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NASA NTRS1990

Lower bound on reliability for Weibull distribution when shape parameter is not estimated accurately

The mathematical relationships between the shape parameter Beta and estimates of reliability and a life limit lower bound for the two parameter Weibull distribution are investigated. It is shown that under rather general conditions, both the reliability lower bound and the allowable life limit lower bound (often called a tolerance limit) have unique global minimums over a range of Beta. Hence lower bound solutions can be obtained without assuming or estimating Beta. The existence and uniqueness of these lower bounds are proven. Some real data examples are given to show how these lower bounds can be easily established and to demonstrate their practicality. The method developed here has proven to be extremely useful when using the Weibull distribution in analysis of no-failure or few-failures data. The results are applicable not only in the aerospace industry but anywhere that system reliabilities are high.

Huang, Zhaofeng↗

NASA NTRS1989

Size distribution of dust grains: A problem of self-similarity

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space.

Henning, TH.↗

NASA NTRS1991

GaP betavoltaic cells as a power source

Maximum power output for the GaP cells of this study was found to be on the order of 1 microW. This resulted from exposure to 200 and 40 KeV electrons at a flux of 2 x 10(exp 9) electrons/sq cm/s, equivalent to a 54 mCurie source. The efficiencies of the cells ranged from 5 to 9 percent for 200 and 40 KeV electrons respectively. The lower efficiency at higher energy is due to a substantial fraction of energy deposition in the substrate, further than a diffusion length from the depletion region of the cell. Radiation damage was clearly observed in GaP after exposure to 200 KeV electrons at a fluence of 2 x 10(exp 12) electrons/sq cm. No discernable damage was observed after exposure to 40 KeV electrons at the same fluence. Analysis indicates that a GaP betavoltaic system would not be practical if limited to low energy beta sources. The power available would be too low even in the ideal case. By utilizing high activity beta sources, such as Sr-90/Y-90, it may be possible to achieve performance that could be suitable for some space power applications. However, to utilize such a source the problem of radiation damage in the beta cell material must be overcome.

Pool, F. S.↗

NASA NTRS1990

Hydrogen and sliding at alpha/beta interfaces of titanium alloys

Emerging evidence that the sliding between alpha and beta interfaces reported in both Ti-Mn alloys and the Ti-4.5Al-5Mo-1.5Cr ('Corona 5') alloy at room temperature is associated with hydrogen suggests that this may be a general problem contributing to Ti alloys' room-temperature creep. The present evaluation of experimental data indicates that while the hydrogen is concentrated at the Ti-Mn alloys' beta phase, no hydride formation at the alpha/beta interfaces has been reported for either the Ti-Mn alloys or Corona 5. If a hydrogen flux is needed, sliding at the alpha-beta interfaces should be a function of total hydrogen content in the alloy.

Margolin, Harold↗

NASA NTRS1991

Steps toward determination of the size and structure of the broad-line region in active galactic nuclei. II - An intensive study of NGC 5548 at optical wavelengths

A large, international program of ground-based optical spectroscopy and photometry of the variable Seyfert 1 galaxy NGC 5548 undertaken in support of an IUE monitoring campaign is described. This contribution presents the data base and describes the methods used to correct for systematic differences between spectra from different sources. Optical continuum and H-beta emission-line light curves are derived from the spectra. The behavior of the optical continuum is qualitatively the same as the behavior of the ultraviolet continuum. Cross-correlation of the ultraviolet and optical continuum measurements does not reveal any significant lag between them. The h-beta emission-line variations show the same basic pattern as seen in the continuum and ultraviolet emission lines, with H-beta lagging behind the continuum by about 20 days. This is significantly larger than the about 10 day lag deduced for Ly-alpha.

Peterson, B. M.↗

NASA NTRS1991

Plasma convection and ion beam generation in the plasma sheet boundary layer

Because of the dawn-dusk electric field E(dd), plasma in the magnetotail convects from the lobe toward the central plasma sheet (CPS). In the absence of space or velocity diffusion due to plasma turbulence, convection would yield a steady state distribution function f = V exp (-2/3) g(v exp 2 V exp 2/3), where V is the flux tube volume. Starting with such a distribution function and a plasma beta which varies from beta greater than 1 in the CPS to beta much smaller than 1 in the lobe, the evolution of the ion distribution function was studied considering the combined effects of ion diffusion by kinetic Alfven waves (KAW) in the ULF frequency range (1-10 mHz) and convection due to E(dd) x B drift in the plasma sheet boundary layer (PSBL) and outer central plasma sheet (OCPS). The results show that, during the early stages after launching the KAWs, a beamlike ion distribution forms in the PSBL and at the same time the plasma density and temperature decrease in the OCPS. Following this stage, ions in the beams convect toward the CPS resulting in an increase of the plasma temperature in the OCPS.

Moghaddam-Taaheri, E.↗

NASA NTRS1991

Optical waveguide formed by cubic silicon carbide on sapphire substrates

Optical confinement in beta silicon carbide (beta-SiC) thin films on sapphire substrate is demonstrated. Measurements are performed on waveguides formed by the mechanical transfer of thin beta-SiC films to sapphire. Recent results of epitaxial films of SiC on sapphire substrates attest to the technological viability of optoelectronic devices made from silicon carbide. Far-field mode patterns are shown. It is believed that this is the first step in validating a silicon carbide optoelectronic technology.

Tang, Xiao↗

NASA NTRS1991

Asymptotic expansions of the kernel functions for line formation with continuous absorption

Asymptotic expressions are obtained for the kernel functions M2(tau, alpha, beta) and K2(tau, alpha, beta) appearing in the theory of line formation with complete redistribution over a Voigt profile with damping parameter a, in the presence of a source of continuous opacity parameterized by beta. For a greater than 0, each coefficient in the asymptotic series is expressed as the product of analytic functions of a and eta. For Doppler broadening, only the leading term can be evaluated analytically.

Hummer, D. G.↗

NASA NTRS1991

Approaches for optimizing the first electronic hyperpolarizability of conjugated organic molecules

Conjugated organic molecules with electron-donating and -accepting moieties can exhibit large electronic second-order nonlinearities, or first hyperpolarizabilities, beta. The present two-state, four-orbital independent-electron analysis of beta leads to the prediction that its absolute value will be maximized at a combination of donor and acceptor strengths for a given conjugated bridge. Molecular design strategies for beta optimization are proposed which give attention to the energetic manipulations of the bridge states. Experimental results have been obtained which support the validity of this approach.

Marder, S. R.↗

NASA NTRS1990

Segmented Ge detectors and mechanical coolers for future gamma-ray astronomy instruments

The effectiveness of a segmented Ge detector in rejecting background events due to the beta decay of internal radioactivity is demonstrated by a laboratory experiment in which radioactivity was produced in the detector by neutron irradiation. A Cf-252 source of neutrons was used to produce, by neutron capture on Ge-74 in the detector itself, Ge-75, which decays by beta emission with a maximum energy of 1188 keV. Simultaneous spectra are taken of the activity in the detector under two conditions: a free spectrum in which all events in the detector are accumulated, and a gated spectrum in which events are accumulated only if they deposit energy in two or more segments. A comparison of the spectra shows that over 85 percent of the beta events are rejected, which is in good agreement with predictions.

Varnell, Larry S.↗

NASA NTRS1991

Linear electro-optic effect in cubic silicon carbide

The first observation is reported of the electrooptic effect of cubic silicon carbide (beta-SiC) grown by a low-pressure chemical vapor deposition reactor using the hydrogen, silane, and propane gas system. At a wavelength of 633 nm, the value of the electrooptic coefficient r41 in beta-SiC is determined to be 2.7 +/- 0.5 x 10 (exp-12) m/V, which is 1.7 times larger than that in gallium arsenide measured at 10.6 microns. Also, a half-wave voltage of 6.4 kV for beta-SiC is obtained. Because of this favorable value of electrooptic coefficient, it is believed that silicon carbide may be a promising candidate in electrooptic applications for high optical intensity in the visible region.

Tang, Xiao↗

NASA NTRS1992

Occultation of a compact radio source by Venus

An occultation of the compact radio source P 0507+17 by Venus on 19 Jul. 1988, was observed in Tidbinbilla, Australia at a frequency of 2.3 GHz. The purpose of this observation was to measure the position of Venus in the radio reference frame. When data from both ingress (Venus dayside) and egress (Venus nightside) were used to solve for the position of Venus in ecliptic longitude and latitude, the results were consistent with zero offsets from the nominal values, with an uncertainty of approximately 0.2 arcsec in both coordinates. By using the nightside data alone, a value of -0.026 +/- 0.04 arcsec was obtained for the linear combination delta(lambda) + 0.51delta(beta), where delta(lambda) and delta(beta) were the offsets from their nominal values of the ecliptic longitude and latitude of Venus. Distortion of a vacuum Fresnel fringe pattern by the Venus troposphere, and especially by the Venus ionosphere, was observed. The dayside ionosphere of Venus caused very large distortions; the amplitude of the first Fresnel fringe in the ingress data was eight times larger than was expected for an airless planet. The observed fringe patterns were modeled by using plausible ionospheres (i.e., consistent with spacecraft measurements of the Venus ionosphere and with solar extreme ultraviolet flux and solar wind pressure measurements at the occultation epoch). However, the range of Venus ionospheric profiles (electron density as a function of altitude) allowed by a priori constraints and by the occultation data was large (e.g., the ionopause height on the dayside was uncertain by a factor of two). This ionospheric uncertainty (particularly on the dayside) translated into a large position uncertainty (0.2 arcsec for the dayside and 0.04 arcsec for the nightside). If it was possible to calibrate the Venus ionosphere by some external means, the accuracy in delta(lambda) and delta(beta) would have been 0.01 arcsec or better.

Linfield, R.↗

NASA NTRS1992

A comparison of lidar inversion methods for cirrus applications

Several methods for inverting the lidar equation are suggested as means to derive the cirrus optical properties (beta backscatter, alpha extinction coefficients, and delta optical depth) at one wavelength. The lidar equation can be inverted in a linear or logarithmic form; either solution assumes a linear relationship: beta = kappa(alpha), where kappa is the lidar ratio. A number of problems prevent us from calculating alpha (or beta) with a good accuracy. Some of these are as follows: (1) the multiple scattering effect (most authors neglect it); (2) an absolute calibration of the lidar system (difficult and sometimes not possible); (3) lack of accuracy on the lidar ratio k (taken as constant, but in fact it varies with range and cloud species); and (4) the determination of boundary condition for logarithmic solution which depends on signal to noise ration (SNR) at cloud top. An inversion in a linear form needs an absolute calibration of the system. In practice one uses molecular backscattering below the cloud to calibrate the system. This method is not permanent because the lower atmosphere turbidity is variable. For a logarithmic solution, a reference extinction coefficient (alpha(sub f)) at cloud top is required. Several methods to determine alpha(sub f) were suggested. We tested these methods at low SNR. This led us to propose two new methods referenced as S1 and S2.

Elouragini, Salem↗

NASA NTRS1992

Theory of small-scale density and electric field fluctuations in the nightside Venus ionosphere

Recently, it has been reported that small-scale (lambda about 0.1-2 km) density irregularities occur during 100-Hz electric field bursts in the nightside ionosphere of Venus. This paper provides a detailed analysis of the lower-hybrid-drift instability as a mechanism to generate the observed irregularities. A fully electromagnetic theory is developed that is relevant to the finite beta plasma in Venus's ionosphere and includes collisional effects (e.g., electron-ion, electron-neutral, and ion-neutral collisions). The key features of the analysis that favor this instability are the following: (1) it is a flute mode and propagates orthogonal to the ambient magnetic field; (2) it is a relatively short wavelength mode and the Doppler-shifted frequency can be greater than about 100 Hz; (3) it can produce both electric field and density fluctuations, as well as magnetic field fluctuations in a finite beta plasma; and (4) it is most unstable in low-beta plasmas so that it is likely to occur in the low-density, high-magnetic-field ionospheric holes. These features are consistent with observational results.

Huba, J. D.↗

NASA NTRS1990

The magnetopause

The magnetopause is the interface between the shocked solar wind in the magnetosheath and the geomagnetic field and plasma in the magnetosphere. This interface is far from simple because both sides of the interface contain magnetized plasma. As a result, there are boundary layers on both sides of the interface so the resulting structure is many-ion-gyroradii thick. There is also substructure which may be much less than an ion gyroradius in thickness. The structure of the magnetopause is also sensitive to the Mach number and beta of the plasma. When the beta is very high, the magnetopause resembles a slow mode wave. When the IMF is southward and the Mach number and/or beta is low the plasma is accelerated much as Dungey predicted. However, at other times reconnection seems to be less steady and perhaps patchy. Ropelike structures are seen which may be connected to the magnetosphere. These structures, which have been called FTEs, are still not fully understood.

Russell, C. T.↗

NASA NTRS1991

Lower bound on reliability for Weibull distribution when shape parameter is not estimated accurately

Huang, Zhaofeng↗

NASA NTRS1993

The Lyman alpha forest of the high-z quasar 0000-263

Medium-resolution (delta(v) = 45 km/s) optical spectra of the bright, high-redshift (z = 4.1) quasar 0000-263 taken at the ESO 3.5-m NTT telescope were analyzed to determine the distribution of column densities, velocities and line widths of the Lyman-alpha forest absorption components. The values of NH, b, and z were determined by fitting Voigt profiles to the lines, and convolving with a Gaussian instrumental response function. Over 350 components with log N(sub H) greater than 13.2 were identified. An analysis of the dependence of the number of components with z reveals that the number evolution of components obeys the power law dN/dz varies as (1+z)(sup gamma), where gamma = 0.5 +/- 0.4 for the sample of 182 lines with log N(sub H) greater than 14.0. The distribution of component strengths is found to obey f(N(sub H)) varies as N(sub h)(sup -beta), where beta = -1.55 for components with log(N(sub H)) is greater than 14.7, and beta = -0.68 for the components with log(N(sub H)) greater than 13.5. A distinct break in the f(N(sub H)) histogram is also observed, at log(N(sub H)) is approximately 14.7. The results are briefly considered in the context of theoretical models of quasar Lyman alpha clouds and their evolution.

Penprase, Bryan↗

NASA NTRS1992

On the electromagnetic fields, Poynting vector, and peak power radiated by lightning return strokes

The initial radiation fields, Poynting vector, and total electromagnetic power that a vertical return stroke radiates into the upper half space have been computed when the speed of the stroke, nu, is a significant fraction of the speed of light, c, assuming that at large distances and early times the source is an infinitesimal dipole. The initial current is also assumed to satisfy the transmission-line model with a constant nu and to be perpendicular to an infinite, perfectly conducting ground. The effect of a large nu is to increase the radiation fields by a factor of (1-beta-sq cos-sq theta) exp -1, where beta = nu/c and theta is measured from the vertical, and the Poynting vector by a factor of (1-beta-sq cos-sq theta) exp -2.

Krider, E. P.↗