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At least 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Electronic energy states

One-electron wave functions are reviewed and approximate solutions of two-electron systems are given in terms of these one-electron functions. The symmetry effects associated with electron spin are reviewed and the effects of electron exchange on energy levels of the two-electron system are given. The coupling of electronic orbital and spin angular momentum is considered next and the Lande interval rule for Russell-Saunders or LS coupling is derived. The configurations possible for various multi-electron LS couplings are enumerated (examples from the first two rows of the periodic table are given), and the meaning of the spectroscopic nomenclature is discussed, particularly with respect to the degeneracies of the electron states involved. Next the nomenclature, symmetries, and degeneracies for electron states of diatomic molecules are discussed, and some examples for N2, O2, and NO are presented. The electronic partition functions and derivative thermodynamic properties are expressed in terms of these energies and degeneracies, and examples are given for some of the simple gas species encountered in the earth's atmosphere.

Source record↗
DOE OSTI2023

Two-pion femtoscopic correlations in Be+Be collisions at $\sqrt{s_{\text {NN}}} = 16.84$ GeV measured by the NA61/SHINE at CERN

This paper reports measurements of two-pion femtoscopic correlations in Be+Be collisions at a beam momentum of 150$A\,\hbox {GeV}\!/\!c$ (energy available in the center-of-mass system for nucleon pair $\sqrt{s_{\text {NN}}} = 16.84$ GeV) by the NA61/SHINE experiment at the CERN SPS accelerator. The obtained momentum space correlation functions can be well described by a Lévy distributed source model. The transverse mass dependence of the Lévy source parameters is presented, and their possible theoretical interpretations are discussed. The results show that the Lévy exponent $\alpha $ is approximately constant as a function of $m_{\text {T}}$ , and far from both the Gaussian case of $\alpha = 2$ or the conjectured value at the critical endpoint, $\alpha = 0.5$. The radius scale parameter R shows a slight decrease in $m_{\text {T}}$ , which can be explained as a signature of transverse flow. Finally, an approximately constant trend of the intercept parameter $\lambda $ as a function of $m_{\text {T}}$ was observed, similar to previous NA44 S + Pb results (obtained with a Gaussian approximation, but unlike RHIC results).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

CrI 3 revisited with a many-body ab initio theoretical approach

CrI 3 has recently been shown to exhibit low-dimensional, long-range magnetic ordering from few layers to single layers of CrI 3 . The properties of CrI 3 bulk and few layered systems are uniquely defined by a combination of short-range intralayer and long-range interlayer interactions; including strong correlations, exchange and spin orbit coupling. Unfortunately, both the long-range van der Waals interactions, which are driven by dynamic, many-body electronic correlations and the competing strong intralayer correlations, present a formidable challenging for the local or semi local mean-field approximations employed in workhorse electronic structure approaches like density functional theory. In this work, we employ a sophisticated many-body approach that can simultaneously describe long- and short-range correlations. Herein, we establish that the fixed-node diffusion Monte Carlo (FNDMC) method reproduces the experimental interlayer separation distance of bulk CrI 3 for the high-temperature, monoclinic phase, with a reliable prediction of the interlayer binding energy. We subsequently employed, the FNDMC results to benchmark the accuracy of several density functional theory exchange-correlation approximations.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Numerical multi-scaling method to solve the linear stochastic partial differential equations

In this paper, we propose a multi-scaling method to solve a class of the stochastic partial differential equations (SPDEs) of Itô-type. By this method, we approximate the solution of the SPDEs with strongly elliptic operator on a finite domain. The method is based on B-spline wavelet approximations; some of these functions are reshaped to satisfy on boundary conditions exactly. We prove the consistency and stability of the method. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

The delta-Eddington approximation for radiative flux transfer

Simple approximations, like the Eddington, are often incapable of coping with the highly asymmetric phase functions typical of particulate scattering. A simple yet accurate method called the delta-Eddington approximation is proposed for determining monochromatic radiative fluxes in an absorbing-scattering atmosphere. In this method, the governing phase function is approximated by a Dirac delta function forward scatter peak and a two-term expansion of the phase function. The fraction of scattering into the truncated forward peak is taken proportional to the square of the phase function asymmetry factor, which distinguishes the delta-Eddington approximation from others of similar nature. The transmission, reflection, and absorption predicted by the delta-Eddington approximation are compared with doubling method calculations for realistic ranges of optical depth, single-scattering albedo, surface albedo, sun angle and asymmetry factor. The approximation is shown to provide an accurate and analytically simple parameterization of radiation to replace the empirism currently encountered in many general circulation and climate models.

Joseph, J. H.↗
DOE OSTI2018

Supersymmetric Dynamics and Zeta-Functions

Boson, fermion, and super oscillators and (statistical) mechanism of cosmological constant; finite approximation of the zeta-function and fermion factorization of the bosonic statistical sum concidered.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 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↗
NASA NTRS1994

AutoClass: A Bayesian Approach to Classification

We describe a Bayesian approach to the untutored discovery of classes in a set of cases, sometimes called finite mixture separation or clustering. The main difference between clustering and our approach is that we search for the "best" set of class descriptions rather than grouping the cases themselves. We describe our classes in terms of a probability distribution or density function, and the locally maximal posterior probability valued function parameters. We rate our classifications with an approximate joint probability of the data and functional form, marginalizing over the parameters. Approximation is necessitated by the computational complexity of the joint probability. Thus, we marginalize w.r.t. local maxima in the parameter space. We discuss the rationale behind our approach to classification. We give the mathematical development for the basic mixture model and describe the approximations needed for computational tractability. We instantiate the basic model with the discrete Dirichlet distribution and multivariant Gaussian density likelihoods. Then we show some results for both constructed and actual data.

Stutz, John↗
NASA NTRS1976

Dynamics of flexible spinning satellites with radial wire antennas

A dynamic analysis is presented for a spin-stabilized spacecraft employing four radial wire antennas with tip masses. The satellite is modelled as a 14-degree-of-freedom system, and the linearized equations of motion are found. The lowest-order vibrational modes and natural frequencies of the gyroscopically coupled system are then determined. Because the satellite spin rate is decreased by antenna deployment, a spin-up maneuver is needed. The response of the time-varying mode equations during spin-up is found for the planar modes in terms of Bessel functions and a Struve function of order -0.25. The particular solution is expressed in various forms, including an infinite series of Bessel functions and a particularly useful asymptotic expansion. An error formula for the latter is derived, showing that it gives good accuracy. A simple approximation to the complementary function is obtained using the Wenzel-Kramers-Brillouin method, and the phase error in the approximation is shown to be small.

Longman, R. W.↗
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↗