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Results for “EXPONENTIAL FUNCTION”

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.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
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 NTRS1994

On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

Gottlieb, David↗
NASA NTRS1987

Strain energy release rates of composite interlaminar end-notch and mixed-mode fracture: A sublaminate/ply level analysis and a computer code

A computer code is presented for the sublaminate/ply level analysis of composite structures. This code is useful for obtaining stresses in regions affected by delaminations, transverse cracks, and discontinuities related to inherent fabrication anomalies, geometric configurations, and loading conditions. Particular attention is focussed on those layers or groups of layers (sublaminates) which are immediately affected by the inherent flaws. These layers are analyzed as homogeneous bodies in equilibrium and in isolation from the rest of the laminate. The theoretical model used to analyze the individual layers allows the relevant stresses and displacements near discontinuities to be represented in the form of pure exponential-decay-type functions which are selected to eliminate the exponential-precision-related difficulties in sublaminate/ply level analysis. Thus, sublaminate analysis can be conducted without any restriction on the maximum number of layers, delaminations, transverse cracks, or other types of discontinuities. In conjunction with the strain energy release rate (SERR) concept and composite micromechanics, this computational procedure is used to model select cases of end-notch and mixed-mode fracture specimens. The computed stresses are in good agreement with those from a three-dimensional finite element analysis. Also, SERRs compare well with limited available experimental data.

Valisetty, R. R.↗
NASA NTRS1989

Responsivity variations in the IRAS survey

The IRAS survey detectors show nonlinear characteristics in their gains and baselines. This behavior can be described by an exponentially decaying gain enhancement, dependent on previously observed flux. The baseline behavior has been modeled by a decaying function composed of the sum of two exponential functions. The scale lengths are 10 arcmin and 1.1 deg for 12 microns, and 8 arcmin and 43 arcmin for 25 microns. Amplitude changes due to this type of hysteresis are less than 1 percent. In addition there is a considerable response of all detectors to particles associated with the South Atlantic Anomaly. Attempts to correct for this effect were performed on the 12- , 60- and 100-micron detectors in the form of bias boosts. This note presents a correction procedure for the 25-micron detectors.

Deul, E. R.↗
NASA NTRS1969

Simple quasi-exponential slope generator

Circuitry for digitally generating an exponentially decaying wave function permits discrete values to be sampled from the exponential waveform for comparison with a binary number of specified accuracy. This exponential-decay generator employs a simple binary counter to count in the sequence of exponential decay.

Anderson, T. O.↗
NASA NTRS1978

Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems

The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.

Brandt, A.↗
NASA NTRS1992

On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function

It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.

Gottlieb, David↗
NASA NTRS1993

Specular scattering on a terrestrial playa and implications for planetary surface studies

Multiangle Advanced Solid State Array Spectroradiometer (ASAS) and Portable Apparatus for Rapid Acquisition of Bidirectional Observations of Land and Atmosphere (PARABOLA) visible and near infrared reflectance data covering the Lunar Lake playa, Nevada, were modeled using specular and volume scattering theory. The volume component used to model the data was based on the Hapke (1986) model and the specular scattering component was based on Fresnel reflection from surface facets with a distribution of tilts. Specular scattering was needed to explain the several-fold increase in reflectance observed at high phase angles in the solar principal plane. Results imply single scattering albedos of approximately 0.93 to 0.95, a real index of refraction value of approximately 1.52 (at a wavelength of 0.66 micron), a small imaginary index of refraction and an exponential facet tilt probability function for the playa. Electron micrographs showed th playa surface to consist of ensembles of smooth, micrometer-scale ellipsoidal particles on gently undulating topography at the millimeter to centimeter scale. The exponential probability function is consistent with this observation. Mars and the icy satellites are discussed as possible places to look for a significant specular scattering component.

Shepard, Michael 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 NTRS1992

ROSAT all-sky survey on the Einstein EMSS sample

The cosmological evolution and the luminosity function (XLF) of X ray selected Active Galactic Nuclei (AGN's) are discussed. The sample used is extracted from the Einstein Observatory Extended Medium Sensitivity Surveys (EMSS) and consists of more than 420 objects. Preliminary results from the ROSAT All-Sky Survey data confirm the correctness of the optical identification of the EMSS sources, thus giving confidence to the results obtained from the analysis of the AGN's sample. The XLF observed at different redshifts (up to z approx. 2) gives direct evidence of cosmological evolution. Data have been analyzed within the framework of luminosity evolution models and the two most common evolutionary forms, L sub x(Z) = L sub x(0) x e(sup Cr) and L sub x(Z) = L sub x(0) x (1 + z)(exp C), have been considered. Luminosity dependent evolution is required if the evolution function has the exponential form, whereas the simpler pure luminosity evolution model is still acceptable if the evolution function has the power law form. Using the whole sample of objects the number-counts and the de-evolved (z = 0) XLF have been derived. A comparison of the EMSS data with preliminary ROSAT results presented at this meeting indicates an overall agreement.

Maccacaro, Tomasso↗
NASA NTRS1992

The evolution of AGN's at x ray wavelengths

The cosmological evolution and the Luminosity Function (LF) of x-ray selected Active Galactic Nuclei (AGN) are discussed. The sample used is extracted from the Einstein Observatory Extended Medium Sensitivity Survey (EMSS) and consists of more than 420 objects. Preliminary results from the Rosat all sky survey data confirm the correctness of the optical identification of the EMSS sources, thus giving confidence to the results obtained from the analysis of the AGN sample. The XLF observed at different redshifts gives direct evidence of cosmological evolution. Data were analyzed within the framework of luminosity evolution models and the two most common evolutionary forms were considered. Luminosity dependent evolution is required if the evolution function has the exponential form, whereas the simpler pure luminosity evolution model is still acceptable if the evolution function has the power law form. Using the whole sample of objects the number counts and the devolved XLF were derived. A comparison of the EMSS Data with preliminary Rosat results indicates an overall agreement.

Maccacaro, Tommaso↗
NASA NTRS1993

The analytical representation of viscoelastic material properties using optimization techniques

This report presents a technique to model viscoelastic material properties with a function of the form of the Prony series. Generally, the method employed to determine the function constants requires assuming values for the exponential constants of the function and then resolving the remaining constants through linear least-squares techniques. The technique presented here allows all the constants to be analytically determined through optimization techniques. This technique is employed in a computer program named PRONY and makes use of commercially available optimization tool developed by VMA Engineering, Inc. The PRONY program was utilized to compare the technique against previously determined models for solid rocket motor TP-H1148 propellant and V747-75 Viton fluoroelastomer. In both cases, the optimization technique generated functions that modeled the test data with at least an order of magnitude better correlation. This technique has demonstrated the capability to use small or large data sets and to use data sets that have uniformly or nonuniformly spaced data pairs. The reduction of experimental data to accurate mathematical models is a vital part of most scientific and engineering research. This technique of regression through optimization can be applied to other mathematical models that are difficult to fit to experimental data through traditional regression techniques.

Hill, S. A.↗
NASA NTRS1992

The properties of X-ray selected active galactic nuclei. II - A deeper look at the cosmological evolution

A detailed study of the cosmological properties of X-ray selected AGN is presented. The data are analyzed within the framework of a pure luminosity evolution (PLE) model and the two most population evolutionary forms. Evidence is found for luminosity-dependent luminosity evolution if the evolution function has the exponential form. The simpler PLE model is more acceptable if the data are fitted with a power-law evolution function. Similar results are obtained in the optical domain from an analysis of a sample of optically selected QSOs with z less than 2.2 and B less than 20.

Della Ceca, Roberto↗
NASA NTRS2010

A Study of Cirrus Ice Particle Size Distribution Using TC4 Observations

An analysis of two days of in situ observations of ice particle size spectra, in convectively generated cirrus, obtained during NASA s Tropical Composition, Cloud, and Climate Coupling (TC4) mission is presented. The observed spectra are examined for their fit to the exponential, gamma, and lognormal function distributions. Characteristic particle size and concentration density scales are determined using two (for the exponential) or three (for the gamma and lognormal functions) moments of the spectra. It is shown that transformed exponential, gamma, and lognormal distributions should collapse onto standard curves. An examination of the transformed spectra, and of deviations of the transformed spectra from the standard curves, shows that the lognormal function provides a better fit to the observed spectra.

Tian, Lin↗
NASA NTRS1984

Function algorithms for MPP scientific subroutines, volume 1

Design documentation and user documentation for function algorithms for the Massively Parallel Processor (MPP) are presented. The contract specifies development of MPP assembler instructions to perform the following functions: natural logarithm; exponential (e to the x power); square root; sine; cosine; and arctangent. To fulfill the requirements of the contract, parallel array and solar implementations for these functions were developed on the PDP11/34 Program Development and Management Unit (PDMU) that is resident at the MPP testbed installation located at the NASA Goddard facility.

Gouch, J. G.↗
NASA NTRS2018

A Simple, Velocity Dependent, Collision Probability Algorithm for Small Combined Hard Body Radii Close Approach Events

Over the last few years progress has been made in the velocity dependent collision probability problem. Recent progress in this problem has been approached via integration of the probability flux into the surface of the combined hard body object. The algorithm presented uses the surface flux approach and is designed to compute the collision probability rate between two objects given their time dependent states and state error covariance matrices. With regards to the computation of the collision probability (Pc) rate, two major differences exist between the development of this algorithm and the usual Pc algorithm. First, the shape of the at-risk volume is assumed to be a cube rather than a sphere. The size of the cube is chosen so that it circumscribes the usual hard body sphere chosen for the spherical Pc problem. This will result in half the length of a side of the cube being equal to the hard body radius (HBR) of the sphere. Second, it is assumed that the HBR of the cube is much smaller than the smallest combined position uncertainty (σ(sub min) > 5*HBR) at each time point of evaluation. This is necessary as the actual collision probability calculation is based on a first order, small variable expansion in the position components of the Gaussian probability density function. This leads to the collision probability rate being to second order in the combined HBR. The collision probability rate is in a concise, closed form containing exponential and error functions.

Frisbee, Joe↗
NASA NTRS1982

The stability of quasi-geostrophic fields induced by potential vorticity sources

A determination of the conditions leading to instabilities which grow in place in quasi-geostrophic fields induced by localized potential vorticity sources is presented. The analysis considers a quasi-geostrophic barotropic flow in a horizontally open domain, and a nondimensional quasi-geostrophic vorticity equation is defined which governs the deviation stream function. Weak forcing is considered, and it is shown that the field induced by the topography is stable while the field induced by the potential vorticity source can be unstable. The growth rate is exponential and a function of nonlinearity and friction, which, if absent, indicates an unstable flowfield. The instability is shown to be capable of changing the flowfield from one quasi-steady state to another, with energy extraction occurring at the source

Merkine, L.-O.↗
NASA NTRS1990

The white dwarf luminosity function - A possible probe of the galactic halo

The dynamically inferred dark halo mass density, amounting to above 0.01 solar masses/cu pc at the sun's Galactocentric radius, can be composed of faint white dwarfs provided that the halo formed in a sufficiently early burst of star formation. The model is constrained by the observed disk white dwarf luminosity function which falls off below log (L/solar L) = -4.4, due to the onset of star formation in the disk. By using a narrow range for the initial mass function and an exponentially decaying halo star formation rate with an e-folding time equal to the free-fall time, all the halo dark matter is allowed to be in cool white dwarfs which lie beyond the falloff in the disk luminosity function. Although it is unlikely that all the dark matter is in these dim white dwarfs, a definite signature in the low-luminosity end of the white dwarf luminosity function is predicted even if they comprise only 1 percent of the dark matter. Current CCD surveys should answer the question of the existence of this population within the next few years.

Tamanaha, Christopher M.↗