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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 1,675 records · Page 93
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

A Fresh Math Perspective Opens New Possibilities for Computational Chemistry

By reformulating the TDDFT problem as a matrix function approximation, making use of a special transformation and taking advantage of the underlying symmetry with respect to a non-Euclidean metric, Yang and his colleagues were able to apply the Lanczos algorithm and a Kernal Polynomial Method (KPM) to approximate the absorption spectrum of several molecules. Both of these algorithms require relatively low-memory compared to non-symmetrical alternatives, which is the key to the computational savings.

Vu, Linda↗
NASA NTRS1996

Relativistic Navigation: A Theoretical Foundation

We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an isolated astronomical N-body system in metric theories of gravity. To do this, we generalize the Fock-Chandrasekhar method of the weak-field and slow-motion approximation (WFSMA) and develop a theory of relativistic reference frames (RF's) for a gravitationally bounded many-extended-body problem. In any proper RF constructed in the immediate vicinity of an arbitrary body, the N-body solutions of the gravitational field equations are formally presented as a sum of the Riemann-flat inertial space-time, the gravitational field generated by the body itself, the unperturbed solutions for each body in the system transformed to the coordinates of this proper RF, and the gravitational interaction term. We develop the basic concept of a general WFSMA theory of the celestial RF's applicable to a wide class of metric theories of gravity and an arbitrary model of matter distribution. We apply the proposed method to general relativity. Celestial bodies are described using a perfect fluid model; as such, they possess any number of internal mass and current multipole moments that explicitly characterize their internal structures. The obtained relativistic corrections to the geodetic equations of motion arise because of a coupling of the bodies' multiple moments to the surrounding gravitational field. The resulting relativistic transformations between the different RF's extend the Poincare group to the motion of deformable self-gravitating bodies. Within the present accuracy of astronomical measurements we discuss the properties of the Fermi-normal-like proper RF that is defined in the immediate vicinity of the extended compact bodies. We further generalize the proposed approximation method and include two Eddington parameters (gamma, Beta). This generalized approach was used to derive the relativistic equations of satellite motion in the vicinity of the extended bodies. Anticipating improvements in radio and laser tracking technologies over the next few decades, we apply this method to spacecraft orbit determination. We emphasize the number of feasible relativistic gravity tests that may be performed within the context of the parameterized WFSMA. Based on the planeto-centric equations of motion of a spacecraft around the planet, we suggested a new null test of the Strong Equivalence Principle (SEP). The experiment to measure the corresponding SEP violation effect could be performed with the future Mercury Orbiter mission. We discuss other relativistic effects, including the perihelion advance and the redshift and geodetic precession of the orbiter's orbital plane about Mercury, as well as the possible future implementation of the proposed formalism in software codes developed for solar-system orbit determination. All the important calculations are completely documented, and the references contain an extensive list of cited literature.

Turyshev, Slava G.↗
DOE OSTI2024

A data-driven sensor placement approach for detecting voltage violations in distribution systems

Stochastic fluctuations in power injections from distributed energy resources (DERs) combined with load variability can cause constraint violations (e.g., exceeded voltage limits) in electric distribution systems. To monitor grid operations, sensors are placed to measure important quantities such as the voltage magnitudes. Here, in this paper, we consider a sensor placement problem which seeks to identify locations for installing sensors that can capture all possible violations of voltage magnitude limits. We formulate a bilevel optimization problem that minimizes the number of sensors and avoids false sensor alarms in the upper level while ensuring detection of any voltage violations in the lower level. This problem is challenging due to the nonlinearity of the power flow equations and the presence of binary variables. Accordingly, we employ recently developed conservative linear approximations of the power flow equations that overestimate or underestimate the voltage magnitudes. By replacing the nonlinear power flow equations with conservative linear approximations, we can ensure that the resulting sensor locations and thresholds are sufficient to identify any constraint violations. Additionally, we apply various problem reformulations to significantly improve computational tractability while simultaneously ensuring an appropriate placement of sensors. Lastly, we improve the quality of the results via an approximate gradient descent method that adjusts the sensor thresholds. We demonstrate the effectiveness of our proposed method for several test cases, including a system with multiple switching configurations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

Presently the training of neural networks relies on data of comparable accuracy but in real applications only a very small set of high-fidelity data is available while inexpensive lower fidelity data may be plentiful. We propose a new composite neural network (NN) that can be trained based on multi-fidelity data. It is comprised of three NNs, with the first NN trained using the low-fidelity data and coupled to two high-fidelity NNs, one with activation functions and another one without, in order to discover and exploit nonlinear and linear correlations, respectively, between the low-fidelity and the high-fidelity data. We first demonstrate the accuracy of the new multi-fidelity NN for approximating some standard benchmark functions but also a 20-dimensional function that is not easy to approximate with other methods, e.g. Gaussian process regression. Subsequently, we extend the recently developed physics-informed neural networks (PINNs) to be trained with multi-fidelity data sets (MPINNs). MPINNs contain four fully-connected neural networks, where the first one approximates the low-fidelity data, while the second and third construct the correlation between the low- and high-fidelity data and produce the multi-fidelity approximation, which is then used in the last NN that encodes the partial differential equations (PDEs). Specifically, by decomposing the correlation into a linear and nonlinear part, the present model is capable of learning both the linear and complex nonlinear correlations between the low- and high-fidelity data adaptively. By training the MPINNs, we can: (1) obtain the correlation between the low- and high-fidelity data, (2) infer the quantities of interest based on a few scattered data, and (3) identify the unknown parameters in the PDEs. In particular, we employ the MPINNs to learn the hydraulic conductivity field for unsaturated flows as well as the reactive models for reactive transport. The results demonstrate that MPINNs can achieve relatively high accuracy based on a very small set of high-fidelity data. Despite the relatively low dimension and limited number of fidelities (two-fidelity levels) for the benchmark problems in the present study, the proposed model can be readily extended to very high-dimensional regression and classification problems involving multi-fidelity data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A Novel Method for Phasor Measurement Unit Sampling Time Error Compensation

This paper focuses on a novel method for successive approximation register analog to digital converter control in synchronized phasor measurement units (PMUs). To compensate for the sampling time error caused by the division remainder between the desirable sampling rate and the oscillator frequency, a variable sampling interval control method is presented by interlacing two integers under a proposed criterion. The frequency of the onboard oscillator is monitored in real-time using the pulse per second (PPS) timing reference from global positioning system. The sampling control is adaptively adjusted each second according to the latest estimated oscillator frequency. The “saw tooth” in phasor angle error and DC offset and spikes in frequency error can be effectively eliminated by applying the proposed method. The simulation and experiment results validate the effectiveness and accuracy of the proposed method, which is believed to be able to greatly improve the performance of PPS-disciplined synchronous sampling methods in PMUs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2004

A Most Probable Point-Based Method for Reliability Analysis, Sensitivity Analysis and Design Optimization

A major step in a most probable point (MPP)-based method for reliability analysis is to determine the MPP. This is usually accomplished by using an optimization search algorithm. The optimal solutions associated with the MPP provide measurements related to safety probability. This study focuses on two commonly used approximate probability integration methods; i.e., the Reliability Index Approach (RIA) and the Performance Measurement Approach (PMA). Their reliability sensitivity equations are first derived in this paper, based on the derivatives of their respective optimal solutions. Examples are then provided to demonstrate the use of these derivatives for better reliability analysis and Reliability-Based Design Optimization (RBDO).

Hou, Gene J.-W.↗
DOE OSTI2018

Basis adaptive sample efficient polynomial chaos (BASE-PC)

For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. Here this paper presents, within the context of uncertainty quantification, a practical implementation using basis adaptation, and coherence motivated sampling, which under assumptions has satisfying guarantees. This implementation is referred to as Basis Adaptive Sample Efficient Polynomial Chaos (BASE-PC). A key component of this is the use of anisotropic polynomial order which admits evolving global bases for approximation in an efficient manner, leading to consistently stable approximation for a practical class of smooth functionals. This fully adaptive, non-intrusive method, requires no a priori information of the solution, and has satisfying theoretical guarantees of recovery. A key contribution to stability is the use of a presented correction sampling for coherence-optimal sampling in order to improve stability and accuracy within the adaptive basis scheme. Theoretically, the method may dramatically reduce the impact of dimensionality in function approximation, and numerically the method is demonstrated to perform well on problems with dimension up to 1000.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Viscous simulation method for unsteady flows past multicomponent configurations

The present algorithm for the numerical simulation of flows about complex configurations (whose multiple and nonsimilar components have arbitraty geometries) employs a hybridization of the domain decomposition techniques for grid generation as well as to reduce computer-memory requirements. A fully vectorized, finite-volume, upwind-biased, approximately factored multigrid method is used to solve 3D Reynolds-averaged unsteady and compressible Navier-Stokes equations simulating supersonic flows past an ogive-nose-cylinder near or within a cavity. The time-averaged surface pressures obtained compare favorably with the wind tunnel data.

Fouladi, Kamran↗
NASA NTRS1984

Supersonic nonlinear potential analysis

The NCOREL computer code was established to compute supersonic flow fields of wings and bodies. The method encompasses an implicit finite difference transonic relaxation method to solve the full potential equation in a spherical coordinate system. Two basic topic to broaden the applicability and usefulness of the present method which is encompassed within the computer code NCOREL for the treatment of supersonic flow problems were studied. The first topic is that of computing efficiency. Accelerated schemes are in use for transonic flow problems. One such scheme is the approximate factorization (AF) method and an AF scheme to the supersonic flow problem is developed. The second topic is the computation of wake flows. The proper modeling of wake flows is important for multicomponent configurations such as wing-body and multiple lifting surfaces where the wake of one lifting surface has a pronounced effect on a downstream body or other lifting surfaces.

Siclari, M. J.↗
NASA NTRS1986

Upwind relaxation algorithms for Euler/Navier-Stokes equations

A description of and results from a solution algorithm for the compressible Navier-Stokes equations are presented. The main features of the algorithm are second or third order accurate upwind discretization of the convection and pressure derivatives and a relaxation scheme for the unfactored implicit backward Euler time method, implemented in a finite-volume formulation. Upwind methods were successfully used to obtain solutions to the Euler equations for flows with strong shock waves. The particular upwind method being used is based on the flux vector splitting technique developed by Van Leer and both second and third order accurate discretizations were developed. Currently, the most widely used implicit solution technique for the Navier-Stokes equations use approximate factorization (AF) methods to treat multidimensional problems. The time integration scheme being used in the present algorithm corresponds to a line Gauss-Seidel relaxation method. This method produces good convergence rates for steady-state flows, and most of the algorithm was vectorized on the NASA Langley VPS 32 computer. The Navier-Stokes algorithm was tested for several two-dimensional flow problems. Solutions for the problems gave excellent results. The presented effort is directed toward the extension of the scheme to the full three-dimensional Navier-Stokes equations.

Thomas, J. L.↗
DOE OSTI2014

Exchange integrals in magnetoelectric hexagonal ferrite (SrCo{sub 2}Ti{sub 2}Fe{sub 8}O{sub 19}): A density functional study

The exchange integrals in magnetoelectric hexagonal ferrite SrCo{sub 2}Ti{sub 2}Fe{sub 8}O{sub 19} have been calculated by using density functional theory. To get 10 inter-sublattice and 3 intra-sublattice exchange integrals, the electronic structures and total energies of 20 spin arrangements have been calculated with General Gradient Approximation (GGA) + U method. The dependence of exchange integrals on U has been studied. The comparison between the exchange integrals in SrFe{sub 12}O{sub 19} and those in SrCo{sub 2}Ti{sub 2}Fe{sub 8}O{sub 19} shows that substitution of Co and Ti decreases the most interactions involving the 12 k sites. The investigation based on our exchange integrals indicates that magnetic interaction between R and S blocks reduces significantly in SrCo{sub 2}Ti{sub 2}Fe{sub 8}O{sub 19}.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Computational simulation of vibrationally resolved spectra for spin‐forbidden transitions

Abstract In this computational study, we illustrate a method for computing phosphorescence and circularly polarized phosphorescence spectra of molecular systems, which takes into account vibronic effects including both Franck‐Condon and Herzberg‐Teller contributions. The singlet and triplet states involved in the phosphorescent emission are described within the harmonic approximation, and the method fully takes mode‐mixing effects into account when evaluating Franck‐Condon integrals. Spin‐orbit couplings, which are responsible for these otherwise forbidden phenomena, are accounted for by means of a relativistic two‐component time‐dependent density functional theory method. The model is applied to two types of chiral systems: camphorquinone, a rigid organic system that allows for an extensive benchmark, and some members of a class of iridium complexes. The merits and shortcomings of the methods are discussed, and some perspectives for future developments are offered.

Egidi, Franco↗
DOE OSTI2016

Automatic software correction of residual aberrations in reconstructed HRTEM exit waves of crystalline samples

Abstract We develop an automatic and objective method to measure and correct residual aberrations in atomic-resolution HRTEM complex exit waves for crystalline samples aligned along a low-index zone axis. Our method uses the approximate rotational point symmetry of a column of atoms or single atom to iteratively calculate a best-fit numerical phase plate for this symmetry condition, and does not require information about the sample thickness or precise structure. We apply our method to two experimental focal series reconstructions, imaging a β-Si 3 N 4 wedge with O and N doping, and a single-layer graphene grain boundary. We use peak and lattice fitting to evaluate the precision of the corrected exit waves. We also apply our method to the exit wave of a Si wedge retrieved by off-axis electron holography. In all cases, the software correction of the residual aberration function improves the accuracy of the measured exit waves.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Integrators

Many electromagnetic measurements detect signals that are the time derivative of the actual quantity of interest. Examples include so-called “B-dot” and “D-dot” detectors that are used for measuring transient magnetic and electric fields. Integration of these signals to recover the quantity of interest is performed either by hardware integrators in the signal line, or by software coding in the analysis programming. Hardware integration is usually done using a classic resistive-capacitive (RC) circuit, or internally in the detector by induction (L/R) or stray capacitance (RC). These hardware integration methods are only approximate, and must be corrected for distortion. This is usually called “droop correction.” In this note, we will examine this correction in some detail. Transient analysis via Laplace transforms will be used to simplify the mathematics. A rudimentary understanding of this method is assumed.

42 ENGINEERING↗
DOE OSTI2020

CASSCF with Extremely Large Active Spaces Using the Adaptive Sampling Configuration Interaction Method

The complete active space self-consistent field (CASSCF) method is the principal approach employed for studying strongly correlated systems. However, exact CASSCF can only be performed on small active spaces of ~20 electrons in ~20 orbitals due to exponential growth in the computational cost. Here, we show that employing the Adaptive Sampling Configuration Interaction (ASCI) method as an approximate Full CI solver in the active space allows CASSCF-like calculations within chemical accuracy (<1 kcal/mol for relative energies) in active spaces with more than ~50 active electrons in ~50 active orbitals, significantly increasing the sizes of systems amenable to accurate multiconfigurational treatment. The main challenge with using any selected CI-based approximate CASSCF is the orbital optimization problem; they tend to exhibit large numbers of local minima in orbital space due to their lack of invariance to active–active rotations (in addition to the local minima that exist in exact CASSCF). We highlight methods that can avoid spurious local extrema as a practical solution to the orbital optimization problem. We employ ASCI-SCF to demonstrate a lack of polyradical character in moderately sized periacenes with up to 52 correlated electrons and compare against heat-bath CI on an iron porphyrin system with more than 40 correlated electrons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Estimating statistical isotropy violation in CMB due to non-circular beam and complex scan in minutes

Mild, unavoidable deviations from circular-symmetry of instrumental beams along with scan strategy can give rise to measurable Statistical Isotropy (SI) violation in Cosmic Microwave Background (CMB) experiments. If not accounted properly, this spurious signal can complicate the extraction of other SI violation signals (if any) in the data. However, estimation of this effect through exact numerical simulation is computationally intensive and time consuming. A generalized analytical formalism not only provides a quick way of estimating this signal, but also gives a detailed understanding connecting the leading beam anisotropy components to a measurable BipoSH characterisation of SI violation. In this paper, we provide an approximate generic analytical method for estimating the SI violation generated due to a non-circular (NC) beam and arbitrary scan strategy, in terms of the Bipolar Spherical Harmonic (BipoSH) spectra. Our analytical method can predict almost all the features introduced by a NC beam in a complex scan and thus reduces the need for extensive numerical simulation worth tens of thousands of CPU hours into minutes long calculations. As an illustrative example, we use WMAP beams and scanning strategy to demonstrate the easability, usability and efficiency of our method. We test all our analytical results against that from exact numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗