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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 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Constrained curve fitting for semi-parametric models with radial basis function networks

Common to many analysis pipelines in lattice gauge theory and the broader scientific discipline is the need to fit a semi-parametric model to data. We propose a fit method that utilizes a radial basis function network to approximate the non-parametric component of such models. The approximate parametric model is fit to data using the basin hopping global optimization algorithm. Parameter constraints are enforced through Gaussian priors. The viability of our method is tested by examining its use in a finite-size scaling analysis of the $q$-state Potts model and $p$-state clock model with $q=2,3$ and $p=4,\infty$.

Peterson, Curtis T.↗
DOE OSTI2019

Multiplicity dependence of light-flavor hadron production in p p collisions at s = 7 TeV

Comprehensive results on the production of unidentified charged particles, $π^±, K^±, K^0_S, K^*(892)^0, p,$ $\bar{p}$, $\phi$ (1020), Λ, $\bar{Λ}$, $\Xi^-$, $\bar{\Xi}^+$, $Ω^-$, and $\bar{Ω}^+$ hadrons in proton-proton ($pp$) collisions at $\sqrt{s}$ = 7 TeV at midrapidity ($|y|$ < 0.5) as a function of charged-particle multiplicity density are presented. In order to avoid autocorrelation biases, the actual transverse momentum ($p$ T ) spectra of the particles under study and the event activity are measured in different rapidity windows. In the highest multiplicity class, the charged-particle density reaches about 3.5 times the value measured in inelastic collisions. While the yield of protons normalized to pions remains approximately constant as a function of multiplicity, the corresponding ratios of strange hadrons to pions show a significant enhancement that increases with increasing strangeness content. Furthermore, all identified particle-to-pion ratios are shown to depend solely on charged-particle multiplicity density, regardless of system type and collision energy. The evolution of the spectral shapes with multiplicity and hadron mass shows patterns that are similar to those observed in $p$-Pb and Pb-Pb collisions at Large Hadron Collider energies. The obtained $p$ T distributions and yields are compared to expectations from QCD-based $pp$ event generators as well as to predictions from thermal and hydrodynamic models. These comparisons indicate that traces of a collective, equilibrated system are already present in high-multiplicity $pp$ collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1984

Multivariate spline methods in surface fitting

The use of spline functions in the development of classification algorithms is examined. In particular, a method is formulated for producing spline approximations to bivariate density functions where the density function is decribed by a histogram of measurements. The resulting approximations are then incorporated into a Bayesiaan classification procedure for which the Bayes decision regions and the probability of misclassification is readily computed. Some preliminary numerical results are presented to illustrate the method.

Guseman, L. F., Jr.↗
NASA NTRS1980

Convolution of a Doppler line by a Gaussian instrument function

A simple and direct method is obtained for assessing the distortion of a Doppler line by a Gaussian instrument function. It is suggested that a close approximation to the width of a Gaussian instrument function, or an almost Gaussian function, may be obtained by measuring a line with a Doppler absorption coefficient. The method is applicable to diode laser measurements, and may be used whenever a Gaussian instrument function is a reasonable approximation to real conditions

Fridovich, B.↗
DOE OSTI2024

LTAU-FF: Loss Trajectory Analysis for Uncertainty in atomistic Force Fields

LTAU (Loss Trajectory Analysis for Uncertainty) is a technique for estimating the uncertainty in a model's predictions for any regression task by approximating the cumulative distribution function (CDF) of the model's errors over the course of training. The approximated CDF, combined with a similarity search algorithm in the model's descriptor space, can then be used to estimate the likelihood that the model's predictions on any given test point will fall below a chosen threshold. LTAU-FF (LTAU in atomistic Force Fields) is the application of LTAU specifically for use with atomistic force fields.

Vita, JoshuaA↗
NASA NTRS1980

Properties of the Io plasma torus inferred from Voyager EUV data

A physical model for the Io plasma torus is constructed to explain the EUV radiative emission observed by the Voyager UV spectrometer. Electron impact excitation rate coefficients for electronic transitions of S III, S IV, O II and O III are calculated by the method of distorted waves (Davis, Kepple, and Blaha, 1976); these coefficients account for the asymmetric shape of the 686 A feature. It is concluded that the electron gas must have a distribution function with a non-Maxwellian tail. An approximate representation of the distribution function as two temperature components requires a cold component of 3.5-4 eV and density of 2000 per cu cm and a hot component of about 100 eV and density of 50-100 per cu cm to satisfy observational constraints.

Strobel, D. F.↗
NASA NTRS1986

An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable

The present adaptive FEM technique for convection-dominated problems is based on a Petrov-Galerkin scheme for spatial approximation, whose typical time-step employs test functions chosen to yield an approximate solution coinciding with the exact solutions at the finite element grid nodes. The derivation of truly local a posteriori error estimates is made possible by this procedure, which is also shown to be a very effective solver by the numerical examples presented.

Demkowicz, L.↗
NASA NTRS1993

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

Starlinger, Alois↗
DOE OSTI2024

Learning Functions Varying along a Central Subspace

Many functions of interest are in a high-dimensional space but exhibit low-dimensional structures. This paper studies regression of an s-Hölder function in $R^D$ which varies along a central subspace of dimension $d$ while $d \ll D$. A direct approximation of $f$ in $R^D$ with an accuracy $\varepsilon$ requires the number of samples in the order of $\varepsilon^{-(2s+D)/s}$. In this paper, we analyze the generalized contour regression (GCR) algorithm for the estimation of the central subspace and use piecewise polynomials for function approximation. GCR is among the best estimators for the central subspace, but its sample complexity is an open question. In this paper, we partially answer this questions by proving that if a variance quantity is exactly known, GCR leads to a mean squared estimation error of $O(n^{-1})$ for the central subspace. The estimation error of this variance quantity is also given in this paper. The mean squared regression error of $f$ is proved to be in the order of $(n/\log n)^{-\frac{2s}{2s+d}}$, where the exponent depends on the dimension of the central subspace instead of the ambient space . This result demonstrates that GCR is effective in learning the low-dimensional central subspace. We also propose a modified GCR with improved efficiency. Here, the convergence rate is validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Polarization options in inclusive DIS off tensor polarized deuteron

In the near future, the Jefferson Lab b 1 experiment will provide the second measurement of tensor polarized asymmetries in inclusive DIS on the deuteron. In this asymmetry, 4 independent tensor polarized structure functions contribute. This necessitates systematic approximations in the extraction of the leading twist structure function b 1 from a single tensor asymmetry measurement. Contamination from higher twist structure functions and kinematic effects is discussed here. Using a deuteron convolution model, we quantify the systematic errors from these approximations for two different choices for the target polarization direction (momentum transfer, electron beam direction). For Jefferson Lab 12 GeV kinematics, the systematic error turns out to be comparable between the two polarization options, while at higher Q 2 values the momentum transfer direction is preferred.

Cosyn, Wim [Florida International University, Miam↗
NASA NTRS1995

Very low mass stars and white dwarfs in NGC 6397

Deep Wide Field/Planetary Camera 2 (WFPC2) images in wide bands centered at 606 and 802 nm were taken with the Hubble Space Telescope (HST) 4.6 min from the center of the galactic globular cluster NGC 6397. The images were used to accurately position approximately 2120 stars detected in the field on a color magnitude diagram down to a limiting magnitude m(sub 814) approximately = m(sub I) approximately = 26 determined reliably and solely by counting statistics. A white dwarf sequence and a rich, narrow cluster main sequence are detected for the first time, the latter stretching from m(sub 814) = 18.5 to m(sub 814) = 24.0 where it becomes indistinguishable from the field population. Two changes of slope of the main sequence at m(sub 814) approximately = 20 and m(sub 814) approximately = 22.5 are evident. The corresponding luminosity function increases slowly from M(sub 814) approximately = 6.5 to 8.5 are expected from ground-based observations but then drops sharply from there dwon to the measurement limit. The corresponding mass function obtained bu using the only presently available mass-luminosity function for the cluster's metallicity rises to a plateau between approximately 0.25 and approximately 0.15 solar mass, but drops toward the expected mass limit of the normal hydrogen burning main sequence at approximately 0.1 solar mass. This result is in clear contrast to that obtained from the ground and implies either a substantial modification of the cluster's initial mass function due to dynamical evolution in its lifetime, or that very low mass stars are not produced in any dynamically significant amount by clusters of this type. The white dwarf sequence is in reasonable agreement with a cooling sequence of models of mass 0.5 solar mass at the canonical distance of NGC 6397 with a scatter that is most likely due to photometric errors, but may also reflect real differences in mass or chemical composition. Contamination from unresolved galaxies, which cannot be reliably identified with our filters, makes it difficult to meaningfully compare the observed white dwarf luminosity function with its theoretical counterpart.

Paresce, Francesco↗
DOE OSTI2018

Electronic optics in graphene in the semiclassical approximation

Highlights: • A rigorous semiclassical theory for the two-dimensional Dirac equation is developed. • We discuss how the use of eikonal coordinates greatly simplifies the theory. • Electronic optics in graphene is developed beyond the standard WKB approximation. • The semiclassical phase essentially affects electron focusing in graphene. - Abstract: We study above-barrier scattering of Dirac electrons by a smooth electrostatic potential combined with a coordinate-dependent mass in graphene. We assume that the potential and mass are sufficiently smooth, so that we can define a small dimensionless semiclassical parameter h≪1. This electronic optics setup naturally leads to focusing and the formation of caustics, which are singularities in the density of trajectories. We construct a semiclassical approximation for the wavefunction in all points, placing particular emphasis on the region near the caustic, where the maximum of the intensity lies. Because of the matrix character of the Dirac equation, this wavefunction contains a nontrivial semiclassical phase, which is absent for a scalar wave equation and which influences the focusing. We carefully discuss the three steps in our semiclassical approach: the adiabatic reduction of the matrix equation to aneffective scalar equation, the construction of the wavefunction using the Maslov canonical operator and the application of the uniform approximation to the integral expression for the wavefunction in the vicinity of a caustic. We consider several numerical examples and show that our semiclassical results are in very good agreement with the results of tight-binding calculations. In particular, we show that the semiclassical phase can have a pronounced effect on the position of the focus and its intensity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, Jeffrey M.↗
NASA NTRS1989

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, J. M.↗
DOE OSTI2026

Thermal exchange-correlation functionals: Capturing quantum electron behavior in warm, dense plasmas

We summarize and give perspective upon recent progress in developing non-empirical constraint-based thermal (i.e., free energy) exchange-correlation (XC) density functionals essential for accurate description of the quantum behavior of electrons in warm, dense plasmas. After delineating the critical role of ground-state functionals for zero-temperature, time-dependent DFT, we outline the underpinnings of local density approximation, generalized gradient approximation (GGA), and meta-GGA XC free-energy functionals. Two basic thermalization principles for upgrading ground-state XC functionals to successful thermal ones are emphasized. Then, we turn to a long-standing challenge, assessment of the accuracy of well-founded functionals. Unlike the ground state, there are a few exact results for large T and P. An exception is path integral Monte Carlo (PIMC) data for dense H/D and He plasmas. For those, we did ab initio molecular dynamics simulations under selected thermodynamic conditions employing five thermal XC functionals: two approximate thermal GGAs, fully thermal GGA, an approximate meta-GGA, and fully thermal meta-GGA. Comparisons with the PIMC data show that functionals thermalized by augmenting a non-thermal functional with a lower-level thermal contribution are inferior to functionals with thermal XC and spatial inhomogeneity effects taken into account at the same level of refinement. We believe this and similar evidence should be convincing to the high-energy density physics community of the necessity of use of proper thermal XC functionals in simulation studies of finite-temperature quantum effects in warm, dense plasmas.

Ab-initio molecular dynamics↗
NASA NTRS1989

Time domain unsteady incompressible cascade airfoil theory for helicopter rotors in hover

A detailed derivation of a finite-time arbitrary-motion incompressible cascade theory is presented for both Laplace and frequency domains. The generalized cascade lift deficiency function is shown to be consistent with the generalized Theodorsen's lift deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity; it also yields a correct value for the zero reduced frequency limit. Efficient numerical procedures are presented for the evaluation of the cascade lift deficiency function. Numerical examples comparing the cascade lift deficiency function with Loewy's (1957) rotary-wing lift deficiency function in frequency domain are presented. Pade approximants of the cascade lift deficiency function are constructed using a Bode plot approach that allows for complex poles. A general-purpose optimization program is used to determine the coefficients of the approximant.

Dinyavari, M. A. H.↗
NASA NTRS1992

Rational approximations from power series of vector-valued meromorphic functions

Let F(z) be a vector-valued function, F: C yields C(sup N), which is analytic at z = 0 and meromorphic in a neighborhood of z = 0, and let its Maclaurin series be given. In this work we developed vector-valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyzed some of the algebraic and analytic properties of the rational approximations thus obtained, and showed that they were akin to Pade approximations. In particular, we proved a Koenig type theorem concerning their poles and a de Montessus type theorem concerning their uniform convergence. We showed how optical approximations to multiple poles and to Laurent expansions about these poles can be constructed. Extensions of the procedures above and the accompanying theoretical results to functions defined in arbitrary linear spaces was also considered. One of the most interesting and immediate applications of the results of this work is to the matrix eigenvalue problem. In a forthcoming paper we exploited the developments of the present work to devise bona fide generalizations of the classical power method that are especially suitable for very large and sparse matrices. These generalizations can be used to approximate simultaneously several of the largest distinct eigenvalues and corresponding eigenvectors and invariant subspaces of arbitrary matrices which may or may not be diagonalizable, and are very closely related with known Krylov subspace methods.

Sidi, Avram↗
DOE OSTI2020

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗