theory Framework of Data Assimilation: 1. The basic framework: dynamical and observation models; 2. Assumptions and approximations; 3. The filtering, smoothing, and prediction problems; 4. Discrete Kalman filter and smoother algorithms; and 5. Example: A retrospective data assimilation system

Cohn, S.↗

NASA NTRS2005

A Search for Transiting Neptune-Mass Extrasolar Planets in High-Precision Photometry of Solar-Type Stars

Tennessee State University operates several automatic photometric telescopes (APTs) at Fairborn Observatory in southern Arizona. Four 0.8 m APTs have been dedicated to measuring subtle luminosity variations that accompany magnetic cycles in solar-type stars. Over 1000 program and comparison stars have been observed every clear night in this program for up to 12 years with a precision of approximately 0.0015 mag for a single observation. We have developed a transit-search algorithm, based on fitting a computed transit template for each trial period, and have used it to search our photometric database for transits of unknown companions. Extensive simulations with the APT data have shown that we can reliably recover transits with periods under 10 days as long as the transits have a depth of at least 0.0024 mag, or about 1.6 times the scatter in the photometric observations. Thus, due to our high photometric precision, we are sensitive to transits of possible short-period Neptune-mass planets that likely would have escaped detection by current radial velocity techniques. Our search of the APT data sets for 1087 program and comparison stars revealed no new transiting planets. However, the detection of several unknown grazing eclipsing binaries from among our comparison stars, with eclipse depths of only a few millimags, illustrates the success of our technique. We have used this negative result to place limits on the frequency of Neptune-mass planets in close orbits around solar-type stars in the Sun's vicinity.

Henry, Stephen M.↗

NASA NTRS2008

Shaping Diffraction-Grating Grooves to Optimize Efficiency

A method of shaping diffraction-grating grooves to optimize the spectral efficiency, spectral range, and image quality of a spectral imaging instrument is under development. The method is based on the use of an advanced design algorithm to determine the possibly complex shape of grooves needed to obtain a desired efficiency-versus-wavelength response (see figure). Then electron- beam fabrication techniques are used to realize the required groove shape. The method could be used, for example, to make the spectral efficiency of the grating in a given wavelength range proportional to the inverse of the spectral efficiency of a photodetector array so that the overall spectral efficiency of the combination of the grating and the photodetector array would be flat. The method has thus far been applied to one-dimensional gratings only, but in principle, it is also applicable to two-dimensional gratings. The algorithm involves calculations in the spatial-frequency domain. The spatial-frequency spectrum of a grating is represented as a diffraction-order spectral-peak-width function multiplied by an efficiency function for a single grating groove. This representation affords computational efficiency and accuracy by making it possible to consider only the response from one grating groove (one period of the grating), instead of from the whole grating area, in determining the response from the entire grating. This combination of efficiency and accuracy is crucial for future extensions of the algorithm to two-dimensional designs and to designs in which polarization must also be taken into account. The algorithm begins with the definition of target values of relative efficiency that represent the desired spectral response of the grating in certain spectral frequencies calculated from the diffraction order and wavelength. The grating period is divided into a number of cells - typically, 100. The phase contribution from each cell is determined from the phase of the incident electromagnetic wave and the height of the grating surface in the cell. The total contribution from all cells to each target value is then calculated. Then a method known to specialists as the optimum-rotation-angle method is used to adjust the height of each cell so that the total response from all cells is optimized. The computation is iterative and continues until the desired response is obtained. In the event that the desired response is unphysical, the algorithm nevertheless strives to generate a grating-grove profile for which the response approximates the desired one as closely as possible.

Backlund, John↗

NASA NTRS2010

Collisional Grooming Models of the Kuiper Belt Dust Cloud

We modeled the three-dimensional structure of the Kuiper Belt (KB) dust cloud at four different dust production rates, incorporating both planet-dust interactions and grain-grain collisions using the collisional grooming algorithm. Simulated images of a model with a face-on optical depth of approximately 10 (exp -4) primarily show an azimuthally- symmetric ring at 40-47 AU in submillimeter and infrared wavelengths; this ring is associated with the cold classical KB. For models with lower optical depths (10 (exp -6) and 10 (exp-7)), synthetic infrared images show that the ring widens and a gap opens in the ring at the location of Neptune; this feature is caused by trapping of dust grains in Neptune's mean motion resonances. At low optical depths, a secondary ring also appears associated with the hole cleared in the center of the disk by Saturn. Our simulations, which incorporate 25 different grain sizes, illustrate that grain-grain collisions are important in sculpting today's KB dust, and probably other aspects of the solar system dust complex; collisions erase all signs of azimuthal asymmetry from the submillimeter image of the disk at every dust level we considered. The model images switch from being dominated by resonantly trapped small grains ("transport dominated") to being dominated by the birth ring ("collision dominated") when the optical depth reaches a critical value of r approximately v/c, where v is the local Keplerian speed.

Kuchner, Marc J.↗

NASA NTRS2006

Phase Sensor for Aligning a Segmented Telescope Mirror

A phase sensor has been developed for use in aligning a segmented telescope mirror to within a fraction of a wavelength in piston. (As used here, piston signifies displacement of a mirror segment along the optical axis of the telescope.) Such precise alignment is necessary in order to realize the full benefit of the large aperture achievable through segmentation. This phase sensor is achromatic. It is based on two-wavelength shearing interferometry, and can be modified to utilize an extended or broad-band (e.g., white) light source. The sensor optics include a ruled diffraction grating and an imaging lens. The sensor can measure the piston shift between segments as well as aberrations of the segments. It can measure the surface error of an individual segment, making it possible to compensate for the error with optimal amount(s) of piston and/or tilt. The precise capture range of the sensor depends partly on the telescope design; the largest relative piston shifts measurable by use of this sensor are of the order of 100 m. The accuracy of the sensor also depends partly on the telescope design; in general, the accuracy is sufficient to enable alignment to within approximately half a wavelength. The interferometric image is digitized and processed by a simple algorithm in real time, and the output of the algorithm can be used to maintain alignment in real time, even in the presence of atmospheric turbulence. The sensor is robust. Through calibration, it can be made insensitive to (and, hence, tolerant of) misalignments and aberrations of its own optics, most aberrations of the telescope as a whole (in contradistinction to aberrations of individual segments), and most aberrations introduced by atmospheric turbulence

Stahl, Philip↗

NASA NTRS1994

Efficient Autonomous Learning for Statistical Pattern Recognition

We describe a neural network learning algorithm that implements differential learning in a generalized backpropagation framework. The algorithm regulates model complexity during the learning procedure, generating the best low-complexity approximation to the Bayer-optimal classifier allowed by the training sample.

Pattern↗

NASA NTRS1975

A general algorithm for relating ground trajectory distance, elapsed flight time, and aircraft airspeed and its application to 4-D guidance

A general solution using an elliptic integral approximation which relates flight time, aircraft airspeed, and ground distance on straight-line and circular-arc trajectory segments is developed. The solution procedure is applicable to both constant and accelerating aircraft flight. In addition, wind shear including both magnitude and heading change is incorporated in the solution. The solution equations are used in a four-dimensional (4-D) control algorithm where both flight time and final airspeed are specified. The results show that the algorithm converges rapidly and accurately.

Foudriat, E. C.↗

NASA NTRS1993

Proposed data compression schemes for the Galileo S-band contingency mission

The Galileo spacecraft is currently on its way to Jupiter and its moons. In April 1991, the high gain antenna (HGA) failed to deploy as commanded. In case the current efforts to deploy the HGA fails, communications during the Jupiter encounters will be through one of two low gain antenna (LGA) on an S-band (2.3 GHz) carrier. A lot of effort has been and will be conducted to attempt to open the HGA. Also various options for improving Galileo's telemetry downlink performance are being evaluated in the event that the HGA will not open at Jupiter arrival. Among all viable options the most promising and powerful one is to perform image and non-image data compression in software onboard the spacecraft. This involves in-flight re-programming of the existing flight software of Galileo's Command and Data Subsystem processors and Attitude and Articulation Control System (AACS) processor, which have very limited computational and memory resources. In this article we describe the proposed data compression algorithms and give their respective compression performance. The planned image compression algorithm is a 4 x 4 or an 8 x 8 multiplication-free integer cosine transform (ICT) scheme, which can be viewed as an integer approximation of the popular discrete cosine transform (DCT) scheme. The implementation complexity of the ICT schemes is much lower than the DCT-based schemes, yet the performances of the two algorithms are indistinguishable. The proposed non-image compression algorith is a Lempel-Ziv-Welch (LZW) variant, which is a lossless universal compression algorithm based on a dynamic dictionary lookup table. We developed a simple and efficient hashing function to perform the string search.

Cheung, Kar-Ming↗

NASA NTRS1995

Femtolensing: Beyond the semiclassical approximation

Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.

Ulmer, Andrew↗

NASA NTRS1978

Updating of ADAPT predictions of sunspot activity

An eigenvector analysis procedure was used to analyze and develop algorithms for predicting sunspot numbers. The predictors in these algorithms consist of sunspot numbers from the preceding two solar cycles and magnetic index data from the preceding cycle. Predictions are presented for cycles 21 and 22. The sunspot activity for cycle 21 is predicted to remain below 100 until early 1980 when it will rapidly reach a peak of approximately 120. The two sigma accuracy on these estimates is approximately 20 sunspot numbers in the region of the peak and 10 sunspot numbers early and late in the cycle. Algorithms were also developed for predicting the period of future sunspot cycles using the same predictor vector.

Hunter, H. C.↗

NASA NTRS1993

A general rough-surface inversion algorithm: Theory and application to SAR data

Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

Moghaddam, M.↗

NASA NTRS1975

Estimation of unmodeled forces on a low-thrust space vehicle

The application of a sequential estimation algorithm, which compensates for random errors in the dynamic model, to the problem of estimating the state of a continuously thrusting solar electric propulsion space vehicle is investigated. The dynamic model errors, due to random anomalies in the propulsion system, are approximated successfully by both first order and second order Gauss-Markov processes to obtain a more accurate and stable orbit determination algorithm. The importance of correct dynamic and measurement modeling in achieving accurate estimates is demonstrated.

Tapley, B. D.↗