Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Function approximation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,675 records · Page 93
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A Data-Driven Approach for High-Impedance Fault Localization in Distribution Systems: Preprint

Accurate and quick identification of high-impedance faults (HIFs) is critical for the reliable operation of distribution systems. Unlike other faults in power grids, HIFs are very difficult to detect by conventional overcurrent relays due to the low fault current. Although HIFs can be affected by various factors, the voltage-current characteristics can substantially imply how the system responds to the disturbance and thus provides opportunities to effectively localize HIFs. In this work, we propose a data-driven approach for the identification of HIF events. To tackle the nonlinearity of the voltage-current trajectory, first, we formulate optimization problems to approximate the trajectory with piecewise functions. Then we collect the function features of all segments as inputs and use the support vector machine approach to efficiently identify HIFs at different locations. Numerical studies on the IEEE 123-node test feeder demonstrate the validity and accuracy of the proposed approach for real-time HIF identification.

explainable artificial intelligence↗
NASA NTRS1980

Grid generation using differential systems techniques

The errors in approximating the derivatives of a function by traditional central differences at grid points of a curvilinear coordinate system were examined. The implications concerning the accuracy of the numerical solution of a partial differential equation are explained by considering several numerical examples. Although this study only considers the two dimensional case, the techniques and implications are equally valid for three dimensional grids. An interesting feature of the error analysis is its simplicity. Most of the results follow by merely working with the truncation terms of some power series expansion. These series expansions also give rise to higher order difference approximations which can significantly reduce error when the grid spacing changes rapidly, as might be the case in problems with shock waves or thin boundary layers.

Thompson, J. F.↗
DOE OSTI2017

Coupled Cluster and Density Functional Studies of Atomic Fluorine Chemisorption on Coronene as Model Systems for Graphene Fluorination

Potential energy curves (PECs) of atomic fluorine adsorption on coronene as a model for graphene or nanocarbon surfaces have been computed. The PECs were obtained by scanning the fluorine atom distance to one of the center carbon atoms of the coronene molecule as model system in a “top” position from 4.0 to1.0 Å in intervals of 0.1 Å using a variety of quantum chemical methods. Various density functional theory (DFT) functionals, such as B3LYP, PBE, PBE0, CAM-B3LYP, and LC-ωPBE; approximate DFT methods such as several levels of the density-functional tight-binding (DFTB) method, as well as ab initio wave function theory methods such as MP2, CCSD, CCSD(T), and G2MS extrapolations, were used to evaluate energies for B3LYP/cc-pVDZ PEC geometries. G2MS is an approximation to the highly accurate CCSD(T)/cc-pVTZ level of theory in our work. We found that fluorine is chemically adsorbed on coronene with a binding energy of 22.9 and 23.3 kcal/mol at the B3LYP/cc-pVDZ and G2MS levels of theory, respectively, and 18.3 and 19.3 kcal/mol after counterpoise correction. Here, we found that pure DFT functionals and their DFTB approximations fail to predict the correct dissociation limit due to the DFT-inherent self-interaction error and various limitations in the DFTB approximation itself.

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

Computer program for calculating and fitting thermodynamic functions

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and free energy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of a least-squares fit, and (3) calculates, as a function of temperture, heats of formation and equilibrium constants. The program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, five methods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for estimating thermodynamic functions for some species is also given.

Mcbride, Bonnie J.↗
DOE OSTI2023

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. Here, this study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1978

Fault-tolerant software for aircraft control systems

Concepts for software to implement real time aircraft control systems on a centralized digital computer were discussed. A fault tolerant software structure employing functionally redundant routines with concurrent error detection was proposed for critical control functions involving safety of flight and landing. A degraded recovery block concept was devised to allow collocation of critical and noncritical software modules within the same control structure. The additional computer resources required to implement the proposed software structure for a representative set of aircraft control functions were discussed. It was estimated that approximately 30 percent more memory space is required to implement the total set of control functions. A reliability model for the fault tolerant software was described and parametric estimates of failure rate were made.

Source record↗
DOE OSTI2020

Characterizing Peatland Microtopography Using Gradient and Microform-Based Approaches

Abstract Peatlands represent an important component of the global carbon cycle, storing 180–621 Gt of carbon (C). Small-scale spatial variations in elevation, frequently referred to as microtopography, influence ecological processes associated with the peatland C cycle, including Sphagnum photosynthesis and methane flux. Microtopography can be characterized with measures of topographic variability and by using conceptual classes (microforms) linked to function: most commonly hummocks and hollows. However, the criteria used to define these conceptual classes are often poorly described, if at all, and vary between studies. Such inconsistencies compel development of explicit quantitative methods to classify microforms. Furthermore, gradient-based characterizations that describe spatial variability without the use of microforms are lacking in the literature. Therefore, the objectives of this study were to (1) calculate peatland microtopographical elevation gradients and measures of spatial variability, (2) develop three microform classification methods intended for specific purposes, and (3) evaluate and contrast classification methods. Our results suggest that at spatial scales much larger than microforms, elevation distributions are unimodal and are well approximated with parametric probability density functions. Results from classifications were variable between methods and years and exhibited significant differences in mean hollow areal coverages of a raised ombrotrophic bog. Our results suggest that the conceptualization and classification of microforms can significantly influence microtopographic structural metrics. The three explicit methods for microform classification described here may be used and built upon for future applications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Estimates of Quantum Tunneling Effects for Hydrogen Diffusion in PuO 2

We detail the estimation of activation energies and quantum nuclear vibrational tunneling effects for hydrogen diffusion in PuO 2 based on Density Functional Theory calculations and a quantum double well approximation. We find that results are relatively insensitive to choice of exchange correlation functional. In addition, the representation of spin in the system and use of an extended Hubbard U correction has only a small effect on hydrogen point defect formation energies when the PuO 2 lattice is held fixed at the experimental density. We then compute approximate activation energies for transitions between hydrogen interstitial sites seeded by a semi-empirical quantum model and determine the quantum tunneling enhancement relative to classical kinetic rates. Our model indicates that diffusion rates in H/PuO 2 systems could be enhanced by more than one order of magnitude at ambient conditions and that these effects persist at high temperature. The method we propose here can be used as a fast screening tool for assessing possible quantum nuclear vibrational effects in any number of condensed phase materials and surfaces, where hydrogen hopping tends to follow well defined minimum energy pathways.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Quantum interference in polyenes

The explicit form of the zeroth Green's function in the Hückel model, approximated by the negative of the inverse of the Hückel matrix, has direct quantum interference consequences for molecular conductance. We derive a set of rules for transmission between two electrodes attached to a polyene, when the molecule is extended by an even number of carbons at either end (transmission unchanged) or by an odd number of carbons at both ends (transmission turned on or annihilated). These prescriptions for the occurrence of quantum interference lead to an unexpected consequence for switches which realize such extension through electrocyclic reactions: for some specific attachment modes the chemically closed ring will be the ON position of the switch. Normally the signs of the entries of the Green's function matrix are assumed to have no physical significance; however, we show that the signs may have observable consequences. In particular, in the case of multiple probe attachments – if coherence in probe connections can be arranged – in some cases new destructive interference results, while in others one may have constructive interference. One such case may already exist in the literature.

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

Concentration dependence of the wings of a dipole-broadened magnetic resonance line in magnetically diluted lattices

The singularities of the time autocorrelation functions (ACFs) of magnetically diluted spin systems with dipole–dipole interaction (DDI), which determine the high-frequency asymptotics of autocorrelation functions and the wings of a magnetic resonance line, are studied. Using the self-consistent fluctuating local field approximation, nonlinear equations are derived for autocorrelation functions averaged over the independent random arrangement of spins (magnetic atoms) in a diamagnetic lattice with different spin concentrations. The equations take into account the specificity of the dipole–dipole interaction. First, due to its axial symmetry in a strong static magnetic field, the autocorrelation functions of longitudinal and transverse spin components are described by different equations. Second, the long-range type of the dipole–dipole interaction is taken into account by separating contributions into the local field from distant and near spins. The recurrent equations are obtained for the expansion coefficients of autocorrelation functions in power series in time. From them, the numerical value of the coordinate of the nearest singularity of the autocorrelation function is found on the imaginary time axis, which is equal to the radius of convergence of these expansions. It is shown that in the strong dilution case, the logarithmic concentration dependence of the coordinate of the singularity is observed, which is caused by the presence of a cluster of near spins whose fraction is small but contribution to the modulation frequency is large. As an example a silicon crystal with different {sup 29}Si concentrations in magnetic fields directed along three crystallographic axes is considered.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

The bispectrum of cosmic string temperature fluctuations including recombination effects

We calculate the cosmic microwave background temperature bispectrum from cosmic strings, including the contributions from the last scattering surface, using a well-established Gaussian model for the string energy-momentum correlation functions, and a simplified model for the cosmic fluid. We check our approximation for the integrated Sachs-Wolfe (ISW) contribution against the bispectrum obtained from the full sky map of the cosmic string ISW signal used by the Planck team, obtaining good agreement. We validate our model for the last scattering surface contribution by comparing the predicted temperature power spectrum with that obtained from a full Boltzmann code treatment applied to the Unconnected Segment Model of a string network. We find that including the last scattering contribution has only a small impact on the upper limit on the string tension resulting from the bispectrum at Planck resolutions, and argue that the bispectrum is unlikely to be competitive with the power spectrum at any resolution.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1999

Low Luminosity States of the Black Hole Candidate GX 339-4: Timing Analysis - 2

Here we present timing analysis of a set of eight Rossi X-ray Timing Explorer (RXTE) observations of the black hole candidate GX 339-4 that were taken during its hard/low state. On long time scales, the RXTE All Sky Monitor data reveal evidence of a 240 day periodicity, comparable to timescales expected from warped, precessing accretion disks. On short timescales all observations save one show evidence of a persistent f(qpo approximately equals 0.3 Hz quasi-periodic oscillations (QPO)). The broad band (10 (exp -3) to 10 (exp2) Hz) power appears to be dominated by two independent processes that can be modeled as very broad Lorentzians with Q approximately less than - 1. The coherence function between soft and hard photon variability shows that if these are truly independent processes, then they are individually coherent, but they are incoherent with one another. This is evidenced by the fact that the coherence function between the hard and soft variability is near unity between 5 x 10 (exp -3) but shows evidence of a dip at f approximately equals 1 Hz. This is the region of overlap between the broad Lorentzian fits to the Power Spectral Density (PSD). Similar to Cyg X-1, the coherence also drops dramatically at frequencies approximately greater than 1O Hz. Also similar to Cyg X-1, the hard photon variability is seen to lag the soft photon variability with the lag time increasing with decreasing Fourier frequency. The magnitude of this time lag appears to be positively correlated with the flux of GX 339-4. We discuss all of these observations in light of current theoretical models of both black hole spectra and temporal variability.

Nowak, Michael A.↗
DOE OSTI2023

Structural relaxation of water during rapid cooling from ambient temperatures

Experiments investigating the properties of deeply supercooled liquid water are needed to develop a comprehensive understanding of water’s anomalous properties. One approach involves transiently heating nanoscale water films into the supercooled region for several nanoseconds at a time and then interrogating the water films after they have quenched to cryogenic temperatures. To relate the results obtained with this approach to other experiments and simulations on supercooled water, it is important to understand how closely the quenched structure tracks the (metastable) equilibrium structure of water as a function of the transient heating temperature. A key step involves quantifying the extent to which water that is transiently heated to ambient temperatures [hyperquenched water (HQW)] subsequently relaxes toward the structure of low-density amorphous (LDA) ice as it cools. We analyzed the infrared reflection–absorption spectra of LDA, HQW, and crystalline ice films to determine their complex indices of refraction. With this information, we estimate that HQW retains ~50%–60% of a structural motif characteristic of water at high temperatures with the balance comprised of a low-temperature motif. This result, along with results from x-ray diffraction experiments on water and amorphous ices, allows one to quantify the fraction of the high-temperature motif at approximately zero pressure as a function of temperature from 150 to 350 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation

The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions that represent radiation-matter interactions. Here, we extend the OMT to include additional vibrational coherence and energy transfer processes. This generalized approximation is applied to a pair of anharmonic chromophores coupled to a bath. The resulting 2D spectra are shown to reflect coherence transfer between normal modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1979

Annihilation in positron-atom collisions - A new approach

Two identities are derived for the exact scattering wave function by using the method of Hiller, Sucher, and Feinberg. It is shown that the resulting identities can be used to improve the calculation of positron annihilation cross sections whenever an approximate positron-atom scattering wave function is known. In addition, the advantages of the method are illustrated with a static model for e(+)-H scattering and then with a more realistic polarized orbital approximation.

Drachman, R. J.↗