Search NASA⌕ Search

SEARCH · Search NASA

Results for “LOGARITHM”

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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

A spectrophotometric survey of cataclysmic variable stars

A sample of dwarf novae and other cataclysmic variable stars were observed using the multichannel spectrophotometer on the 5-m Hale reflector. A preliminary qualitative description of the continuum distributions is given and a discussion of the Balmer emission-line fluxes is made. For the spectral energy distributions, the logarithm of the monochromatic flux density is plotted against the inverse of the wavelength. It is concluded that the presence or absence of evident flux from a late-type stellar component is consistent with the standard picture which has been developed for the structure of cataclysmic variable stars. The presence of the Balmer jump in emission or absorption can be understood in terms of the relative importance of an optically thick accreting disk characteristic of nova-like variables and dwarf novae in outburst and an optically thin outer accreting disk characteristic of quiescent dwarf novae.

Oke, J. B.↗
NASA NTRS1982

Numerical comparisons of nonlinear convergence accelerators

As part of a continuing program of numerical tests of convergence accelerators, the iterated Aitken's Delta-squared method, Wynn's epsilon algorithm, Brezinski's theta algorithm, and Levin's u transform are compared on a broad range of test problems: linearly convergence alternating, monotone, and irregular-sign series, logarithmically convergent series, power method and Bernoulli method sequences, alternating and monotone asymptotic series, and some perturbation series arising in applications. In each category either the epsilon algorithm or the u transform gives the best results of the four methods tested. In some cases differences among methods are slight, and in others they are quite striking.

Smith, D. A.↗
NASA NTRS1982

Fragmentation of ice by low velocity impact

Low-velocity impact experiments (0.14 to 1 km/s) carried out in polycrystalline water ice targets at 257 and 81 K reveal interactions which are assigned to four fragmentation classes: cratering, erosion, disruption, and total fragmentation. The specific kinetic energies for the transitions between these classes are found to be about one to two orders of magnitude below those for silicate rocks. The mass vs. cumulative number distribution of fragments in the experiments is described by a simple power law, similar to that observed in fragmented rocks both in the laboratory and in nature. The logarithmic slopes of cumulative number vs. fragment weight range from -0.9 to -1.8; they decrease with increasing projectile energy and are approximately independent of target temperature. The shapes of fragments resulting from erosion and disruption of ice targets are found to be significantly less spherical for 257 K targets than for 81 K targets. Fragment sphericity increases with increasing projectile energy at 257 K; however, no similar trend is observed for 81 K ice.

Lange, M. A.↗
NASA NTRS1982

An operational large-scale marine planetary boundary layer model

A marine planetary boundary layer (PBL) model is presented and compared with data from sea-based experiments. The PBL model comprises two layers, the outer an Ekman-Taylor layer with stratification-dependent secondary flow, and the logarithmic surface layer corrected for stratification and humidity effects and variable surface roughness. Corrections are noted for air much warmer than water in stable conditions and for low wind speeds. The layers are analytically defined along with similarity relations and a resistance law for inclusion in a program. An additional interfacial layer correction is developed and shown to be significant for heat flux calculations. Experimental data from GOASEX were used to predict the windfield in the Gulf of Alaska, and JASIN data was used for windfields SE of Iceland. The JASIN-derived wind field predictions were accurate to within 1 m/sec and 10 deg in a 200 km triangle.

Brown, R. A.↗
NASA NTRS1981

A statistical analysis of simulated data from potential stratospheric satellite missions

A simplified one-dimensional model is used to analyze simulated data from typical proposed satellite measurements of trace species in the stratosphere. Uncertainties are introduced in simulated species concentration measurements and applied to the basic physical and chemical model data. The results of the calculations are then used to predict uncertainties in the species concentrations computed by the model. Candidate satellite missions can be evaluated for net information acquired by applying the error analysis. An abbreviated depiction of the computational procedure is given, and sample histograms based on an accumulation of 200 calculations are shown for H2O2 and ClNO3, demonstrating that emergent species distributions are roughly Gaussian in the logarithm of number density. Calculated vertical concentration profiles for these two species are presented.

Nealy, J. E.↗
NASA NTRS1982

The ionization structure of planetary nebulae. 3: NGC 7009

Spectrophotometric observations of emission line intensities were made in 8 positions in the planetary nebula NGC 7009. For the 6 brightest positions, the coverage is from 1400 A to 10,000 A. Standard equations used to correct for the existence of elements in other than the optical observable ionization stages give results over a wide range of ionization that are consistent and agree with abundances calculated using ultraviolet lines. This result is particularly gratifying for N because previously the standard formula gave inconsistent abundances in NGC 7009. The major outstanding problem is that the lambda 4267 CII line implies a C(2+) abundance as much as 12 times greater than that determined from the UV lines. This discrepancy is greatest nearest the central star, as is the case in the planetary nebula NGC 6720. The logarithmic abundances (relative to H=12.00) are: He=11.07, 0=8.68, N=8.10, Ne=8.16, C=8.18, Ar=6.36, and S=7.12. The average of the Ne, Ar, and S abundances agrees to within 5% of that for NGC 6720, but the O, N, nd C abundances average 1.9 times lower in NGC 7009, suggesting that here may have been mixing of processed material in the planetary precursor in NGC 6720.

Barker, T.↗
NASA NTRS1982

Computations and turbulent flow modeling in support of helicopter rotor technology

Efforts continue to investigate the applicability of the Deiwert's time dependent numerical airfoil calculation code to the simulation of two dimensional airfoil flows with large amounts of separation present. A modified logarithmic region mixing length term produced substantial differences in the calculated flow fields for the large separation of the M=0.4, high angle of attack cases. Reasons are given for interest in applying that model to previously investigated cases of the 64A010 airfoil section at Mach number 0.8 for angles of attack of 4 deg and 6.2 deg. The effects of these turbulence models at alterations and the time dependent behavior from impulsively started conditions are discussed.

Rose, W. C.↗
NASA NTRS1983

A basis for the analysis of surface geometry of spiral bevel gears

Geometrical procedures helpful in the fundamental studies of the surface geometry of spiral bevel gears are summarized. These procedures are based upon: (1) fundamental gear geometry and kinematics as exposited by Buckingham, et al; (2) formulas developed from differential geometry; and (3) geometrical concepts developed in recent papers and reports on spiral bevel gear surface geometry. Procedures which characterize the geometry so that the surface parametric equations, the principal radii of curvature, and the meshing kinematics are systematically determined are emphasized. Initially, the focus in on theoretical, logarithmic spiral bevel gears as defined by Buckingham. The gears, however, are difficult to fabricate and are sometimes considered to be too straight. Circular-cut spiral bevel gears are an alternative to this. Surface characteristics of crown circular cut gears are analyzed.

Huston, R. L.↗
NASA NTRS1983

A class of nonideal solutions. 1: Definition and properties

A class of nonideal solutions is defined by constructing a function to represent the composition dependence of thermodynamic properties for members of the class, and some properties of these solutions are studied. The constructed function has several useful features: (1) its parameters occur linearly; (2) it contains a logarithmic singularity in the dilute solution region and contains ideal solutions and regular solutions as special cases; and (3) it is applicable to N-ary systems and reduces to M-ary systems (M or = N) in a form-invariant manner.

Zeleznik, F. J.↗
NASA NTRS1983

Solar radio burst and in situ determination of interplanetary electron density

A few interplanetary electron density scales which were derived from the analysis of interplanetary solar radio burst are discussed and compared to a model derived from 1974 to 1980 Helios 1 and 2 in situ density observations made in the 0.3 to 1.0 AU range. The Helios densities were normalized to 1976 with the aid of IMP and ISEE data at 1 AU, and were then sorted into 0.1 AU bins and logarithmically averaged within each bin. The best fit to these 1976-normalized, bin averages is N(R(AU)) = 6.1 R(-2.10)/cu cm. This model is in rather good agreement with the solar burst determination if the radiation is assumed to be on the second harmonic of the plasma frequency. This analysis also suggests that the radio emissions tend to be produced in regions denser than the average where the density gradient decreases faster with distance than the observed R(-2.10).

Bougeret, J. L.↗
NASA NTRS1982

The rotation of comet nuclei

Spin-vector research on cometary nuclei is reviewed with emphasis on the actual determination of rotation period and spin-axis orientation. The rotation periods of 47 comets are compared with those of 41 asteroids with diameters of not more than 40 km. It is shown that the median periods for the comets is 15.0 hr as compared with 6.8 hr for the asteroids and that the preliminary distribution curve for the logarithms of the comet periods is not Gaussian and is flatter than the corresponding curve for the asteroids. Slow accumulation at low relative velocities is suggested as the cause of the longer comet rotation periods.

Whipple, F. L.↗
NASA NTRS1983

Effects of solution mass transport on the ECC ozonesonde background current

Measurement of the mass transport rate constant for the electrochemical concentration cell in an ozonesonde as a function of the pressure is reported. The investigation was performed to accurately model the residual current present in the ECC cell in the absence of ozone. The convective mass transport for two sondes were determined while maintaining a sufficiently negative cathodic potential to eliminate electron transfer at the cathode surface. A sonde was placed in a bell jar and subjected to varying pressure levels. When the background current was kept below 0.1 microamp and pressure was from 100-1000 mb, the necessary correction term for the pressure was independent of pressure. However, below 100 mb, a logarithmic decrease in the background current with pressure is expected. Present practices, involving a sensitivity to oxygen, are calculated to result in overestimation of the total ozone between 1000-10 mb by 0.0096 atm-cm with a background current of 0.1 microamp at 1000 mb.

Thornton, D. C.↗
NASA NTRS1983

Spectrophotometry of the broad absorption-line QSO PHL 5200

Spectrophotometric observations of PHL 5200 conducted from 1974 to 1979 are presented. The semiforbidden C III 1909 and Mg II 2799 emission lines give an emission redshift of 1.981 + or - 0.002 using the peak of the profile. The semiforbidden C III 1909/C IV 1549 emission line ratio, after correction for absorption, is more than the average for normal quasars. In addition, the spectrum shows more structure between C IV 1549 emission and semiforbidden C III 1909 emission than in the case of normal quasars. The absorption profiles are investigated by using symmetrical logarithmic profiles to model the emission lines. The residual intensities at different wavelengths in the absorption troughs are employed to map optical depth as a function of velocity, assuming that the absorption region covers a small part of the sky as seen from the central source. Spectra from five observing seasons are compared, and no apparent changes in the C IV and Si IV absorption troughs are found.

Junkkarinen, V. T.↗
NASA NTRS1983

A non-spherically symmetric model for absorption regions near quasars

An approximate analytic solution of the radiative-transfer equation is used to estimate upper limits on the fraction of sky covered (Omega/4pi) by absorption regions near broad absorption-line quasars. The resonance scattering of line radiation tends to 'fill in' absorption troughs, and regions with large Omega/4pi produce troughs that are severely 'filled in'. PHL 5200 and several other broad absorption line quasars have absorption troughs that are flat-bottomed and deep. It is noted that these quasars probably have small Omega/4pi. Simple solutions are obtained for the case of large optical depth and a point central source using a two-stream model for the radiation field. It is shown that the scattered radiation can produce flat-bottomed absorption troughs if the logarithmic velocity derivative in the outflow is constant. For a large class of models, Omega/4pi is approximately less than the residual intensity (the fraction left after absorption) in a deep flat-bottomed absorption trough.

Junkkarinen, V. T.↗
NASA NTRS1983

Effects of solution mass transport on the ECC ozonesonde background current

A technique is developed to measure the effective mass transport parameter for the electrochemical concentration cell (ECC) ozonesonde in order to determine the mass transport rate constant for the ECC as a function of pressure. It is shown that a pressure dependent factor in the background current originates in a convective mass transport parameter. It is determined that for atmospheric pressures greater than 100 mb the mass transport parameter is a constant, while at pressures less than 100 mb it decreases logarithmically with pressure. It is suggested that the background current correction is directly correlated to the mass transport parameter pressure dependence. The presently used background current correction, which is based on the partial pressure of oxygen, is found to lead to an overestimation of the integrated ozone value in the troposphere for the ECC ozonesonde data.

Thornton, D. C.↗
NASA NTRS1983

The depletion of calcium in the Rho Ophiuchi cloud

Data on the interstellar Ca II H and K lines toward HD 147889, a star deeply embedded in the rho Ophiuchi dark cloud, were obtained at the Mauna Kea Observatory of the University of Hawaii, using a multi-anode microchannel array (MAMA) detector. An upper limit on the Ca II column density of 1.7 x 10 to the 11th/sq cm was derived, which, together with ionization considerations and an estimated lower limit on the total hydrogen column density, implies that the calcium-to-hydrogen ratio in this line of sight is 0.00000795 or less, relative to the solar value. The logarithmic depletion is up to -5.10, the largest yet measured, and implies that gas-grain interaction in this region has proceeded to a much greater degree than is typical of diffuse clouds.

Snow, T. P.↗
NASA NTRS1981

The influence of environmental effects on the mechanical properties of graphite/epoxy laminates

The time dependent deformational and creep rupture processes in graphite/epoxy laminates are examined as a function of temperature and stress level. The role of accelerated characterization of design materials is discussed, and the use of a nonlinear time-temperature-stress-superposition principle in the determination of compliance master curves as a function of stress and temperature is considered. Creep rupture analytical models are discussed as applied to polymer-matrix composites, and the data is shown to be in general agreement with a logarithmic stress and temperature-dependent delayed fracture model. Comparisons between creep and rupture experiments and phenomenological models are presented.

Brinson, H. F.↗
NASA NTRS1983

A preliminary global oceanic cloud climatology from satellite albedo observations

A predictive relationship is developed between over-ocean cloud system albedo and the cloud amount present, using as a data base ERB satellite microwave readings at 0.5-0.7 micron and the USAF three-dimensional nephanalysis archive. The ERB data provided global coverage at a resolution of 2.5 x 2.5 deg during the 1974-78 period. Regression analyses were performed on the amounts and albedos for several years of data for one month in order to detect seasonal variations. A logarithmic relationship was found between the cloud system albedo and cloud amount over the oceans, with negligible seasonal variance. The analysis is noted to apply only where low surface albedos are encountered, and further work to extend the study to continental vegetated areas is indicated.

Hughes, N. A.↗