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.

SourceResearch connectionFrom yearThrough year

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

At least 145 records · Page 8

All sources NASA NTRS DOE OSTI

NASA NTRS1987

Atlas of Absorption Lines from 0 to 17900 Cm (sup)-1

Plots of logarithm (base 10) of absorption line strength versus wavenumber from 0 to 17900/cm(sup)-1 are shown for the 28 atmospheric gases (H2O, CO2, O3, N2O, CO, CH4, O2, NO, SO2, NO2, NH3, HNO3, OH, HF, HCl, HBr, HI, ClO, OCS, H2CO, HOCl, N2, HCN, CH3Cl, H2O2, C2H2, C2H6, PH3), which appear in the 1986 Air Force Geophysics Laboratory high-resolution transmission molecular absorption data base (HITRAN) compilation, and for O(P-3), O-18 isotopic ozone, and HO2 from the 1984 JPL compilation in the 0- to 200/cm(sup)-1 region, and infrared solar CO lines at 4500 K. Also shown are plots of logarithm (base 10) of approximate infrared absorption cross sections of 11 heavy molecules versus wavenumber. The cross-section data cover 700 to 1800/cm(sup)-1 and are included as a separate data file in the 1986 HITRAN database.

Park, J. H.↗

NASA NTRS1986

Numerical study of sink-flow boundary layers

Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 x 10 to the -6th and 3.0 x 10 to the -6th, are presented. The three-dimensional, time-dependent Navier-Stokes equations are solved numerically, using a spectral method, with about one million degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones and Launder (1972) is observed. The two effects of the favorable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of R(theta) for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 x 10 to the -6th, corresponding to a Reynolds number R(theta) of about 330.

Spalart, Philippe R.↗

NASA NTRS1987

Comparing barrier algorithms

A barrier is a method for synchronizing a large number of concurrent computer processes. After considering some basic synchronization mechanisms, a collection of barrier algorithms with either linear or logarithmic depth are presented. A graphical model is described that profiles the execution of the barriers and other parallel programming constructs. This model shows how the interaction between the barrier algorithms and the work that they synchronize can impact their performance. One result is that logarithmic tree structured barriers show good performance when synchronizing fixed length work, while linear self-scheduled barriers show better performance when synchronizing fixed length work with an imbedded critical section. The linear barriers are better able to exploit the process skew associated with critical sections. Timing experiments, performed on an eighteen processor Flex/32 shared memory multiprocessor, that support these conclusions are detailed.

Arenstorf, Norbert S.↗

NASA NTRS1986

Numerical simulation of boundary layers. Part 3: Turbulence and relaminarization in sink flows

Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 and 3.0 x 10 to the -6 power, are presented. The three-dimensional, time-dependent Navier-Stokes equations are solved numerically using a spectral method, with about 10 to the -6 degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones and Launder is observed. Two effects of the favorable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At very low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of the Reynolds number for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 x 10 to the -6 power, corresponding to a Reynolds number, based on momentum thickness, of about 330.

Spalart, Philippe R.↗

NASA NTRS1988

Experimental results on atomic oxygen corrosion of silver

The results of an experimental study of the reaction kinetics of silver with atomic oxygen in 10 degree increments over the temperature range of 0 to 70 C is reported. The silver specimens, of the order of 10,000 A in thickness, were prepared by thermal evaporation onto 3 inch diameter polished silicon wafers. There were later sliced into pieces having surface areas of the order of 1/4 to 1/2 square inch. Atomic oxygen was generated by a gas discharge in a commercial plasmod asher operating in the megahertz frequency range. The sample temperature within the chamber was controlled by means of a thermoelectric unit. Exposure of the silver specimens to atomic oxygen was incremental, with oxide film thickness measurements being carried out between exposures by means of an automated ellipsometer. For the early growth phase, the data can be described satisfactorily by a logarithmic growth law: the oxide film thickness increases as the logarithm of the exposure time. Furthermore, the oxidation process is thermally activated, the rate increasing with increasing temperature. However, the empirical activation energy parameter deduced from Arrhenius plots is quite low, being of the order of 0.1 eV.

Fromhold, Albert T.↗

NASA NTRS1989

Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data

The values of the Normalized Radar Backscattering Cross Section (NRCS), sigma (o), obtained by a scatterometer are random variables whose variance is a known function of the expected value. The probability density function can be obtained from the normal distribution. Models for the expected value obtain it as a function of the properties of the waves on the ocean and the winds that generated the waves. Point estimates of the expected value were found from various statistics given the parameters that define the probability density function for each value. Random intervals were derived with a preassigned probability of containing that value. A statistical test to determine whether or not successive values of sigma (o) are truly independent was derived. The maximum likelihood estimates for wind speed and direction were found, given a model for backscatter as a function of the properties of the waves on the ocean. These estimates are biased as a result of the terms in the equation that involve natural logarithms, and calculations of the point estimates of the maximum likelihood values are used to show that the contributions of the logarithmic terms are negligible and that the terms can be omitted.

Pierson, Willard J., Jr.↗

NASA NTRS1989

Comparing barrier algorithms

Arenstorf, Norbert S.↗

NASA NTRS1989

Pressure dependence of the melting temperature of metals

A new method for the analysis of the experimental data for the pressure dependence of the melting temperature of metals is presented. The method combines Lindemann's law, the Debye model, and a first-order equation of state with the experimental observation that the Grueneisen parameter divided by the volume is constant. It is observed that, based on these assumptions, in the absence of phase transitions, plots of the logarithm of the normalized melting temperature versus the logarithm of the normalized pressure are straight lines. It is found that the normalized-melting--temperature versus normalized-pressure curves accurately satisfy the linear relationship for Al, Ag, Au, Cs, Cu, K, Na, Pt, and Rb. In addition, this technique provides a sensitive tool for detecting phase transitions.

Schlosser, Herbert↗

NASA NTRS1937

A simplified application of the method of operators to the calculation of disturbed motions of an airplane

A simplified treatment of the application of Heaviside's operational methods to problems of airplane dynamics is given. Certain graphical methods and logarithmic formulas that lessen the amount of computation involved are explained. The problem representing a gust disturbance or control manipulation is taken up and it is pointed out that in certain cases arbitrary control manipulations may be dealt with as though they imposed specific constraints on the airplane, thus avoiding the necessity of any integration. The application of the calculations described in the text is illustrated by several examples chosen to show the use of the methods and the practicability of the graphical and logarithmic computations described.

Jones, Robert T↗

NASA NTRS1994

Evaluation of bio-optical algorithms to remotely sense marine primary production from space

In situ bio-optical measurements from several oceanographic campaigns were analyzed to derive a direct relationship between water column primary production P (sub t) ocean color as expressed by the ratio of reflectances R (sub 1) at 440 nm and R (sub 3) at 550 nm and photosynthetically available radiation (PAR). The study is restricted to the Morel case I waters for which the following algorithm is proposed: log (P(sub f)) = -4.286 - 1.390 log (R(sub 1)/R(sub3)) + 0.621 log (PAR), with P(sub t) in g C m(exp -2)/d and PAR in J m(exp -2)/d. Using this algorithm the rms accuracy of primary production estimate is 0.17 on a logarithmic scale, i.e., a factor of 1.5. Using spectral reflectance measurements in the entire visible spectral range, the central wavelength, spectral bandwidth, and radiometric noise level requirements are investigated for the channels to be used by an ocean color space mission dedicated to estimating global marine primary production and the associated carbon fluxes. Nearly all the useful information is provided by two channels centered at 440 nm and 550 nm, but the accuracy of primary production estimate appears weakly sensitive to spectral bandwidth, which, consequently, may be enlarged by several tens of nanometers. The sensitivity to radiometric noise, on the contrary, is strong, and a noise equivalent reflectance of 0.005 degraded the accuracy on the primary production estimate by a factor 2 (0.14-0.25 on a logarithmic scale). The results should be applicable to evaluating the primary production of oligotrophic and mesotrophic waters, which constitute most of the open ocean.

Berthelot, Beatrice↗

NASA NTRS1995

Gas phase abundances and conditions along the sight line to the low-halo, inner galaxy star HD 167756

We present high-resolution (3.5 km/s) Goddard High Resolution Spectrograph (GHRS) measurements of the Mg II, Si II, Cr II, Fe II, and Zn II lines toward HD 167756, a low-latitude halo star at a distance of 4 kpc in the direction l = 351.5 deg, b = -12.3 and at a Galactic altitude of z = -0.85 kpc. Supplemental Na I, Ca II, and H I data are also presented for comparison with the UV lines. Our analysis centers on converting the observed absoprtion-line data into measures of the apparent column density per unit velocity. N(sub a)(v), over the velocity range -25 less than or = v(sub lsr) less than 30 km/s for each species observed. We use these N(sub a)(v) profiles to construct logarithmic abundance ratios of Mg II, Si II, Cr II, Fe II, and Ca II relative to Zn II, normalized to solar abundances, as a function of velocity. Compared to Zn, these species show an underabundance relative to their solar values, with the largest underabundances occurring in the v(sub lsr) approximately equals 5 km/s component(s), for which we find logarithmic abundances A(sub Si/Zn) greater than -0.38, A(Mg/Zn) = -0.82, A(sub Cr/Zn) = -1.18, and A(sub Fe/Zn) greater than 1.40 dex. We show that ionization effects, abundance gradients, or intrinsic abundance variability cannot be significant sources for the underabundances observed. The most likely explanation is gas phase depletion of elements onto dust grains. Comparisons with the gas phase abundances along other diffuse, warm gas sight lines, like the halo sight line to HD 93521, support this interpretation as do the derived physical properties of the sight line.

Cardelli, Jason A.↗

NASA NTRS1993

New limb-darkening coefficients for modeling binary star light curves

We present monochromatic, passband-specific, and bolometric limb-darkening coefficients for a linear as well as nonlinear logarithmic and square root limb-darkening laws. These coefficients, including the bolometric ones, are needed when modeling binary star light curves with the latest version of the Wilson-Devinney light curve progam. We base our calculations on the most recent ATLAS stellar atmosphere models for solar chemical composition stars with a wide range of effective temperatures and surface gravitites. We examine how well various limb-darkening approximations represent the variation of the emerging specific intensity across a stellar surface as computed according to the model. For binary star light curve modeling purposes, we propose the use of a logarithmic or a square root law. We design our tables in such a manner that the relative quality of either law with respect to another can be easily compared. Since the computation of bolometric limb-darkening coefficients first requires monochromatic coefficients, we also offer tables of these coefficients (at 1221 wavelength values between 9.09 nm and 160 micrometer) and tables of passband-specific coefficients for commonly used photometric filters.

Van Hamme, W.↗

NASA NTRS1995

Large-eddy simulations with wall models

The near-wall viscous and buffer regions of wall-bounded flows generally require a large expenditure of computational resources to be resolved adequately, even in large-eddy simulation (LES). Often as much as 50% of the grid points in a computational domain are devoted to these regions. The dense grids that this implies also generally require small time steps for numerical stability and/or accuracy. It is commonly assumed that the inner wall layers are near equilibrium, so that the standard logarithmic law can be applied as the boundary condition for the wall stress well away from the wall, for example, in the logarithmic region, obviating the need to expend large amounts of grid points and computational time in this region. This approach is commonly employed in LES of planetary boundary layers, and it has also been used for some simple engineering flows. In order to calculate accurately a wall-bounded flow with coarse wall resolution, one requires the wall stress as a boundary condition. The goal of this work is to determine the extent to which equilibrium and boundary layer assumptions are valid in the near-wall regions, to develop models for the inner layer based on such assumptions, and to test these modeling ideas in some relatively simple flows with different pressure gradients, such as channel flow and flow over a backward-facing step. Ultimately, models that perform adequately in these situations will be applied to more complex flow configurations, such as an airfoil.

Cabot, W.↗

NASA NTRS1995

High-temperature oxidation behavior of reaction-formed silicon carbide ceramics

The oxidation behavior of reaction-formed silicon carbide (RFSC) ceramics was investigated in the temperature range of 1100 to 1400 C. The oxidation weight change was recorded by TGA; the oxidized materials were examined by light and electron microscopy, and the oxidation product by x-ray diffraction analysis (XRD). The materials exhibited initial weight loss, followed by passive weight gain (with enhanced parabolic rates, k(sub p)), and ending with a negative (logarithmic) deviation from the parabolic law. The weight loss arose from the oxidation of residual carbon, and the enhanced k(sub p) values from internal oxidation and the oxidation of residual silicon, while the logarithmic kinetics is thought to have resulted from crystallization of the oxide. The presence of a small amount of MoSi, in the RFSC material caused a further increase in the oxidation rate. The only solid oxidation product for all temperatures studied was silica.

Ogbuji, Linus U. J. T.↗

NASA NTRS1996

Symmetries in Turbulent Boundary Layer Flows

The objective is the development of a new theory which enables the algorithmic computation of all self-similar mean velocity profiles. The theory is based on Liegroup analysis and unifies a large set of self-similar solutions for the mean velocity of stationary parallel turbulent shear flows. The results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the middle of a Couette flow and in the middle of a rotating channel flow, and a new exponential mean velocity profile not previously reported. Experimental results taken in the outer parts of a high Reynolds number flat-plate boundary layer, strongly support the exponential profile. From experimental as well as from DNS data of a turbulent channel flow the algebraic scaling law could be confirmed in both the center region and in the near wall region. In the case of the logarithmic law of the wall, the scaling with the wall distance arises as a result of the analysis and has not been assumed in the derivation. The crucial part of the derivation of all the different mean velocity profiles is to consider the invariance of the equation for the velocity fluctuations at the same time as the invariance of the equation for the velocity product equations. The latter is the dyad product of the velocity fluctuations with the equation for the velocity fluctuations. It has been proven that all the invariant solutions are also consistent with similarity of all velocity moment equations up to any arbitrary order.

Oberlack, M.↗

NASA NTRS1999

Double Resonances and Spectral Scaling in the Weak Turbulence Theory of Rotating and Stratified Turbulence

In rotating turbulence, stably stratified turbulence, and in rotating stratified turbulence, heuristic arguments concerning the turbulent time scale suggest that the inertial range energy spectrum scales as k(exp -2). From the viewpoint of weak turbulence theory, there are three possibilities which might invalidate these arguments: four-wave interactions could dominate three-wave interactions leading to a modified inertial range energy balance, double resonances could alter the time scale, and the energy flux integral might not converge. It is shown that although double resonances exist in all of these problems, they do not influence overall energy transfer. However, the resonance conditions cause the flux integral for rotating turbulence to diverge logarithmically when evaluated for a k(exp -2) energy spectrum; therefore, this spectrum requires logarithmic corrections. Finally, the role of four-wave interactions is briefly discussed.

Rubinstein, Robert↗

NASA NTRS1994

Nonlinear Optical Image Processing with Bacteriorhodopsin Films

The transmission properties of some bacteriorhodopsin film spatial light modulators are uniquely suited to allow nonlinear optical image processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude transmission feature of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. The bacteriorhodopsin film displays the logarithmic amplitude response for write beam intensities spanning a dynamic range greater than 2.0 orders of magnitude. We present experimental results demonstrating the principle and capability for several different image and noise situations, including deterministic noise and speckle. Using the bacteriorhodopsin film, we successfully filter out image noise from the transformed image that cannot be removed from the original image.

Downie, John D.↗

NASA NTRS2002

Optimal Design of Functionally Graded Metallic Foam Insulations

The focus of our work has been on developing an insight into the physics that govern the optimum design of thermal insulation for use in thermal protection systems of launch vehicle. Of particular interest was to obtain optimality criteria for designing foam insulations that have density (or porosity) distributions through the thickness for optimum thermal performance. We investigate the optimum design of functionally graded thermal insulation for steady state heat transfer through the foam. We showed that the heat transfer in the foam has competing modes, of radiation and conduction. The problem assumed a fixed inside temperature of 400 K and varied the aerodynamic surface heating on the outside surface from 0.2 to 1.0 MW/sq m. The thermal insulation develops a high temperature gradient through the thickness. Investigation of the model developed for heat conduction in foams showed that at high temperatures (as on outside wall) intracellular radiation dominates the heat transfer in the foam. Minimizing radiation requires reducing the pore size, which increases the density of the foam. At low temperatures (as on the inside wall), intracellular conduction (of the metal and air) dominates the heat transfer. Minimizing conduction requires increasing the pore size. This indicated that for every temperature there was an optimum value of density that minimized the heat transfer coefficient. Two optimization studies were performed. One was to minimize the heat transmitted though a fixed thickness insulation by varying density profiles. The second was to obtain the minimum mass insulation for specified thickness. Analytical optimality criteria were derived for the cases considered. The optimality condition for minimum heat transfer required that at each temperature we find the density that minimizes the heat transfer coefficient. Once a relationship between the optimum heat transfer coefficient and the temperature was found, the design problem reduced to the solution of a simple nonlinear differential equation. Preliminary results of this work were presented at the American Society of Composites meeting, and the final version was submitted for publication in the AIAA Journal. In addition to minimizing the transmitted heat, we investigated the optimum design for minimum weight given an acceptable level of heat transmission through the insulation. The optimality criterion developed was different from that obtained for minimizing beat transfer coefficient. For minimum mass design, we had to find for a given temperature the optimum density, which minimized the logarithmic derivative of the insulation thermal conductivity with respect to its density. The logarithmic derivative is defined as the ratio of relative change in the dependent response (thermal conductivity) to the relative change in the independent variable (density). The results have been documented as a conference paper that will be presented at the upcoming AIAA.

Haftka, Raphael T.↗