Search NASA⌕ Search

SEARCH · Search NASA

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 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Beyond Limber: efficient computation of angular power spectra for galaxy clustering and weak lensing

Angular two-point statistics of large-scale structure observables are important cosmological probes. To reach the high accuracy required by the statistical precision of future surveys, some of these statistics may need to be computed without the commonly employed Limber approximation; the exact computation however requires integration over Bessel functions, and a brute-force evaluation is slow to converge. Here, we present a new method based on our generalized FFTLog algorithm for the efficient computation of angular power spectra beyond the Limber approximation. The new method significantly simplifies the calculation and improves the numerical speed and stability. It is easily extended to handle integrals involving derivatives of Bessel functions, making it equally applicable to numerically more challenging cases such as contributions from redshift-space distortions and Doppler effects. We implement our method for galaxy clustering and galaxy-galaxy lensing power spectra. We find that using the Limber approximation for galaxy clustering in future analyses like LSST Year 1 and DES Year 6 may cause significant biases in cosmological parameters, indicating that going beyond the Limber approximation is necessary for these analyses.

weak gravitational lensing↗
DOE OSTI2024

Non-mercury methylating microbial taxa are integral to understanding links between mercury methylation and elemental cycles in marine and freshwater sediments

The goal of this study was to explore the role of non-mercury (Hg) methylating taxa in mercury methylation and to identify potential links between elemental cycles and Hg methylation. Statistical approaches were utilized to investigate the microbial community and biochemical functions in relation to methylmercury (MeHg) concentrations in marine and freshwater sediments. Sediments were collected from the methylation zone (top 15 cm) in four Hg-contaminated sites. Both abiotic (e.g., sulfate, sulfide, iron, salinity, total organic matter, etc.) and biotic factors (e.g., hgcA, abundances of methylating and non-methylating taxa) were quantified. Random forest and stepwise regression were performed to assess whether non-methylating taxa were significantly associated with MeHg concentration. Co-occurrence and functional network analyses were constructed to explore associations between taxa by examining microbial community structure, composition, and biochemical functions across sites. Regression analysis showed that approximately 80% of the variability in sediment MeHg concentration was predicted by total mercury concentration, the abundances of Hg methylating taxa, and the abundances of the non-Hg methylating taxa. The co-occurrence networks identified Paludibacteraceae and Syntrophorhabdaceae as keystone non Hg methylating taxa in multiple sites, indicating the potential for syntrophic interactions with Hg methylators. Strong associations were also observed between methanogens and sulfate-reducing bacteria, which were likely symbiotic associations. The functional network results suggested that non-Hg methylating taxa play important roles in sulfur respiration, nitrogen respiration, and the carbon metabolism-related functions methylotrophy, methanotrophy, and chemoheterotrophy. Interestingly, keystone functions varied by site and did not involve carbon- and sulfur-related functions only. In conclusion, our findings highlight associations between methylating and non-methylating taxa and sulfur, carbon, and nitrogen cycles in sediment methylation zones, with implications for predicting and understanding the impact of climate and land/sea use changes on Hg methylation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Small bimetallic clusters Agn-1M (M = Au, Co, Cu, Ni, Pd, Pt; n = 3, 9, 15): Density functional theory and genetic algorithm

We investigated the effect of size and composition on the properties of bimetallic nanoclusters. The geometric structures, stabilities, and electronic properties of size-selected Ag n-1 M (M = Au, Co, Cu, Ni, Pd, Pt; n = 3, 9, 15) bimetallic nanoclusters are systematically analyzed using spin-polarized density functional theory (DFT) within the generalized gradient approximation (GGA). We determine the most stable geometries for these clusters using a genetic algorithm (GA) in combination with DFT. Our results show that doping pure silver clusters with an M atom (transition metal), referred to as a “guest atom”, increases the stability as compared to pure Ag n (n = 3, 9, 15) clusters. The results for various properties including formation energy per atom, electronic structure, magnetic moments, and vibrational density of states (VDOS) are evaluated as a function of both size and composition of the system. The adsorption of selected bimetallic clusters on hydroxylated alumina substrate shows weak binding and minor changes in geometric properties except for Ag 8 Pt.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Capturing multireference excited states by constrained-density-functional theory

The computation of excited electronic states with commonly employed (approximate) methods is challenging, typically yielding states of lower quality than the corresponding ground state for a higher computational cost. In this work, we present a mean-field method that extends the previously proposed excited constrained-density-functional theory (XCDFT) from single Slater determinants to ensemble one-body reduced density matrices for computing low-lying excited states. The method still retains an associated computational complexity comparable to a semilocal density functional theory (DFT) calculation while at the same time it is capable of approaching states with multireference character. Further, we benchmark the quality of this method on well-established test sets, finding good descriptions of the electronic structure of multireference states and maintaining an overall accuracy for the predicted excitation energies comparable to semilocal time-dependent DFT.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Towards a Deeper Fundamental Understanding of (Al,Sc)N Ferroelectric Nitrides

Density functional theory (DFT) calculations, within the virtual crystal alloy approximation, are performed, along with the development of a Landau-type model employing a symmetry-allowed analytical expression of the internal energy and having parameters determined from first principles, to investigate properties and energetics of Al1-xScxN ferroelectric nitrides in their hexagonal forms. These DFT computations and this model predict the existence of two different types of minima, namely, the fourfold-coordinated wurtzite (WZ) polar structure and a five-fold coordinated paraelectric hexagonal phase (denoted as H5), for any Sc composition up to 40%. The H5 minimum progressively becomes the lowest-energy state within hexagonal symmetry as the Sc concentration increases from 0 to 0.4. Furthermore, the model points to several key findings. Examples include the crucial role of the coupling between polarization and strains to create the WZ minimum, in addition to polar and elastic energies, and that the origin of the H5 state overcoming the WZ phase as the global minimum within hexagonal symmetry when increasing the Sc composition mostly lies in the compositional dependency of only two parameters-one linked to the polarization and another one being purely elastic in nature. Other examples are that forcing Al1-xScxN systems to have no or a weak change in lattice parameters when heating them allows us to reproduce their finite-temperature polar properties well and that a value of the axial ratio close to that of the ideal WZ structure implies a large polarization at low temperatures but not necessarily at high temperatures because of the ordered-disordered character of the temperature-induced formation of the WZ state. Such findings should allow for a better fundamental understanding of (Al,Sc)N ferroelectric nitrides, which may be used to design efficient devices having, e.g., low operating voltages.

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

Structural, Elastic, and Electronic Properties of CeN and LuN Using: Ab Initio Study

We report on the electronic, structural, and elastic property calculations conducted for the rare-earth (RE) nitride compounds in the rocksalt structure (CeN and LuN compounds) using the full-potential linear muffin-tin orbital method (FP-LMTO) based on the spin density functional theory (DFT) calculations using the LSDA + U approach (local spin density approximation with Hubbard-U corrections). The LSDA + U approximation is applied to the 4f as well as 5d states. Various space groups were considered including the NaCl (Fm-3m (225)), the cesium chloride [CsCl(Pm-3m (221))], and the zinc blende [ZnS(F-43m 216))]. Our obtained results indicate that the NaCl-type structure is stable than all the other phases, while the predicted elastic constants were found to satisfy the mechanical stability. The related mechanical properties such as the anisotropy factor (A), Poisson’s ratio (υ), Young’s modulus (E), and the shear modulus (G) for the same NaCl structure were also calculated. Finally, the band structure calculations of the CeN and LuN have revealed half-metallic and semiconductor behaviour, respectively. The obtained results are presented and in-depth discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Approximating the particle distribution in rotating and tandem mirror traps

Steady-state distribution functions can be used to calculate stability conditions for modes, radiation energy losses and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true distributions such as the relative speeds of different transport processes while possessing computational advantages over their numerical counterparts. In this paper, we motivate and present a closed-form ana- lytic model for a distribution of particles in a centrifugal or tandem mirror. We find that our model outperforms other known models in approximating numerical steady- state simulations outside of a narrow range of low confining potentials. We demonstrate the model’s suitability in the high confining potential regime for applications such as loss-cone stability thresholds, fusion yields and available energy.

Li, G.X.↗
DOE OSTI2025

Approximating the particle distribution in rotating and tandem mirror traps

Steady-state distribution functions can be used to calculate stability conditions for modes, radiation energy losses and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true distributions such as the relative speeds of different transport processes while possessing computational advantages over their numerical counterparts. In this paper, we motivate and present a closed-form analytic model for a distribution of particles in a centrifugal or tandem mirror. We find that our model outperforms other known models in approximating numerical steady-state simulations outside of a narrow range of low confining potentials. We demonstrate the model’s suitability in the high confining potential regime for applications such as loss-cone stability thresholds, fusion yields and available energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

An Exchange-Correlation Functional Capturing Bulk Surface and Confinement Physics

Due to its balance of accuracy and computational cost, density functional theory has become the method of choice for computing the electronic structure and related properties of materials. However, present-day semilocal approximations to the exchange-correlation energy of density functional theory break down for materials containing d and f electrons. In this report we summarize our progress in addressing this issue. We describe the construction of the BSC exchange-correlation functional within the subsystem functional formalism which enables us to capture bulk, surface, and confinement physics with a single exchange-correlation functional. We report on the initial assessment of this functional within the jellium surface system and demonstrate that the BSC functional captures the confinement physics more accurately than standard semilocal exchange-correlation functionals. We conclude by outlining our future research objectives which focus on refining the functional form of the BSC functional and achieving significantly more accurate energetics of materials containing f and d electrons than existing semilocal functionals.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Low-Energy E1 Strength Distributions of {sup 68}Ni

We study the effects of the coupling between one- and two-phonon components of the wave functions on the low-energy electric dipole response of {sup 6}8Ni in a microscopic model based on an effective Skyrme interaction SLy5. The finite rank separable approach for the quasiparticle random phase approximation is used. The effect of phonon-phonon coupling leads to the fragmentation of the E1 strength to a lower energy and improves the agreement with available experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Probability of Loss of Assured Safety in Systems with Multiple Time-Dependent Failure Modes: Incorporation of Delayed Link Failure in the Presence of Aleatory Uncertainty.

Probability of loss of assured safety (PLOAS) is modeled for weak link (WL)/strong link (SL) systems in which one or more WLs or SLs could potentially degrade into a precursor condition to link failure that will be followed by an actual failure after some amount of elapsed time. The following topics are considered: (i) Definition of precursor occurrence time cumulative distribution functions (CDFs) for individual WLs and SLs, (ii) Formal representation of PLOAS with constant delay times, (iii) Approximation and illustration of PLOAS with constant delay times, (iv) Formal representation of PLOAS with aleatory uncertainty in delay times, (v) Approximation and illustration of PLOAS with aleatory uncertainty in delay times, (vi) Formal representation of PLOAS with delay times defined by functions of link properties at occurrence times for failure precursors, (vii) Approximation and illustration of PLOAS with delay times defined by functions of link properties at occurrence times for failure precursors, and (viii) Procedures for the verification of PLOAS calculations for the three indicated definitions of delayed link failure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Effect of Fe Doping and O Vacancies on the Magnetic Properties of Rutile TiO{sub 2}

Magnetism sources of Fe doping and O vacancies, which coexist in the presence of rutile TiO{sub 2}, are controversial and require a resolution. The effects of Fe doping and point defect on the magnetism of rutile TiO{sub 2} were studied using geometry optimization and energy calculation based on the first principle generalized gradient approximation + U method (GGA+U) of density functional theory. Fe/Vo ratio is 1:1 in rutile TiO{sub 2}. The next closest distance between Fe and Vo is 0.04082 nm. The formation energy of the doping system is the smallest. This doping system has the highest stability. The coexistence of Fe doping and O vacancy achieved ferromagnetic long-range order. The different ratios of Fe/Vo are 1:1, 1:2, 2:1, and 2:2. The magnetic properties of the doping system are significantly different. At a ratio of 2:1, the magnetic moment is the largest among all doping systems. Moreover, the Curie temperature of the doping system can be higher than room temperature. These findings can obtain dilute magnetic semiconductors with potential application value. At a Fe/V{sub O} ratio of 2:2, the Ti{sub 14}Fe{sub 2}O{sub 30} system produces a half-metallic property of 100% electron spin polarizability. This is the most valuable application for designing and preparing novel spintronic injection source dilute magnetic semiconductors. The magnetic source is mainly mediated by the holes generated by Fe doping and O vacancy complexes, thereby causing the spin polarization double exchange effect on the electron of Ti–3d orbital atoms near the O vacancy, O–2p electron orbital, and Fe–3d electron orbital. This feature is consistent with the following theories: the mean field approximation and the double exchange mechanism theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Characterizing the impact of model error in hydrologic time series recovery inverse problems

Hydrologic models are commonly over-smoothed relative to reality, owing to computational limitations and to the difficulty of obtaining accurate high-resolution information. When used in an inversion context, such models may introduce systematic biases which cannot be encapsulated by an unbiased “observation noise” term of the type assumed by standard regularization theory and typical Bayesian formulations. Despite its importance, model error is difficult to encapsulate systematically and is often neglected. In this paper, model error is considered for an important class of inverse problems that includes interpretation of hydraulic transients and contaminant source history inference: reconstruction of a time series that has been convolved against a transfer function (i.e., impulse response) that is only approximately known. Using established harmonic theory along with two results established here regarding triangular Toeplitz matrices, upper and lower error bounds are derived for the effect of systematic model error on time series recovery for both well-determined and over-determined inverse problems. It is seen that use of additional measurement locations does not improve expected performance in the face of model error. A Monte Carlo study of a realistic hydraulic reconstruction problem is presented, and the lower error bound is seen informative about expected behavior. Finally, a possible diagnostic criterion for blind transfer function characterization is also uncovered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Experimental determination of the valence band offsets of ZnGeN 2 and (ZnGe) 0.94 Ga 0.12 N 2 with GaN

A predicted type-II staggered band alignment with an approximately 1.4 eV valence band offset at the ZnGeN 2 /GaN heterointerface has inspired novel band-engineered III-N/ZnGeN 2 heterostructure-based device designs for applications in high performance optoelectronics. We report on the determination of the valence band offset between metalorganic chemical vapor deposition grown (ZnGe) 1- x Ga 2 x N 2 , for x = 0 and 0.06, and GaN using x-ray photoemission spectroscopy. The valence band of ZnGeN 2 was found to lie 1.45–1.65 eV above that of GaN. This result agrees well with the value predicted by first-principles density functional theory calculations using the local density approximation for the potential profile and quasiparticle self-consistent GW calculations of the band edge states relative to the potential. For (ZnGe) 0.94 Ga 0.12 N 2 the value was determined to be 1.29 eV, ~10%–20% lower than that of ZnGeN 2 . The experimental determination of the large band offset between ZnGeN 2 and GaN provides promising alternative solutions to address challenges faced with pure III-nitride-based structures and devices.

Physics↗
DOE OSTI2022

Analytic gradients for compressed multistate pair-density functional theory

Photochemical reactions often involve states that are closely coupled due to near degeneracies, for example by proximity to conical intersections. Therefore, a multistate method is used to accurately describe these states; for example, ordinary perturbation theory is replaced by quasidegenerate perturbation theory. Multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to approximate the full dynamical correlation energy of strongly correlated systems, and we recently proposed compressed multistate pair-density functional theory (CMS-PDFT) to treat closely coupled states. In the present paper, we report the implementation of analytic gradients for CMS-PDFT in both OpenMolcas and PySCF, and here we illustrate the use of these gradients by applying the method to the excited states of formaldehyde and phenol.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Cluster decomposition of full configuration interaction wave functions: A tool for chemical interpretation of systems with strong correlation

Approximate full configuration interaction (FCI) calculations have recently become tractable for systems of unforeseen size, thanks to stochastic and adaptive approximations to the exponentially scaling FCI problem. The result of an FCI calculation is a weighted set of electronic configurations, which can also be expressed in terms of excitations from a reference configuration. The excitation amplitudes contain information on the complexity of the electronic wave function, but this information is contaminated by contributions from disconnected excitations, i.e., those excitations that are just products of independent lower-level excitations. The unwanted contributions can be removed via a cluster decomposition procedure, making it possible to examine the importance of connected excitations in complicated multireference molecules which are outside the reach of conventional algorithms. We present an implementation of the cluster decomposition analysis and apply it to both true FCI wave functions, as well as wave functions generated from the adaptive sampling CI algorithm. Furthermore, the cluster decomposition is useful for interpreting calculations in chemical studies, as a diagnostic for the convergence of various excitation manifolds, as well as as a guidepost for polynomially scaling electronic structure models. Applications are presented for (i) the double dissociation of water, (ii) the carbon dimer, (iii) the π space of polyacenes, and (iv) the chromium dimer. While the cluster amplitudes exhibit rapid decay with an increasing rank for the first three systems, even connected octuple excitations still appear important in Cr 2 , suggesting that spin-restricted single-reference coupled-cluster approaches may not be tractable for some problems in transition metal chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Implications of the fractional charge of hydroxide at the electrochemical interface

Rational design of materials that efficiently convert electrical energy into chemical bonds will ultimately depend on a thorough understanding of the electrochemical interface at the atomic level. Towards this goal, the use of density functional theory (DFT) at the generalized gradient approximation (GGA) level has been applied widely in the past 15 years. In the calculation of electrochemical reaction energetics using GGA-DFT, it is frequently implicitly assumed that ions in the Helmholtz plane have unit charge. However, the ion charge is observed to be fractional near the interface through both a capacitor model and through Bader charge partitioning. In this work, we show that this spurious charge transfer can be effectively mitigated by continuum charging of the electrolyte. Finally, we show that, similar to hydronium, the observed fractional charge of hydroxide is not due to a GGA level self-interaction error, as the partial charge is observed even when using hybrid level exchange–correlation functionals.

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

Effects of interaction strength of associating groups on linear and star polymer dynamics

A small number of associating groups incorporated onto a polymer backbone have dramatic effects on the mobility and viscoelastic response of the macromolecules in melts. These associating groups assemble, driving the formation of clusters, whose lifetime affects the properties of the polymers. In this study, we probe the effects of the interaction strength on the structure and dynamics of two topologies, linear and star polymer melts, and further investigate blends of associative and non-associating polymers using molecular dynamics simulations. Polymer chains of approximately one entanglement length are described by a bead–spring model, and the associating groups are incorporated in the form of interacting beads with an interaction strength between them that is varied from 1 to 20 k B T. We find that, for all melts and blends, interaction of a few k B T between the associating groups drives cluster formation, where the size of the clusters increases with increasing interaction strength. These clusters act as physical crosslinkers, which slow the chain mobility. Blends of chains with and without associating groups macroscopically phase separate for interaction strength between the associating groups of a few k B T and above. For weakly interacting associating groups, the static structure function S(q) is well fit by functional form predicted by the random phase approximation where a clear deviation occurs as phase segregation takes place, providing a quantitative assessment of phase segregation.

36 MATERIALS SCIENCE↗