Search NASA⌕ Search

SEARCH · Search NASA

Results for “exponential”

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 343 records · Page 19

Long-time creep behavior of the niobium alloy C-103

The creep behavior of C-103 was studied as a function of stress, temperature, and grain size for test times to 19000 hr. Over the temperature range 827 to 1204 C and the stress range 6.89 to 138 MPa, only tertiary (accelerating) creep was observed. The creep strain epsilon can be related to time t by an exponential relation epsilon = epsilon(0) + K e raised to power (st) - 1), where epsilon (0) is initial creep strain, K is the tertiary creep strain parameter, and s is the tertiary creep rate parameter. The observed stress exponent 2.87 is similar to the three power law generally observed for secondary (linear) creep of Class I solid solutions. The apparent activation energy 374 kj/g mol is close to that observed for self diffusion of pure niobium. The initial tertiary creep rate was slightly faster for fine grained than for coarse-grained material. The strain parameter K can be expressed as a combination of power functions of stress and grain size and an exponential function of temperature. Strain time curves generated by using calculated values for K and s showed reasonable agreement with observed curves to strains of at least 4 percent. The time to 1 percent strain was related to stress, temperature, and grain size in a similar manner as the initial tertiary creep rate.

Titran, R. H.↗

Feasibility of quasi-random band model in evaluating atmospheric radiance

The use of the quasi-random band model in evaluating upwelling atmospheric radiation is investigated. The spectral transmittance and total band adsorptance are evaluated for selected molecular bands by using the line by line model, quasi-random band model, exponential sum fit method, and empirical correlations, and these are compared with the available experimental results. The atmospheric transmittance and upwelling radiance were calculated by using the line by line and quasi random band models and were compared with the results of an existing program called LOWTRAN. The results obtained by the exponential sum fit and empirical relations were not in good agreement with experimental results and their use cannot be justified for atmospheric studies. The line by line model was found to be the best model for atmospheric applications, but it is not practical because of high computational costs. The results of the quasi random band model compare well with the line by line and experimental results. The use of the quasi random band model is recommended for evaluation of the atmospheric radiation.

Tiwari, S. N.↗

Investigation of the effects of inlet shapes on fan noise radiation

The effect of inlet shape on forward radiated fan tone noise directivities was investigated under experimentally simplified zero flow conditions. Simulated fan tone noise was radiated to the far field through various shaped zero flow inlets. Baseline data were collected for the simplest baffled and unbaffled straight pipe inlets. These data compared well with prediction. The more general inlet shapes tested were the conical, circular, and exponential surfaces of revolution and an asymmetric inlet achieved by cutting a straight pipe inlet at an acute angle. Approximate theories were developed for these general shapes and some comparisons with data are presented. The conical and exponential shapes produced directivities that differed considerably from the baseline data while the circular shape produced directivities similar to the baseline data. The asymmetric inlet produced asymmetric directivities with significant reductions over the straight pipe data for some angles.

Clark, T. L.↗

Time-average fluxes of heavy ions at the geostationary orbit

Measurements of average proton, helium, carbon, and oxygen fluxes at 6.6 earth radii are reported. The data represent averages obtained on ATS 6 between June 15 and Oct. 3, 1974. The energy range covered was 0.36-1.1 MeV for protons and approximately 1-4 MeV for the heavier ions. The results indicate that above about 1 MeV the heavier ion fluxes dominate over the proton flux on the energy/ion scale. Using two different spectral dependencies to fit the data, the carbon to oxygen concentration ratio for energies above 1 MeV was found to be 0.43 for the power law spectrum and 0.44 for the exponential spectrum. Thus in either case the abundance ratio is consistent with the solar origin of the particles. Similarly, the helium to oxygen concentration ratio is found to be 0.17 for the power law spectrum and 0.28 for the exponential spectrum. This is inconsistent with the solar wind ratio, which is about 10. The results quoted above are based on a very small portion of the distribution function above 1 MeV.

Konradi, A.↗

The low-energy galactic cosmic ray carbon, nitrogen, and oxygen isotopic composition

It is found that C, N, and O elemental and isotopic ratios in the galactic cosmic rays measured near the earth with the IMP 7 telescope of the University of Chicago have had the values N/O = 0.25 + or 0.02; C/O = 1.06 + or - 0.03; C-13/C = 0.04-0.10; N-15/N = 0.47 + or - 0.06; and O-18/O less than or equal to 0.03. It is noted that these results are confirmed by IMP 8 measurements. The measurements are extrapolated back to the cosmic ray source using exponential and truncated exponential path length distributions whose parameters have been determined by fitting cosmic ray B/C and sub-Fe/Fe ratios measured previously.

Guzik, T. G.↗

Energetic particle spectra in finite shocks - The earth's bow shock

Particle acceleration and escape at the earth's bow shock wave are discussed in order to account for reported exponential fast particle spectra. A model is presented of particle acceleration in a finite two-dimensional shock perpendicular to the magnetic field, with particle parallel and perpendicular diffusion coefficients inversely proportional to each other. It is shown that the exponential particle energy per unit charge spectra observed by Ipavich et al. (1979) for the case of a radial solar wind magnetic field may be obtained if the fast particles escape the shock by means of resonant diffusion to unconnected field lines. The calculated e-folding value of the energy/charge ratio is found to be independent of the level of turbulence near the shock and in good agreement with observations. For the case of a nonradial solar wind magnetic field, the model is noted to predict that convection may be the dominant means of escape. It is also pointed out that the parallel and perpendicular diffusion coefficients may be measured indirectly at the bow shock.

Eichler, D.↗

Penetrating transmission zeros in the design of robust servomechanism systems

In the design of a robust servomechanism system, it is well known that the system cannot track a reference signal whose frequency coincides with the transmission zeros of the system. This paper proposes a new design method for overcoming this difficulty. The controller to be used employs a sampler and holding device with exponential decay. It is shown that the transmission zeros of the discretized system can be shifted by changing the rate of the exponential decay of the holding device. Thus, it is possible to design a robust controller for the discretized system to track any reference signal of given frequency, even if the given frequency coincides with the transmission zeros of the original continuous-time system.

Wang, S. H.↗

Current QSO statistics - Implications for the intergalactic medium

The results of numerous QSO surveys have been compiled and analyzed to form a single spatially averaged QSO ionizing function that is independent of evolution mode (number density or luminosity). An intergalactic medium (IGM) that satisfies the observational constraints may now have a density with respect to closure of approximately 0.1, which is substantially less than hitherto modeled. The aggregate of QSO data also indicate that if evolution is due to number density, then, when split into luminosity classes, an exponential in look-back time fits the data better than a power law, and the evolution rates increase roughly with absolute luminosity if analyzed by the exponential.

Sherman, R. D.↗

Thermodynamics and kinetics of the sulfation of porous calcium silicate

The sulfation of plasma sprayed calcium silicate in flowing SO2/air mixtures at 900 and 1000 C was investigated thermogravimetrically. Reaction products were analyzed using electron microprobe and X-ray diffraction analysis techniques, and results were compared with thermodynamic predictions. The percentage, by volume, of SO2 in air was varied between 0.036 and 10 percent. At 10 percent SO2 the weight gain curve displays a concave downward shoulder early in the sulfation process. An analytical model was developed which treats the initial process as one which decays exponentially with increasing time and the subsequent process as one which decays exponentially with increasing weight gain. At lower SO2 levels the initial rate is controlled by the reactant flow rate. At 1100 C and 0.036 percent SO2 there is no reaction, in agreement with thermodynamic predictions.

Miller, R. A.↗

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.↗

Stationary state model for normal metal tunnel junction phenomena

A model applicable to normal metal tunnel junctions is presented. This model, referred to herein as the stationary state model, is an extension of the extended basis function theory of Kleinman and Duke (1972). Under the assumption that elastic tunneling is the dominant transport mechanism under static bias, the theory has been extended to include the case where there is an ac component of bias potential, and the fluctuation spectrum has been derived. In this approach structure eigenstates are used as the basis, allowing observables to be evaluated without recourse to the perturbation theory inherent in the transfer Hamiltonian model. Comparison is made to the appropriate results of the first order transfer Hamiltonian model, and it is found that there is close but not always exact agreement to lowest order in the tunneling exponential. The stationary state model should be accurate with large barrier transmission, as it includes all orders of the tunneling exponential. The model as presented here should be applicable to normal metal tunnel junctions, where elastic tunneling is the dominant transport mechanism (under static bias), up to infrared excitation frequencies.

Whiteley, S. R.↗

Snowmelt runoff modeling in simulation and forecasting modes with the Martinec-Mango model

The Martinec-Rango snowmelt runoff model was applied to two watersheds in the Rio Grande basin, Colorado-the South Fork Rio Grande, a drainage encompassing 216 sq mi without reservoirs or diversions and the Rio Grande above Del Norte, a drainage encompassing 1,320 sq mi without major reservoirs. The model was successfully applied to both watersheds when run in a simulation mode for the period 1973-79. This period included both high and low runoff seasons. Central to the adaptation of the model to run in a forecast mode was the need to develop a technique to forecast the shape of the snow cover depletion curves between satellite data points. Four separate approaches were investigated-simple linear estimation, multiple regression, parabolic exponential, and type curve. Only the parabolic exponential and type curve methods were run on the South Fork and Rio Grande watersheds for the 1980 runoff season using satellite snow cover updates when available. Although reasonable forecasts were obtained in certain situations, neither method seemed ready for truly operational forecasts, possibly due to a large amount of estimated climatic data for one or two primary base stations during the 1980 season.

Shafer, B.↗

Hypersonic slender-wedge analysis with gradual change in angle of attack

The behavior of a narrow cross-section wedge wing moving at a high Mach number and subjected to an angle of attack changing exponentially with time is investigated. This type of wedge wing is commonly employed as a lifting surface in hypersonic vehicles. The time history of wall shear, heat transfer, displacement thickness, and viscous induced pressure are determined. Results show that for the same change in angle of attack, the flow attains the final steady state much faster when the change is exponential than when the change is made impulsively. In addition, the unsteady character of the flow is primarily confined to the initial stages of the change in the angle of attack.

Gupta, R. N.↗

Ultraviolet photometry of dwarf novae in outburst

Broad-band photometry from the Astronomical Netherlands Satellite of five dwarf novae at 1550, 1800, 2200, 2500, and 3300 A is presented. EM Cyg in standstill exhibits a flux excess at 3300 A. The lack of a strong extinction feature at 2200 A is seen as suggesting that the reddening is small toward all five systems. Using an independent estimate of the distances, mass flux rates are derived by fitting steady-state, optically thick accretion disk models to the observed UV luminosity. The rate is found to be 3 x 10 to the 17th g/s for Z Cam and EM Cyg in outburst and a factor of 3 smaller of Z Cam in standstill. The models, however, do not reproduce the slope of the Balmer continuum. Of special interest are the observations of outburst rises of SS Aur, SU UMa, and EM Cyg. SS Aur exhibits an exponential increase at a rate of 3.5 mag in 0.5 d. The outburst in EM Cyg also reveals an exponential rise, but at a rate of only 1.2 mag per day.

Wu, C.-C.↗

Thermally induced spin rate ripple on spacecraft with long radial appendages

A thermally induced spin rate ripple hypothesis is proposed to explain the spin rate anomaly observed on ISEE-B. It involves the two radial 14.5 meter beryllium copper tape ribbons going in and out of the spacecraft hub shadow. A thermal lag time constant is applied to the thermally induced ribbon displacements which perturb the spin rate. It is inferred that the averaged thermally induced ribbon displacements are coupled to the ribbon angular motion. A possible exponential build up of the inplane motion of the ribbon which in turn causes the spin rate ripple, ultimately limited by damping in the ribbon and spacecraft is shown. It is indicated that qualitative increase in the oscillation period and the thermal lag is fundamental for the period increase. found that numerical parameter values required to agree with in orbit initial exponential build up are reasonable; those required for the ripple period are somewhat extreme.

Fedor, J. V.↗

Software reliability: Additional investigations into modeling with replicated experiments

The effects of programmer experience level, different program usage distributions, and programming languages are explored. All these factors affect performance, and some tentative relational hypotheses are presented. An analytic framework for replicated and non-replicated (traditional) software experiments is presented. A method of obtaining an upper bound on the error rate of the next error is proposed. The method was validated empirically by comparing forecasts with actual data. In all 14 cases the bound exceeded the observed parameter, albeit somewhat conservatively. Two other forecasting methods are proposed and compared to observed results. Although demonstrated relative to this framework that stages are neither independent nor exponentially distributed, empirical estimates show that the exponential assumption is nearly valid for all but the extreme tails of the distribution. Except for the dependence in the stage probabilities, Cox's model approximates to a degree what is being observed.

Nagel, P. M.↗

Discrete approximation methods for parameter identification in delay systems

Approximation schemes for parameter identification problems in which the governing state equation is a linear functional differential equation of retarded type are constructed. The basis of the schemes is the replacement of the parameter identification problem having an infinite dimensional state equation by a sequence of approximating parameter identification problems in which the states are given by finite dimensional discrete difference equations. The difference equations are constructed using linear semigroup theory and rational function approximations to the exponential. Sufficient conditions are given for the convergence of solutions to the approximating problems, which can be obtained using conventional methods, to solutions to the original parameter identification problem. Finite difference and spline based schemes using Paderational function approximations to the exponential are constructed, and shown to satisfy the sufficient conditions for convergence. A discussion and analysis of numerical results obtained through the application of the schemes to several examples is included.

Rosen, I. G.↗

Atmospheric attenuation for correlated satellite communication ground sites

Link margin estimates are calculated for 30/20 GHz satellite communication systems employing closely-spaced (4 to 100 km) 'dual diversity' switched ground sites. The link margin estimates are based on a new analysis in which the bivariate rain attenuation density function for two correlated ground sites is modelled by an exponential density function. The results of the exponential density function analysis enable derivation of a direct relation between rain margin estimates and probability of exceedance (link availability). Margins typically in the range 2 to 12 dB are calculated for various ground site separations and summarized for seven city locations and five satellite orbit positions over the U.S. The results can be easily extended to other EHF satellite frequencies and other locations.

Christopher, P.↗