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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Incompressible fluid ellipsoids in halos. I - The second-harmonic oscillations of the Maclaurin spheroids

The structure and stability of Maclaurin spheroids embedded in rigid uniform-density oblate spheroidal halos are determined by the tensor virial-equation method. These spheroid-halo systems can be thought of as crude fluid analogs of disk galaxies with halos. The halos are assumed to have the same center, the same axis of symmetry, and the same equatorial radius as the Maclaurin spheroids. Only halos with lower eccentricity than the Maclaurin spheroids are considered. The dynamic instability of the toroidal (barlike) modes is suppressed when m, the ratio of the halo mass to Maclaurin spheroid mass, is greater than 3 pi/8 for spherical halos and when m is greater than 1/2 for halos congruent to the Maclaurin spheroids. Intermediate halo flattenings yield intermediate critical m-values. On the other hand, a neutral point of the toroidal modes in the rotating and inertial frames occurs for all m and for all allowed halo flattenings. Growth rates for secular instability beyond the neutral point are calculated, and the eigenfrequencies of all second-harmonic modes are given for select cases. The Ostriker-Peebles (1973) conjecture concerning the stability of disk galaxies against barlike perturbations appears to be incorrect.

Durisen, R. H.↗
NASA NTRS1976

Sound scattering by rigid oblate spheroids, with implication to pressure gradient microphones

The frequency limit below which sound scattering by a microphone body is sufficiently small to permit accurate pressure gradient measurements was determined. The sound pressure was measured at various points on the surface of a rigid oblate spheroid illuminated by spherical waves generated by a point source at a large distance from the spheroid, insuring an essentially plane sound field. The measurements were made with small pressure microphones flush mounted from the inside of the spheroid model. Numerical solutions were obtained for a variety of spheroid shapes, including that of the experimental model. Very good agreement was achieved between the experimental and theoretical results. It was found that scattering effects are insignificant if the ratio of the major circumference of the spheroid to the wavelength of the incident sound is less than about 0.7, this number being dependent upon the shape of the spheroid. This finding can be utilized in the design of pressure gradient microphones.

Maciulaitis, A.↗
DOE OSTI2025

Sedimentation and shear-induced dynamics of spheroids in fluids with spatial viscosity variations

A generalized reciprocal theorem is used to relate the force and torque induced on a particle in an inertia-less fluid with small variation in viscosity to integrals involving Stokes flow fields and the spatial dependence of viscosity. These resistivity expressions are analytically evaluated using spheroidal harmonics and then used to obtain the mobility of the spheroid during sedimentation, and in linear flows, of a fluid with linear viscosity stratification. The coupling between the rotational and translational motion induced by stratification rotates the spheroid’s centerline, creating a variety of rotational and translational dynamics dependent upon the particle’s aspect ratio, κ, and the component of the stratification unit vector in the gravity direction, d g . Spheroids with 0.55 ⪅ κ ⪅ 2.0 exhibit the largest variety of settling behaviors. Interestingly, this range covers most microplastics and typical microorganisms. One of the modes include a stable orientation dependent only on κ and d g , but independent of initial orientation, thus allowing for the potential control of settling angles and sedimentation rates. In a simple shear flow, cross-streamline migration occurs due to the stratification-induced force generated on the particle. Similarly, a particle no longer stays at the stagnation point of a uniaxial extensional flow. While fully analytical results are obtained for spheroids, numerical simulations provide a source of validation. These simulations also provide additional insights into the stratification-induced force- and torque-producing mechanisms through the stratification-induced stress, which is not accessed in the reciprocal theorem-based analytical calculations.

Geophysical and Geological Flows: Stratified flows↗
NASA NTRS1980

Light scattering by randomly oriented spheroidal particles

A study of the light scattering properties of randomly oriented, identical spheroidal particles is presented. A computation method was developed to integrate the Asano and Yamomoto solution (1975) for scattering from a homogeneous spheroid over all particle orientations; the extinction and scattering cross-sections, the asymmetry factor, and scattering matrix elements are calculated for randomly oriented prolate and oblate spheroids and compared with the calculations for spheres and laboratory measurements. The angular scattering behavior of spheroids is found to be different from that of the spheres for side scattering to backscattering directions, and prolate and oblate spheroids of the same shape parameter have similar angular scattering patterns.

Asano, S.↗
NASA NTRS1983

Some constraints on the color-magnitude diagram of giants in the galactic spheroid

The color-magnitude diagram of giants in the Galactic spheroid is shown to be important in determining the number-color histogram of stars brighter than B = 19 mag. This result is demonstrated by comparing a standard Galaxy model with observations of 391 stars in a field in the direction of Aquarius (l = 36.5 deg, b = -51.1 deg). More than 80 percent of the spheroid stars and 40 percent of all stars in this magnitude range and direction are predicted to be giants. At most, a few percent of the spheroid stars in the current sample can lie on the main sequence bluer than the turn-off onto the giant branch near B - V approximately 0.4. The available observations suggest that the blue tip of the horizontal branch of the spheroid must be sparsely populated about a factor of 10 less than would be expected if the color-magnitude diagram of the spheroid were the same as diagrams for any of the globular clusters M3, M13, or M92. The total dispersion in colors (measurement errors and intrinsic dispersion) has a standard deviation in B - V color that is less than 0.2 mag.

Bahcall, J. N.↗
NASA NTRS1979

Light scattering properties of spheroidal particles

In the present paper, the light scattering characteristics of spheroidal particles are evaluated within the framework of a scattering theory developed for a homogeneous isotropic spheroid. This approach is shown to be well suited for computing the scattering quantities of spheroidal particles of fairly large sizes (up to a size parameter of 30). The effects of particle size, shape, index of refraction, and orientation on the scattering efficiency factors and the scattering intensity functions are studied and interpreted physically. It is shown that, in the case of oblique incidence, the scattering properties of a long slender prolate spheroid resemble those of an infinitely long circular cylinder.

Asano, S.↗
NASA NTRS1983

The galactic spheroid

Analytic approximations and numerical simulations are used to derive the characteristic behavior of star counts in a galactic spheroidal population, whose visible stars' stellar luminosity function is obtainable for galactocentric distances between about 4 and 12 kpc from star count observations above 30 deg galactic latitude. The total densities of stars and of mass in the spheroid at the solar position are evaluated using different assumed luminosity functions, in order to extrapolate the measured values to a wider range of absolute magnitudes. The upper limits to the frequency of intermediate population stars are derived for the absolute visual magnitude range of 5-8. If such stars occur in either a flat disk with a scale height of 3 kpc or a spheroid with an ellipticity of 0.5, their local surface density is less than 1.8 times that of the spheroid.

Bahcall, J. N.↗
NASA NTRS1992

Bar-spheroid interaction in galaxies

N-body simulation and linear analysis is employed to investigate the secular evolution of barred galaxies, with emphasis on the interaction between bars and spheroidal components of galaxies. This interaction is argued to drive secular transfer of angular momentum from bars to spheroids, primarily through resonant coupling. A moderately strong bar, having mass within corotation about 0.3 times the enclosed spheroid mass, is predicted to shed all its angular momentum typically in less than about 10 exp 9 yr. Even shorter depletion time scales are found for relatively more massive bars. It is suggested either that spheroids around barred galaxies are structured so as to inhibit strong coupling with bars, or that bars can form by unknown processes long after disks are established. The present models reinforce the notion that bars can drive secular evolution in galaxies.

Hernquist, Lars↗
NASA NTRS1961

An Investigation of the Natural Frequencies and Mode Shapes of Liquids in Oblate Spheroidal Tanks

An experimental investigation was conducted to gain some understanding of the character of the free vibration modes of liquids In oblate spheroidal tanks applicable in missile and space vehicle systems, Measured natural frequencies were obtained for the lowest three or four, antisymmetric modes of oscillation as a function of the liquid depth for three orientations of each of several such tanks of different size and oblateness. The orientations considered were such that: (a) the equator of the spheroid was horizontal and oscillations were along a diameter of the circular liquid surface; (b) the equator of the spheroid was vertical and the oscillations were along the minor axis of the elliptical liquid surface; and (c) the equator of the spheroid was vertical and the oscillations were along the major axis of the elliptical liquid surface; The frequency data are presented as dimensionless parameters developed for each orientation to permit the application of the experimental results to the prediction of the natural frequencies of tanks of different size and oblateness. Photographs we re made of representative surface wave or mode, shapes for each orientation.

Leonard, H. Wayne↗
NASA NTRS1999

WFPC2 Observations of the URSA Minor Dwarf Spheroidal Galaxy

We present our analysis of archival Hubble Space Telescope Wide Field Planetary Camera 2 (WFPC2) observations in F555W (approximately V) and F814W (approximately I) of the central region of the Ursa Minor dwarf spheroidal galaxy. The V versus V - I color-magnitude diagram features a sparsely populated blue horizontal branch, a steep thin red giant branch, and a narrow subgiant branch. The main sequence reaches approximately 2 magnitudes below the main-sequence turnoff (V(sup UMi, sub TO) approximately equals 23.27 +/- 0.11 mag) of the median stellar population. We compare the fiducial sequence of the Galactic globular cluster M92 (NGC 6341). The excellent match between Ursa Minor and M92 confirms that the median stellar population of the UMi dSph galaxy is metal poor ([Fe/H](sub UMi) approximately equals [Fe/H](sub M92) approximately equals -2.2 dex) and ancient (age(sub UMi)approximately equalsage(sub M92) approximately equals 14 Gyr). The B - V reddening and the absorption in V are estimated to be E(B - V) = 0.03 +/- 0.01 mag and A(sup UMi, sub V) = 0.09 +/- 0.03 mag. A new estimate of the distance modulus of Ursa Minor, (m - M)(sup UMi, sub 0) = 19.18 +/- 0.12 mag, has been derived based on fiducial-sequence fitting M92 [DELTA.V(sub UMi - M92) = 4.60 +/- 0.03 mag and DELTA(V - I)(sub UMi - M92) = 0.010 +/- 0.005 mag] and the adoption of the apparent V distance modulus for M92 of (m - M)(sup M92, sub V) = 14.67 +/- 0.08 mag (Pont et al. 1998, A&A, 329, 87). The Ursa Minor dwarf spheroidal galaxy is then at a distance of 69 +/- 4 kpc from the Sun. These HST observations indicate that Ursa Minor has had a very simple star formation history consisting mainly of a single major burst of star formation about 14 Gyr ago which lasted approximately < 2 Gyr. While we may have missed minor younger stellar populations due to the small field-of-view of the WFPC2 instrument, these observations clearly show that most of the stars in the central region Ursa Minor dwarf spheroidal galaxy are ancient. If the ancient Galactic globular clusters, like M92, formed concurrently with the early formation of the Milky Way galaxy itself, then the Ursa Minor dwarf spheroidal is probably as old as the Milky Way.

Mighell, Kenneth J.↗
NASA NTRS2000

Convection in Slab and Spheroidal Geometries

Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

Porter, David H.↗
NASA NTRS1992

The RBE-LET relationship for rodent intestinal crypt cell survival, testes weight loss, and multicellular spheroid cell survival after heavy-ion irradiation

This report presents data for survival of mouse intestinal crypt cells, mouse testes weight loss as an indicator of survival of spermatogonial stem cells, and survival of rat 9L spheroid cells after irradiation in the plateau region of unmodified particle beams ranging in mass from 4He to 139La. The LET values range from 1.6 to 953 keV/microns. These studies examine the RBE-LET relationship for two normal tissues and for an in vitro tissue model, multicellular spheroids. When the RBE values are plotted as a function of LET, the resulting curve is characterized by a region in which RBE increases with LET, a peak RBE at an LET value of 100 keV/microns, and a region of decreasing RBE at LETs greater than 100 keV/microns. Inactivation cross sections (sigma) for these three biological systems have been calculated from the exponential terminal slope of the dose-response relationship for each ion. For this determination the dose is expressed as particle fluence and the parameter sigma indicates effect per particle. A plot of sigma versus LET shows that the curve for testes weight loss is shifted to the left, indicating greater radiosensitivity at lower LETs than for crypt cell and spheroid cell survival. The curves for cross section versus LET for all three model systems show similar characteristics with a relatively linear portion below 100 keV/microns and a region of lessened slope in the LET range above 100 keV/microns for testes and spheroids. The data indicate that the effectiveness per particle increases as a function of LET and, to a limited extent, Z, at LET values greater than 100 keV/microns. Previously published results for spread Bragg peaks are also summarized, and they suggest that RBE is dependent on both the LET and the Z of the particle.

Non-NASA Center↗
NASA NTRS1977

Transformations from an oblate spheroid to a plane and vice versa: The equations used in the cartographic projection program MAP2

The relationships between the coordinates of a point on the surface on an oblate spheroid and the coordinates of the projection of that point in several common map projections are discussed. Because several of the projections are conformal, the theory of conformally mapping an oblate spheroid to the plane is summarized. For each projection considered, the equations which map the spheroid to the plane and their inverses are given.

Elliott, D. A.↗
NASA NTRS1981

Electrostatic disruption of a charged conducting spheroid

Electrostatic disruption of elongated parent grains following sudden charging to high electrostatic potentials is proposed as a specific mechanism for the appearance of striae or pseudosynchronic bands which have been observed in several comets. The polar and equatorial electrostatic tension for axis ratios between 0.01 and 1000 are calculated, and the polar pressure is found to be larger than the equatorial pressure for prolate spheroids. The electrostatic polar pressure profile along the polar axis for prolate spheroids is calculated, and the pressure is found to increase monotonically from a minimum at the center to a maxima at the ends. This indicates that as a prolate spheroid of uniform tensile strength is charged up, it will continue to chip off at the ends when the electrostatic pressure there exceeds the uniform tensile strength of the grain. The result can be a prolate grain or a grain which continues chipping until it explodes.

Hill, J. R.↗
NASA NTRS1982

Discovery of carbon stars in the Draco dwarf spheroidal galaxy

A grating prism survey of the Draco dwarf spheroidal galaxy that is 97% areally complete has led to the discovery of three carbon stars. Membership of these stars in Draco is firmly established from luminosity, proper motion, and radial velocity considerations. Optical and preliminary infrared photometry suggest that the Draco carbon stars are more closely related to the CH stars in omega Cen than to the luminous carbon stars found in the Fornax and Carina dwarfs. One of the carbon stars possesses an unusual emission line spectrum which might be indicative of either a very hot degenerate companion or a preplanetary evolutionary stage. Carbon stars have now been located in all four of the dwarf spheroidals that have been examined using transmission grating prism techniques. The rarity of these stars in galactic globulars, systems with which the dwarf spheroidals are often compared, indicates a fundamental population difference whose cause is not yet fully understood.

Aaronson, M.↗
NASA NTRS1986

Liquid-vapor interface locations in a spheroidal container under low gravity

As a part of the general study of liquid behavior in low gravity environments, an experimental investigation was conducted to determine if there are equilibrium liquid-vapor interface configurations that can exist at more than one location in oblate spheroidal containers under reduced gravity conditions. Static contact angles of the test liquids on the spheroid surface were restricted to near 0 deg. The experiments were conducted in a low gravity environment. An oblate spheroidal tank was tested with an eccentricity of 0.68 and a semimajor axis of 2.0 cm. Both quantitative and qualitative data were obtained on the liquid-vapor interface configuration and position inside the container. The results of these data, and their impat on previous work in this area, are discussed. Of particular interest are those equilibrium interface configurations that can exist at multiple locations in the container.

Carney, M. J.↗
NASA NTRS1986

A numerical study of separation on a spheroid at incidence

The three-dimensional incompressible, steady and laminar flow field around a prolate spheroid at incidence is considered. The parabolized Navier-Stokes equations are solved numerically. The method can handle vortex types as well as bubble type flow separation because the pressure is one of the dependent variables. Here, the distribution of the skin friction is reported for two test cases. The first test case is a prolate spheroid of aspect ratio of 4:1 at 6 degrees incidence and Reynolds number of 1 million (based on half the major axis). The second case is a spheroid with a 6:1 aspect ratio at 10 degrees incidence and Reynolds number of 0.8 x 1 million. The properties of the flow field near the body are discussed on the basis of the pattern of the skin friction lines, and the shape of the separation lines. Favorable agreement with experimental results is obtained.

Rosenfeld, M.↗
NASA NTRS1993

Stable Ni isotopes and Be-10 and Al-26 in metallic spheroids from Meteor Crater, Arizona

The Canyon Diablo spheroids, which are found around Meteor Crater, Arizona, are nickel-enriched objects with diameters from less than 0.1 to several mm. Previous studies have suggested that the enrichment of nickel resulted either from shock-melting of S-rich areas followed by solidification of the liquids under strongly non-equilibrium conditions at rapid cooling rates during flight outward from the crater or from the selective oxidation of iron. Isotopic studies are an effective tool for constraining the degree of open-system evaporation experienced by a system. The purpose of this study was to see whether Ni isotopes had been fractionated by volatilization during spheroid formation. In addition, the cosmogenic nuclides Be-10 and Al-26 were measured to try to estimate the depths in the parent meteorite from which the spheroids came.

Xue, S.↗