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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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Energetic electrons in the Jovian magnetosphere

Results are reported for a detailed analysis of Pioneer 10 data on energetic particle species in the magnetodisk region of Jupiter's magnetosphere. It is shown that the observed counting rates in the magnetodisk (beyond 20 Jupiter radii) were caused primarily by electrons with energies exceeding 0.06 MeV. Absolute omnidirectional electron intensities in the magnetodisk are presented for five integral energy ranges, and a model electron differential energy spectrum is found to fit the intensities throughout most of the encounter trajectory. It is suggested that the observed spectral shape results from losses of high-energy electrons by pitch-angle scattering. Observed equatorial energy spectra are used to compute distribution functions for several values of the first adiabatic invariant, mu. The radial profiles of the functions are found to have maxima at about 50 Jupiter radii inbound as well as at about 90 radii outbound and to diminish strongly for lesser radii. The large decreases in density are shown to require strong losses, and resonant electron whistler-mode pitch-angle scattering is suggested as a loss mechanism.

Baker, D. N.↗
NASA NTRS1981

Ellipsoidal corrections for geoid undulation computations using gravity anomalies in a cap

Ellipsoidal correction terms have been derived for geoid undulation computations when the Stokes equation using gravity anomalies in a cap is combined with potential coefficient information. The correction terms are long wavelength and depend on the cap size in which its gravity anomalies are given. Using the regular Stokes equation, the maximum correction for a cap size of 20 deg is -33 cm, which reduces to -27 cm when the Stokes function is modified by subtracting the value of the Stokes function at the cap radius. Ellipsoidal correction terms were also derived for the well-known Marsh/Chang geoids. When no gravity was used, the correction could reach 101 cm, while for a cap size of 20 deg the maximum correction was -45 cm. Global correction maps are given for a number of different cases. For work requiring accurate geoid computations these correction terms should be applied.

Rapp, R. H.↗
DOE OSTI2018

Survey geometry and the internal consistency of recent cosmic shear measurements

Here, we explore the impact of an update to the typical approximation for the shape noise term in the analytic covariance matrix for cosmic shear experiments that assumes the absence of survey boundary and mask effects. We present an exact expression for the number of galaxy pairs in this term based on the the survey mask, which leads to more than a factor of three increase in the shape noise on the largest measured scales for the Kilo-Degree Survey (KIDS-450) real-space cosmic shear data. We compare the result of this analytic expression to several alternative methods for measuring the shape noise from the data and find excellent agreement. This update to the covariance resolves any internal model tension evidenced by the previously large cosmological best-fit $\chi^2$ for the KiDS-450 cosmic shear data. The best-fit $\chi^2$ is reduced from 161 to 121 for 118 degrees of freedom. We also apply a correction to how the multiplicative shear calibration uncertainty is included in the covariance. This change, along with a previously known update to the reported effective angular values of the data vector, jointly shift the inferred amplitude of the correlation function to higher values. Lastly, we find that this improves agreement of the KiDS-450 cosmic shear results with Dark Energy Survey Year 1 and Planck results.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1972

A class of neutral functional differential equations.

Formulation and study of the initial value problem for neutral functional differential equations. The existence, uniqueness, and continuation of solutions to this problem are investigated, and an analysis is made of the dependence of the solutions on the initial conditions and parameters, resulting in the derivation of a continuous dependence theorem in which the fundamental mathematical principles underlying the continuous dependence problem for a very general system of nonlinear neutral functional differential equations are separated out.

Melvin, W. R.↗
DOE OSTI2019

What Is the Fractional Laplacian? A Comparative Review with New Results

The fractional Laplacian in $\mathbb{R}^{d}$, which we write as (–Δ) α/2 with, α ϵ (0, 2) has multiple equivalent characterizations. Furthermore, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the literature as to which definition of the fractional Laplacian in bounded domains is most appropriate for a given application. The Riesz (or integral) definition, for example, admits a nonlocal boundary condition, where the value of a function must be prescribed on the entire exterior of the domain in order to compute its fractional Laplacian. Yet, the spectral definition requires only the standard local boundary condition. These differences, among others, lead us to ask the question: “What is the fractional Laplacian?” Beginning from first principles, we compare several commonly used definitions of the fractional Laplacian theoretically, through their stochastic interpretations as well as their analytical properties. Next, we present quantitative comparisons using a sample of state-of-the-art methods. We discuss recent advances on nonzero boundary conditions and present new methods to discretize such boundary value problems: radial basis function collocation (for the Riesz fractional Laplacian) and nonharmonic lifting (for the spectral fractional Laplacian). In our numerical studies, we aim to compare different definitions on bounded domains using a collection of benchmark problems. We consider the fractional Poisson equation with both zero and nonzero boundary conditions, where the fractional Laplacian is defined according to the Riesz definition, the spectral definition, the directional definition, and the horizon-based nonlocal definition. We verify the accuracy of the numerical methods used in the approximations for each operator, and we focus on identifying differences in the boundary behaviors of solutions to equations posed with these different definitions. Through our efforts, we aim to further engage the research community in open problems and assist practitioners in identifying the most appropriate definition and computational approach to use for their mathematical models in addressing anomalous transport in diverse applications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Phase function, backscatter, extinction, and absorption for standard radiation atmosphere and El Chichon aerosol models at visible and near-infrared wavelengths

Tabular values of phase function, Legendre polynominal coefficients, 180 deg backscatter, and extinction cross section are given for eight wavelengths in the atmospheric windows between 0.4 and 2.2 microns. Also included are single scattering albedo, asymmetry factor, and refractive indices. These values are based on Mie theory calculations for the standard rediation atmospheres (continental, maritime, urban, unperturbed stratospheric, volcanic, upper atmospheric, soot, oceanic, dust, and water-soluble) assest measured volcanic aerosols at several time intervals following the El Chichon eruption. Comparisons of extinction to 180 deg backscatter for different aerosol models are presented and related to lidar data.

Whitlock, C. H.↗
NASA NTRS1975

Determination of discontinuities in the derivative of a piecewise-smooth function on the basis of the results of measurements

A piecewise-smooth function with discontinuity in the first derivative on a given interval is considered. The values of the function are measured at a sequence of points in the interval and a random error is included in the measurements. A method is proposed to estimate the position of the discontinuity in the derivative. Regression lines are associated with each measurement point and account for k - 1 points preceding or following the point. The estimate for the position of the discontinuity is the measurement point with the largest angle between the regression lines. The error in the estimate is analyzed and the results are verified.

Gurin, L. S.↗
NASA NTRS1992

Fuzzy knowledge base construction through belief networks based on Lukasiewicz logic

In this paper, a procedure is proposed to build a fuzzy knowledge base founded on fuzzy belief networks and Lukasiewicz logic. Fuzzy procedures are developed to do the following: to assess the belief values of a consequent, in terms of the belief values of its logical antecedents and the belief value of the corresponding logical function; and to update belief values when new evidence is available.

Lara-Rosano, Felipe↗
NASA NTRS2012

Advisory Algorithm for Scheduling Open Sectors, Operating Positions, and Workstations

Air traffic controller supervisors configure available sector, operating position, and work-station resources to safely and efficiently control air traffic in a region of airspace. In this paper, an algorithm for assisting supervisors with this task is described and demonstrated on two sample problem instances. The algorithm produces configuration schedule advisories that minimize a cost. The cost is a weighted sum of two competing costs: one penalizing mismatches between configurations and predicted air traffic demand and another penalizing the effort associated with changing configurations. The problem considered by the algorithm is a shortest path problem that is solved with a dynamic programming value iteration algorithm. The cost function contains numerous parameters. Default values for most of these are suggested based on descriptions of air traffic control procedures and subject-matter expert feedback. The parameter determining the relative importance of the two competing costs is tuned by comparing historical configurations with corresponding algorithm advisories. Two sample problem instances for which appropriate configuration advisories are obvious were designed to illustrate characteristics of the algorithm. Results demonstrate how the algorithm suggests advisories that appropriately utilize changes in airspace configurations and changes in the number of operating positions allocated to each open sector. The results also demonstrate how the advisories suggest appropriate times for configuration changes.

Bloem, Michael↗
NASA NTRS1974

Quantitative values of blood flow through the human forearm, hand, and finger as functions of temperature

A literature search was made to obtain values of human forearm, hand and finger blood flow as functions of environmental temperature. The sources used include both government and laboratory reports and the research presented in the open literature. An attempt was made to review many of the more quantitative noninvasive determinations and to collate the results in such a way as to yield blood flow values for each body segment as continuous functions of temperature. A brief review of the various ways used to measure blood flow is included along with an abstract of each work from which data was taken.

Montgomery, L. D.↗
NASA NTRS2020

Evaluation of Fatigue Damage Accumulation Functions for Delamination Initiation and Propagation

The present report follows on the cohesive fatigue damage model methodology proposed in NASA-TP-2018-219838. In that report, an empirical function describing the incremental damage due to cyclic loading was used to calculate fatigue damage within a cohesive formulation. The form of the function was developed such that, when integrated at a constant stress amplitude from no damage to failure, it produces a life versus load response that is consistent with an S-N diagram. Therefore, the parameters of the damage model could be obtained by fitting the model predictions to an S-N diagram. The finite element analyses performed demonstrate that the cohesive fatigue accumulation function provides a link between the S-N diagram that describes crack initiation, and the Paris law that characterizes the rate of crack propagation. However, when the model was proposed, it was not known whether the form of the damage accumulation function associated with a desired S-N diagram is unique and, if not, if the link between S-N and the Paris law is unique and independent of the fatigue function selected. In the effort described herein, several alternative forms of the damage function that reproduce the desired features of S-N diagrams were found and evaluated. The effects of each of these functions on the predicted parameters of the Paris law and the propagation threshold are discussed. The results indicate that the predicted exponent m of the Paris law is indeed independent of the damage accumulation function. However, different functions predict different values for the pre-factor C of the Paris law. Therefore, the proper damage accumulation function must be selected by comparison with experiments. One of the new damage accumulation functions proposed herein was found to be particularly useful for analysis because of the ease with which the model parameters can be determined with a minimal amount of experimental information. The effectiveness of the proposed methodology and damage function was demonstrated by conducting analyses of a double cantilever beam test, a mixed-mode bending test, and a three-point bending test of a skin/doubler specimen. The results indicate that the same set of model parameters can provide accurate predictions of the rate of fatigue crack propagation for a variety of material interfaces, mode mixities, load levels, and stress ratios.

Cohesive elements↗
NASA NTRS1962

The Restricted Three-Body-Problem as a Perturbation of Euler's Problem of Two Fixed Centers and Its Application to Lunar Trajectories

The restricted Three-Body-Problem considers the motion of an infinitesimal mass under the gravitational attraction of two finite masses, which revolve about their common center of gravity in coplanar circles. It is well known that Euler's problem of two fixed centers, consisting of the motion of an infinitesimal mass under the gravitational attraction of two finite masses fixed in space, can be solved by elliptic functions. The idea presented here is to take the solution of Euler's problem as the solution of the restricted Three-Body-Problem by allowing the initial values to be functions of time now. Differential equations for the perturbed initial values are established. These equations can be given in closed form by using the fact that the transformation to the perturbed initial values of Euler's problem is canonical. Thus, an approximation can be obtained for the solution of the restricted Three-Body-Problem. The method can also be used to represent classes of neighboring trajectories for guidance purposes.

Euler equation↗
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 NTRS2008

Quantum-Inspired Maximizer

A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).

Zak, Michail↗
DOE OSTI2023

Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) projection of data to the causal space; (2) estimation of pole locations; and (3) semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. Furthermore, it is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗