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.

SourceResearch connectionFrom yearThrough year

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

At least 325 records · Page 18

All sources NASA NTRS DOE OSTI

NASA NTRS1974

Multiple eigenvalues of sound-absorbing circular and annular ducts

Eigenvalue equations of the form D(lambda) = 0 are studied for acoustic modes in circular and annular ducts without flow. The ducts have locally reacting walls with arbitrary wall admittance. It is shown that circular ducts may have double eigenvalues, or wall admittances where both D(lambda) and D prime (lambda) are zero. These double eigenvalues are formed by the coalescence of the lowest-order eigenfunction with some higher-order eigenfunction. The eigenfunctions, or acoustic modes, associated with the double eigenvalues are found to be orthogonal to themselves so that the standard expansion formula for the acoustic field, which is obtained from a separation-of-variables analysis, is invalid. An alternate expansion formula for the acoustic field is derived. This alternate formula shows that the coalesced acoustic mode is linearly amplified by the transmission distance and exponentially attenuated at the expected rate. The expansion formula also reveals a new eigenfunction, or acoustic mode, which is exponentially attenuated at the same rate as the coalesced eigenfunction.

Zorumski, W. E.↗

NASA NTRS1974

Design data for radars based on 13.9 GHz Skylab scattering coefficient measurements

The author has identified the following significant results. Measurements made at 13.9 GHz with the radar scatterometer on Skylab have been combined to produce median curves of the variation of scattering coefficient with angle of incidence out to 45 deg. Because of the large number of observations, and the large area averaged for each measured data point, these curves may be used as a new design base for radars. A reasonably good fit at larger angles is obtained using the theoretical expression based on an exponential height correlation function and also using Lambert's law. For angles under 10 deg, a different fit based on the exponential correlation function, and a fit based on geometric optics expressions are both reasonably valid.

Moore, R. K.↗

NASA NTRS1975

Almost periodic solutions to difference equations

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

Bayliss, A.↗

NASA NTRS1975

Turbulence in a gaseous hydrogen-liquid oxygen rocket combustion chamber

The intensity of turbulence and the Lagrangian correlation coefficient for a LOX-GH2 rocket combustion chamber was determined from experimental measurements of tracer gas diffusion. A combination of Taylor's turbulent diffusion theory and a numerical method for solving the conservation equations of fluid mechanics was used to calculate these quantities. Taylor's theory was extended to consider the inhomogeneity of the turbulence field in the axial direction of the combustion chamber, and an exponential function was used to represent the Lagrangian correlation coefficient. The results indicate that the value of the intensity of turbulence reaches a maximum of 14% at a location about 7" downstream from the injector. The Lagrangian correlation coefficient associated with this value is given by the above exponential expression where alpha = 10,000/sec.

Lebas, J.↗

NASA NTRS1976

All-sky monitor observations of the decay of A0620-00 (Nova monocerotis 1975)

The All-Sky X-ray Monitor onboard Ariel 5 has observed the 3-6 keV decline of the bright transient X-ray source A0620-00 on a virtually continuous basis during the period September 1975 - March 1976. The source behavior on timescales 100 minutes is characterized by smooth, exponential decays interrupted by substantial increases in October and February. The latter increase was an order-of-magnitude rise above the extrapolated exponential fall-off, and was followed by a final rapid decline. Upper limits of 2.5% and 10% were found for any periodicities in the range 0d.2 - 10d during the early and later decay phases, respectively. A probable correlation between the optical and 3-6 keV emission from A0620-00 was noted, effectively ruling out models involving traditional optical novae in favor of Roche-lobe overflow in a binary system. The existing data on the transient X-ray sources is consistent with two distinct luminosity-lifetime classes of these objects.

Kaluzienski, L. J.↗

NASA NTRS1977

Shuttle program: Ground tracking data program document shuttle OFT launch/landing

The equations for processing ground tracking data during a space shuttle ascent or entry, or any nonfree flight phase of a shuttle mission are given. The resulting computer program processes data from up to three stations simultaneously: C-band station number 1; C-band station number 2; and an S-band station. The C-band data consists of range, azimuth, and elevation angle measurements. The S-band data consists of range, two angles, and integrated Doppler data in the form of cycle counts. A nineteen element state vector is used in Kalman filter to process the measurements. The acceleration components of the shuttle are taken to be independent exponentially-correlated random variables. Nine elements of the state vector are the measurement bias errors associated with range and two angles for each tracking station. The biases are all modeled as exponentially-correlated random variables with a typical time constant of 108 seconds. All time constants are taken to be the same for all nine state variables. This simplifies the logic in propagating the state error covariance matrix ahead in time.

Lear, W. M.↗

NASA NTRS1977

All-Sky Monitor observations of the decay of A0620-00 /Nova Monocerotis 1975/

The All-Sky X-ray Monitor on board Ariel-5 has observed the 3-6 keV decline of the bright transient X-ray source A0620-00 on a virtually continuous basis during the period 1975 September-1976 March. The source behavior on time scales greater than about 100 minutes is characterized by smooth, exponential decays interrupted by substantial increases in October and February. The latter increase was an order-of-magnitude rise above the extrapolated exponential falloff, and was followed by a final rapid decline below a level of about 0.05 per sq cm per sec by late March. Upper limits of 2.5% and 10% were found for any periodicities in the range 0.2-10 days during the early and later decay phases, respectively. A probable correlation between the optical and 3-6 keV emission from A0620-00 has been noted, effectively ruling out models involving traditional optical novae in favor of Roche-lobe overflow in a binary system. The existing data on the transient X-ray sources are consistent with two distinct luminosity-lifetime classes of these objects.

Kaluzienski, L. J.↗

NASA NTRS1977

The response of the dayside aurora to sharp northward and southward transitions of the interplanetary magnetic field and to magnetospheric substorms

Latitudinal shifts of the discrete dayside aurora are examined with respect to variations in the interplanetary magnetic field (IMF) and to magnetospheric substorms. Within 10-15 min after steplike southward (northward) transitions in the IMF the dayside auroral oval moves equatorward (poleward). In at least some cases the auroral shift is similar to an exponential relaxation in latitude from an initial to a final steady state value; for these cases the average exponential time constant is estimated to be 17 min. Substorm features in the dayside aurora include (1) an equatorward shift by 1-3 deg of the equatorward discrete auroral boundary, (2) a brightening of the discrete aurora near substorm onset, (3) the formation of multiple auroral bands, and (4) poleward motion of short-lived individual auroral arcs occurring nearly coincident in time with the equatorward boundary shifts, the average poleward velocity of these arcs being approximately 800 m/s.

Horwitz, J. L.↗

NASA NTRS1976

Studies on color-center formation in glass utilizing measurements made during 1 to 3 MeV electron irradiation

The coloring of NBS 710 glass was studied using a facility for making optical absorption measurements during and after electron irradiation. The induced absorption contains three Gaussian shaped bands. The color center growth curves contain two saturating exponential and one linear components. After irradiation the coloring decays can be described by three decreasing exponentials. At room temperature both the coloring curve plateau and coloring rate increases with increasing dose rate. Coloring measurements made at fixed dose rate but at increasing temperature indicate: (1) The coloring curve plateau decreases with increasing temperature and coloring is barely measurable near 400 C. (2) The plateau is reached more rapidly as the temperature increases. (3) The decay occurring after irradiation cannot be described by Arrhenius kinetics. At each temperature the coloring can be explained by simple kinetics. The temperature dependence of the decay can be explained if it is assumed that the thermal untrapping is controlled by a distribution of activation energies.

Swyler, K. J.↗

NASA NTRS1978

A double shooting scheme for certain unstable and singular boundary value problems

A scheme is presented to obtain the unique bounded solution for an exponentially unstable linear system. The scheme consists of choosing random data at large initial values and integrating forwards and backwards until accurate regular boundary values are obtained. Proofs of convergence are given for the case that the homogeneous equation has an exponential dichotomy. Applications to other types of problems are discussed and numerical results are presented.

Bayliss, A.↗

NASA NTRS1978

The rain parameter diagram - Methods and applications

A rain parameter diagram is presented which displays the relationships between all rainfall parameters defined in terms of an exponential drop size distribution. Special emphasis is given to remotely measurable quantities such as radar reflectivity, microwave attenuation, and optical extinction. Although an exponential distribution is used to construct the diagram, it is shown to have general application for arbitrary size distributions and for a wide variety of rainfall-related problems. Some of the problems are: analysis of the sources of error which result from the use of empirical rainfall relations; depiction of the physical differences between different types of rainfall and of the similarity between all empirical relations which apply to the same type of rainfall; and determination of the accuracy with which remote measurements must be made to obtain accurate rain parameters. A set of overlays is shown for four common radar wavelengths and four temperatures which display the relationships between microwave attenuation and the other rainfall parameters. These diagrams can be used to determine rainfall parameters remotely in dual-measurement techniques.

Ulbrich, C. W.↗

NASA NTRS1978

Three-dimensional galaxy simulations

A three-dimensional fully self-consistent computer model was used to determine the evolution of galaxies consisting of 100,000 simulation stars with exponential radial density variation. Comparison with two-dimensional (infinitesimally thin disk) simulations showed only a very slight stabilizing effect due to the additional degree of freedom. The addition of a fully self-consistent, nonrotating, exponential core/halo component resulted in considerable stabilization. The most pronounced instabilities present were those due to the Jeans' instability in the outer regions of the disk, while at the same time a relatively slowly-growing bar instability appeared. The two-dimensional disk, plus core/halo simulation, showed the usual fast-growing instability leading to bar formation.

Hohl, F.↗

NASA NTRS1978

Decay of homogeneous turbulence from a given state at higher Reynolds number

The turbulence equations are closed by specification of initial conditions (using either a Taylor or an exponential series) and by a modified Kovasznay-type closure. Good results for large times are obtained only for the initial-conditions closure used with four or more terms of an exponential series. The evolution of all of the initially-specified spectra can be calculated rather well from the theory. From a fundamental standpoint the method thus seems to be satisfactory.

Deissler, R. G.↗

NASA NTRS1978

Prediction of solar energetic particle event histories using real-time particle and solar wind measurements

The comparatively well-ordered magnetic structure in the solar corona during the decline of Solar Cycle 20 revealed a characteristic dependence of solar energetic particle injection upon heliographic longitude. When analyzed using solar wind mapping of the large scale interplanetary magnetic field line connection from the corona to the Earth, particle fluxes display an approximately exponential dependence on heliographic longitude. Since variations in the solar wind velocity (and hence the coronal connection longitude) can severely distort the simple coronal injection profile, the use of real-time solar wind velocity measurements can be of great aid in predicting the decay of solar particle events. Although such exponential injection profiles are commonplace during 1973-1975, they have also been identified earlier in Solar Cycle 20, and hence this structure may be present during the rise and maximum of the cycle, but somewhat obscured by greater temporal variations in particle injection.

Roelof, E. C.↗

NASA NTRS1978

Decay of homogeneous turbulence from a given state at higher Reynolds number

Deissler, R. G.↗

NASA NTRS1978

Observations of the hard X-ray spectrum of the impulsive phase of solar flares

The impulsive solar hard X-ray spectrum provides a direct diagnostic on the impulsive energy release of the flare. The data from the hard X-ray (14-342 keV) spectrometer on OSO 7 have been examined for events covering a wide energy range to determine the photon spectrum more precisely. This resulted in a sample of 38 events. The data have been fitted with either single- or double-power laws, and with an exponential spectrum, as from thermal bremsstrahlung. The chi-squared statistic between two-parameter fits strongly favors the exponential fit, particularly at peak intensity when the widest energy range is sampled. This result supports a single-temperature thermal source of the impulsive solar hard X-rays with temperatures in the range 4.7-31 keV and emission measures in the range from 8.4 x 10 to the 43rd to 6.0 x 10 to the 46th per cu cm. The temperature reaches a single maximum and then rapidly decays, but the emission measure usually increases throughout, even after temperature maximum, for data with 10-s resolution.

Elcan, M. J.↗

NASA NTRS1979

Study on the application of NASA energy management techniques for control of a terrestrial solar water heating system

This paper addresses the potential for enhanced solar system performance through sophisticated control of the collector loop flow rate. Computer simulations utilizing the TRNSYS solar energy program were performed to study the relative effect on system performance of eight specific control algorithms. Six of these control algorithms are of the proportional type: two are concave exponentials, two are simple linear functions, and two are convex exponentials. These six functions are typical of what might be expected from future, more advanced, controllers. The other two algorithms are of the on/off type and are thus typical of existing control devices. Results of extensive computer simulations utilizing actual weather data indicate that proportional control does not significantly improve system performance. However, it is shown that thermal stratification in the liquid storage tank may significantly improve performance.

Swanson, T. D.↗

NASA NTRS1979

A computer program for thermal radiation from gaseous rocket exhuast plumes (GASRAD)

A computer code is presented for predicting incident thermal radiation from defined plume gas properties in either axisymmetric or cylindrical coordinate systems. The radiation model is a statistical band model for exponential line strength distribution with Lorentz/Doppler line shapes for 5 gaseous species (H2O, CO2, CO, HCl and HF) and an appoximate (non-scattering) treatment of carbon particles. The Curtis-Godson approximation is used for inhomogeneous gases, but a subroutine is available for using Young's intuitive derivative method for H2O with Lorentz line shape and exponentially-tailed-inverse line strength distribution. The geometry model provides integration over a hemisphere with up to 6 individually oriented identical axisymmetric plumes, a single 3-D plume, Shading surfaces may be used in any of 7 shapes, and a conical limit may be defined for the plume to set individual line-of-signt limits. Intermediate coordinate systems may specified to simplify input of plumes and shading surfaces.

Reardon, J. E.↗