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NASA NTRS1986

Scattering from mirrors contaminated by particulates - A model

A model has been used to fit the bidirectional reflectance distribution function for a variety of samples with different angles of incidence and degrees of contamination and roughness by the proper adjustment of six parameters. Exponential and Gaussian composite surface height autocorrelation functions are used to simulate the data at the small and medium angles, and a perturbation of these functions with two additional parameters allows the fit of the upward and downward curve portions of the data at the large angles. Good agreement is found with previous results. The present approach is the same as the classical dispersion equation in treating the index of refraction of optical materials.

Wang, Yaujen↗

NASA NTRS1995

Microlensing by the galactic bar

We compute the optical depth and duration distribution of microlensing events towrd Baade's window in a model composed of a Galactic disk and a bar. The bar model is a self-consistent dynamical model built out of individual orbits that has been populated to be consistent with the COBE maps of the Galaxy and kinematic observations of the Galactic bulge. We find that most of the lenses are in the bulge with a line-of-sight distance 6.25 kpc (adopting R(sub 0) = 8 kpc). The microlensing optical depth of a 2 x 10(exp 10) solar mass bar plus a truncated disk is (2.2 +/- 0.45) x 10(exp -6), consistent with the large optical depth (3.2 +/- 1.2) x 10(exp -6) found by Udalski et al. (1994). This model optical depth is enhanced over the predictions of axisymmetric models by Kiraga & Paczynski (1994) by slightly more than a factor of 2, since the bar is elongated along the line of sight. The large Einstein radius and small transverse velocity dispersion also predict a longer event duration in the self-consistent bar model than in the Kiraga-Paczynski model. The event rate and duration distribution also depend on the lower mass cutoff of the lens mass function. With a 0.1 solar mass cutoff, five to seven events (depending on the contribution of disk lenses) with a logarithmic mean duration of 20 days are expected for the Optical Gravitational Lensing Experiment (OGLE) according to our model, while Udalski et al. (1994) observed nine events with durations from 8 to 62 days. On the other hand, if most of the lenses are brown dwarfs, our model predicts too many short-duration events. A Kolmogorov-Smirnov test finds only 7% probability for the model with 0.01 solar mass cutoff to be consistent with current data.

Zhao, Hongsheng↗

NASA NTRS1993

A deep x-ray survey of the Pleiades cluster and the B6-A3 main sequence stars in Orion

We have obtained deep ROSAT images of three regions within the Pleiades open cluster. We have detected 317 X-ray sources in these ROSAT PSPC images, 171 of which we associate with certain probable members of the Pleiades cluster. We detect nearly all Pleiades members with spectral types later than G0 and within 25 arcminutes of our three field centers where our sensitivity is highest. This has allowed us to derive for the first time the luminosity function for the G, K, and M dwarfs of an open cluster without the need to use statistical techniques to account for the presence of upper limits in the data sample. Because of our high X-ray detection frequency down to the faint limit of the optical catalog, we suspect that some of our unidentified X-ray sources are previously unknown, very low-mass members of the Pleiades. A large fraction of the Pleiades members detected with ROSAT have published rotational velocities. Plots of L(sub x)/L(sub bol) versus spectroscopic rotational velocity show tightly correlated 'saturation' type relations for stars with (B - V)(sub O) greater than 0.60. For each of several color ranges, X-ray luminosities rise rapidly with increasing rotation rate until v sin i approximately equals 15 km/s, and then remain essentially flat for rotation rates up to at least v sin i approximately equal to 100 km/s. The dispersion in rotation among low-mass stars in the Pleiades is by far the dominant contributor to the dispersion in L(subx) at a given mass. Only about 35 percent of the B.A. and early F stars in the Pleiades are detected as X-ray sources in our survey. There is no correlation between X-ray flux and rotation for these stars. The X-ray luminosity function for the early-type Pleiades stars appears to be bimodal, with only a few exceptions. We either detect these stars at fluxes in the range found for low-mass stars or we derive X-ray limits below the level found for most Pleiades dwarfs. The X-ray spectra for the early-type Pleiades stars detected by ROSAT are indistinguishable from the spectra of the low-mass Pleiades members. We believe that the simple explanation for this behavior is that the early-type Pleiades stars are not themselves intrinsic X-ray sources and that the X-ray sources and that the X-ray emission actually arises from low-mass companions to these stars.

Caillault, Jean-Pierre↗

NASA NTRS1985

Clustered impacts - Experiments and implications

The characteristics of impact by clusters of projectiles are experimentally studied by launching grouped projectiles of aluminum shot, steel shot, iron filings, and sand. Cratering efficiency is considered as a function of a dimensionless parameter related to projectile size and impact velocity. The effects of different target and projectile densities on cratering efficiency are examined. Crater morphology is addressed by considering a typical example, reviewing the systematics between cluster dispersion and crater morphology for vertical impacts, and examining oblique angle impacts which have relevance for planetary secondary cratering processes. These results are compared with impacts by single bodies with different strengths. The evolution of the ejecta plume for clustered impacts is compared to that for single-body impacts for vertical and oblique impacts from 1.3 to 1.8 km/s. The experimental results are discussed in the context of planetary surface processes, emphasizing processes in an atmosphere-free environment and secondary impact cratering.

Schultz, P. H.↗

NASA NTRS1983

Finite element or Galerkin type semidiscrete schemes

A finite element of Galerkin type semidiscrete method is proposed for numerical solution of a linear hyperbolic partial differential equation. The question of stability is reduced to the stability of a system of ordinary differential equations for which Dahlquist theory applied. Results of separating the part of numerical solution which causes the spurious oscillation near shock-like response of semidiscrete scheme to a step function initial condition are presented. In general all methods produce such oscillatory overshoots on either side of shocks. This overshoot pathology, which displays a behavior similar to Gibb's phenomena of Fourier series, is explained on the basis of dispersion of separated Fourier components which relies on linearized theory to be satisfactory. Expository results represented.

Durgun, K.↗

NASA NTRS1985

Analysis/forecast experiments with a multivariate statistical analysis scheme using FGGE data

A three-dimensional, multivariate, statistical analysis method, optimal interpolation (OI) is described for modeling meteorological data from widely dispersed sites. The model was developed to analyze FGGE data at the NASA-Goddard Laboratory of Atmospherics. The model features a multivariate surface analysis over the oceans, including maintenance of the Ekman balance and a geographically dependent correlation function. Preliminary comparisons are made between the OI model and similar schemes employed at the European Center for Medium Range Weather Forecasts and the National Meteorological Center. The OI scheme is used to provide input to a GCM, and model error correlations are calculated for forecasts of 500 mb vertical water mixing ratios and the wind profiles. Comparisons are made between the predictions and measured data. The model is shown to be as accurate as a successive corrections model out to 4.5 days.

Baker, W. E.↗

NASA NTRS1992

Evolving, dynamical models for collapsed-core globular clusters - M15 and NGC 6624

The stellar populations of the collapsed-core globular clusters M15 and NGC 6624 are investigated by fitting observed surface-brightness and projected velocity-dispersion profiles. The present evolving cluster models were generated by the direct Fokker-Planck method and incorporate realistic stellar mass spectra and energy input from binaries formed by three-body interactions. An evolved power-law mass function with nonluminous remnants of maximum mass 1.0-1.4 solar mass is adopted. M15 is found to be best fitted by postcollapse evolving models with a mass-function slope of x = 0.9 (where x = 1.35 corresponds to the Salpeter mass function) and a maximum remnant mass of 1.3 solar mass. Postcollapse core oscillations, driven by energy input from hard binaries, can produce sufficiently rapid core expansion to explain the resolution of the core of M15 by HST observations reported by Lauer et al. (1991).

Grabhorn, Robert P.↗

NASA NTRS2009

Spatial Modulation Improves Performance in CTIS

Suitably formulated spatial modulation of a scene imaged by a computed-tomography imaging spectrometer (CTIS) has been found to be useful as a means of improving the imaging performance of the CTIS. As used here, "spatial modulation" signifies the imposition of additional, artificial structure on a scene from within the CTIS optics. The basic principles of a CTIS were described in "Improvements in Computed- Tomography Imaging Spectrometry" (NPO-20561) NASA Tech Briefs, Vol. 24, No. 12 (December 2000), page 38 and "All-Reflective Computed-Tomography Imaging Spectrometers" (NPO-20836), NASA Tech Briefs, Vol. 26, No. 11 (November 2002), page 7a. To recapitulate: A CTIS offers capabilities for imaging a scene with spatial, spectral, and temporal resolution. The spectral disperser in a CTIS is a two-dimensional diffraction grating. It is positioned between two relay lenses (or on one of two relay mirrors) in a video imaging system. If the disperser were removed, the system would produce ordinary images of the scene in its field of view. In the presence of the grating, the image on the focal plane of the system contains both spectral and spatial information because the multiple diffraction orders of the grating give rise to multiple, spectrally dispersed images of the scene. By use of algorithms adapted from computed tomography, the image on the focal plane can be processed into an image cube a three-dimensional collection of data on the image intensity as a function of the two spatial dimensions (x and y) in the scene and of wavelength (lambda). Thus, both spectrally and spatially resolved information on the scene at a given instant of time can be obtained, without scanning, from a single snapshot; this is what makes the CTIS such a potentially powerful tool for spatially, spectrally, and temporally resolved imaging. A CTIS performs poorly in imaging some types of scenes in particular, scenes that contain little spatial or spectral variation. The computed spectra of such scenes tend to approximate correct values to within acceptably small errors near the edges of the field of view but to be poor approximations away from the edges. The additional structure imposed on a scene according to the present method enables the CTIS algorithms to reconstruct acceptable approximations of the spectral data throughout the scene.

Bearman, Gregory H.↗

NASA NTRS1994

A deep imaging survey of the Pleiades with ROSAT

We have obtained deep ROSAT images of three regions within the Pleiades open cluster. We have detected 317 X-ray sources in these ROSAT Position Sensitive Proportional Counter (PSPC) images, 171 of which we associate with certain or probable members of the Pleiades cluster. We detect nearly all Pleiades members with spectral types later than G0 and within 25 arcminutes of our three field centers where our sensitivity is highest. This has allowed us to derive for the first time the luminosity function for the G, K, amd M dwarfs of an open cluster without the need to use statistical techniques to account for the presence of upper limits in the data sample. Because of our high X-ray detection frequency down to the faint limit of the optical catalog, we suspect that some of our unidentified X-ray sources are previously unknown, very low-mass members of Pleiades. A large fraction of the Pleiades members detected with ROSAT have published rotational velocities. Plots of L(sub X)/L(sub Bol) versus spectroscopic rotational velocity show tightly correlated `saturation' type relations for stars with ((B - V)(sub 0)) greater than or equal to 0.60. For each of several color ranges, X-ray luminosities rise rapidly with increasing rotation rate until c sin i approximately equal to 15 km/sec, and then remains essentially flat for rotation rates up to at least v sin i approximately equal to 100 km/sec. The dispersion in rotation among low-mass stars in the Pleiades is by far the dominant contributor to the dispersion in L(sub X) at a given mass. Only about 35% of the B, A, and early F stars in the Pleiades are detected as X-ray sources in our survey. There is no correlation between X-ray flux and rotation for these stars. The X-ray luminosity function for the early-type Pleiades stars appears to be bimodal -- with only a few exceptions, we either detect these stars at fluxes in the range found for low-mass stars or we derive X-ray limits below the level found for most Pleiades dwarfs. The X-ray spectra for the early-type Pleiades stars detected by ROSAT are indistinguishable from the spectra of the low-mass Pleiades members. We believe that the simplest explanation for this behavior is that the early-type Pleiades stars are not themselves intrinsic X-ray sources and that the X-ray emission actually arises from low-mass companions to these stars.

Stauffer, J. R.↗

NASA NTRS1989

Online submicron particle sizing by dynamic light scattering using autodilution

Efficient production of a wide range of commercial products based on submicron colloidal dispersions would benefit from instrumentation for online particle sizing, permitting real time monitoring and control of the particle size distribution. Recent advances in the technology of dynamic light scattering (DLS), especially improvements in algorithms for inversion of the intensity autocorrelation function, have made it ideally suited to the measurement of simple particle size distributions in the difficult submicron region. Crucial to the success of an online DSL based instrument is a simple mechanism for automatically sampling and diluting the starting concentrated sample suspension, yielding a final concentration which is optimal for the light scattering measurement. A proprietary method and apparatus was developed for performing this function, designed to be used with a DLS based particle sizing instrument. A PC/AT computer is used as a smart controller for the valves in the sampler diluter, as well as an input-output communicator, video display and data storage device. Quantitative results are presented for a latex suspension and an oil-in-water emulsion.

Nicoli, David F.↗

NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗

NASA NTRS2001

Dynamics of Aqueous Foam Drops

We develop a model for the nonlinear oscillations of spherical drops composed of aqueous foam. Beginning with a simple mixture law, and utilizing a mass-conserving bubble-in-cell scheme, we obtain a Rayleigh-Plesset-like equation for the dynamics of bubbles in a foam mixture. The dispersion relation for sound waves in a bubbly liquid is then coupled with a normal modes expansion to derive expressions for the frequencies of eigenmodal oscillations. These eigenmodal (breathing plus higher-order shape modes) frequencies are elicited as a function of the void fraction of the foam. A Mathieu-like equation is obtained for the dynamics of the higher-order shape modes and their parametric coupling to the breathing mode. The proposed model is used to explain recently obtained experimental data.

Akhatov, Iskander↗

NASA NTRS2003

Concentration and Velocity Gradients in Fluidized Beds

In this work we focus on the height dependence of particle concentration, average velocity components, fluctuations in these velocities and, with the flow turned off, the sedimentation velocity. The latter quantities are measured using Particle Imaging Velocimetry (PIV). The PIV technique uses a 1-megapixel camera to capture two time-displaced images of particles in the bed. The depth of field of the imaging system is approximately 0.5 cm. The camera images a region with characteristic length of 2.6 cm for the small particles and 4.7 cm. for the large particles. The local direction of particle flow is determined by calculating the correlation function for sub-regions of 32 x 32 pixels. The velocity vector map is created from this correlation function using the time between images (we use 15 to 30 ms). The software is sensitive variations of 1/64th of a pixel. We produce velocity maps at various heights, each consisting of 3844 velocities. We break this map into three vertical zones for increased height information. The concentration profile is measured using an expanded (1 cm diameter) linearly polarized HeNe Laser incident on the fluidized bed. A COHU camera (gamma=1, AGC off) with a lens and a polarizer images the transmitted linearly polarized light to minimize the effects of multiply scattered light. The intensity profile (640 X 480 pixels) is well described by a Gaussian fit and the height of the Gaussian is used to characterize the concentration. This value is compared to the heights found for known concentrations. The sedimentation velocity is estimated using by imaging a region near the bottom of the bed and using PIV to measure the velocity as a function of time. With a nearly uniform concentration profile, the time can be converted to height information. The stable fluidized beds are made from large pseudo-monodisperse particles (silica spheres with radii (250-300) microns and (425-500) microns) dispersed in a glycerin/water mix. The Peclet number is sufficiently large that Brownian motion of the particles can be ignored and the Reynolds number sufficiently small that particle inertia is negligible. A packed particle bed is used to randomize and disperse the flowing fluid introduced by a peristaltic pump. The bed itself is a rectangular glass cell 8 cm wide (x), 0.8 cm deep and a height of 30.5 cm (z). The depth of field of the camera is approximately 0.5 cm so depth information is averaged. Over flow fluid is returned to the reservoir making a closed loop system. In these experiments the particles form a sediment approximately 5.7 cm high with the pump off and expand to 22 cm with the pump on. For the smaller particles the pump velocity is .5 millimeters per second and 1.1 millimeters per second for the large particles. At this concentration the bed has a very well defined top where particle concentration rapidly drops to zero.

McClymer, James P.↗

NASA NTRS1992

The formation of cosmic structure in a texture-seeded cold dark matter cosmogony

The growth of density fluctuations induced by global texture in an Omega = 1 cold dark matter (CDM) cosmogony is calculated. The resulting power spectra are in good agreement with each other, with more power on large scales than in the standard inflation plus CDM model. Calculation of related statistics (two-point correlation functions, mass variances, cosmic Mach number) indicates that the texture plus CDM model compares more favorably than standard CDM with observations of large-scale structure. Texture produces coherent velocity fields on large scales, as observed. Excessive small-scale velocity dispersions, and voids less empty than those observed may be remedied by including baryonic physics. The topology of the cosmic structure agrees well with observation. The non-Gaussian texture induced density fluctuations lead to earlier nonlinear object formation than in Gaussian models and may also be more compatible with recent evidence that the galaxy density field is non-Gaussian on large scales. On smaller scales the density field is strongly non-Gaussian, but this appears to be primarily due to nonlinear gravitational clustering. The velocity field on smaller scales is surprisingly Gaussian.

Gooding, Andrew K.↗

NASA NTRS1995

Brightest cluster galaxies as standard candles

We investigate the use of brightest cluster galaxies (BCGs) as standard candles for measuring galaxy peculiar velocities on large scales. We have obtained precise large-format CCD surface photometry and redshifts for an all-sky, volume-limited (z less than or = 0.05) sample of 199 BCG. We reinvestigate the Hoessel (1980) relationship between the metric luminosity, L(sub m), within the central 10 kpc/h of the BCGs and the logarithmic slope of the surface brightness profile, alpha. The L(sub m)-alpha relationship reduces the cosmic scatter in L(sub m) from 0.327 mag to 0.244 mag, yielding a typical distance accuracy of 17% per BCG. Residuals about the L(sub m)-alpha relationship are independent of BCG luminosity, BCG B - R(sub c) color, BCG location within the host cluster, and richness of the host cluster. The metric luminosity is independent of cluster richness even before correcting for its dependence on alpha, which provides further evidence for the unique nature of the BCG luminosity function. Indeed, the BCG luminosity function, both before and after application of the alpha-correction, is consistent with a single Gaussian distribution. Half the BCGs in the sample show some evidence of small color gradients as a function of radius within their central 50 kpc/h regions but with almost equal numbers becoming redder as becoming bluer. However, with the central 10 kpc/h the colors are remarkably constant -- the mean B - R(sub c) color is 1.51 with a dispersion of only 0.06 mag. The narrow photometric and color distributions of the BCGs, the lack of 'second-parameter' effects, as well as the unique rich cluster environment of BCGs, argue that BCGs are the most homogeneous distance indicators presently available for large-scale structure research.

Postman, Marc↗

NASA NTRS1994

The whistler heat flux instability: Threshold conditions in the solar wind

Solar wind electrons are observed often to consist of two components: a core and a halo. The anisotropics and relative average speeds of these components correspond to a heat flux that has the potential to excite several different electromagetic instabilities; wave-particle scattering by the resulting enhanced fluctuations can limit this heat flux. This manuscript describes theoretical studies using the linear Vlasco dispersion equation for drifting bi-Maxwellian component distributions in a homogeneous plasma to examine the threshold of the whistler heat flux instability. Expressions for this threshold are obtained from two different parametric baselines: a local model that yields scalings as functions of local dimensionless plasma paramaters, and a global model based on average electron properties observed during the in-eliptic phase of the Ulysses mission. The latter model yields an expression for the heat flux at threshold of the whistler instability as a function of helisopheric radius that scales in the same way as the average heat flux observed form Ulysses and that provides an approximate upper bound for that same quantity. This theoretical scaling is combined with the observational results to yield a semi-empirical closure relation for the average electron heat flux in the solar wind between 1 and 5 AU.

Gary, S. Peter↗

NASA NTRS2002

The Velocity Distribution of Isolated Radio Pulsars

We infer the velocity distribution of radio pulsars based on large-scale 0.4 GHz pulsar surveys. We do so by modelling evolution of the locations, velocities, spins, and radio luminosities of pulsars; calculating pulsed flux according to a beaming model and random orientation angles of spin and beam; applying selection effects of pulsar surveys; and comparing model distributions of measurable pulsar properties with survey data using a likelihood function. The surveys analyzed have well-defined characteristics and cover approx. 95% of the sky. We maximize the likelihood in a 6-dimensional space of observables P, dot-P, DM, absolute value of b, mu, F (period, period derivative, dispersion measure, Galactic latitude, proper motion, and flux density). The models we test are described by 12 parameters that characterize a population's birth rate, luminosity, shutoff of radio emission, birth locations, and birth velocities. We infer that the radio beam luminosity (i) is comparable to the energy flux of relativistic particles in models for spin-driven magnetospheres, signifying that radio emission losses reach nearly 100% for the oldest pulsars; and (ii) scales approximately as E(exp 1/2) which, in magnetosphere models, is proportional to the voltage drop available for acceleration of particles. We find that a two-component velocity distribution with characteristic velocities of 90 km/ s and 500 km/ s is greatly preferred to any one-component distribution; this preference is largely immune to variations in other population parameters, such as the luminosity or distance scale, or the assumed spin-down law. We explore some consequences of the preferred birth velocity distribution: (1) roughly 50% of pulsars in the solar neighborhood will escape the Galaxy, while approx. 15% have velocities greater than 1000 km/ s (2) observational bias against high velocity pulsars is relatively unimportant for surveys that reach high Galactic absolute value of z distances, but is severe for spatially bounded surveys; (3) an important low-velocity population exists that increases the fraction of neutron stars retained by globular clusters and is consistent with the number of old objects that accrete from the interstellar medium; (4) under standard assumptions for supernova remnant expansion and pulsar spin-down, approx. 10% of pulsars younger than 20 kyr will appear to lie outside of their host remnants. Finally, we comment on the ramifications of our birth velocity distribution for binary survival and the population of inspiraling binary neutron stars relevant to some GRB models and potential sources for LIGO.

Arzoumanian, Z.↗

NASA NTRS1992

Possible observational consequences of primordial binaries in globular clusters

The paper investigates the observational consequences of the evolution of a primordial binary population in a globular cluster. For those binary systems which begin mass transfer at orbital periods of less than about 1 d, the system is expected to evolve to a contact binary stage and to eventually merge to form a single star. At longer orbital periods, the binary system will enter into a common envelope stage. For periods less than about 10 d, the system is likely to merge, and the outcome of the evolution is a single red giant star. For systems characterized by orbital periods greater than about 15 d, a detached red dwarf-white dwarf binary system is expected to change. As a consequence of the mergers, a range in masses for the red giant stars is possible, leading to a color spread on the RGB of the color magnitude diagram. The luminosity function of stars at high luminosities is expected to steepen as a result of tidal interaction in the binary. It is suggested that the formation of cataclysmic variables via primordial binaries is expected only in loosely bound clusters of low-velocity dispersion.

Taam, Ronald E.↗