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At least 1,567 records · Page 87
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Locating the Discontinuities of a Bounded Function by the Partial Sums of its Fourier Series I: Periodical Case

A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.

Kvernadze, George↗
DOE OSTI2024

Effect of XC functionals and dispersion corrections on the DFT‐computed structural and vibrational properties of SrCl 2 –NaCl and ZrF 4 –LiF

Density functional theory (DFT) calculations were performed to examine the impact of exchange–correlation (XC) functionals and van der Waals corrections (specifically the D3 method) on the structural and vibrational properties of the SrCl 2 –NaCl and ZrF 4 –LiF salt systems. Multiple XC functionals, including the local density approximation (LDA), the generalized gradient approximation using the Perdew–Burke–Ernzerhof (PBE) model, and its modified form suitable for solids (PBEsol), the dispersion-corrected PBE-D3 and PBEsol-D3, were considered. Of these functionals, LDA was found to exhibit the highest degree of error, while PBEsol and PBE-D3 displayed the least error. Underestimated lattice parameters compared with experimental values were observed to result in higher force constants, leading to an overprediction of vibrational frequencies. Conversely, an overestimation of lattice parameters was associated with lower vibrational frequencies. The methodology presented in this study yielded results that are in good agreement with experiment, irrespective of the method (finite differences vs. density functional perturbation theory) employed for calculating infrared and Raman spectra. It was further demonstrated that for alkali halides with weak Raman scattering, utilizing a supercell constructed from primitive cells better predicts Raman features than does the use of conventional cells.

Raman↗
DOE OSTI2016

ωB97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation

A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation is presented in this paper. The final 12-parameter functional form is selected from approximately 10 × 10 9 candidate fits that are trained on a training set of 870 data points and tested on a primary test set of 2964 data points. The resulting density functional, ωB97M-V, is further tested for transferability on a secondary test set of 1152 data points. For comparison, ωB97M-V is benchmarked against 11 leading density functionals including M06-2X, ωB97X-D, M08-HX, M11, ωM05-D, ωB97X-V, and MN15. Encouragingly, the overall performance of ωB97M-V on nearly 5000 data points clearly surpasses that of all of the tested density functionals. Finally, in order to facilitate the use of ωB97M-V, its basis set dependence and integration grid sensitivity are thoroughly assessed, and recommendations that take into account both efficiency and accuracy are provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

How Well Can the M06 Suite of Functionals Describe the Electron Densities of Ne, Ne 6+ , and Ne 8+ ?

The development of better approximations to the exact exchange-correlation functional is essential to the accuracy of density functionals. A recent study indicated that functionals with few parameters offer more accurate electron densities than recently developed many-parameter functionals for light closed-shell atomic systems. In this study, we calculated electron densities, their gradients, and Laplacians of Ne, Ne 6+ , and Ne 8+ using 19 electronic structure methods, and we compared them to the CCSD reference results. Two basis sets, namely, aug-cc-pωCV5Z and aug-cc-pV5Z, are utilized in the calculations. We found that the choice of basis set has a significant impact on the errors and rankings of some of the selected methods. The errors of electron densities, their gradients, and Laplacians calculated with the aug-cc-pV5Z basis set are substantially reduced, especially for Minnesota density functionals, as compared to the results using the aug-cc-pωCV5Z basis set (a larger basis set utilized in earlier work (Medvedev et al. Science2017, 355, 49–52)). The rankings of the M06 suite of functionals among the 19 methods are greatly improved with the aug-cc-pV5Z basis set. Furthermore, the performances of the HSE06, BMK, MN12-L, and MN12-SX functionals are also improved with the aug-cc-pV5Z basis set. The M06 suite of functionals is capable of providing accurate electron densities, gradients, and Laplacians using the aug-cc-pV5Z basis set, and thus it is suitable for a wide range of applications in chemistry and physics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

Approximate Solutions Of Equations Of Steady Diffusion

Rigorous analysis yields reliable criteria for "best-fit" functions. Improved "curve-fitting" method yields approximate solutions to differential equations of steady-state diffusion. Method applies to problems in which rates of diffusion depend linearly or nonlinearly on concentrations of diffusants, approximate solutions analytic or numerical, and boundary conditions of Dirichlet type, of Neumann type, or mixture of both types. Applied to equations for diffusion of charge carriers in semiconductors in which mobilities and lifetimes of charge carriers depend on concentrations.

Edmonds, Larry D.↗
DOE OSTI2019

Comparison of first principles and semi-empirical models of the structural and electronic properties of Ge{sub 1−x}Sn{sub x} alloys

We present and compare three distinct atomistic models—based on first principles and semi-empirical approaches—of the structural and electronic properties of Ge{sub 1−x}Sn{sub x} alloys. Density functional theory calculations incorporating Heyd–Scuseria–Ernzerhof (HSE), local density approximation (LDA) and modified Becke–Johnson (mBJ) exchange-correlation functionals are used to perform structural relaxation and electronic structure calculations for a series of Ge{sub 1−x}Sn{sub x} alloy supercells. Based on HSE calculations, a semi-empirical valence force field (VFF) potential and sp{sup 3}s{sup ∗} tight-binding (TB) Hamiltonian are parametrised. Comparing the HSE, LDA+mBJ and VFF+TB models, and using the HSE results as a benchmark, we demonstrate that: (1) LDA+mBJ calculations provide an accurate first principles description of the electronic structure at reduced computational cost, (2) the VFF potential is sufficiently accurate to circumvent the requirement to perform first principles structural relaxation, and (3) VFF+TB calculations provide a good quantitative description of the alloy electronic structure in the vicinity of the band edges. Our results also emphasise the importance of Sn-induced band mixing in determining the nature of the conduction band structure of Ge{sub 1−x}Sn{sub x} alloys. The theoretical models and benchmark calculations we present inform and enable predictive, computationally efficient and scalable atomistic calculations for disordered alloys and nanostructures. This provides a suitable platform to underpin further theoretical investigations of the properties of this emerging semiconductor alloy.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2015

Half-metallic antiferromagnetism in double perovskite BiPbCrCuO{sub 6}

The electronic structure and magnetic properties of BiPbCrCuO{sub 6} double perovskite are investigated based on first-principles density functional calculations with generalized gradient approximation (GGA) and GGA incorporated with Coulomb correlation interaction U (GGA + U). The results suggest the half-metallic (HM) and antiferromagnetic (AFM) properties of BiPbCrCuO{sub 6} double perovskite. The HM-AFM property of the double perovskite is caused by the double-exchange mechanism between neighboring Cr{sup 5+}(t{sub 2g}{sup 1}↓) and Cu{sup 2+}(t{sub 2g}{sup 3}↑t{sub 2g}{sup 3}↓e{sub g}{sup 2}↑e{sub g}↓) via the intermediate O{sup 2−}(2s{sup 2}2p{sup 6}) ion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

QCD factorization with multihadron fragmentation functions

Important aspects of quantum chromodynamics (QCD) factorization theorems are the properties of the objects involved that can be identified as universal. One example is that the definitions of parton densities and fragmentation functions for different types of hadrons differ only in the identity of the nonperturbative states that form the matrix elements, but are otherwise the same. This leads to independence of perturbative calculations on nonperturbative details of external states. It also lends support to interpretations of correlation functions as encapsulations of intrinsic nonperturbative properties. These characteristics have usually been presumed to still hold true in fragmentation functions even when the observed nonperturbative state is a small-mass cluster of n hadrons rather than simply a single isolated hadron. However, the multidifferential aspect of cross sections that rely on these latter types of fragmentation functions complicates the treatment of kinematical approximations in factorization derivations. That has led to recent claims that the operator definitions for fragmentation functions need to be modified from the single hadron case with nonuniversal prefactors. With such concerns as our motivation, we retrace the steps for factorizing the unpolarized semi-inclusive e + e − annihilation cross section and confirm that they do apply without modification to the case of a small-mass multihadron observed in the final state. In particular, we verify that the standard operator definition from single hadron fragmentation, with its usual prefactor, remains equally valid for the small-mass n -hadron case with the same hard parts and evolution kernels, whereas the more recently proposed definitions with nonuniversal prefactors do not. Our results reaffirm the reliability of most past phenomenological applications of dihadron fragmentation functions. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

A comparison of polynomial approximations and artificial neural nets as response surfaces

Artificial neural nets and polynomial approximations were used to develop response surfaces for several test problems. Based on the number of functional evaluations required to build the approximations and the number of undetermined parameters associated with the approximations, the performance of the two types of approximations was found to be comparable. A rule of thumb is developed for determining the number of nodes to be used on a hidden layer of an artificial neural net, and the number of designs needed to train an approximation is discussed.

Carpenter, William C.↗
NASA NTRS1993

Effect of design selection on response surface performance

Artificial neural nets and polynomial approximations were used to develop response surfaces for several test problems. Based on the number of functional evaluations required to build the approximations and the number of undetermined parameters associated with the approximations, the performance of the two types of approximations was found to be comparable. A rule of thumb is developed for determining the number of nodes to be used on a hidden layer of an artificial neural net and the number of designs needed to train an approximation is discussed.

Carpenter, William C.↗
DOE OSTI2014

Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory

We investigate fundamental properties of meta-generalized-gradient approximations (meta-GGAs) to the exchange-correlation energy functional, which have an implicit density dependence via the Kohn-Sham kinetic-energy density. To this purpose, we construct the most simple meta-GGA by expressing the local exchange-correlation energy per particle as a function of a fictitious density, which is obtained by inverting the Thomas-Fermi kinetic-energy functional. This simple functional considerably improves the total energy of atoms as compared to the standard local density approximation. The corresponding exchange-correlation potentials are then determined exactly through a solution of the optimized effective potential equation. These potentials support an additional bound state and exhibit a derivative discontinuity at integer particle numbers. We further demonstrate that through the kinetic-energy density any meta-GGA incorporates a derivative discontinuity. However, we also find that for commonly used meta-GGAs the discontinuity is largely underestimated and in some cases even negative.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Simple Models of Lateral Heterostructures

General analytical expressions for densities of states of a lateral heterostructure, formed by the contact of two square semi-infinite lattices with single-band and two-band spectra, were obtained in the tight-binding approximation by the Green’s function method. The semi-elliptical density of states was used for numerical estimates, and the model of two interacting dimers was proposed to estimate the charge transfer. Application of this approach to description of lateral epitaxial and graphene-like heterostructures is discussed.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2021

Approximating and incorporating model uncertainty in an inversion for seismic source functions: Preliminary results

We present preliminary work on propagating model uncertainty into the estimation of the time domain source time functions of the seismic source. Our method is based on an estimated model covariance function, which we estimate from the data. The model covariance function is then used to construct a suite of surrogate Greens functions which we use in a Monte Carlo type inversion scheme. The result is a probability density function of the six independent source time functions, each of which corresponds to an individual component of the seismic moment tensor. We compare the results of our method with those obtained using a computationally expensive finite difference Monte Carlo method and find that our new method produces results that are deficient in low frequencies. The advantage of our new method, which we term the Karhunen-Loeve Monte Carlo (KLMC) method, is that is several orders of magnitude faster than our current method, which uses a finite difference scheme to produce the suite of forward models.

42 ENGINEERING↗
DOE OSTI2020

A Multi-Function AAA Algorithm Applied to Frequency-Dependent Line Modeling: Preprint

We present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages respect to the popular Vector Fitting (VF) algorithm using examples of approximations of admittance matrices discussed in a very recent paper and by the creators of VF. We show that not only MIAAA outperforms VF in terms of achieving better accuracy using a smaller number of poles, but also has no numerical issues to achieve convergence. In contrast to VF, MIAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Assessing density functionals for describing methane dissociative chemisorption on Pt(110)-(2×1) surface

In this work, we explore the suitability of several density functionals with the generalized gradient approximation (GGA) and beyond for describing the dissociative chemisorption of methane on the reconstructed Pt(110)-(2×1) surface. The bulk and surface structures of the metal, methane adsorption energy, and dissociation barrier are used to assess the functionals. A van der Waals corrected GGA functional (optPBE-vdW) and a metaGGA functional with van der Waals correction (MS PBEl-rVV10) are selected for ab initio molecular dynamics calculations of the sticking probability. Our results suggest that the use of these two functionals may lead to a better agreement with existing experimental results, thus serving as a good starting point for future development of reliable machine-learned potential energy surfaces for the dissociation of methane on the Pt(110)-(2×1) surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1948

The Problem of Torsion in Prismatic Members of Circular Segmental Cross Section

The problem is solved by approximation, by setting up a function complying with the differential equation of the stress function, and determining the coefficients appearing in it in such a way that the boundary condition is fulfilled as nearly as possible. For the semicircle, for which the solution is known, the method yields very accurate values; the approximated stress distribution is in good agreement with the accurately computed distribution. Stress and strain measurements indicate that the approximate solution is in sufficiently exact agreement with reality for segmental cross sections.

Weigand, A.↗