Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Truncated 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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Quasi-exospheric heat flux of solar-wind electrons

Density, bulk-velocity, and heat-flow moments are calculated for truncated Maxwellian distributions representing the cool and hot populations of solar-wind electrons, as realized at the base of a hypothetical exosphere. The electrostatic potential is calculated by requiring charge quasi-neutrality and the absence of electrical current. Plasma-kinetic coupling of the cool-electron and proton bulk velocities leads to an increase in the electrostatic potential and a decrease in the heat-flow moment. If the velocities differ by the Alfven speed along the magnetic field, for example, the potential rises to 72.6 V and the heat flux falls to 0.0272 erg/sq cm per sec. In each case, the heat flux is carried mainly by the quasi-exospheric hot electrons.

Eviatar, A.↗
NASA NTRS1992

A self-consistent field method for galactic dynamics

The present study describes an algorithm for evolving collisionless stellar systems in order to investigate the evolution of systems with density profiles like the R exp 1/4 law, using only a few terms in the expansions. A good fit is obtained for a truncated isothermal distribution, which renders the method appropriate for galaxies with flat rotation curves. Calculations employing N of about 10 exp 6-7 are straightforward on existing supercomputers, making possible simulations having significantly smoother fields than with direct methods such as tree-codes. Orbits are found in a given static or time-dependent gravitational field; the potential, phi(r, t) is revised from the resultant density, rho(r, t). Possible scientific uses of this technique are discussed, including tidal perturbations of dwarf galaxies, the adiabatic growth of central masses in spheroidal galaxies, instabilities in realistic galaxy models, and secular processes in galactic evolution.

Hernquist, Lars↗
NASA NTRS1961

Applications of Power Spectral Analysis Methods to Maneuver Loads Obtained on Jet Fighter Airplanes During Service Operations

Power spectral densities of normal load factor have been obtained for two service operational training flights of a Republic F-84G airplane and three service operational training flights of a North American F-86A airplane in order to indicate the load-factor frequency content and possible uses of power spectral methods in analyzing maneuver load data. It was determined that the maneuvering load-factor time histories appeared to be described by a truncated normal distribution. The power spectral densities obtained were relatively level at frequencies below 0.03 cycle per second and varied inversely with approximately the cube of the frequency at the higher frequencies. In general, the frequency content was very low above 0.2 cycle per second. The load-factor peak distributions were estimated fairly well from the spectrum analysis. In addition, peak load data obtained during service operations of fighter-type airplanes with flight time totaling about 24,000 hours were examined and appeared to agree reasonably well with the type of equations obtained from spectrum peak-load distributions.

Mayer, John P.↗
NASA NTRS1981

Interpretation of cosmic ray composition - The path length distribution

The chemical composition of cosmic ray nuclei, the value of Z varying between 3 and 28, and being between a few hundred MeV/nucleon and a few hundred GeV/nucleon, is compared with a consistent set of propagation calculations. These include the effects of spallation (energy-dependent cross sections are used), escape, ionization loss in the interstellar medium, and deceleration in the solar cavity. The amount of matter traversed by cosmic rays is found to be approximately 7 g/sq cm, independent of energy between 100 MeV/nucleon and 2 GeV/nucleon. Above 2 GeV/nucleon, the escape length varies as the -0.4 + or 0.1 power of the energy. In addition, a procedure has been developed to measure the shape of the cosmic ray path length distribution. Utilizing the ratio of Fe secondaries to Fe in the cosmic rays, presently available data are found to be consistent with an exponential distribution and they eliminate models in which the path length distribution is severely truncated. To tie down the shape of the distribution more precisely, new measurements of the cosmic ray composition, presently becoming available from experiments on the HEAO 3 satellite, will have to be coupled with improved measurements of the energy dependence of partial and total cross sections.

Protheroe, R. J.↗
NASA NTRS1994

Photoionization of disk galaxies: An explanation of the sharp edges in the H I distribution

We have reproduced the observed radial truncation of the H I distribution in isolated spiral galaxies with a model in which extragalactic radiation photoionizes the gaseous disk. For a galactic mass distribution model that reproduces the observed rotation curves, including dark matter in the disk and halo, the vertical structure of the gas is determined self-consistently. The ionization structure and column densities of H and He ions are computed by solving the radiation transfer equation for both continuum and lines. Our model is similar to that of Maloney, and the H I structure differs by less than 10%. The radial structure of the column density of H I is found to be more sensitive to the extragalactic radiation field than to the distribution of mass. For this reason, considerable progress can be made in determining the extragalactic flux of ionizing photons, phi(sub ex), with more 21 cm observations of isolated galaxies. However, owing to the uncertainty of the radial distribution of total hydrogen at large radii, inferring the extragalactic flux by comparing the observed edges to photoionization models is somewhat subjective. We find 1 x 10(exp 4)/sq cm/s is less than or approximately phi(sub ex) is less than or approximately 5 x 10(exp 4)/sq cm/s, corresponding to 2.1 is less than or approximately iota(sub 0) is less than or approximately 10.5 x 10(exp -23) ergs/sq cm/s/Hz/sr for a 1/nu spectrum. Although somewhat higher, our inferred range of iota(sub 0) is consistent with the large range of values obtained by Kulkarni & Fall from the 'proximity effect' toward Quasi-Stellar Objects (QSOs) at approximately 0.5.

Dove, James B.↗
NASA NTRS1985

Finite difference solutions of the Euler equations in the vicinity of sharp edges

Attempts have been made to explain why finite difference solutions of the Euler equations can describe flows with large vortical structures around sharp-edged bodies. The present paper is concerned with the influence of a singular sharp edge on the truncation error for a set of discretized Euler equations. An analysis is conducted of the distribution of the truncation error of one finite difference approximation of the Euler equations near a sharp edge of a thin plate. The analysis leads to a determination of the size of the region of the neighborhood of such a singularity. Attention is given to the consistency of a discretization of the Euler equations, and numerical experiments.

Hartwich, P.-M.↗
NASA NTRS1990

Doppler radar imaging of spherical planetary surfaces

This paper describes a technique for using echo power-spectra for making radar images of spherical planetary targets. In developing the Doppler-radar imaging system, the target's reflectivity distribution is expanded in a truncated spherical harmonic series; the distribution of echo power in rotational phase and the Doppler frequency are obtained in form of a system of linear equations which express the echo spectra as functions of the series coefficients. To estimate the coefficients from an observed phase-Doppler distribution, the inversion is cast as a least-squares problem, and is solved using singular value decompositions, yielding a linear imaging system which can be fully characterized by its impulse response as a function of latitude. Simulations were designed and used to explore the capabilities of Doppler radar imaging, and the sensitivity of imaging to such factors as subradar altitude coverage and signal-to-noise ratio was investigated.

Hudson, R. Scott↗
NASA NTRS1968

Independent doubly truncated gamma variables

Density and distribution functions of the sum of independent variables, each having a truncated gamma density function, were derived for use in the measurement of complex physical phenomena.

Lavender, D. E.↗
NASA NTRS1989

Voids in the Ly-alpha forest

The general issue of using the Ly-alpha absorbers in quasar spectra as tracers of the large-scale matter distribution is discussed, emphasizing complications due to evolutionary effects and line blending. Then, a novel method of statistical analysis of the line data appropriate for studying large-scale structure is described. This method circumvents the problem of line blending by truncating the interval distribution at the low end. It also explicitly takes z-dependent effects into account. As an example, the method is applied to an 18-quasar spectrum sample of 417 lines.

Duncan, Robert C.↗
NASA NTRS2019

Bayesian Estimation of Earth’s Undiscovered Mineralogical Diversity Using Noninformative Priors

Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.

Bayesian statistics↗
NASA NTRS1983

The propagation of ultraheavy cosmic ray nuclei

The propagation of ultraheavy cosmic ray nuclei (Z greater than 30) has been studied using a model based on the leaky-box formalism. This model has been used to examine the possible composition of the source, the path length distribution, and the mean escape length of the confinement region. Various abundance ratios have been found that have a sensitive dependence on one or more of these factors. Comparison of the theoretical values of these ratios with published data suggests that the source composition is similar to that of solar system matter, but that in the Pt-Pb region, enrichment in material produced by the r-process cannot be ruled out. Data for the secondary-to-primary ratio (Ru-44 - Cd-48)/(Sn-50 - Ba-56) show the presence of significantly more secondaries than are predicted, even when a truncated path length distribution is used in the model.

Brewster, N. R.↗
NASA NTRS1974

Modal analysis and control of flexible manipulator arms

The possibility of modeling and controlling flexible manipulator arms was examined. A modal approach was used for obtaining the mathematical model and control techniques. The arm model was represented mathematically by a state space description defined in terms of joint angles and mode amplitudes obtained from truncation on the distributed systems, and included the motion of a two link two joint arm. Three basic techniques were used for controlling the system: pole allocation with gains obtained from the rigid system with interjoint feedbacks, Simon-Mitter algorithm for pole allocation, and sensitivity analysis with respect to parameter variations. An improvement in arm bandwidth was obtained. Optimization of some geometric parameters was undertaken to maximize bandwidth for various payload sizes and programmed tasks. The controlled system is examined under constant gains and using the nonlinear model for simulations following a time varying state trajectory.

Neto, O. M.↗
NASA NTRS1979

Collective plasma effects associated with the continuous injection model of solar flare particle streams

A modified continuous injection model for impulsive solar flares that includes self-consistent plasma nonlinearities based on the concept of marginal stability is presented. A quasi-stationary state is established, composed of a hot truncated electron Maxwellian distribution confined by acoustic turbulence on the top of the loop and energetic electron beams precipitating in the chromosphere. It is shown that the radiation properties of the model are in accordance with observations.

Vlahos, L.↗
NASA NTRS1982

The source abundances of galactic cosmic rays

The galactic cosmic ray source abundances have been determined from two complete datasets, one at low and the other at high energy. For both exponential and truncated exponential pathlength distributions (PLD), the two sets of source abundances show significant differences for the primary elements, i.e., the Fe/O ratio. An energy dependent PLD reduces but does not eliminate the discrepancy, and this may indicate an energy dependence in the source composition. New source abundances for Na, P, Cl, Ca, and Mn are derived.

Dwyer, R. D.↗
NASA NTRS1986

Wing/body interference flow investigation

The concept of using parametric bicubic patch surface definitions with bilinear vorticity or biquadratic doublet distributions was tested by modeling the vortex sheet and predicting its shape numerically in the vicinity of the wing. For the purpose of computing induced velocities, it was shown that higher order of vorticity would not improve the truncation error. The bilinear distribution, used to model the tip vorticity, was satisfactory but gave rise to some difficulty. The bicubic geometric surface representation proved very suitable for curved surfaces such as the rolled-up vortex sheet, with the surface fit scheme failing only for complex wings, far downstream beyond the region of concern.

Vogel, J. M.↗
NASA NTRS1976

Appendage modal coordinate truncation criteria in hybrid coordinate dynamic analysis

The paper examines the validity of the assumption that certain appendage-distributed (modal) coordinates can be truncated from a system model without unacceptable degradation of fidelity in hybrid coordinate dynamic analysis for attitude control of spacecraft with flexible appendages. Alternative truncation criteria are proposed and their interrelationships defined. Particular attention is given to truncation criteria based on eigenvalues, eigenvectors, and controllability and observability. No definitive resolution of the problem is advanced, and exhaustive study is required to obtain ultimate truncation criteria.

Likins, P.↗
NASA NTRS1983

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 pathlength distributions or quantitative solutions to Galactic propagation models. These relations can be used to propagate abundances from the source or to the source, and the method described here allows a simple propagation of abundance uncertainties. A simultaneous analysis of B/C and (21-25)Fe indicates a need for truncation of the pathlength distribution.

Margolis, S. H.↗
NASA NTRS2011

Drop Size Distribution Measurements Supporting the NASA Global Precipitation Measurement Mission: Infrastructure and Preliminary Results

Global Precipitation Measurement Mission (GPM) retrieval algorithm validation requires datasets that characterize the 4-D structure, variability, and correlation properties of hydrometeor particle size distributions (PSD) and accumulations over satellite fields of view (5 -- 50 km). Key to this process is the combined use of disdrometer and polarimetric radar platforms. Here the disdrometer measurements serve as a reference for up-scaling dual-polarimetric radar observations of the PSD to the much larger volumetric sampling domain of the radar. The PSD observations thus derived provide a much larger data set for assessing DSD variability, and satellite-based precipitation retrieval algorithm assumptions, in all three spatial dimensions for a range of storm types and seasons. As one component of this effort, the GPM Ground Validation program recently acquired five 3rd generation 2D Video disdrometers as part of its Disdrometer and Radar Observations of Precipitation Facility (DROP), currently hosted in northern Alabama by the NASA Marshall Space Flight Center and the University of Alabama in Huntsville. These next-generation 2DVDs were operated and evaluated in different phases of data collection under the scanning domain of the UAH ARMOR C-band dual-polarimetric radar. During this period approximately 7500 minutes of PSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSDs were then used as input to T-matrix code for computation of polarimetric radar moments at C-band. The combined dataset was then analyzed with two basic objectives in mind: 1) the investigation of seasonal variability in the rain PSD parameters as observed by the 2DVDs; 2) the use of combined polarimetric moments and observed gamma distribution parameters in a functional form to retrieve PSD parameters in 4-D using the ARMOR radar for precipitation occurring in different seasons and for different rain system types. Preliminary results suggest that seasonal variations in the DSD parameters do occur, but are most pronounced when comparing tropical PSDs to either winter or summer convective precipitation. For example the previously documented shift to relatively smaller drop diameters in higher number concentrations for equivalent rain rate bins was observed in tropical storm rainbands occurring over Huntsville. On a more inter seasonal basis empirical fits between parameters such as D0 and ZDR do not appear to exhibit robust seasonal biases- i.e., one fit seems to work for all seasons within acceptable standard error (O[10%]) for estimates of D0. In polarimetric retrievals of the vertical variability in PSD (rain layer) for a tropical rainband we find that the Do varies with height when partitioned by specified precipitation categories (e.g., convective or stratiform, heavy and light stratiform etc.) but this variation is of order 10-20% and is smaller than the difference in D0 observed between the basic delineation of convective and stratiform precipitation types. Currently we are expanding our analysis of the vertical structure of the PSD to include several seasonally and/or dynamically-different storm system types (e.g., winter convection and stratiform events; summer mid-latitude convective etc.) sampled by ARMOR. The study will present the results of our combined analyses.

Petersen, Walter A.↗