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Results for “Density functional approximations”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Independent Component Analysis of Textures

A common method for texture representation is to use the marginal probability densities over the outputs of a set of multi-orientation, multi-scale filters as a description of the texture. We propose a technique, based on Independent Components Analysis, for choosing the set of filters that yield the most informative marginals, meaning that the product over the marginals most closely approximates the joint probability density function of the filter outputs. The algorithm is implemented using a steerable filter space. Experiments involving both texture classification and synthesis show that compared to Principal Components Analysis, ICA provides superior performance for modeling of natural and synthetic textures.

Manduchi, Roberto↗
NASA NTRS1980

Time correlation functions in classical dense fluids

The velocity autocorrelation functions and memory functions of dense classical fluids may be directly obtained from the static radial distribution function g(r) in an approximate way. Following the Mori projection operator formalism, the memory functions may be related to the fluctuating force correlation. At low densities, these functions may be evaluated by following the trajectories of particle pairs in the interatomic potential. At higher densities, the force correlation functions can be evaluated approximately from particle pair trajectories via the potential of the mean force. The results for argon fluids at various densities and temperatures agree satisfactorily with the molecular dynamics and the Enskog values. The decrease of the diffusion coefficient with density is partly due to the nature of g(r) which reflects the stronger clustering of atoms at higher densities.

Tsang, T.↗
NASA NTRS1989

Probability density and exceedance rate functions of locally Gaussian turbulence

A locally Gaussian model of turbulence velocities is postulated which consists of the superposition of a slowly varying strictly Gaussian component representing slow temporal changes in the mean wind speed and a more rapidly varying locally Gaussian turbulence component possessing a temporally fluctuating local variance. Series expansions of the probability density and exceedance rate functions of the turbulence velocity model, based on Taylor's series, are derived. Comparisons of the resulting two-term approximations with measured probability density and exceedance rate functions of atmospheric turbulence velocity records show encouraging agreement, thereby confirming the consistency of the measured records with the locally Gaussian model. Explicit formulas are derived for computing all required expansion coefficients from measured turbulence records.

Mark, W. D.↗
NASA NTRS1971

Two-way coherent tracking systems.

Review of some results pertinent to the development of nonlinear theory on two-way coherent tracking systems. In particular, the model of cascaded systems is presented, and approximations to steady state probability density functions of the two-way system phase and Doppler error are developed. From these, certain numerical results required in the design and planning of these systems are derived.

Lindsey, W. C.↗
NASA NTRS1992

Electronic and total energy properties of ternary and quaternary semiconductor compounds, alloys, and superlattices: Theoretical study of Cu/graphite bonding

The goals of the research were to provide a fundamental science basis for why the bonding of Cu to graphite is weak, to critically evaluate the previous analysis of the wetting studies with particular regard to the values used for the surface energies of Cu and graphite, and to make recommendations for future experiments or other studies which could advance the understanding and solution of this technological problem. First principles electronic structure calculations were used to study the problem. These are based on density functional theory in the local density approximation and the use of the linear muffin-tin orbital band structure method. Calculations were performed for graphite monolayers, single crystal graphite with the hexagonal AB stacking, bulk Cu, Cu(111) surface, and Cu/graphite superlattices. The study is limited to the basal plane of graphite because this is the graphite plane exposed to Cu and graphite surface energies and combined with the measured contact angles to evaluate the experimental adhesion energy.

Lambrecht, Walter R. L.↗
NASA NTRS2014

Reconstructing the Sky Location of Gravitational-Wave Detected Compact Binary Systems: Methodology for Testing and Comparison

The problem of reconstructing the sky position of compact binary coalescences detected via gravitational waves is a central one for future observations with the ground-based network of gravitational-wave laser interferometers, such as Advanced LIGO and Advanced Virgo. Different techniques for sky localization have been independently developed. They can be divided in two broad categories: fully coherent Bayesian techniques, which are high latency and aimed at in-depth studies of all the parameters of a source, including sky position, and "triangulation-based" techniques, which exploit the data products from the search stage of the analysis to provide an almost real-time approximation of the posterior probability density function of the sky location of a detection candidate. These techniques have previously been applied to data collected during the last science runs of gravitational-wave detectors operating in the so-called initial configuration. Here, we develop and analyze methods for assessing the self consistency of parameter estimation methods and carrying out fair comparisons between different algorithms, addressing issues of efficiency and optimality. These methods are general, and can be applied to parameter estimation problems other than sky localization. We apply these methods to two existing sky localization techniques representing the two above-mentioned categories, using a set of simulated inspiralonly signals from compact binary systems with a total mass of equal to or less than 20M solar mass and nonspinning components. We compare the relative advantages and costs of the two techniques and show that sky location uncertainties are on average a factor approx. equals 20 smaller for fully coherent techniques than for the specific variant of the triangulation-based technique used during the last science runs, at the expense of a factor approx. equals 1000 longer processing time.

technique used↗
NASA NTRS2016

Potential Sources of Polarized Light from a Plant Canopy

Field measurements have demonstrated that sunlight polarized during a first surface reflection by shiny leaves dominates the optical polarization of the light reflected by shiny-leafed plant canopies having approximately spherical leaf angle probability density functions ("Leaf Angle Distributions" - LAD). Yet for other canopies - specifically those without shiny leaves and/or spherical LADs - potential sources of optically polarized light may not always be obvious. Here we identify possible sources of polarized light within those other canopies and speculate on the ecologically important information polarization measurements of those sources might contain.

Polarized Light↗
NASA NTRSDate not supplied

Higher-Order Statistical Moments of Predicted Sonic Boom Waveforms Through Turbulence

Sonic booms generated by supersonic aircraft are affected by turbulence in the atmospheric boundary layer through which they propagate. Turbulence effects lead to random variability of the sonic boom waveforms measured on the ground, complicating the prediction of such waveforms. As an initial effort to predict the waveform variability, the solution of the coherent or mean sonic boom waveform has previously been formulated by the author. The current paper extends the formulation to derive an expression of the second-order statistical moment necessary to calculate the variance of the spectral amplitudes. Since the derivation uses a full wave equation, results using the derived expression will be compared with those obtained using a parabolic approximation. In order to fully quantify the uncertainty of our predictions, the higher order statistical moments are also formulated and are shown to be approximately zero. Consequently, the probability density function (pdf) of the spectral amplitudes is predicted to be Gaussian. The formulation is further extended to determine the pdf of the loudness of sonic booms and quantify the uncertainties associated with the loudness prediction. Results from the formulation are compared with available flight test data.

sonic booms↗
NASA NTRS1996

Downlink Probability Density Functions for EOS-McMurdo Sound

The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.

Christopher, P.↗
NASA NTRS1980

Analytic and approximate boundary-fitted coordinate systems for fluid flow simulation

A method for constructing a direct functional relation between the computational and physical domains such that boundaries in the computational domain map into boundaries in the physical domain is presented. This method which is called the 'two-boundary technique' is based on generating functions that represent two disconnected boundaries in the physical domain and an independent function which connects one boundary with another to generate grids. The suggested connecting functions are simple linear and cubic parametric polynomials with parameters based on position and derivatives at the disconnected boundaries. The boundaries can be defined by analytical, approximate, and tension spline functions; the grid density in specified regions is controlled by embedding contraction functions in either the boundary representation or the connecting function.

Smith, R. E.↗
NASA NTRS1991

Luminosity function of quasars at large redshifts from grism surveys

We have carried out a systematic search for emission-line objects through photometrically calibrated CCD grism surveys with the Palomar 200-inch telescope in transit mode, covering 62 square degrees. These surveys have yielded 141 quasars detected by their C IV or Ly-alpha emission in the redshift range 2.0 - 4.7. We use this sample and the known flux limits to derive the slope of the luminosity function and the space density above a given line luminosity, as a function of redshift. While space densities are approximately constant at redshifts 2.0 - 3.0, they are declining steeply for redshifts larger than 3.

Schmidt, Maarten↗
NASA NTRS2003

Interfacial Reaction Studies Using ONIOM

In this report, we focus on the calculations of the energetics and chemical kinetics of heterogeneous reactions for Organometallic vapor phase epitaxy (OMVPE). The work described in this report builds upon our own previous thermochemical and chemical kinetics studies. The first of these articles refers to the prediction of thermochemical properties, and the latter one deals with the prediction of rate constants for gaseous homolytic dissociation reactions. The calculations of this investigation are at the microscopic level. The systems chosen consisted of a gallium nitride (GaN) substrate, and molecular nitrogen (N2) and ammonia (NH3) as adsorbants. The energetics for the adsorption and the adsorbant dissociation processes were estimated, and reaction rate constants for the dissociation reactions of free and adsorbed molecules were predicted. The energetics for substrate decomposition was also computed. The ONIOM method, implemented in the Gaussian98 program, was used to perform the calculations. This approach has been selected since it allows dividing the system into two layers that can be treated at different levels of accuracy. The atoms of the substrate were modeled using molecular mechanics6 with universal force fields, whereas the adsorbed molecules were approximated using quantum mechanics, based on density functional theory methods with B3LYP functionals and 6-311G(d,p) basis sets. Calculations for the substrate were performed in slabs of several unit cells in each direction. The N2 and NH3 adsorbates were attached to a central location at the Ga-lined surface.

Cardelino, Beatriz H.↗
NASA NTRS2018

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.

Corbetta, M.↗
NASA NTRS2019

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.

stochastic calculus↗
NASA NTRS1978

Feature selection for best mean square approximation of class densities

A criterion for linear feature selection is proposed which is based on mean square apporximation of class density functions. It is shown that for the widest possible class of approximants, the criterion reduces to Devijver's Bayesian distance. For linear approximants the criterion is equivalent to well known generalized Fisher criteria.

Peters, C.↗
NASA NTRS1980

The unique determination of density from high-order potentials

The existence of higher-order potentials is postulated, and that the density function can be determined from this set of potentials is demonstrated. Moreover, it is shown that there is a one-to-one correspondence between such potentials and the density function, provided it is continuous. Finally, it is noted that this demonstration includes a method of constructing the density function from the set of potentials as well as indicating how to approximate the density from incomplete knowledge of the potentials.

Johnson, G. G.↗
NASA NTRS2023

Efficient Calibration of Expensive Computational Models

Accounting for uncertainty when calibrating expensive computational models is a common challenge faced by scientists and engineers. Often Bayesian techniques are adopted to estimate a probability density function over the model parameters given noisy empirical data. The methods used to perform this type of probabilistic calibration are computationally prohibitive in that they require a large number of evaluations of the expensive model. In these cases, surrogate modeling -- that is, using a fast-to-evaluate, lower fidelity stand-in for the original computational model -- may be the only option to alleviate this computational burden. However, the upfront cost of generating training data to build a surrogate model can itself be expensive. As such, it is important to be judicious when selecting training points at which the full-fidelity model is evaluated. Here, an active learning approach is proposed that enables efficient selection of training points using approximate samples of the calibrated parameter probability density function. In this way, the training points can be concentrated in regions where the calibration algorithm requires high model accuracy.

active learning↗