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 1,747 records · Page 97
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance

Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation.

algorithmic development↗
DOE OSTI2019

Controlling the Infrared Dielectric Function through Atomic-Scale Heterostructures

Surface phonon polaritons (SPhPs), the surface-bound electromagnetic modes of a polar material resulting from the coupling of light with optic phonons, offer immense technological opportunities for nanophotonics in the infrared (IR) spectral region. However, once a particular material is chosen, the SPhP characteristics are fixed by the spectral positions of the optic phonon frequencies. Here, we provide a demonstration of how the frequency of these optic phonons can be altered by employing atomic-scale superlattices (SLs) of polar semiconductors using AlN/GaN SLs as an example. Using second harmonic generation (SHG) spectroscopy, we show that the optic phonon frequencies of the SLs exhibit a strong dependence on the layer thicknesses of the constituent materials. Furthermore, new vibrational modes emerge that are confined to the layers, while others are centered at the AlN/GaN interfaces. As the IR dielectric function is governed by the optic phonon behavior in polar materials, controlling the optic phonons provides a means to induce and potentially design a dielectric function distinct from the constituent materials and from the effective-medium approximation of the SL. We show that atomic-scale AlN/GaN SLs instead have multiple Reststrahlen bands featuring spectral regions that exhibit either normal or extreme hyperbolic dispersion with both positive and negative permittivities dispersing rapidly with frequency. Apart from the ability to engineer the SPhP properties, SL structures may also lead to multifunctional devices that combine the mechanical, electrical, thermal, or optoelectronic functionality of the constituent layers. We propose that this effort is another step toward realizing user-defined, actively tunable IR optics and sources.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Electrostatic twisted modes in multi-component dusty plasmas

Various electrostatic twisted modes are re-investigated with finite orbital angular momentum in an unmagnetized collisionless multi-component dusty plasma, consisting of positive/negative charged dust particles, ions, and electrons. For this purpose, hydrodynamical equations are employed to obtain paraxial equations in terms of density perturbations, while assuming the Gaussian and Laguerre-Gaussian (LG) beam solutions. Specifically, approximated solutions for potential problem are studied by using the paraxial approximation and expressed the electric field components in terms of LG functions. The energy fluxes associated with these modes are computed and corresponding expressions for orbital angular momenta are derived. Numerical analyses reveal that radial/angular mode numbers as well as dust number density and dust charging states strongly modify the LG potential profiles attributed to different electrostatic modes. Our results are important for understanding particle transport and energy transfer due to wave excitations in multi-component dusty plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

New fractional derivatives applied to the Korteweg–de Vries and Korteweg–de Vries–Burger’s equations

In this paper, we extend the model of the Korteweg–de Vries (KDV) and Korteweg–de Vries–Burger’s (KDVB) to new model time fractional Korteweg–de Vries (TFKDV) and time fractional Korteweg–de Vries-Burger’s (TFKDVB) with Liouville–Caputo (LC), Caputo–Fabrizio (CF), and Atangana-Baleanu (AB) fractional time derivative equations, respectively. We utilize the q-homotopy analysis transform method (q-HATM) to compute the approximate solutions of TFKDV and TFKDVB using LC, CF and AB in Liouville–Caputo sense. We study the convergence analysis of q-HATM by computing the Residual Error Function (REF) and finding the interval of the convergence through the h-curves. Also, we find the optimal values of h so that, we assure the convergence of the approximate solutions. The results are very effective and accurate in solving the TFKDV and TFKDVB.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Energy Band Structure and Optical Properties of LiNaSO{sub 4} Crystals

The energy band structure of a LiNaSO{sub 4} has been calculated within the framework of density functional theory for space group P31c. It has been established that bandgap width E{sub g} in the GGA approximation is 5.49 eV. The valence band top is generally formed of oxygen p-electrons, while the conduction band bottom is composed of lithium and sodium s-states. The effect of the cationic substitution Na → K → Rb → NH{sub 4} on the electron structure of LiBSO{sub 4} group crystals is considered. Based on the calculated dielectric functions, the spectral dependences of the refractive indices and extinction coefficient of a crystal were calculated and compared with experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Solutions of the bi-confluent Heun equation in terms of the Hermite functions

We construct an expansion of the solutions of the bi-confluent Heun equation in terms of the Hermite functions. The series is governed by a three-term recurrence relation between successive coefficients of the expansion. We examine the restrictions that are imposed on the involved parameters in order that the series terminates thus resulting in closed-form finite-sum solutions of the bi-confluent Heun equation. A physical application of the closed-form solutions is discussed. We present the five six-parametric potentials for which the general solution of the one-dimensional Schrödinger equation is written in terms of the bi-confluent Heun functions and further identify a particular conditionally integrable potential for which the involved bi-confluent Heun function admits a four-term finite-sum expansion in terms of the Hermite functions. This is an infinite well defined on a half-axis. We present the explicit solution of the one-dimensional Schrödinger equation for this potential and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and construct an accurate approximation for the bound-state energy levels. - Highlights: • The bi-confluent Heun functions are expanded in terms of the Hermite functions. • The restrictions leading to closed-form finite-sum solutions are identified. • The five bi-confluent Heun potentials for the Schrödinger equation are presented. • A new conditionally integrable Schrödinger potential is derived. • An accurate approximation for the bound-state energy levels is constructed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

An increasing stellar baryon fraction in bright galaxies at high redshift

Recent observations have shown that the characteristic luminosity of the rest-frame ultraviolet (UV) luminosity function does not significantly evolve at 4 < z < 7 and is approximately M{sub UV}{sup ∗}∼−21. We investigate this apparent non-evolution by examining a sample of 173 bright, M{sub UV} < −21 galaxies at z = 4–7, analyzing their stellar populations and host halo masses. Including deep Spitzer/IRAC imaging to constrain the rest-frame optical light, we find that M{sub UV}{sup ∗} galaxies at z = 4–7 have similar stellar masses of log(M/M{sub ⊙}) = 9.6–9.9 and are thus relatively massive for these high redshifts. However, bright galaxies at z = 4–7 are less massive and have younger inferred ages than similarly bright galaxies at z = 2–3, even though the two populations have similar star formation rates and levels of dust attenuation for a fixed dust-attenuation curve. Matching the abundances of these bright z = 4–7 galaxies to halo mass functions from the Bolshoi ΛCDM simulation implies that the typical halo masses in ∼M{sub UV}{sup ∗} galaxies decrease from log(M{sub h}/M{sub ⊙}) = 11.9 at z = 4 to log(M{sub h}/M{sub ⊙}) = 11.4 at z = 7. Thus, although we are studying galaxies at a similar stellar mass across multiple redshifts, these galaxies live in lower mass halos at higher redshift. The stellar baryon fraction in ∼M{sub UV}{sup ∗} galaxies in units of the cosmic mean Ω{sub b}/Ω{sub m} rises from 5.1% at z = 4 to 11.7% at z = 7; this evolution is significant at the ∼3σ level. This rise does not agree with simple expectations of how galaxies grow, and implies that some effect, perhaps a diminishing efficiency of feedback, is allowing a higher fraction of available baryons to be converted into stars at high redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Effect of hydrostatic pressure on the structural and electronic properties of Cd{sub 0.75}Cr{sub 0.25}S

In this paper we present the results obtained from first principle calculations of the effect of hydrostatic pressure on the structural and electronic properties of Cd{sub 1-x}Cr{sub x}S diluted magnetic semiconductor in Zinc Blende (B3) phase at x=0.25. High pressure behavior of Cd{sub 1-x}Cr{sub x}S has been investigated between 0 GPa to 100 GPa The calculations have been performed using Density functional theory as implemented in the Spanish Initiative for Electronic Simulations with Thousands of Atoms code using local density approximation as exchange-correlation (XC) potential. Calculated electronic band structures of Cd{sub 1-x}Cr{sub x}S are discussed in terms of contribution of Cr 3d{sup 5} 4s{sup 1}, Cd 4d{sup 10} 5s{sup 2}, S 3s{sup 2} 3p{sup 4} orbital’s. Study of band structures shows half-metallic ferromagnetic nature of Cd{sub 0.75}Cr{sub 0.25}S with 100% spin polarization. Under application of external pressure, the valence band and conduction band are shifted upward which leads to modification of electronic structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A Corrected Score Function Framework for Modelling Circadian Gene Expression

Many biological processes display oscillatory behaviour based on an approximately 24 h internal timing system specific to each individual. One process of particular interest is gene expression, for which several circadian transcriptomic studies have identified associations between gene expression during a 24 h period and an individual's health. A challenge with analysing data from these studies is that each individual's internal timing system is offset relative to the 24 h day-night cycle, where day–night cycle time is recorded for each collected sample. Laboratory procedures can accurately determine each individual's offset and determine the internal time of sample collection. However, these laboratory procedures are labour-intensive and expensive. Here, in this paper, we propose a corrected score function framework to obtain a regression model of gene expression given internal time when the offset of each individual is too burdensome to determine. A feature of this framework is that it does not require the probability distribution generating offsets to be symmetric with a mean of zero. Simulation studies validate the use of this corrected score function framework for cosinor regression, which is prevalent in circadian transcriptomic studies. Illustrations with data from three circadian transcriptomic studies further demonstrate that the proposed framework consistently mitigates bias relative to using a score function that does not account for this offset.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

A note on the reliability of goal-oriented error estimates for Galerkin finite element methods with nonlinear functionals

Here, we consider estimating the discretization error in a nonlinear functional J (u) in the setting of an abstract variational problem: find u ϵ $\mathscr{V}$ such that B (u, φ) = L (φ) ∀φ ϵ $\mathscr{V}$, as approximated by a Galerkin finite element method. Here, $\mathscr{V}$ is a Hilbert space, B (. , .) is a bilinear form, and L (∙) is a linear functional. We consider well-known error estimates η of the form J (u) - J (u h ) ≈ η = L (z) - B (u h , z), where u h denotes a finite element approximation to u, and z denotes the solution to an auxiliary adjoint variational problem. We show that there exist nonlinear functionals for which error estimates of this form are not reliable, even in the presence of an exact adjoint solution z. An estimate η is said to be reliable if there exists a constant C ϵ $\mathbb{R}$ >0 independent of u h such that |J (u) - J (u h )| ≤ C|η|. We present several example pairs of bilinear forms and nonlinear functionals where reliability of η is not achieved.

A posteriori↗
DOE OSTI2017

One-Dimensional Fluids with Second Nearest–Neighbor Interactions

As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest–neighbor probability distribution function, p{sub 1}(r), is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearest–neighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of p{sub 1}(r) is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest–neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Quantum and classical behavior in interacting bosonic systems

It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Nonempirical Range-Separated Hybrid Functional with Spatially Dependent Screened Exchange

Electronic structure calculations based on density functional theory (DFT) have successfully predicted numerous ground-state properties of a variety of molecules and materials. However, exchange and correlation functionals currently used in the literature, including semilocal and hybrid functionals, are often inaccurate to describe the electronic properties of heterogeneous solids, especially systems composed of building blocks with large dielectric mismatch. Here, in this study, we present a dielectric-dependent range-separated hybrid functional, screened-exchange range-separated hybrid (SE-RSH), for the investigation of heterogeneous materials. We define a spatially dependent fraction of exact exchange inspired by the static Coulomb-hole and screened-exchange (COHSEX) approximation used in many-body perturbation theory, and we show that the proposed functional accurately predicts the electronic structure of several nonmetallic interfaces, three- and two-dimensional, pristine, and defective solids and nanoparticles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Triple Excitations in Green’s Function Coupled Cluster Solver for Studies of Strongly Correlated Systems in the Framework of Self-Energy Embedding Theory

Embedding theories became important approaches used for accurate calculations of both molecules and solids. In these theories, a small chosen subset of orbitals is treated with an accurate method, called an impurity solver, capable of describing higher correlation effects. Ideally, such a chosen fragment should contain multiple orbitals responsible for the chemical and physical behavior of the compound. Handling a large number of chosen orbitals presents a very significant challenge for the current generation of solvers used in the physics and chemistry community. Here, we develop a Green’s function coupled cluster singles doubles and triples (GFCCSDT) solver that can be used for a quantitative description in both molecules and solids. This solver allows us to treat orbital spaces that are inaccessible to other accurate solvers. At the same time, GFCCSDT maintains high accuracy of the resulting self-energy. Moreover, in conjunction with the GFCCSD solver, it allows us to test the systematic convergence of computational studies. Developing the CC family of solvers paves the road to fully systematic Green’s function embedding calculations in solids. In this paper, we focus on the investigation of GFCCSDT self-energies for a strongly correlated problem of SrMnO 3 solid. Subsequently, we apply this solver to solid MnO showing that an approximate variant of GFCCSDT is capable of yielding a high accuracy orbital resolved spectral function.

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

Comparison of the electromagnetic responses of C 12 obtained from the Green's function Monte Carlo and spectral function approaches

Here, the electromagnetic responses of carbon obtained from the Green's function Monte Carlo and spectral function approaches using the same dynamical input are compared in the kinematical region corresponding to momentum transfer in the range 300–570 MeV. The results of our analysis, aimed at pinning down the limits of applicability of the approximations involved in the two schemes, indicate that the factorization ansatz underlying the spectral function formalism provides remarkably accurate results down to momentum transfer as low as 300 MeV. On the other hand, it appears that at 570 MeV relativistic corrections to the electromagnetic current not included in the Monte Carlo calculations may play a significant role in the transverse channel.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Biotic Interactions Are More Important than Propagule Pressure in Microbial Community Invasions

ABSTRACT Microbial probiotics are intended to improve functions in diverse ecosystems, yet probiotics often fail to establish in a preexisting microbiome. This is a species invasion problem. The relative importance of the two major factors controlling establishment in this context—propagule pressure (inoculation dose and frequency) and biotic interactions (composition of introduced and resident communities)—is unknown. We tested the effect of these factors in driving microbial composition and functioning following 12 microbial community invasions (e.g., introductions of many microbial invaders) in microcosms. Ecosystem functioning over a 30-day postinvasion period was assessed by measuring activity (respiration) and environment modification (dissolved organic carbon abundance). To test the dependence on environmental context, experiments were performed in two resource environments. In both environments, biotic interactions were more important than propagule pressure in driving microbial composition and community function, but the magnitude of effect varied by environment. Successful invaders comprised approximately 8% of the total number of operational taxonomic units (OTUs). Bacteria were better invaders than fungi, with average relative abundances of 7.4% ± 6.8% and 1.5% ± 1.4% of OTUs, respectively. Common bacterial invaders were associated with stress response traits. The most resilient bacterial and fungal families, in other words, those least impacted by invasions, were linked to antimicrobial resistance or production traits. Illuminating the principles that determine community composition and functioning following microbial invasions is key to efficient community engineering. IMPORTANCE With increasing frequency, humans are introducing new microbes into preexisting microbiomes to alter functioning. Example applications include modification of microflora in human guts for better health and those of soil for food security and/or climate management. Probiotic applications are often approached as trial-and-error endeavors and have mixed outcomes. We propose that increased success in microbiome engineering may be achieved with a better understanding of microbial invasions. We conducted a microbial community invasion experiment to test the relative importance of propagule pressure and biotic interactions in driving microbial community composition and ecosystem functioning in microcosms. We found that biotic interactions were more important than propagule pressure in determining the impact of microbial invasions. Furthermore, the principles for community engineering vary among organismal groups (bacteria versus fungi).

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Electronic properties of single-layer CoO 2 /Au(111)

Here we report direct measurements via angle-resolved photoemission spectroscopy (ARPES) of the electronic dispersion of single-layer (SL) CoO 2 . The Fermi contour consists of a large hole pocket centered at the $\overline{\Gamma}$ point. To interpret the ARPES results, we use density functional theory (DFT) in combination with the multi-orbital Gutzwiller Approximation (DFT+GA), basing our calculations on crystalline structure parameters derived from x-ray photoelectron diffraction and low-energy electron diffraction. Our calculations are in good agreement with the measured dispersion. We conclude that the material is a moderately correlated metal. We also discuss substrate effects, and the influence of hydroxylation on the CoO 2 SL electronic structure.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer

The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C 2 singlet ground state is known from correlated wave function theory to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B 2 , C 2 , O 2 , and F 2 in the local spin density approximation (LSDA), the Perdew–Burke–Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C 2 . Here, this work shows that spin symmetry breaking in singlet C 2 , which involves the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that underbinding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry breaking with an advanced density functional might reliably describe strong correlation. This article also discusses some general aspects of symmetry breaking and the insights into strong correlation that symmetry breaking can bring. The normally correlated low-lying triplet excited state has the right vertical excitation energy in SCAN but not in LSDA or PBE, where the triplet is a false ground state. Fractional occupation numbers are found only for the symmetry-unbroken singlet and only in LSDA and PBE GGA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗