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NASA NTRS1982

Evolution of the cluster X-ray luminosity function slope

The results of an X-ray survey of 58 clusters of galaxies at moderate and high redshifts are reported. Using a luminosity-limited subsample of 25 objects, it is found that to a redshift of 0.5 the slope of the luminosity function of distant clusters is independent of redshift and consistent with that of nearby clusters. The time scale for change in the slope must be greater than 9 billion years. The implications of the data for theoretical models are discussed. In particular, Perrenod's models (1980) with high Omega are excluded by the present data.

Henry, J. P.↗

NASA NTRS1984

Deployment of a Secondary Concentrator to Increase the Intercept Factor of a Dish with Large Slope Errors

The testing of a hyperbolic trumpet non-imaging secondary concentrator with a parabolic dish having slope errors of about 10 mrad is reported. The trumpet, which has a concentration ratio of 2.1, increased the flux through a 141-mm focal aperture by 72%, with an efficiency of 96%, thus demonstrating its potential for use in tandem with cheap dishes having relatively large slope errors.

Ortabasi, U.↗

NASA NTRS1984

Ultrasonic velocity measurement using phase-slope cross-correlation methods

Computer implemented phase-slope and cross-correlation methods are introduced for measuring time delays between pairs of broadband ultrasonic pulse-echo signals for determining velocity in engineering materials. The phase-slope and cross-correlation methods are compared with the overlap method which is currently in wide use. Comparison of digital versions of the three methods shows similar results for most materials having low ultrasonic attenuation. However, the cross-correlation method is preferred for highly attenuating materials. An analytical basis for the cross-correlation method is presented. Examples are given for the three methods investigated to measure velocity in representative materials in the megahertz range.

Hull, D. R.↗

NASA NTRS1985

Tiltmeter Indicates Sense of Slope

Tiltmeter indicates sense and magnitude of slope used in locations where incline not visible to operator. Use of direct rather than alternating current greatly simplifies design of instrument capable of indicating sense of slope.

Lonborg, J. O.↗

NASA NTRS1985

Measurement of ultrasonic velocity using phase-slope and cross-correlation methods

Hull, D. R.↗

NASA NTRS1986

On the varying slope of velocity spectra

Spectra of zonal, meridional and vertical wind velocity, measured during a 24 hour period with the spaced-antenna technique indicate quite a variable slope as a function of height. It is found that the spectral slope (1h to 24h) of all three components correlates with the mean horizontal wind velocity. A possible conclusion is that the frequency dependence of power density of horizontal and vertical fluctuation component apparently depends on the mean wind velocity. However, the vertical spectra at periods larger than about 1 hour can also be influenced by spillover (due to finite radar antenna beam width) from the horizontal fluctuation component or by a Doppler shift.

Rottger, J.↗

NASA NTRS1987

Source of the optical red-slope in iron-rich meteorites

The relationship between ordinary chondrites and S-type asteroids is an unresolved issue in meteorite science. S-type asteroids exhibit a positively red-sloped spectrum that is interpreted to indicate the presence of elemental iron on the surfaces. The characteristic red-sloped spectrum of iron-rich meteorites is produced by only the specular component of the reflectance. Complex metallic surfaces can be modeled as linear mixtures of specular and nonspecular components. It is the geometry of the metal on a surface and its interaction with surrounding material, rather than the absolute amount of metal, that determine the redness of resulting spectra. In order to distinguish between ordinary chondrite and differentiated parent bodies it is important to understand how regolith processes affect the nature and form of metal on asteroid surfaces.

Britt, Daniel T.↗

NASA NTRS1986

Number-counts slope estimation in the presence of Poisson noise

The slope determination of a power-law number flux relationship in the case of photon-limited sampling. This case is important for high-sensitivity X-ray surveys with imaging telescopes, where the error in an individual source measurement depends on integrated flux and is Poisson, rather than Gaussian, distributed. A bias-free method of slope estimation is developed that takes into account the exact error distribution, the influence of background noise, and the effects of varying limiting sensitivities. It is shown that the resulting bias corrections are quite insensitive to the bias correction procedures applied, as long as only sources with signal-to-noise ratio five or greater are considered. However, if sources with signal-to-noise ratio five or less are included, the derived bias corrections depend sensitively on the shape of the error distribution.

Schmitt, Juergen H. M. M.↗

NASA NTRS1988

The dependence of sea surface slope on atmospheric stability and swell conditions

A tower-mounted optical device is used to measure the two-orthogonal components of the sea surface slope. The results indicate that an unstable stratification at the air-sea interface tends to enhance the surface roughness. The presence of a long ocean swell system steers the primary direction of shortwave propagation away from wind direction, and may increase or reduce the mean square slope of the sea surface.

Hwang, Paul A.↗

NASA NTRS1990

The effects of oppositely sloping boundaries with Ekman dissipation in a nonlinear baroclinic system

The present analytical and numerical examination of the effect of the slope Delta with dissipation delta on baroclinic flows in linear and nonlinear systems uses a modified Eady channel model with oppositely sloping top and bottom Ekman layers, and truncates the spectral wave solution up to six components. Comparisons are made wherever possible with results from beta-plane dissipative systems. In the linear system, the combined effect of Delta and delta strongly stabilizes long waves. In a nonlinear system without wave-wave interaction, Delta stabilizes the flow even for small delta and reduces the domain of vacillation while enlarging the domain of single-wave steady state.

Weng, H.-Y.↗

NASA NTRS1991

Slope variations on the surface of Phobos

It has been suggested that slope fluctuations on the scale of pixel dimensions could be determined by statistical photoclinometry. A closer study of the surface of Phobos reveals variations in the scattering properties of single particles and microstructures formed by the particles. In the present context, the photoclinometric method of brightness moments is extended to account for these variations by allowing statistical fluctuations in the phase function of the assumed Lommel-Seeliger scattering law. The mean slope on the investigated regions of Phobos has been found to vary from about 12 deg on a 61 m scale to about 7 deg on a 216 - 272 m scale. On the same scales, a value of the order of 2 percent has been obtained for the standard deviation of the scattering phase function. Hints of a fractal-like scale-invariance have been noticed in the covariance function of brightness.

Muinonen, Karri↗

NASA NTRS1992

Sea surface mean square slope from Ku-band backscatter data

A surface mean-square-slope parameter analysis is conducted for 14-GHz airborne radar altimeter near-nadir, quasi-specular backscatter data, which in raw form obtained by least-squares fitting of an optical scattering model to the return waveform show an approximately linear dependence over the 7-15 m/sec wind speed range. Slope data are used to draw inferences on the structure of the high-wavenumber portion of the spectrum. A directionally-integrated model height spectrum that encompasses wind speed-dependent k exp -5/2 and classical Phillips k exp -3 power laws subranges in the range of gravity waves is supported by the data.

Jackson, F. C.↗

NASA NTRS1994

Applications of interferometrically derived terrain slopes: Normalization of SAR backscatter and the interferometric correlation coefficient

Terrain slopes, which can be measured with Synthetic Aperture Radar (SAR) interferometry either from a height map or from the interferometric phase gradient, were used to calculate the local incidence angle and the correct pixel area. Both are required for correct thematic interpretation of SAR data. The interferometric correlation depends on the pixel area projected on a plane perpendicular to the look vector and requires correction for slope effects. Methods for normalization of the backscatter and interferometric correlation for ERS-1 SAR are presented.

Werner, Charles L.↗

NASA NTRS1995

Estimating Slopes In Images Of Terrain By Use Of BRDF

Proposed method of estimating slopes of terrain features based on use of bidirectional reflectivity distribution function (BRDF) in analyzing aerial photographs, satellite video images, or other images produced by remote sensors. Estimated slopes integrated along horizontal coordinates to obtain estimated heights; generating three-dimensional terrain maps. Method does not require coregistration of terrain features in pairs of images acquired from slightly different perspectives nor requires Sun or other source of illumination to be low in sky over terrain of interest. On contrary, best when Sun is high. Works at almost all combinations of illumination and viewing angles.

Scholl, Marija S.↗

NASA NTRS1996

Improving CAP-TSD steady pressure solutions through airfoil slope modification

A modification of airfoil section geometry is examined for improvement of the leading edge pressures predicted by the Computational Aeroelasticity Program - Transonic Small Disturbance (CAP-TSD). Results are compared with Eppler solutions to assess improvement. Preliminary results indicate that a fading function modification of section slopes is capable of significant improvements in the pressures near the leading edge computed by CAP-TSD. Application of this modification to airfoil geometry before use in CAP-TSD is shown to reduce the nonphysical pressure peak predicted by the transonic small disturbance solver. A second advantage of the slope modification is the substantial reduction in sensitivity of CAP-TSD steady pressure solutions to the computational mesh.

Mitterer, Kent F.↗

NASA NTRS1996

Measurement of Ocean Surface Slope By AIRSAR

A new technique has been developed to measure ocean surface slopes by polarimetric synthetic aperture radar (SAR). This technique has the potential of estimating surface slop in the along-track direction at an accuracy of a fraction of a degree. Experimental results using the NASA/JPL AIRSAR P-, L-, and C-band data from the Gulfstream 90 Experiment showed a sudden slope change at a converging current front.

Lee, J. S.↗

NASA NTRS2002

Age of the Mars Global Northerly Slope: Evidence From Utopia Planitia

Recent results from the Mars Orbiter Laser Altimeter (MOLA) experiment on Mars Global Surveyor (MGS) indicate that most of Mars is characterized by a very gentle, roughly northerly slope. Detailed mapping in north-central Arabia Terra combined with superposition relations and crater counts indicate that, in that region at least, this northerly slope must have been formed no later than Late Hesperian, with the most likely time of formation being Late Hesperian. Current research in Utopia Planitia intended as a test of extant models for the formation of giant polygons has turned up good evidence for a Late Hesperian age for the northerly tilt in this region as well, as will be discussed.

McGill, George E.↗

NASA NTRS2005

Analysis of Slope Limiters on Irregular Grids

This paper examines the behavior of flux and slope limiters on non-uniform grids in multiple dimensions. Many slope limiters in standard use do not preserve linear solutions on irregular grids impacting both accuracy and convergence. We rewrite some well-known limiters to highlight their underlying symmetry, and use this form to examine the proper - ties of both traditional and novel limiter formulations on non-uniform meshes. A consistent method of handling stretched meshes is developed which is both linearity preserving for arbitrary mesh stretchings and reduces to common limiters on uniform meshes. In multiple dimensions we analyze the monotonicity region of the gradient vector and show that the multidimensional limiting problem may be cast as the solution of a linear programming problem. For some special cases we present a new directional limiting formulation that preserves linear solutions in multiple dimensions on irregular grids. Computational results using model problems and complex three-dimensional examples are presented, demonstrating accuracy, monotonicity and robustness.

Berger, Marsha↗