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NASA NTRS1991

Asymptotic behavior of curvature of surface elements in isotropic turbulence

The asymptotic behavior of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. Several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times, the (first five) moments of the logarithm of characteristic curvature and shape factor asymptote to values that are independent of the initial curvature or shape. This evidence strongly suggests that the asymptotic pdf's of the curvature and shape of material elements are stationary and independent of initial conditions. Irrespective of initial curvature or shape, the asymptotic shape of a material surface is cylindrical with a high probability.

Girimaji, S. S.↗

NASA NTRS1991

The semi-infinite strip problem in the mechanics of composite materials

Many problems, ranging from interface-fiber fracture to determining the strength of fiber-matrix interfaces in composites, can be greatly assisted by a complete understanding of the boundary value problem of a semi-infinite strip. The specific boundary value problem of a semi-infinite strip with symmetric tractions on the transverse edges and normal loads on the end is investigated in the present study. The nature of the singular behavior in the slope of the end vertical displacement at the corner points is found. An asymptotic analysis of the solution shows that, depending on the nature of the applied stresses in the vicinity of the corner points, the singularity in the slope of the end vertical displacement may either be a power or logarithmic type, both, or not exist at all. Illustrative examples, for which exact or numerical results are known, are given. Numerical procedures are also given. The direct application of the results of the paper are illustrated for several problems in the mechanics of composite materials.

Kaw, Autar K.↗

NASA NTRS1990

Three-dimensional potential flows from functions of a 3D complex variable

Potential, or ideal, flow velocities can be found from the gradient of an harmonic function. An ordinary complex valued analytic function can be written as the sum of two real valued functions, both of which are harmonic. Thus, 2D complex valued functions serve as a source of functions that describe two-dimensional potential flows. However, this use of complex variables has been limited to two-dimensions. Recently, a new system of three-dimensional complex variables has been developed at the NASA Ames Research Center. As a step toward application of this theory to the analysis of 3D potential flow, several functions of a three-dimensional complex variable have been investigated. The results for two such functions, the 3D exponential and 3D logarithm, are presented in this paper. Potential flows found from these functions are investigated. Important characteristics of these flows fields are noted.

Kelly, Patrick↗

NASA NTRS1991

Spray characterization using planar laser imaging

Results on the application of a planar polarization ratio technique to spray and soot particle measurements are presented and compared with the phase Doppler particle analyzer (PDPA) measurements. With the assumption of a logarithmic normal distribution, reasonable agreement between the two techniques were obtained, demonstrating the capability of the planar polarization ratio technique to differentiate regions containing soot particles from those containing droplets. A comparison of quantitative measurement capabilities of the two techniques showed that the planar polarization ratio technique can be applied to complicated combustion environments for at least semiquantitative investigation of sprays.

Pal, S.↗

NASA NTRS1991

Statistical properties of shock-accelerated ions in the outer heliosphere

Reported here are statistical studied of interplanetary protons (about 0.5-1.5 MeV) as measured by the Voyager 2 spacecraft in the outer heliosphere between about 1 and 22 AU. The acceleration processes which produce the fluctuations in intensity of the protons throughout the interval studied are caused by solar flare-generated shock waves and corotating shock structures in the solar wind. It is found that the proton count rates can be represented by a lognormal distribution, independent of the phase of the solar cycle in which the measurements were made. Power spectra of the logarithm of the counts show that for frequencies in the range of about 0.02-0.5 cycles per day, the spectra can be characterized as about f exp -2. At lower frequencies, the spectra turn over and flatten. Over the entire frequency range studied, about 0.002-0.5 cycles per day, the spectra are therefore nonfractal. The rollover in the spectra at about 100 days probably represents the reorganization time for solar wind streams within the coronal source at the sun.

Lanzeroti, L. J.↗

NASA NTRS1992

Software For Generating Graphs And Charts

Common Graphics Library (CGL) computer program designed to enable users to generate graphs and charts of quality sufficient for publication or optical projection. Quickly and easily generates linear, logarithmic, bar, pie, and composite charts. Features of linear charts include automatic scaling, increasing or decreasing numerical axes, and character axes. Features of pie charts include segment labels, exploded segments, and chart keys. One of general features, horizontal or vertical orientation of figures. Written in ANSI FORTRAN 77.

Hammond, Dana P.↗

NASA NTRS1990

Planar Laser Imaging of Sprays for Liquid Rocket Studies

A planar laser imaging technique which incorporates an optical polarization ratio technique for droplet size measurement was studied. A series of pressure atomized water sprays were studied with this technique and compared with measurements obtained using a Phase Doppler Particle Analyzer. In particular, the effects of assuming a logarithmic normal distribution function for the droplet size distribution within a spray was evaluated. Reasonable agreement between the instrument was obtained for the geometric mean diameter of the droplet distribution. However, comparisons based on the Sauter mean diameter show larger discrepancies, essentially because of uncertainties in the appropriate standard deviation to be applied for the polarization ratio technique. Comparisons were also made between single laser pulse (temporally resolved) measurements with multiple laser pulse visualizations of the spray.

Lee, W.↗

NASA NTRS1991

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

Presented here is a preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. The authors show that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Ashrafi, S.↗

NASA NTRS1991

Magnetic relaxation in the 110 K superconducting phase in Bi-Sr-Ca-Cu-O thin films

We have investigated the time dependence of remnant moment decay in a highly oriented, nearly single high T(sub c) phase Bi-Sr-Ca-Cu-O thin film. A strictly logarithmic time dependence was observed over a 20 K temperature range for observation intervals of 2000 seconds. The normalized decay rate exhibits a peak around 14 K and has a relatively weak magnetic field dependence. These data are then compared with existing data on the YBCO and Eu-based superconductors.

Tanaka, Atsushi↗

NASA NTRS1991

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

A preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity is presented. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. It is shown that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Ashrafi, S.↗

NASA NTRS1992

Measuring the Weibull modulus of microscope slides

The objectives are that students will understand why a three-point bending test is used for ceramic specimens, learn how Weibull statistics are used to measure the strength of brittle materials, and appreciate the amount of variation in the strength of brittle materials with low Weibull modulus. They will understand how the modulus of rupture is used to represent the strength of specimens in a three-point bend test. In addition, students will learn that a logarithmic transformation can be used to convert an exponent into the slope of a straight line. The experimental procedures are explained.

Sorensen, Carl D.↗

NASA NTRS1992

Lidar analysis techniques for use in the atmospheric boundary layer

There is a growing body of observational and theoretical evidence which suggests that local climate characteristics are associated with variations in the earth's surface. The link between surface variability and local-scale processes must be made if we are to improve our understanding of the feedback mechanisms involved in surface-atmosphere dynamics. However, to understand these interactions, the surface-atmosphere interface must be studied as a large-scale spatial system. Lidars are ideal tools to study the spatial properties of the atmosphere. The described techniques were developed for use with the Los Alamos Water Raman-Lidar, but are applicable to many other types of lidar. The methodology of the analysis of lidar data is summarized in order to determine meteorological parameters in the atmospheric boundary layer. The techniques are not exhaustive but are intended to show the depth and breadth of the information which can be obtained from lidars. Two methods for the computation of water-vapor fluxes were developed. The first uses the fact that the water vapor concentration in the vertical direction follows a logarithmic profile when corrected for atmospheric stability. The second method involves using inertial dissipation techniques in which lidar-derived spatial and temporal power spectra are used to determine the flux.

Eichinger, William E.↗

NASA NTRS1991

Interstellar gas phase abundance of carbon, oxygen, nitrogen, copper, gallium, germanium, and krypton toward Zeta Ophiuchi

An analysis of weak (less than 10 mA) UV interstellar absorption line data obtained for the line of sight to the O9.5 IV star Zeta Oph is presented. Measurements of weak semiforbidden lines of N I, O I, Cu II, and a new UV detection of Na I are reported along with a small upper limit for C II. Interstellar detections of Ga II, Ge II, and Kr I are also presented. Ga, Ge, and Kr represent the heaviest elements detected in the ISM. A comparison of the derived column densities to cosmic abundances shows Ga to be depleted by about -1.2 dex while Ge is overabundant by +0.2 dex. Assuming Kr to be undepleted, a logarithmic cosmic abundance of Kr/H = 2.95 is obtained on the scale where H = 12.00.

Cardelli, Jason A.↗

NASA NTRS1992

The three-dimensional turbulent boundary layer near a plane of symmetry

The asymptotic structure of the three-dimensional turbulent boundary layer near a plane of symmetry is considered in the limit of large Reynolds number. A self-consistent two-layer structure is shown to exist wherein the streamwise velocity is brought to rest through an outer defect layer and an inner wall layer in a manner similar to that in two-dimensional boundary layers. The cross-stream velocity distribution is more complex and two terms in the asymptotic expansion are required to yield a complete profile which is shown to exhibit a logarithmic region. The flow in the inner wall layer is demonstrated to be collateral to leading order; pressure-gradient effects are formally of higher order but can cause the velocity profile to skew substantially near the wall at the large but finite Reynolds numbers encountered in practice. The governing set of ordinary differential equations describing a self-similar flow is derived. The calculated numerical solutions of these equations are matched asymptotically to an inner wall-layer solution and the results show trends that are consistent with experimental observations.

Degani, A. T.↗

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 NTRS1992

Estimation of excitation energy of diatomic molecules in expanding nonequilibrium flows

The energy contained in the highly excited vibrational and rotational states in a diatomic gas in a thermochemical nonequilibrium state during expansion is estimated. The estimation is made on the assumption that the populations of the vibrational and rotational states, when normalized by their respective equilibrium values, are describable by simple functions containing no more than four arbitrary parameters. A cubic polynomial, a logarithmic-cubic polynomial, and a bimodal step function are used for this purpose. The four parameters are determined by imposing conditions known at the ground state and the dissociation limit and the mass conservation law. The energy in excess of that accounted for by assuming a Boltzmann distribution of these states, defined here as excess excitation energy, is calculated for N2, O2, NO, CO, OH, and H2. A calculation made for a typical nozzle flow shows that the excess energy may reach 6 percent of the total enthalpy of the flow, and that the flow velocity may decrease by as much as 4 percent due to the nonequilibrium excitation phenomenon.

Park, Chul↗

NASA NTRS1991

Pressure dependence of the melting temperature of solids - Rare-gas solids

A method presented by Schlosser et al. (1989) for analyzing the pressure dependence of experimental melting-temperature data is applied to rare-gas solids. The plots of the logarithm of the reduced melting temperature vs that of the reduced pressure are straight lines in the absence of phase transitions. The plots of the reduced melting temperatures for Ar, Kr, and Xe are shown to be approximately straight lines.

Schlosser, Herbert↗

NASA NTRS1991

Unsupervised segmentation of polarimetric SAR data using the covariance matrix

An unsupervised selection of polarimetric features useful for the segmentation and analysis of polarimetric synthetic aperture radar (SAR) data is presented. The technique is based on multidimensional clustering of the parameters composing the polarimetric covariance matrix of the data. Clustering is performed on the logarithm of these quantities. Once the polarimetric cluster centers have been determined, segmentation of the polarimetric data into regions is performed using a maximum likelihood polarimetric classifier. Segmentation maps are further improved using a Markov random field to describe the statistics of the regions and computing the maximum of the product of the local conditional densities. Examples with real polarimetric SAR imagery are given to illustrate the potential of this method.

Rignot, Eric↗