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At least 145 records · Page 8

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NASA NTRS1977

Simple analytical solutions for spherically symmetric production and modulation of energetic solar particles

Exact analytical solutions are presented for the standard time-independent spherically symmetric convection-diffusion-adiabatic deceleration equation governing the transport of cosmic rays in the interplanetary medium for the case in which particles are produced with spherical symmetry at the sun. It is assumed that the solar-wind speed is constant and radial, and that the spatial diffusion coefficient has a power-law dependence on momentum. The Green's function describing the modulation of a monoenergetic production of particles is presented. The solutions provide a useful basis for the study of time-integrated properties of energetic solar-flare particle spectra.

Gross, M. W.↗

NASA NTRS1978

Thermal limit for spherical accretion and X-ray bursts

A mechanism is described whereby the rate of spherical accretion on a collapsed object and the resulting X-ray luminosity can be limited by thermal heating and evaporation of the accreting gas. The luminosity limit can be a factor of the order of 100 below the corresponding Eddington limit. Steady accretion flow is not possible within a range above this limit, and X-ray bursts can be produced by accretion surges resulting from the cooling and collapse of a heated gas shell above a critical optical depth. The luminosity and approximate recurrence rate of the bursts from NGC 6624 and other burst sources may then be understood. A general model for bursters is proposed in which massive (about 10 to 100 solar masses) black holes, from massive stars and the cores of disrupted globular clusters, undergo supercritical spherical accretion in interstellar clouds. Both X-ray and gamma-ray bursts are predicted to have similar hard X-ray (about 200 keV) spectra, though high average accretion rates and central optical depths also yield a comparable luminosity at around 5 keV from a Comptonized blackbody spectrum in the X-ray bursts and associated steady sources.

Grindlay, J. E.↗

NASA NTRS1979

Lash-free spherical bearing

Grooved and chamfered spherical bearing can maintain close contact between its ball and race, even when it is vibrated. Bearing thus eliminates major cause of wear and loosening in spherical bearings: pounding of ball on race under vibration.

Hein, L. A.↗

NASA NTRS1979

Calculated scan characteristics of a large spherical reflector antenna

A previously published numerical method to calculate the radiation properties of parabolic reflectors has been modified to also include very large spherical reflectors. The method has been verified by comparing the calculated and the measured results for a 120-wavelength spherical reflector.

Agrawal, P. K.↗

NASA NTRS1980

Convective flows of viscous fluid in spherical layers. Certain astrophysical applications

The convective stability of a viscous liquid in spherical layers is investigated taking into consideration rotation, the latitudinal temperature gradient, and shear flow. The results of calculating nonlinear convective motion in spherical layers are examined. A discussion is given of the applicability of the results obtained to studying convection in astrophysical objects.

Yavorskaya, I. M.↗

NASA NTRS1980

The NASA/MSFC global reference atmospheric model: MOD 3 (with spherical harmonic wind model)

Improvements to the global reference atmospheric model are described. The basic model includes monthly mean values of pressure, density, temperature, and geostrophic winds, as well as quasi-biennial and small and large scale random perturbations. A spherical harmonic wind model for the 25 to 90 km height range is included. Below 25 km and above 90 km, the GRAM program uses the geostrophic wind equations and pressure data to compute the mean wind. In the altitudes where the geostrophic wind relations are used, an interpolation scheme is employed for estimating winds at low latitudes where the geostrophic wind relations being to mesh down. Several sample wind profiles are given, as computed by the spherical harmonic model. User and programmer manuals are presented.

Justus, C. G.↗

NASA NTRS1980

Orthogonality of spherical harmonic coefficients

Orthogonality relations are obtained for the spherical harmonic coefficients of functions defined on the surface of a sphere. Following a brief discussion of the orthogonality of Fourier series coefficients, consideration is given to the values averaged over all orientations of the coordinate system of the spherical harmonic coefficients of a function defined on the surface of a sphere that can be expressed in terms of Legendre polynomials for the special case where the function is the sum of two delta functions located at two different points on the sphere, and for the case of an essentially arbitrary function. It is noted that the orthogonality relations derived have found applications in statistical studies of the geomagnetic field.

Mcleod, M. G.↗

NASA NTRS1981

Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion

To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1 deg-averaged surface free-air gravity anomalies of POGO satellite magnetometer data for the United States, Mexico, and Central America illustrate the capabilities of the method.

Von Frese, R. R. B.↗

NASA NTRS1981

Laboratory studies on a spherically curved Bragg spectrometer for cosmic X-ray spectroscopy

A spherical array of twenty LiF 200 crystals was built to test the performances of a freestanding, self-focussing spherical crystal cosmic X-ray spectrometer. Measurements presently available show that the size of the image for a point source at infinite distance would be 3 mm (FWHM) along the focalisation axis and 2.1 mm (FWHM) along the dispersion axis. The mosaic spread on individual crystals is less than 0.1 degree. A slightly systematic deviation from the ideal bending (0.1 degree) is observed at the edges of most crystals and this appears to be the major limitation to spectrometer performance.

Cantin, M.↗

NASA NTRS1982

Sensitivity of selected geomagnetic properties to truncation level of spherical harmonic expansions

The model dependence of Gauss coefficients associated with a lack of spherical harmonic orthogonality on a nonuniform Magsat data grid is shown to be minor, where the fitting level exceeds the harmonic order by a value of approximately four. The shape of the magnetic energy spectrum outside the core, and the sensitivity to truncation level of magnetic contour location and the number of their intersections on the core-mantle boundary, suggest that spherical harmonic expansions of the main geomagnetic field should be truncated at a truncation level value of not more than eight if they are to be extrapolated to the core.

Benton, E. R.↗

NASA NTRS1983

High speed spherical roller-bearing analysis and comparison with experimental performance

The capabilities of a spherical roller bearing analysis/design tool, Spherbean (spherical bearing analysis) are described. Capabilities of the analysis are demonstrated and verified by comparison with experimental data. A practical design problem is presented where the computer program is used to improve a particular bearing's performance.

Kleckner, R. J.↗

NASA NTRS1983

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocity and attenuation of ultrasonic waves in two-phase media are determined for cases of distributed spheres and localized damage. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with spherical inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results or moduli, velocity and/or attenuation as functions of concentration of inclusion material, or porosity, are graphically displayed.

Fu, L. S.↗

NASA NTRS1983

Modeling of G333.6-0.2 as a spherical H II region

The radio and IR observations of the H II region G333.6-0.2 are matched with a detailed spherical model with a density distribution which has a uniform-density core of radius 0.05 pc, a power-law intermediate zone, and a uniform-density halo. A stellar radiation field is required that is somewhat different from those predicted by available model atmospheres. Of the stellar models of Kurucz, the Teff = 34,000 K and log g = 3.5 model best fits the observed ratio of helium to hydrogen recombination lines. A good fit to all the observations in obtained with an S(2+) ionizing flux which is a factor of 20 times less than predicted by the Kurucz atmosphere. Current model atmospheres may not be appropriate because a single stable star with Teff = 34,000 K fails by at least an order of magnitude to produce the ionizing luminosity. The small radius of the constant-density core implies a short dynamical lifetime of approximately 5000 years for this spherical model; this may indicate that a nonspherical blister geometry is more appropriate for this H II region.

Rubin, R. H.↗

NASA NTRS1984

Thermal evaporation of spherical clouds - Effects of viscous stresses

The thermal evaporation of a cold spherical cloud embedded in hot gas is analyzed, including the effects of viscous stresses as well as 'saturation' of the conductive heat flux, for the case of equal electron and ion temperatures. The relevant transport properties for an H-He plasma are discussed, including the modification of these transport coefficients when temperature or velocity gradients become large. The fluid-dynamical equations for steady spherical evaporation are given and cast into dimensinless form. Numerical integration of these equations and the results are discussed, emphasizing the novel features of the viscous solutions, astrophysical implications, and uncertainties in the physics.

Giuliani, J. L., Jr.↗

NASA NTRS1982

The numerical design of a spherical baroclinic experiment for Spacelab flights

The near-zero G environment of Spacelab is the basis of a true spherical experimental model of synoptic scale baroclinic atmospheric processes, using a radial dielectric body force analogous to gravity over a volume of liquid within two concentric spheres. The baroclinic motions are generated by corotating the spheres and imposing thermal boundary conditions, such that the liquid is subjected to a stable radial gradient and a latitudinal gradient. Owing to mathematical difficulties associated with the spherical geometry, quantitative design criteria can be acquired only by means of numerical models. The procedure adopted required the development of two computer codes based on the Navier-Stokes equations. The codes, of which the first calculates axisymmetric steady flow solutions and the second determines the growth or decay rates of linear wave perturbations with different wave numbers, are combined to generate marginal stability curves.

Fowlis, W. W.↗

NASA NTRS1984

Adaptive spherical lens

This paper reports the creation of a tandem liquid crystal cell arrangement capable of simulating the performance of a spherical lens. Electrical modulation of the index of refraction creates focusing behavior. The modulation is induced by a set of electrodes whose individual voltages are arranged to provide a cylindrical exit wave front for a uniform plane-wave input. Two such cells with orthogonal electrodes arranged in cascade create spherical lens performance. Experimental evidence using a lens with a relatively small number of electrodes is presented. Applications for such structures, once improved, would include real-time focus adjustment for optical disk readers and hand-held photographic equipment as well as aberration compensation for long path-length optical systems.

Kowel, S. T.↗

NASA NTRS1984

Ultrasonic wave propagation in two-phase media - Spherical inclusions

Fu, L. S.↗

NASA NTRS1984

Line transfer in static and expanding spherical atmospheres

The integral-operator method is extended to line and continuum transfer calculations for static and expanding spherical radiating atmospheres. A relationship is defined between radiative transfer and the source function at particular optical depths. Linearized equations are developed for the mean intensity, monochromatic scattering, line transfer, and line transfer with absorption. Numerical solutions are obtained for each equation, as well as for background absorption and scattering, partial redistribution when the line source is frequency dependent, and line transfer in connection with the expansion velocity. Finally, a solution is found for spherical expansion in concert with partial redistribution and Doppler line broadening.

Avrett, E. H.↗