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Results for “functional 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.

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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Scenario generation for stochastic optimization problems via the sparse grid method

We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid method can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The Effects of Ru and Rh Substitutions on the Magneto-electronic and Optical Properties of the TbNi{sub 5} Intermetallic Compound: An Ab Initio Investigation

In this study, we have performed the first-principles investigation of the structural, electronic, magnetic, and optical properties of TbNi{sub 5}, TbNi{sub 3}Ru{sub 2}, and TbNi{sub 3}Rh{sub 2} compounds. The full-potential linearized augmented plane waves with local orbitals method is used in the framework of density functional theory (DFT) employing the generalized gradient approximation (GGA) for the exchange correlation functional as implemented in WIEN2k package. The structural properties are reposed on the evaluation of the equilibrium lattice parameters of these compounds under hexagonal structure such as lattice constants (a and c), bulk modulus (B), and its first pressure derivative (B{sup ′}). The spin-polarized electronic structures, including band structure and density of states, are calculated employing the GGA plus band correlated Hubbard parameter (GGA + U) scheme. The results show that density of states and magnetic moment of the pure TbNi{sub 5} compound are changed by doping. These changes are observed in the appearance of additional peaks on the spectral density of states (DOS) and in the augmentation of the total magnetic moment of TbNi{sub 3}X{sub 2} (X = Ru and Rh) intermetallic compounds. Based on the electronic structure results, the frequency dependents of optical conductivity are estimated in all the spectra and interpreted in the interband optical absorption part.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Double-core excitations in formamide can be probed by X-ray double-quantum-coherence spectroscopy

The attosecond, time-resolved X-ray double-quantum-coherence four-wave mixing signals of formamide at the nitrogen and oxygen K-edges are simulated using restricted excitation window time-dependent density functional theory and the excited core hole approximation. These signals, induced by core exciton coupling, are particularly sensitive to the level of treatment of electron correlation, thus providing direct experimental signatures of electron and core-hole many-body effects and a test of electronic structure theories.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The effect of Coulomb interactions on thermoelectric properties of quantum dots

Thermoelectric effects in a quantum dot coupled to the source and drain charge reservoirs are explored using a nonequilibrium Green's functions formalism beyond the Hartree-Fock approximation. Thermal transport is analyzed within a linear response regime. A transition from Coulomb blockade regime to Kondo regime in thermoelectric transport through a single-level quantum dot is traced using unified approximations for the relevant Green's functions.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Half-metallic ferromagnetism in full-Heusler compounds ACaX{sub 2} (A = K and Rb; X = N and O)

Electronic structure and magnetic properties of hypothetical ACaX{sub 2} (A = K and Rb; X= N and O) compounds in full-Heusler phase have been investigated based on density functional theory (DFT) within the local density approximation (LDA). The electronic band structures and density of states of these compounds show that the spin-down electrons have metallic, and the spin-up electrons have a semi conducting gap resulting in stable half-metallic ferromagnetic behaviour. The strong spin polarization of 2p states of N and O atoms is found to be the origin of ferromagnetism which results in a total magnetic moment of 3{sub μB} and 1{sub μB} respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

The effect of Coulomb interactions on nonlinear thermovoltage and thermocurrent in quantum dots

In the present work, we theoretically study the nonlinear regime of charge transport through a quantum dot coupled to the source and drain reservoirs. The investigation is carried out using a nonequilibrium Green’s function formalism beyond the Hartree-Fock approximation. Employed approximations for the relevant Green’s functions allow to trace a transition from Coulomb blockade regime to Kondo regime in the thermoelectric transport. Effects arising when electrons move in response to thermal gradient applied across the system are discussed, including experimentally observed thermovoltage zeros.

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

Structural, electronic and elastic properties of RERu{sub 2} (RE=Pr and Nd) Laves phase intermetallic compounds

We have performed the first-principles calculations to study the structural, electronic and elastic properties of RERu{sub 2} (RE = Pr and Nd) Laves phase intermetallic compounds using full-potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT) within the generalized gradient approximation (GGA) for exchange and correlation potential. The optimized lattices constant are in reasonable agreement with available experimental data. The electronic properties are analyzed in terms of band structures, total and partial density of states, which confirm their metallic character. The calculated elastic constants infer that these compounds are mechanically stable in C15 (MgCu{sub 2} type) structure and found to be ductile in nature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A new method for analyzing and visualizing plasma simulations using a phase-space tessellation

We apply a novel phase-space interpolation technique referred to as the simplex-in-cell (SIC) method to analyze two- and three-dimensional particle-in-cell (PIC) simulations of electromagnetic plasmas. SIC relies on a discretization of the initial phase-space distribution function into simplices, which allows an approximation to the full, continuously defined distribution function to be constructed at any later time in the simulation. This allows densities, currents, and even full momentum distribution functions to be measured at any point in the simulation domain without averaging over control volumes. The SIC approach applies to any PIC simulation for which a tessellation of the initial particle distribution can be constructed. In this study, we use outputs from standard PIC simulations of the Weibel instability and compare physical quantities such as charge and current densities calculated in postprocessing using SIC and standard particle deposits. Using 2D simulations with 1–65 536 particles-per-cell, we find that SIC eliminates discrete particle noise and in some cases can reach a given noise level using ~1000 times fewer simulation particles than with standard particle deposition schemes. In regions of low density, such as between current filaments, SIC is able to capture small amplitude features even with fewer particles than gridpoints due to the deformable nature of the SIC volume elements. Here, by calculating momentum distributions, we show how SIC can capture low density tails in the spectrum using far fewer particles than are necessary for standard particle deposits. We calculate the charge density on spatial grids of increasing resolution to demonstrate the ability of SIC to reveal fine-scale details that are not accessible with standard particle deposits. Finally, we show how SIC can be extended to 3D and give an example of its use to calculate the charge density from 3D PIC simulations of the Weibel instability. These results motivate the future implementation of SIC directly in the simulation force calculation for a novel low-noise electromagnetic plasma simulation method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Toward improved property prediction of 2D materials using many-body quantum Monte Carlo methods

The field of 2D materials has grown dramatically in the past two decades. 2D materials can be utilized for a variety of next-generation optoelectronic, spintronic, clean energy, and quantum computing applications. These 2D structures, which are often exfoliated from layered van der Waals materials, possess highly inhomogeneous electron densities and can possess short- and long-range electron correlations. The complexities of 2D materials make them challenging to study with standard mean-field electronic structure methods such as density functional theory (DFT), which relies on approximations for the unknown exchange-correlation functional. To overcome the limitations of DFT, highly accurate many-body electronic structure approaches such as diffusion Monte Carlo (DMC) can be utilized. In the past decade, DMC has been used to calculate accurate magnetic, electronic, excitonic, and topological properties in addition to accurately capturing interlayer interactions and cohesion and adsorption energetics of 2D materials. Here, this approach has been applied to 2D systems of wide interest, including graphene, phosphorene, MoS 2 , CrI 3 , VSe 2 , GaSe, GeSe, borophene, and several others. In this review article, we highlight some successful recent applications of DMC to 2D systems for improved property predictions beyond standard DFT.

2D materials↗
DOE OSTI2017

Is the Collecting Surface of a Flat One-Sided Probe Constant when Measuring the Ion Distribution Function?

The correctness of the known plane single-ended probe method for measuring the anisotropic ion distribution functions in a gas-discharge plasma has been considered. Analysis has been performed for positive probe potentials relative to the plasma with magnitudes on the order of the mean ion energy, which as a rule is much lower than the mean electron energy. We have analyzed the dependence of the collection surface area of a plane probe on its potential in this range. The structure of the near-probe layer has been determined for an isotropic electron distribution function of the Maxwellian or Druvestein type and an anisotropic ion distribution function. These results are used to derive analytic relations for the correction to the second derivative of the probe current with respect to the plane probe potential. It has been shown that, when the ion distribution function is measured in a wide range of conditions in the gas-discharge plasma, when the approximation of a collisionless probe layer is applicable, and the probe does not perturb the plasma, the dependence of the collection surface area of the probe on the potential can be disregarded in this range.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

First Principles Calculation of the Entropy of Liquid Aluminum

The information required to specify a liquid structure equals, in suitable units, its thermodynamic entropy. Hence, an expansion of the entropy in terms of multi-particle correlation functions can be interpreted as a hierarchy of information measures. Utilizing first principles molecular dynamics simulations, we simulate the structure of liquid aluminum to obtain its density, pair and triplet correlation functions, allowing us to approximate the experimentally measured entropy and relate the excess entropy to the information content of the correlation functions. We discuss the accuracy and convergence of the method.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Identifying finite-time coherent sets from limited quantities of Lagrangian data

A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Solving Stochastic Dynamic Programming Problems: A Mixed Complementarity Approach

We detail a mixed complementarity problem (MCP) formulation of continuous state dynamic programming problems (DP-MCP). We write the solution to projection methods in value function iteration (VFI) as a joint set of optimality conditions that characterize maximization of the Bellman equation; and approximation of the value function. The MCP approach replaces the iterative component of projection based VFI with a one-shot solution to a square system of complementary conditions. We provide three numerical examples to illustrate our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Increasing the applicability of density functional theory. IV. Consequences of ionization-potential improved exchange-correlation potentials

This paper's objective is to create a “consistent” mean-field based Kohn-Sham (KS) density functional theory (DFT) meaning the functional should not only provide good total energy properties, but also the corresponding KS eigenvalues should be accurate approximations to the vertical ionization potentials (VIPs) of the molecule, as the latter condition attests to the viability of the exchange-correlation potential (V{sub XC}). None of the prominently used DFT approaches show these properties: the optimized effective potential V{sub XC} based ab initio dft does. A local, range-separated hybrid potential cam-QTP-00 is introduced as the basis for a “consistent” KS DFT approach. The computed VIPs as the negative of KS eigenvalue have a mean absolute error of 0.8 eV for an extensive set of molecule's electron ionizations, including the core. Barrier heights, equilibrium geometries, and magnetic properties obtained from the potential are in good agreement with experiment. A similar accuracy with less computational efforts can be achieved by using a non-variational global hybrid variant of the QTP-00 approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Unsupervised Learning for Equitable DER Control: Preprint

In the context of managing distributed energy resources (DERs) within distribution networks (DNs), this work focuses on the task of developing local controllers. We propose an unsupervised learning framework to train functions that can closely approximate optimal power flow (OPF) solutions. The primary aim is to establish specific conditions under which these learned functions can collectively guide the network towards desired configurations asymptotically, leveraging an incremental control approach. The flexibility of the proposed methodology allows to integrate fairness-driven components into the cost function associated with the OPF problem. This addition seeks to mitigate power curtailment disparities among DERs, thereby promoting equitable power injections across the network. To demonstrate the effectiveness of the proposed approach, power flow simulations are conducted using the IEEE 37-bus feeder. The findings not only showcase the guaranteed system stability but also underscore its improved overall performance.

asymptotic stability↗
DOE OSTI2014

Electric double layer for a size-asymmetric electrolyte around a spherical colloid

We have studied the structure of a size-asymmetric electrolyte on charged colloids by a density functional perturbation theory. The hard-sphere contribution has been approximated as the direct pair correlation function with the coupling parameter, whereas the electronic contribution has been approximated as the mean-spherical approximation in the bulk phase. The calculated results for the ionic density distributions and mean electrostatic potentials are in very good agreement with the computer simulations over a wide range of colloid sizes and electrolyte concentrations. The present theory provides better structural results than the hypernetted-chain equation based on the mean spherical approximation. We have confirmed that the overcharging appears when the counterions are larger than the coions. The overcharging disappears everywhere when the electrostatic repulsion becomes strong enough, while the charge reversal is observed when the coions are larger than the counterions, and the reversal effect appears for a size-asymmetric electrolyte at high surface charge densities. The charge reversal occurs even for the point of zero charge, mainly due to the depletion force between two ions. The present theory is able to provide interesting insights about the charge reversal and overcharging phenomena occurring at the interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗