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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
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.↗
DOE OSTI2025

Decoherence dynamics in molecular qubits: Exponential, Gaussian and beyond

In this article, we examine how the structure of system–bath interactions can determine commonly encountered temporal decoherence patterns, such as Gaussian and exponential decay, in molecular and other qubits coupled to a thermal bosonic bath. The analysis, based on a pure dephasing picture that admits analytical treatment, shows that decoherence, in general, is neither purely Gaussian nor exponential but rather the exponential of oscillatory functions, with periods determined by the bath’s frequencies. For initially unentangled qubit-bath states, Gaussian decay is always present at early times. It becomes increasingly dominant with increasing temperature, qubit–bath interaction strength, and bath correlation time. Initial system–bath entanglement that arises due to displacement in the position of the bath states preserves the Gaussian decay. By contrast, strict exponential decay arises only in very specific models that we isolate. However, it becomes dominant for times longer than the bath correlation time or for early times when there is initial entanglement due to momentum displacement of the bath states. For molecular electronic decoherence, the long-time exponential regime plays a limited role as it emerges after most coherence is lost. Thus, the Gaussian decay provides a more suitable (albeit imperfect) model of such decoherence. Furthermore, we discuss the connection between electronic decoherence dynamics and electronic spectroscopic line shape theory, where Gaussian spectral peaks correspond to Gaussian coherence decay and Lorentzian peaks correspond to exponential coherence decay. We find that Gaussian spectral peaks, usually associated with inhomogeneous broadening, can emerge from the entangling unitary system–bath dynamics even when there is no inhomogeneity in the initial conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Cluster spin glass correlations and dynamics in Zn 0.5⁢ Mn 0.5⁢ Te

Here, we present a combined magnetometry, muon spin-relaxation (𝜇⁢SR), and neutron-scattering study of the insulating spin glass Zn 0.5 ⁢Mn 0.5 ⁢Te, for which magnetic Mn 2+ and nonmagnetic Zn 2+ ions are randomly distributed on a face-centered cubic lattice. The magnetometry and 𝜇⁢SR results confirm a spin freezing transition around 𝑇 𝑓 ≈ 23 K, with the spin-fluctuation rate decreasing gradually and somewhat inhomogeneously through the sample volume as the temperature decreases toward 𝑇 𝑓 . Characteristic spin-correlation times well above 𝑇 𝑓 are on the order of 10 −10 s, much slower than typically observed in canonical spin glasses but in line with expectations for a cluster spin glass. Using magnetic pair distribution function (mPDF) analysis and reverse Monte Carlo (RMC) modeling of the magnetic diffuse neutron-scattering data, we show that the spin-glass ground state consists of clusters of spins exhibiting short-range-ordered type-III antiferromagnetic correlations with a locally ordered moment of 3.1⁢(1)⁢𝜇 B between nearest-neighbor spins. The type-III correlations decay exponentially as a function of spin separation distance with a correlation length of approximately 5 Å. The diffuse magnetic scattering and corresponding mPDF show no significant changes across 𝑇 𝑓 , indicating that the dynamically fluctuating short-range spin correlations in the paramagnetic state retain the same basic type-III configuration that characterizes the spin-glass state; the only change apparent from the neutron-scattering data is a gradual reduction of the correlation length and locally ordered moment with increasing temperature. Taken together, these results paint a unique and detailed picture of the local magnetic structure and dynamics in Zn 0.5 ⁢Mn 0.5⁢ Te and provide strong evidence that this material is best described as a cluster spin glass. In addition, this work showcases a statistical method for extracting diffuse scattering signals from neutron powder diffraction data, which we developed to facilitate the mPDF and RMC analysis of the neutron data. This method has the potential to be broadly useful for neutron powder diffraction experiments on a variety of materials with short-range atomic or magnetic order.

magnetism↗
NASA NTRS1995

Exponentially accurate approximations to piece-wise smooth periodic functions

A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.

Greer, James↗
NASA NTRS1993

Dynamic tests on the NASA Langley CSI evolutionary model

A modal analysis study, representing one of the anticipated 'Cooperative Spacecraft Structural Dynamics Experiments on the NASA Langley CSI Evolutionary Model', was carried out as a sub-task under the NASA/DLR collaboration in dynamics and control of large space systems. The CSI evolutionary testbed (CEM) is designed for the development of Controls-Structures Interaction (CSI) technology to improve space science platform pointing. For orbiting space structures like large flexible trusses, new identification challenges arise due to their specific dynamic characteristics (low frequencies and high modal density) on the one hand, and the limited possibilities of exciting such structures and measuring their responses on orbit on the other. The main objective was to investigate the modal identification potential of several different types of forcing functions that could possibly be realized with on-board excitation equipment using a minimum number of exciter locations as well as response locations. These locations were defined in an analytical test prediction process used to study the implications of measuring and analyzing the responses thus produced. It turned out that broadband excitation is needed for a general modal survey, but if only certain modes are of particular interest, combinations of exponentially decaying sine functions provide favorable excitation conditions as they allow to concentrate the available energy on the modes being of special interest. From a practical point-of-view structural nonlinearities as well as noisy measurements make the analysis more difficult, especially in the low frequency range and when the modes are closely spaced.

Troidl, H.↗
NASA NTRS1984

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.↗
DOE OSTI2026

A variational framework for residual-based adaptivity in neural PDE solvers and operator learning

Residual-based adaptive strategies are widely used in scientific machine learning yet remain largely heuristic. We introduce a variational framework that formalizes these methods through convex transformations of the residual, where different transformations correspond to distinct objective functionals. For instance, exponential weights target uniform error minimization, while linear weights recover quadratic error minimization. This perspective reveals adaptive weighting as a means of selecting sampling distributions that optimize a primal objective, directly linking discretization choices to error metrics. This principled approach yields three key benefits: it enables systematic design of adaptive schemes, reduces discretization error by lowering estimator variance, and enhances learning dynamics by improving gradient signal-to-noise ratio. Extending the framework to operator learning, we demonstrate substantial performance gains across diverse optimizers and architectures. Our results provide a theoretical perspective for residual-based adaptivity and establish a foundation for principled discretization and training.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Neutrons in the moon

Neutron fluxes for energies between 15 MeV and thermal at depths of 0 to 300 g/sq cm in the moon are calculated by the discrete ordinate mathod with the ANISN code. With the energy spectrum of Lingenfelter et al. (1972). A total neutron-production rate for the moon of 26 plus or minus neutrons/sq cm sec is determined from the Ar-37 activity measurements in the Apollo 16 drill string, which are found to have a depth dependence in accordance with a neutron source function that decreases exponentially with an attenuation length of 155 g/sq cm.

Kornblum, J. J.↗
NASA NTRS1974

Buckling of cylindrical shells with random imperfections

Buckling of long cylindrical shells with random imperfections subjected to axial loads is treated using the method of truncated hierarchy. A system of homogeneous variational equations is set up to examine the existence of bifurcation in the neighborhood of the equilibrium state. These equations are linear and involve stationary random coefficients. The truncated-hierarchy method is applied, and characteristic equations are obtained. Various exponential cosine correlation functions associated with asymmetric imperfections are examined numerically. Qualitatively, the results obtained are as anticipated.

Fersht, R. S.↗
NASA NTRS1977

Turbulent scattering in an exponential atmosphere - A wave-optical solution

The thin-screen model for scattering of radiation by a turbulent atmosphere is generalized to the case where the mean phase change decreases exponentially as a function of distance across the screen. This is of interest because it models the effect of turbulent scattering in an isothermal average atmosphere. We present both the change in average intensity and average bending angle in terms of the r-m-s scattering angle introduced by the turbulence. We find, for example, that the effect of turbulent scattering on the mean scattering angle (and hence Doppler residuals) is approximately the same as that obtained from more heuristic calculations. The effect depends on wavelength only to the extent that the refractivity is a function of wavelength.

Hubbard, W. B.↗
NASA NTRS1976

A Landsat study of water quality in Lake Okeechobee

This paper uses multiple regression techniques to investigate the relationship between Landsat radiance values and water quality measurements. For a period of over one year, the Central and Southern Florida Flood Control District sampled the water of Lake Okeechobee for chlorophyll, carotenoids, turbidity, and various nutrients at the time of Landsat overpasses. Using an overlay map of the sampling stations, Landsat radiance values were measured from computer compatible tapes using a GE image 100 and averaging over a 22-acre area at each station. These radiance values in four bands were used to form a number of functions (powers, logarithms, exponentials, and ratios), which were then compared with the ground measurements using multiple linear regression techniques. Several dates were used to provide generality and to study possible seasonal variations. Individual correlations were presented for the various water quality parameters and best fit equations were examined for chlorophyll and turbidity. The results and their relationship to past hydrological research were discussed.

Gervin, J. C.↗