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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Three-dimensional reconstruction of x-ray emission volumes in magnetized liner inertial fusion from sparse projection data using a learned basis

The ability to visualize x-ray and neutron emission from fusion plasmas in 3D is critical to understand the origin of the complex shapes of the plasmas in experiments. Unfortunately, this remains challenging in experiments that study a fusion concept known as Magnetized Liner Inertial Fusion (MagLIF) due to a small number of available diagnostic views. Here, we present a basis function-expansion approach to reconstruct MagLIF stagnation plasmas from a sparse set of x-ray emission images. A set of natural basis functions is “learned” from training volumes containing quasi-helical structures whose projections are qualitatively similar to those observed in experimental images. Tests on several known volumes demonstrate that the learned basis outperforms both a cylindrical harmonic basis and a simple voxel basis with additional regularization, according to several metrics. Two-view reconstructions with the learned basis can estimate emission volumes to within 11% and those with three views recover morphology to a high degree of accuracy. The technique is applied to experimental data, producing the first 3D reconstruction of a MagLIF stagnation column from multiple views, providing additional indications of liner instabilities imprinting onto the emitting plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Universal reduced basis for the calibration of covariant energy density functionals

The reduced basis method is used to construct a “universal” basis of Dirac orbitals that may be applicable throughout the nuclear chart to calibrate covariant energy density functionals. Relative to the successful development of a reduced basis emulator for the nonrelativistic Schrödinger equation, the Dirac equation adds an extra layer of complexity due to the existence of negative energy states, which complicates building an efficient reduced basis. However, once this problem is mitigated, the resulting reduced basis is able to accurately and efficiently reproduce the high-fidelity model at a fraction of the computational cost. We are confident that the resulting reduced basis will serve as a foundational element in developing rapid and accurate emulators. In turn, these emulators will play a critical role in the Bayesian optimization of covariant energy density functionals.

Bayesian methods↗
NASA NTRS1982

Application of the reduced basis method to nonlinear transient thermal analysis

An effort to apply the reduced basis method to nonlinear transient thermal analysis is described. The method combines the classical Rayleigh-Ritz and modal superposition techniques with contemporary finite element methods to retain modeling versatility as the degrees of freedom in a problem are reduced. The essence of the method is to use a few thermal modes from eigenvalue analyses as basis vectors to represent the temperature response for a given thermal problem similar to the use of vibration modes to represent displacements in a dynamic response problem. Approximate temperature distributions were obtained using the reduced basis method for a small section of the Shuttle Orbiter lower wing undergoing reentry heating. Good agreement was obtained between the reduced basis method solutions and full system solutions with reductions in the degrees of freedom of up to a factor of four. The good agreement indicates the reduced basis method has the potential for significant reduction in computing effort for thermal analysis; however, considerable work remains to determine techniques for selecting the type and number of basis vectors needed for approximate solutions to more complex transient thermal problems.

Shore, C. P.↗
NASA NTRS1989

Near Hartree-Fock quality Gaussian type orbital basis sets for the first- and third-row atoms

Energy-optimized, near Hartree-Fock (NHF) quality Gaussian type orbital (GTO) basis sets are reported for the second-row (Li to Ne) and fourth-row (K to Kr) atoms. The most accurate basis sets reported for the second row are (18s 13p) sets which are with 4 micro E(H) of the numerical Hartree-Fock (NHF) results. For B to Ne basis sets with more than 15s functions are quadruple zeta in the valence space. For the second-row transition metal atoms the (20s 12p 9d) basis sets are triple zeta in the valence space and are approximately equivalent to Clementi and Roetti's accurate Slater type orbital sets. Supplementing the (20s 12p 9d) basis sets optimized for the lowest state with the 4s(2)3d(n) occupation with a diffuse d function gives self-consistent-field energy separations to the 4s(1)3d(n+1) and 3d(n+2) states which are within 100 micro E(H) of the NHF results. The most accurate basis sets for the transition metal atoms are with 30 micro E(H) of the NHF results. In addition, energy optimized sets are reported for He(3P), Li(2P) and Be(3P).

Partridge, Harry↗
NASA NTRS2022

Structural Shape Sensing from Strain Data Using the Basis Function Method

An aircraft shape must be measured during flight to implement an active trim shape control, such as an active dihedral control for a highly flexible aircraft with a high-aspect-ratio wing, and an active sonic boom control for a supersonic transport aircraft. A basis function method for linear as well as geometrically nonlinear structural shape sensing is proposed in this study. Basis functions can be mode shapes, linear static deformation shapes, or geometrically nonlinear static deformation shapes. The proposed basis function method is validated using a high-aspect-ratio wing, a swept test plate, and the National Aeronautics and Space Administration Low Boom Flight Demonstration mission X-59 Quiet Supersonic Technology (QueSST) aircraft (Lockheed Martin, Bethesda, Maryland). A large structural deformation of a high-aspect-ratio wing is successfully captured using the proposed basis function method with less than 0.3-percentprediction error at the wing-tip section. The basis function method gives excellent deformation prediction, even with stress concentration. Performance of the basis functions is compared using the X-59 stabilator sample case. In most of the sample load cases, static deformations give a better correlation with the target deformation than do mode shapes. Wing shape sensing with sparse strain data is also demonstrated in this study using the X-59 QueSST aircraft. Predicted structural deformations match reasonably with the target deformations even without strain gauges on some structural components. The predicted deformations have a good match with the target deformations.

Chan-gi Pak↗
DOE OSTI2026

Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit

We benchmark the accuracy of Dunning correlation-consistent Gaussian basis sets for computing frequencydependent second-order hyperpolarizabilities relevant to second-harmonic generation (SHG), using multiresolution analysis (MRA) as a reference. Basis set errors are analyzed using a unit-sphere representation of the effective hyperpolarizability vector, enabling direct assessment of directional error structure. We introduce a relative RMS total error metric that integrates directional deviations over the unit sphere and complement it with signed projection errors that distinguish over- and underestimation. Unsupervised clustering based on these signed directional metrics reveals four distinct convergence behaviors across a set of 68 molecules. Unitsphere visualizations of representative systems show that basis set errors are often highly anisotropic and localized along specific bond directions, even when global error measures appear small. Doubly augmented basis sets consistently outperform singly augmented ones, and core-polarization functions are required for uniform convergence in second-row systems. Overall, this work demonstrates that directional analysis combined with clustering provides a robust framework for understanding basis set convergence in nonlinear optical response properties.

Basis sets↗
DOE OSTI2025

Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories

Traditional SU⁡(𝑁) lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) 𝑉 𝜆 of the SU⁡(𝑁) gauge symmetry. On a lattice, the elements of this basis are tensor networks comprising dimer tensors on the links labeled by a set of irreps {𝜆 ℓ } and monomer tensors on sites labeled by {𝜆 𝑠 }. These tensors naturally define a local site Hilbert space, ℋ$^𝑔_𝑠$, on which gauge transformations act. Gauss’s law introduces an additional index 𝛼 𝑠 =1,2,…,𝒟⁡(ℋ$^𝑔_𝑠$) that labels an orthonormal basis of the gauge-invariant subspace of ℋ$^𝑔_𝑠$. This monomer-dimer tensor-network (MDTN) basis, |{𝜆 𝑠 },{𝜆 ℓ },{𝛼 𝑠 }⟩, of the physical Hilbert space enables the construction of new qubit-regularized SU⁡(𝑁) gauge theories that are free of sign problems while preserving key features of traditional LGTs. Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized SU(2) and SU(3) gauge theory in 𝑑 =2 and 𝑑 =3 spatial dimensions, formulated using the MDTN basis, and show that they reproduce the universal results of traditional LGTs at these transitions. Additionally, in 𝑑 =1, we demonstrate using a plaquette chain that the string tension at zero temperature can be continuously tuned to zero by adjusting a model parameter that plays the role of the gauge coupling in traditional LGTs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1975

Solutions to Kuessner's integral equation in unsteady flow using local basis functions

The computational procedure and numerical results are presented for a new method to solve Kuessner's integral equation in the case of subsonic compressible flow about harmonically oscillating planar surfaces with controls. Kuessner's equation is a linear transformation from pressure to normalwash. The unknown pressure is expanded in terms of prescribed basis functions and the unknown basis function coefficients are determined in the usual manner by satisfying the given normalwash distribution either collocationally or in the complex least squares sense. The present method of solution differs from previous ones in that the basis functions are defined in a continuous fashion over a relatively small portion of the aerodynamic surface and are zero elsewhere. This method, termed the local basis function method, combines the smoothness and accuracy of distribution methods with the simplicity and versatility of panel methods. Predictions by the local basis function method for unsteady flow are shown to be in excellent agreement with other methods. Also, potential improvements to the present method and extensions to more general classes of solutions are discussed.

Fromme, J. A.↗
NASA NTRS1992

On the performance of large Gaussian basis sets for the computation of total atomization energies

The total atomization energies of a number of molecules have been computed using an augmented coupled-cluster method and (5s4p3d2f1g) and 4s3p2d1f) atomic natural orbital (ANO) basis sets, as well as the correlation consistent valence triple zeta plus polarization (cc-pVTZ) correlation consistent valence quadrupole zeta plus polarization (cc-pVQZ) basis sets. The performance of ANO and correlation consistent basis sets is comparable throughout, although the latter can result in significant CPU time savings. Whereas the inclusion of g functions has significant effects on the computed Sigma D(e) values, chemical accuracy is still not reached for molecules involving multiple bonds. A Gaussian-1 (G) type correction lowers the error, but not much beyond the accuracy of the G1 model itself. Using separate corrections for sigma bonds, pi bonds, and valence pairs brings down the mean absolute error to less than 1 kcal/mol for the spdf basis sets, and about 0.5 kcal/mol for the spdfg basis sets. Some conclusions on the success of the Gaussian-1 and Gaussian-2 models are drawn.

Martin, J. M. L.↗
NASA NTRS1995

A Comparison of Correlation-Consistent and Pople-Type Basis Sets

Correlation-consistent basis sets are compared with Pople-type basis sets for the calculation of atomization energies using the G2(B3LYP/MP2/CC) approach. Without a higher-level correction, the smallest errors are found for the augmented- correlation-consistent polarized valence triple zeta plus tight d basis sets. However, after inclusion of a higher-level correction, the combination of the 6-311G** basis set for the high-level correlation treatment and 6-311+G(3df,2p) for the MP2 step yields the best results. At the spin-unrestricted CCSD(T) level and for the basis set considered in this work, the G2(B3LYP/MP2/CC) approach works better than the PCIX approach for the atomization energies of the 55 G2 molecules.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1998

Atomization Energies of SO and SO2; Basis Set Extrapolation Revisted

The addition of tight functions to sulphur and extrapolation to the complete basis set limit are required to obtain accurate atomization energies. Six different extrapolation procedures are tried. The best atomization energies come from the series of basis sets that yield the most consistent results for all extrapolation techniques. In the variable alpha approach, alpha values larger than 4.5 or smaller than 3, appear to suggest that the extrapolation may not be reliable. It does not appear possible to determine a reliable basis set series using only the triple and quadruple zeta based sets. The scalar relativistic effects reduce the atomization of SO and SO2 by 0.34 and 0.81 kcal/mol, respectively, and clearly must be accounted for if a highly accurate atomization energy is to be computed. The magnitude of the core-valence (CV) contribution to the atomization is affected by missing diffuse valence functions. The CV contribution is much more stable if basis set superposition errors are accounted for. A similar study of SF, SF(+), and SF6 shows that the best family of basis sets varies with the nature of the S bonding.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1999

TiCl, TiH and TiH+ Bond Energies, a Test of a Correlation Consistent Ti Basis Set

Correlation consistent basis sets are developed for Ti atom. The polarization functions are optimized for the average of the 3F and 5F states. One series of correlation consistent basis sets is for 3d and 4s correlation, while the second series includes 3s and 3p correlation as well as 3d and 4s correlation. These basis sets are tested using the Ti 3F-5F separation and the dissociation energies of TiCl X4Phi, TiH X4Phi, and TiH(+) X3Phi. The CCSD(T) complete basis set limit values are determined by extrapolation. The Douglas Kroll approach is used to compute the scalar relativistic effect. Spin-orbit effects are taken from experiment and/or computed at the CASSCF level. The Ti 3F-5F separation is in excellent agreement with experiment, while the TiCl, TiH, and TiH(+) bond energies are in good agreement with experiment. Extrapolation with the valence basis set is consistent with other atoms, while including 3s and 3p correlation appears to make extrapolation.

Bauschlicher, Charles W., Jr.↗
NASA NTRS2003

Meshless Local Petrov-Galerkin Euler-Bernoulli Beam Problems: A Radial Basis Function Approach

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Compactly and noncompactly supported radial basis functions are considered. The non-compactly supported cubic radial basis function is found to perform very well. Results obtained from the radial basis MLPG method are comparable to those obtained using the conventional MLPG method for mixed boundary value problems and problems with discontinuous loading conditions.

Raju, I. S.↗
NASA NTRS2007

Zernike-like Orthogonal Basis Functions for Wavefront Characterization over Sampled, Irregular Apertures

For optical systems with circular apertures, wavefronts are often analyzed using Zernike polynomials, and individual Zernike functions are associated with familiar optical aberrations. For systems with noncircular apertures, or in practical situations in which wavefronts are measured at a limited number of points in the aperture, the Zernike polynomials are no longer an orthogonal basis for the measured data. Although there are an endless number of ways to create a basis for such measured data, a "Zernike-like" basis is useful to connect with our experience with the usual optical aberrations. In this paper, the steps required to identify a Zernike-like basis for wavefronts over sampled, irregular apertures are presented, based on the Gram-Schmidt orthogonalization technique. The benefits of analyzing optical wavefronts using an orthogonal basis specific to an optical system's aperture shape and wavefront sampling, instead of using the traditional Zernike polynomials, are detailed in two examples, from image-based wavefront sensing on a segmented-aperture telescope (the James Webb Space Telescope Testbed Telescope at Ball Aerospace) and from interferometer characterization for surface metrology of a hexagonal mirror segment.

Aronstein, David L.↗
NASA NTRS2015

Mock Certification Basis for an Unmanned Rotorcraft for Precision Agricultural Spraying

This technical report presents the results of a case study using a hazard-based approach to develop preliminary design and performance criteria for an unmanned agricultural rotorcraft requiring airworthiness certification. This case study is one of the first in the public domain to examine design and performance criteria for an unmanned aircraft system (UAS) in tandem with its concept of operations. The case study results are intended to support development of airworthiness standards that could form a minimum safety baseline for midsize unmanned rotorcraft performing precision agricultural spraying operations under beyond visual line-of-sight conditions in a rural environment. This study investigates the applicability of current methods, processes, and standards for assuring airworthiness of conventionally piloted (manned) aircraft to assuring the airworthiness of UAS. The study started with the development of a detailed concept of operations for precision agricultural spraying with an unmanned rotorcraft (pp. 5-18). The concept of operations in conjunction with a specimen unmanned rotorcraft were used to develop an operational context and a list of relevant hazards (p. 22). Minimum design and performance requirements necessary to mitigate the hazards provide the foundation of a proposed (or mock) type certification basis. A type certification basis specifies the applicable standards an applicant must show compliance with to receive regulatory approval. A detailed analysis of the current airworthiness regulations for normal-category rotorcraft (14 Code of Federal Regulations, Part 27) was performed. Each Part 27 regulation was evaluated to determine whether it mitigated one of the relevant hazards for the specimen UAS. Those regulations that did were included in the initial core of the type certification basis (pp. 26-31) as written or with some simple modifications. Those regulations that did not mitigate a recognized hazard were excluded from the certification basis. The remaining regulations were applicable in intent, but the text could not be easily tailored. Those regulations were addressed in separate issue papers. Exploiting established regulations avoids the difficult task of generating and interpreting novel requirements, through the use of acceptable, standardized language. The rationale for the disposition of the regulations was assessed and captured (pp. 58-115). The core basis was then augmented by generating additional requirements (pp. 38-47) to mitigate hazards for an unmanned sprayer that are not covered in Part 27.

Hayhurst, Kelly J.↗
DOE OSTI2020

Electronic couplings for singlet fission: Orbital choice and extrapolation to the complete basis set limit

Abstract For the search for promising singlet fission candidates, the calculation of the effective electronic coupling, which is required to estimate the singlet fission rate between the initially excited state (S 0 S 1 ) and the multiexcitonic state ( 1 TT, two triplets on neighboring molecules, coupled into a singlet), should be sufficiently reliable and fast enough to explore the configuration space. We propose here to modify the calculation of the effective electronic coupling using a nonorthogonal configuration interaction approach by: (a) using only one set of orbitals, optimized for the triplet state of the molecules, to describe all molecular electronic states, and (b) only taking the leading configurations into consideration. Furthermore, we also studied the basis set convergence of the electronic coupling, and we found, by comparison to the complete basis set limit obtained using the cc‐pV n Z series of basis sets, that both the aug‐cc‐pVDZ and 6–311++G** basis sets are a good compromise between accuracy and computational feasibility. The proposed approach enables future work on larger clusters of molecules than dimers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Accelerated basis adaptation in homogeneous chaos spaces

Polynomial chaos expansions (PCE) provide an efficient approach to uncertainty quantification (UQ) and have been adapted to diverse applications across the spectrum of science and engineering. For situations involving large stochastic parameterizations, the curse of dimensionality renders PCE-based methods computationally prohibitive. A basis adaptation approach for PCE was proposed by Tipireddy and Ghanem (2014) which transforms the input random variables through an isometry such that sufficient probabilistic characterization of specific quantities of interest (QoI) is concentrated in an algebraic manifold embedded in the linear span of the dominant transformed variables. While quite versatile, that original version of the PCE basis adaptation exhibited slow convergence for a number of problems of practical significance. In the present paper, we propose two novel methods to accelerate the convergence of the original basis adaptation approach, thus expanding its reach while also providing insight into its performance. In the first method, information gained from a pilot PCE representation is used to correct the mean and Gaussian coefficients in the adapted space. By taking advantages of probabilistic information in higher dimensional adaptation gleaned from an initial adaptation, the second method updates the rotation matrix used to identify the dominant transformed variables. In this manner, the new rotation matrix concentrates even more probabilistic information in its first few dimensions. These two method can be combined to achieve even better performance, the combined method is referred to as sequentially optimized adaptation method. Here, the methods are demonstrated on an analytical test function and a model of a space structure with several sub-components and a non-smooth quantity of interest representing the maximum acceleration over time. Both methods achieve accelerated convergence of the basis adaptation approach with negligible additional costs.

Accelerated convergence↗
DOE OSTI2023

Reproducibility of calculations on Li species with correlation-consistent basis sets

Here we have found that two different basis set series, both labeled cc-pVxZ, are widely available and widely used for calculation on Li compounds such that calculations that should be the same are different, causing a reproducibility problem. Here we study the magnitude of the disagreement of these nominally-the-same basis sets for wave function and density functional calculations of Li clusters. We find deviations among the basis sets of as large as 22 millihartrees. In most cases one obtains lower energies with the noncanonical choices. Therefore, it is important to specify which version of the basis set is used for calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗