Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Exponential distribution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

ETARA PC version 3.3 user's guide: Reliability, availability, maintainability simulation model

A user's manual describing an interactive, menu-driven, personal computer based Monte Carlo reliability, availability, and maintainability simulation program called event time availability reliability (ETARA) is discussed. Given a reliability block diagram representation of a system, ETARA simulates the behavior of the system over a specified period of time using Monte Carlo methods to generate block failure and repair intervals as a function of exponential and/or Weibull distributions. Availability parameters such as equivalent availability, state availability (percentage of time as a particular output state capability), continuous state duration and number of state occurrences can be calculated. Initial spares allotment and spares replenishment on a resupply cycle can be simulated. The number of block failures are tabulated both individually and by block type, as well as total downtime, repair time, and time waiting for spares. Also, maintenance man-hours per year and system reliability, with or without repair, at or above a particular output capability can be calculated over a cumulative period of time or at specific points in time.

Hoffman, David J.↗
NASA NTRS1991

Solar F10.7 radiation - A short term model for Space Station applications

A new method is described for statistically modeling the F10.7 component of solar radiation for 91-day intervals. The resulting model represents this component of the solar flux as a quasi-exponentially correlated, Weibull distributed random variable, and thereby demonstrates excellent agreement with observed F10.7 data. Values of the F10.7 flux are widely used in models of the earth's upper atmosphere because of its high correlation with density fluctuations due to solar heating effects. Because of the direct relation between atmospheric density and drag, a realistic model of the short term fluctuation of the F10.7 flux is important for the design and operation of Space Station Freedom. The method of modeling this flux described in this report should therefore be useful for a variety of Space Station applications.

Vedder, John D.↗
NASA NTRS1992

Mg II absorption in the spectra of 103 QSOs - Implications for the evolution of gas in high-redshift galaxies

Spectra of 103 low- and intermediate-redshift QSOs with a resolution of 4-6 A were obtained in order to investigate the statistics of the M II 2796, 2803 absorption systems over the redshift range of 0.2-2.2. New emission-line redshifts, based mostly on Mg II 2800 and semiforbidden 1909, were determined for the QSOs. The mean number density of Mg II absorbers per unit redshift range decreased from 0.97 +/-0.10 for a rest equivalent width threshold of 0.3 A to 0.27 +/-0.05 for a threshold of 1.0 A. The results are in agreement with comparable previous work. The observed equivalent width distribution could be fitted with either exponential or power-law analytic distributions, with parameters in line with those found in earlier studies. Statistical tests show that the Mg II absorbers are uniformly distributed in both comoving coordinates and velocity relative to the QSO.

Steidel, Charles C.↗
NASA NTRS1987

Cosmic-ray propagation in the Galaxy and in the heliosphere - The path-length distribution at low energy

The energy dependence of the path-length distribution of cosmic rays at low energies, below relativistic velocities, is studied, and its implications for models of cosmic-ray confinement and propagation in the Galaxy and Galactic halo, including the effects of a possible Galactic wind, are studied. It is found that the mean free path in Galactic propagation must be fully energy-dependent, with the mean of an exponential path-length distribution increasing with increasing energy below 1 GeV per nucleon and decreasing with increasing energy above 1 GeV per nucleon. This indicates that, at low energies, diffusion is not the controlling process. The path-length distribution is not purely exponential but is depleted in short path lengths at low energies. This depletion is energy-dependent, being largest at low energies and decreasing with increasing energy.

Garcia-Munoz, M.↗
NASA NTRS1990

Probabilistic structural analysis of a truss typical for space station

A three-bay, space, cantilever truss is probabilistically evaluated using the computer code NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) to identify and quantify the uncertainties and respective sensitivities associated with corresponding uncertainties in the primitive variables (structural, material, and loads parameters) that defines the truss. The distribution of each of these primitive variables is described in terms of one of several available distributions such as the Weibull, exponential, normal, log-normal, etc. The cumulative distribution function (CDF's) for the response functions considered and sensitivities associated with the primitive variables for given response are investigated. These sensitivities help in determining the dominating primitive variables for that response.

Pai, Shantaram S.↗
NASA NTRS2003

Rock Size-Frequency Distributions at the Mars Exploration Rover Landing Sites: Impact Hazard and Accessibility

The Viking and Mars Pathfinder landing sites and a wide variety of rocky locations on the Earth show size-frequency distributions that follow an exponential when expressed in cumulative fractional area covered by rocks of a given diameter or larger versus diameter plots. Mars lander rock distributions have been fit by an equation of the form: Fk(D) = k exp [-q(k) D], where Fk(D) is the cumulative fractional area covered by rocks of diameter D or larger, k is the total area covered by all rocks, and an exponential q(k) = 1.79 + 0.152/k, which governs how abruptly the area covered by rocks decreases with increasing diameter. These distributions form a family of noncrossing curves that flatten out at small rock diameter at a total rock abundance of 5-40%. Model rock size-frequency distributions indicate a low probability of impacting hazardous rocks during MER landing. Rocks large enough to analyze and abrade by the rover should be plentiful within an easy Sol's drive.

Golombek, M. P.↗
NASA NTRS2010

A Study of Cirrus Ice Particle Size Distribution Using TC4 Observations

An analysis of two days of in situ observations of ice particle size spectra, in convectively generated cirrus, obtained during NASA s Tropical Composition, Cloud, and Climate Coupling (TC4) mission is presented. The observed spectra are examined for their fit to the exponential, gamma, and lognormal function distributions. Characteristic particle size and concentration density scales are determined using two (for the exponential) or three (for the gamma and lognormal functions) moments of the spectra. It is shown that transformed exponential, gamma, and lognormal distributions should collapse onto standard curves. An examination of the transformed spectra, and of deviations of the transformed spectra from the standard curves, shows that the lognormal function provides a better fit to the observed spectra.

Tian, Lin↗
NASA NTRS1999

A Diagnostic Analysis of the Kennedy Space Center LDAR Network: Data Characteristics - 1

An analytical framework is developed in which to analyze climatological VHF (66 MHz) radiation measurements taken by the Kennedy Space Center Lightning Detection and Ranging (LDAR) network. A 19-month noise-filtered sample of LDAR observations is examined using this framework. It is found that the climatological VHF source density as observed by LDAR falls off approximately 10 dB every 71 km of ground range away from the network centroid (a 31 km e-folding scale). From this framework it is inferred that the underlying source distribution is likely inverse exponential in amplitude, with a log-slope of 126-147 mW(sup -1/2). The underlying vertical distribution of VHF sources is approximately normally distributed with a mean altitude of 9 km and a standard deviation of 2.7 km; this implies that the loss of below-horizon sources has a negligible effect on column-integrated source densities within 200 km ground range. At medium to far ranges, location errors are primarily radial and have a slightly asymmetric distribution whose first moment increases as range squared. Error moments estimated from observed lightning are significantly higher than those from aircraft-based signal generator or analytic solution estimates, suggesting that timing errors arising from poor signal identification and discrimination may dominate over timing errors arising from nominal sensor resolution. The VHF source properties of individual LDAR-observed flashes are computed and an analytic expression for flash detection efficiency vs. range is derived. This reveals nearly constant flash detection efficiency to 80-94 km range from the network centroid.

Boccippio, D. J.↗
NASA NTRS1985

Proton-air inelastic cross section at S(1/2) = 30 TeV

The distribution of the maxima of high energy cosmic ray induced extensive air showers in the atmosphere was measured as a function of atmospheric depth. From the exponential tail of this distribution, it was determined that the proton-air inelastic cross section at 30 TeV center-of-mass energy to be 540 + or - 40mb.

Baltrusaitis, R. M.↗
NASA NTRS1973

Bayesian estimation of life parameters in the Weibull distribution.

Development of a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter theta, Bayesian estimates of theta and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. Bhattacharya's results (1967) for the one-parameter exponential life-testing distribution are reduced to a special case of these results. A fully Bayesian analysis of both the scale and shape parameters is developed by assuming independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of Monte Carlo simulation and numerical-integration techniques. In both cases, a computer simulation is carried out, and a comparison is made between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior.

Canavos, G. C.↗
NASA NTRS1975

Solar models of low neutrino-counting rate - The depleted Maxwellian tail

Evolutionary sequences for the sun are presented which confirm that the Cl-37 neutrino counting rate will be greatly reduced if the high-energy tail of the Maxwellian distribution of relative energies is progressively depleted. Thermonuclear reaction rates and pressure are reevaluated for a distribution function modified by the correction factor suggested by Clayton (1974), and the effect of the results on solar models calculated with a simple Henyey code is discussed. It is shown that if the depletion is characterized by a certain exponential dependence on the distribution function, the counting rate will fall below 1 SNU for a distribution function of not less than 0.01. Suggestions are made for measuring the distribution function in the sun by means of neutrino spectroscopy and photography.

Clayton, D. D.↗
NASA NTRS2022

Characteristics of Multi-scale Current Sheets in the Solar Wind at 1 au Associated with Magnetic Reconnection and the Case for a Heliospheric Current Sheet Avalanche

Wind spacecraft measurements are analyzed to obtain a current sheet (CS) normal width dcs-distribution of 3374 confirmed magnetic reconnection exhausts in the ecliptic plane of the solar wind at 1 AU. The dcs-distribution displays a nearly exponential decay from a peak at dcs=25 di to a median at dcs=85 di and a 95th percentile at dcs=905 di with a maximum exhaust width at dcs=8077 di. A magnetic field ϴ-rotation angle distribution increases linearly from a relatively few high-shear events toward a broad peak at 35o<ϴ<65o. The azimuthal φ-angles of the CS normal directions of 430 thick dcs≥500 di exhausts are consistent with a dominant Parker-spiral magnetic field and a CS normal along the ortho-Parker direction. The CS normal orientations of 370 kinetic-scale dcs<25 di exhausts are isotropic in contrast, and likely associated with Alfvénic solar wind turbulence. We propose that the alignment of exhaust normal directions from narrow dcs~15-25 di widths to well beyond dcs~500 di with an ortho-Parker azimuthal direction of a large-scale HCS is a consequence of CS bifurcation and turbulence within the HCS exhaust that may trigger reconnection of the adjacent pair of bifurcated CSs. The proposed HCS-31 avalanche scenario suggests that the underlying large-scale parent HCS closer to the Sun evolves with heliocentric distance to fracture into many, more or less aligned, secondary current sheets due to reconnection. A few wide exhaust-associated HCS-like CSs could represent a population of HCSs that failed to reconnect as frequently between the Sun and 1 AU as other HCSs.

Stefan Eriksson↗
NASA NTRS1986

The cosmic-ray source composition

The cosmic-ray source composition is shown to be related to the observed cosmic-ray abundances by a set of linear equations which are valid for either ad hoc path length distributions or quantitative solutions of galactic propagation models. In the limit of no ionization energy loss, this method is exact for all path length distributions and can replace more detailed numerical integrations; it provides a simple way to calculate directly the source composition implied by a particular set of cross sections, observed abundances, and propagation model. This method is used to determine the source abundances of the galactic cosmic rays in a model-independent manner. Compared to a simple exponential, the path length distribution required by observations is deficient in the contributions from short (not greater than 0.5 g/sq cm) paths at energies of a few GeV per nucleon.

Margolis, S. H.↗
NASA NTRS1982

Numerical solution of viscous flow in unbounded fluid

Incompressible viscous flow fields induced by initial vorticity distributions with bounded support or exponential decay in the far field are investigated. A numerical scheme for the solution of the vorticity distribution and the velocity field is presented with special emphasis on the treatment of the boundary data. The efficiency of the scheme is demonstrated. The present method has been applied to the study of the merging and collision of vortex rings.

Liu, C. H.↗
NASA NTRS1975

Measurement of the fluxes of galactic cosmic-ray H-2 and He-3 in 1972-1973

This paper reports measurements of the fluxes of cosmic-ray H-2 and He-3 during 1972-1973, carried out by instruments on board the IMP-7 and Pioneer 10 spacecraft. Energy spectra are generally consistent with a positive slope of unity, as would be expected for modulated secondary components. A self-consistent data set is proposed spanning the period from 1965 to 1973 wherein all spectra have the same kinematic behavior. The measured spectra for 1972-1973 are compared with calculated interstellar spectra, and it is concluded that only very broad limits can be placed on the amount of modulation. Ratios of the form H-2/He-4 and He-3/He-4 are examined and compared with calculated values based on an assumed exponential path-length distribution for galactic propagation. It is concluded that unless extreme assumptions are made about the modulation (e.g., no energy loss), it is impossible to reconcile the simple theory and observation. A nearby source is apparently required to supply enough low-energy He-4 to account for the low values of the H-2/He-4 and He-3/He-4 ratios. The possible relationship between this source and the recently discovered enhancements of cosmic-ray N and O is discussed.

Teegarden, B. J.↗
NASA NTRS1982

Wall interference evaluation from pressure measurements on control surfaces

Conventional methods for the calculation of wall interference corrections are based on boundary conditions which require a knowledge of ventilated wall porosity parameters, and which are unsuitable for deformed walls. The method described uses a simple exponential decay of pressure distribution beyond the most upstream and downstream limits in order to evaluate Mach number and incidence corrections given by the method proposed by Papelier et al. (1978). It is found that, while the upstream contribution to incidence correction is significant, the upstream and downstream contributions to Mach number correction are negligible.

Gopinath, R.↗
NASA NTRS1983

Optimal design and use of retry in fault tolerant real-time computer systems

A new method to determin an optimal retry policy and for use in retry of fault characterization is presented. An optimal retry policy for a given fault characteristic, which determines the maximum allowable retry durations to minimize the total task completion time was derived. The combined fault characterization and retry decision, in which the characteristics of fault are estimated simultaneously with the determination of the optimal retry policy were carried out. Two solution approaches were developed, one based on the point estimation and the other on the Bayes sequential decision. The maximum likelihood estimators are used for the first approach, and the backward induction for testing hypotheses in the second approach. Numerical examples in which all the durations associated with faults have monotone hazard functions, e.g., exponential, Weibull and gamma distributions are presented. These are standard distributions commonly used for modeling analysis and faults.

Lee, Y. H.↗