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 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Embedded function methods for supersonic turbulent boundary layers

The development of embedded functions to represent the mean velocity and total enthalpy distributions in the wall layer of a supersonic turbulent boundary layer is considered. The asymptotic scaling laws (in the limit of large Reynolds number) for high speed compressible flows are obtained to facilitate eventual implementation of the embedded functions in a general prediction method. A self-consistent asymptotic structure is derived, as well as a compressible law of the wall in which the velocity and total enthalpy are logarithmic within the overlap zone, but in the Howarth-Dorodnitsyn variable. Simple outer region turbulence models are proposed (some of which are modifications of existing incompressible models) to reflect the effects of compressibility. As a test of the methodology and the new turbulence models, a set of self-similar outer region profiles is obtained for constant pressure flow; these are then coupled with embedded functions in the wall layer. The composite profiles thus obtained are compared directly with experimental data and good agreement is obtained for flows with Mach numbers up to 10.

He, J.↗
NASA NTRS1990

On the Lagrangian description of unsteady boundary-layer separation. II - The spinning sphere

A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A Lagrangian numerical scheme is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian computations broke down at the first occurrence of separation, it is found that the Lagrangian computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time.

Van Dommelen, Leon L.↗
NASA NTRS1990

Performance analysis of a generalized concurrent error detection procedure

A general procedure for error detection in complex systems, called the data block capture and analysis monitoring process, is described and analyzed. It is assumed that, in addition to being exposed to potential external fault sources, a complex system will in general always contain embedded hardware and software fault mechanisms which can cause the system to perform incorrect computations and/or produce incorrect output. Thus, in operation, the system continuously moves back and forth between error and no-error states. These external fault sources or internal fault mechanisms are extremely difficult to detect. The data block capture and analysis monitoring process is concerned with detecting deviations from the normal performance of the system, known as errors, which are symptomatic of fault conditions. The process consists of repeatedly recording a fixed amount of data from a set of predetermined observation lines of the system being monitored (i.e., capturing a block of data) and then analyzing the captured block in an attempt to determine whether the system is functioning correctly. The performances of linear, quadratic, and logarithmic data analysis algorithms are rigorously characterized in terms of the probability of correctly detecting an error, the expectation and variance of the number of false alarms per error, and the expectation and variance of the latency in detection of errors. Insight into the nature of the general problem of error detection is obtained.

Blough, Douglas M.↗
NASA NTRS1990

Rare-gas liquids - Equation of state and reduced-pressure, reduced-bulk-modulus, and reduced-sound-velocity functions

This paper is concerned with verification of the applicability of the Vinet et al. (1987) universal equation of state to the liquid phase of the rare-gas elements under pressure. As previously observed in solids and liquids metals, to a good approximation, in the absence of phase transitions, plots of the logarithms of the reduced pressure function, of the reduced sound velocity, and of the reduced bulk modulus, are all linear functions of 1 - X over the entire experimental pressure range. The results obtained on the rare-gas liquids are comparable in accuracy to those obtained in previous work on solids and liquid metals.

Schlosser, Herbert↗
NASA NTRS1990

Deep-level dominated electrical characteristics of Au contacts on beta-SiC

Electrical characteristics of Au contacts on beta-SiC films, grown epitaxially on both nominal and off-axis (100) silicon substrates, are reported. An analysis of the logarithmic I-V plots of the Au/beta-SiC diodes revealed information pertaining to the deep states present in the materials. It was found that while the beta-SiC films grown on nominally (100) oriented substrates show the presence of two deep levels located between 0.26 and 0.38 eV below the conduction bandedge, the beta-SiC films deposited on off-axis substrates have only one deep level, located about 0.49 eV below the conduction bandedge for the 2-deg off (100) substrates and 0.57 eV for the 4-deg off (100) substrates. The presence of the shallower deep states in the beta-SiC films grown on nominal (100) substrates is attributed to the electrical activity of antiphase domain boundaries.

Das, K.↗
NASA NTRS1990

A simple analytic model for the evolution of captured galactic disks

The general analytic solution developed by Steinman-Cameron and Durisen and published in 1988 for the evolution of dissipative nonplanar disks is applied to captured galactic disks in model galaxies with nonspherical, scale-free, logarithmic gravitational potentials. Such potentials produce flat rotation curves, similar to those seen in real galaxies. In this case, the analytic solution yields a self-similar structure for the warps and twists that develop while the disks is settling. Being scale-free in a simple, analytic form, this solution is completely defined by only a few dimensionless fitting parameters. As a result, it can be utilized as a mathematical tool to fit settling disks in real galaxies. The minimum time it takes for a disk to settle into a steady state orientation is also a scale-free quantity when expressed in units of the precession period or the orbit period. For realistic parameters, settling times are on the order of one-half to two periods. The use of the time-dependent structure of settling disks as a probe of the three-dimensional mass distribution of the host galaxies, including dark halos, is discussed.

Steiman-Cameron, Thomas Y.↗
NASA NTRS1991

Waveform-Generating Program

GENERATE (Digital Generation of Complex Waveforms) computer program is flexible and reliable software tool for advanced generation of waveforms. User employs standard arithmetic operator (+, -, x, /, and parentheses) to simulate any combination of eight commonly used basic waveforms at desired amplitude and frequency. Creates data file based on user's selections from menu. Provides necessary equations describing eight basic waveforms and enables user to combine them arithmetically. Basic waveforms offered as building blocks; sine, ramp, exponential, logarithmic, step, clipped sine, square, and sawtooth. Also contains routine for plotting output waveform data on terminal with Tektronics (or equivalent) emulator, providing visual confirmation of desirability of waveform. Developed by use of VMS FORTRAN on DEC VAX 3600 computer.

Hopson, Charles B.↗
NASA NTRS1990

Laser-induced fluorescence of phosphors for remote cryogenic thermometry

Remote cryogenic temperature measurements can be made by inducing fluorescence in phosphors with temperature-dependent emissions and measuring the emission lifetimes. The thermographic phosphor technique can be used for making precision, noncontact, cryogenic-temperature measurements in electrically hostile environments, such as high dc electric or magnetic fields. The National Aeronautics and Space Administration is interested in using these thermographic phosphors for mapping hot spots on cryogenic tank walls. Europium-doped lanthanum oxysulfide (La2O2S:Eu) and magnesium fluorogermanate doped with manganese (Mg4FGeO6:Mn) are suitable for low-temperature surface thermometry. Several emission lines, excited by a 337-nm ultraviolet laser, provide fluorescence lifetimes having logarithmic dependence with temperature from 4 to above 125 K. A calibration curve for both La2O2S:Eu and Mg4FGeO6:Mn is presented, as well as emission spectra taken at room temperature and 11 K.

Beshears, D. L.↗
NASA NTRS1989

Dust of Orionid meteor shower in the Earth atmosphere before and after Halley's Comet

Among the interesting questions concerning meteor streams associated with Comet Halley is the question of whether or not the activity of a meteor stream was connected with the approach of the comet to the terrestrial orbit in 1985 to 1986. Meteoric aerosols getting to the upper atmosphere can be detected by twilight sounding, as has been done previously. It turns out that not only parameters describing some properties of aerosol can be obtained by twilight sounding, but also characteristics concerning the structure of the stream can be derived. Among the yearly active streams, the Orionides have always attracted the attention of scientists. The period of activity of the Orionides is October 18 to 26, and the maximum stream activity is October 21. In detecting aerosol layers in the terrestrial atmosphere, a notion of the logarithmic intensity gradient of scattered twilight light is used, d log I/dH, where I is intensity and H is the real twilight beam height, which is a function of the wavelength observed. A photoelectric photometer with an interference filter at the wavelength of 610 nm is used. The observation were carried out in two points of the solar vertical; the zenith angle of the observation points was + or - 60 degrees. The recording was carried on continuously in each direction during a minute, then the system was switched to the other direction. A calibration standard was recorded before each observation. The observation dates in the Orionid periods of 1984, 1986, and 1987 are given.

Mateshvili, G.↗
NASA NTRS1991

Maximum-entropy probability distributions under Lp-norm constraints

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

Dolinar, S.↗
NASA NTRS1991

An experimental analysis of critical factors involved in the breakdown process of leading edge vortex flows

Experimental crosswire measurements of the flowfield above a 70 and 75 degree flat plate delta wing were performed at a Reynolds number of 250,000. Survey grids were taken normal to the platform at a series of chordwise locations for angles of attack of 20 and 30 degrees. Axial and azimuthal vorticity distributions were derived from the velocity fields. The dependence of circulation on distance from the vortex core as well as on chordwise location was examined. The effects of nondimensionalization in comparison with other experimental data was made. The circulation distribution scales with the local semispan and grows approximately linearly in the chordwise direction. For regions of the flow outside of the vortex subcore, the circulation at any chordwise station was observed to vary logarithmically with distance from the vortex axis. The circulation was also found to increase linearly with angle of incidence at a given chordwise station. A reduction in the local circulation about the vortex axis occurred at breakdown. The spanwise distribution of axial vorticity was severely altered through the breakdown region and the spanwise distribution of axial vorticity present appeared to reach a maximum immediately preceding breakdown. The local concentration of axial vorticity about the vortex axis was reduced while the magnitude of the azimuthal vorticity decreased throughout the breakdown zone. The axial vorticity components with a negative sense, found in the secondary vortex, remained unaffected by changes in wing sweep or angle of attack, in direct contrast to the positive components. The inclusion of the local wing geometry into a previously derived correlation parameter indicated that the circulation of growing leading edge vortex flows were similar at corresponding radii from the vortex axis. It was concluded that the flow over a delta wing, upstream of the breakdown regions and away from the apex and trailing edge regions, is conical. In addition, the dominating factors leading to the onset of breakdown are felt to be the local circulation of the vortex and the accompanying pressure field.

Visser, Kenneth D.↗
NASA NTRS1991

Nonlinear dynamics of global atmospheric and Earth-system processes

General Circulation Model (GCM) studies of the atmospheric response to change boundary conditions are discussed. Results are reported on an extensive series of numerical studies based on the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM) general circulation model. In these studies the authors determined the response to systematic changes in atmospheric CO2 ranging from 100 to 1000 ppm; to changes in the prescribed sea surface temperature (SST) in the Gulf of Mexico, such as occurred during the deglaciation phase of the last ice age; to changes in soil moisture over North America; and to changes in sea ice extent in the Southern Hemisphere. Study results show that the response of surface temperature and other variables is nearly logarithmic, with lower levels of CO2 implying greater sensitivity of the atmospheric state to changes in CO2. It was found that the surface temperature of the Gulf of Mexico exerts considerable control over the storm track and behavior of storm systems over the North Atlantic through its influence on evaporation and the source of latent heat. It was found that reductions in soil moisture can play a significant role in amplifying and maintaining North American drought, particularly when a negative soil moisture anomaly prevails late in the spring.

Saltzman, Barry↗
NASA NTRS1990

Determination of the thermal stability of fluids by tensimetry - Instrumentation and procedure

A computerized tensimeter and experimental procedure for determination of the thermal decomposition temperature (T sub d) of perfluoro alkylethers were developed and tested. Both the apparatus and the procedure are described in detail. Results of testing with bis(2-ethylhexyl) phthalate and trimethylolpropane triheptanoate demonstrate that the reciprocal of the decomposition temperature is a linear function of the logarithm of the gas volume/heated liquid volume ratio. The T sub d obtained for each compound at a gas volume/heated liquid volume ration of one was similar to the value previously reported using an isoteniscope technique. Results of testing with a polymer of hexafluoropropylene oxide demonstrate that this instrument and procedure can be used to determine the T sub d of perfluoro alkylethers.

Helmick, Larry S.↗
NASA NTRS1991

UGC galaxies stronger than 25 mJy at 4.85 GHz

UGC galaxies in the declination band +5 to +75 deg were identified by position coincidence with radio sources stronger than 25 mJy on the Green Bank 4.85 GHz sky maps. Candidate identifications were confirmed or rejected with the aid of published aperture-synthesis maps and new 4.86 GHz VLA maps having 15 or 18 arcsec resolution, resulting in a sample of 347 nearby radio galaxies plus five new quasar-galaxy pairs. The radio energy sources in UGC galaxies were classified as 'starbursts' or 'monsters' on the basis of their infrared-radio flux ratios, infrared spectral indices, and radio morphologies. The rms scatter in the logarithmic infrared-radio ratio q is not more than 0.16 for starburst galaxies selected at 4.85 GHz. Radio spectral indices were obtained for nearly all of the UGC galaxies, and S0 galaxies account for a disproportionate share of the compact flat-spectrum (alpha less than 0.5) radio sources. The extended radio jets and lobes produced by monsters are preferentially, but not exclusively, aligned within about 30 deg of the optical minor axes of their host galaxies. The tendency toward minor-axis ejection appears to be independent of radio-source size and is strongest for elliptical galaxies.

Condon, J. J.↗
NASA NTRS1991

The ionization structure of planetary nebulae. X - NGC 2392

Spectrophotometric observations of emission-line intensities over the spectral range 1400 to 7200 A were made in six positions in the planetary nebula NGC 2392. Standard equations used to correct for the existence of elements in other than the optically observable ionization stages give consistent results for the different positions that are in excellent agreement with abundances calculated using ultraviolet lines, and there is no evidence for any abundance gradient in the nebula. The logarithmic abundances agree well with determinations by Aller and Keyes.

Barker, Timothy↗
NASA NTRS1991

Ultraviolet variability of NGC 5548 - Dynamics of the continuum production region and geometry of the broad-line region

Data from the 1989-1990 IUE monitoring of the Seyfert galaxy NGC 5548 are used here to analyze the continuum variability properties of the galaxy and to derive the structure or its emission-line region. The mean shape of the UV continuum is well fit by an accretion disk model with a given black hole mass and an additional component required to reproduce the observed soft X-ray flux. The continuum fluctuation power spectrum is very steep, with most of the variance coming from about 1 yr time scales. The entire optical/UV continuum rises and falls almost simultaneously, so that the logarithmic slope of the power spectrum is nearly the same for all bands, but the flux at higher photon frequencies varies with larger amplitude. The emission-line material around the nucleus may best be described by a highly ionized inner zone of high and nearly constant pressure that stretches about 4-14 light-days from the center and an outer, more weakly ionized zone of considerably lower ionization at least 20-30 light-days out.

Krolik, J. H.↗
NASA NTRS1991

Temperature dependence of the anisotropy in magnetic relaxation in YBa2Cu3O(7-x) thin films

The relaxation of diamagnetic magnetization in the c-axis-aligned YBa2Cu3O(7-x) thin film is studied as a function of orientation and temperature in the range of 5-50 K at H = 0.2 T. The magnetization M(T,H) in the orientations H parallel to c and H perpendicular to c and at all the temperatures is found to decrease logarithmically with time t. The activation energy for the movement of flux lines U is found to be 30-110 meV in the range 5-50 K. For H parallel c, U increases continuously with T, whereas for H perpendicular c, U has two apparent maxima: at T = 10 K and T greater than 50 K. These results are discussed in terms of the thermally activated flux motion model.

Vitta, Satish↗
NASA NTRS1990

On the Goertler vortex instability mechanism at hypersonic speeds

The linear instability of the hypersonic boundary layer on a curved wall is considered. As a starting point real-gas effects are ignored and the viscosity of the fluid is taken to be related to the temperature either by Chapman's Law or by Sutherland's Law. It is shown that the flow is susceptible to Goertler vortices. If Chapman's Law is used the vortices are trapped in the logarithmically thin adjustment layer in which the temperature of the basic flow changes rapidly to its free stream value and the nonuniqueness of the neutral stability curve associated with incompressible Goertler vortices is shown to disappear at high Mach numbers if the appropriate 'fast' streamwise dependence of the instability is built into the disturbance flow structure. If, on the other hand, Sutherland's Law is used, the vortices are found to spread into an O(1) region and the concept of a unique neutral stability curve is not tenable because of the nonparallel effects. For both laws the leading order terms in the expansions of the Goertler number are independent of the wave number and are due to the curvature of the basic state.

Hall, P.↗