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NASA NTRS1989

Objective analysis of pseudostress over the Indian Ocean using a direct-minimization approach

A technique not previously used in objective analysis of meteorological data is used here to produce monthly average surface pseudostress data over the Indian Ocean. An initial guess field is derived and a cost functional is constructed with five terms: approximation to initial guess, approximation to climatology, a smoothness parameter, and two kinematic terms. The functional is minimized using a conjugate-gradient technique, and the weight for the climatology term controls the overall balance of influence between the climatology and the initial guess. Results from various weight combinations are presented for January and July 1984. Quantitative and qualitative comparisons to the subject analysis are made to find which weight combination provides the best results. The weight on the approximation to climatology is found to balance the influence of the original field and climatology.

Legler, David M.↗

DOE OSTI2015

Metal cluster structures and properties from Born-Oppenheimer molecular dynamics

Density functional theory (DFT) Born-Oppenheimer molecular dynamics (BOMD) simulations of metal clusters are presented. The calculations have been performed with the deMon2k [1] code employing all-electron basis sets and local and non-local functionals. The capability to perform reasonable long (∼ 100 ps) first-principle BOMD simulations in order to explore potential energy landscape of metallic clusters will be presented [2,3]. The evolution of the cluster structures and properties, such as polarizability and heat capacity, with temperature is discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1975

A grid of model atmospheres for metal-deficient giant stars. I

A grid of flux-constant model atmospheres for stars with effective temperatures between 3750 and 6000 K, log g between 0.75 and 3.0, and (A/H) between -3.0 and 0.0 has been constructed. The line absorption is approximated by opacity distribution functions. Metal lines and molecular lines, including those from the infrared bands of CO and CN, are taken into account. The variation of the structure of the models with metal abundance and microturbulence parameter is found to be quite regular and not very drastic. The surface cooling produced by CO is important for all the models with a maximum temperature of 5000 K, while CN mainly causes a backwarming effect but is not very important for solar CNO abundances. The effects of convection, estimated by using the mixing-length approximation, are important only for the coldest models. The models compare very well with models from overlapping regions of other grids. A solar model consistent with the grid models is found to agree satisfactorily with empirical solar model atmospheres. The careful use of scaled solar models for stars with (A/H) approximately equal to zero is justified.

Gustafsson, B.↗

DOE OSTI2020

Confirmation of the PPLB Derivative Discontinuity: Exact Chemical Potential at Finite Temperatures of a Model System

The landmark 1982 paper of Perdew, Parr, Levy, and Balduz (often called PPLB) laid the foundation for our modern understanding of the role of the derivative discontinuity in density functional theory, which drives much development to account for its effects. A simple model for the chemical potential at vanishing temperature played a crucial role in their argument. We investigate the validity of this model in the simplest non-trivial system to which it can be applied and which can be easily solved exactly, the Hubbard dimer. We find exact agreement in the crucial zero-temperature limit, and show the model remains accurate for a significant range of temperatures. We identify how this range depends on the strength of correlations. We extend the model to approximate free energies accounting for the derivative discontinuity, a feature missing in standard semilocal approximations. Here, we provide a correction to this approximation to yield even more accurate free energies. We discuss the relevance of these results for warm dense matter.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Production of light-flavor hadrons in pp collisions at $\sqrt{s}~=~7\text { and }\sqrt{s} = 13 \, \text { TeV} $

The production of $\pi ^{\pm }$ , $\mathrm{K}^{\pm }$ , $\mathrm{K}^{0}_{S}$ , $\mathrm{K}^{*}(892)^{0}$ , $\mathrm{p}$ , $\phi (1020)$ , $\Lambda $ , $\Xi ^{-}$ , $\Omega ^{-}$ , and their antiparticles was measured in inelastic proton–proton (pp) collisions at a center-of-mass energy of $\sqrt{s}$ = 13 TeV at midrapidity ( $|y|<0.5$ ) as a function of transverse momentum ( $p_{\mathrm{T}}$ ) using the ALICE detector at the CERN LHC. Furthermore, the single-particle $p_{\mathrm{T}}$ distributions of $\mathrm{K}^{0}_{S}$ , $\Lambda $ , and $\overline{\Lambda }$ in inelastic pp collisions at $\sqrt{s} = 7$ TeV are reported here for the first time. The $p_{\mathrm{T}}$ distributions are studied at midrapidity within the transverse momentum range $0\le p_{\mathrm{T}}\le 20$ GeV/ c , depending on the particle species. The $p_{\mathrm{T}}$ spectra, integrated yields, and particle yield ratios are discussed as a function of collision energy and compared with measurements at lower $\sqrt{s}$ and with results from various general-purpose QCD-inspired Monte Carlo models. A hardening of the spectra at high $p_{\mathrm{T}}$ with increasing collision energy is observed, which is similar for all particle species under study. The transverse mass and $x_{\mathrm{T}}\equiv 2p_{\mathrm{T}}/\sqrt{s}$ scaling properties of hadron production are also studied. As the collision energy increases from $\sqrt{s}$ = 7–13 TeV, the yields of non- and single-strange hadrons normalized to the pion yields remain approximately constant as a function of $\sqrt{s}$ , while ratios for multi-strange hadrons indicate enhancements. The $p_\mathrm{{T}}$ -differential cross sections of $\pi ^{\pm }$ , $\mathrm {K}^{\pm }$ and $\mathrm {p}$ ( $\overline{\mathrm{p}}$ ) are compared with next-to-leading order perturbative QCD calculations, which are found to overestimate the cross sections for $\pi ^{\pm }$ and $\mathrm{p}$ ( $\overline{\mathrm{p}}$ ) at high $p_\mathrm{{T}}$ .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2000

General Purpose Fortran Program for Discrete-Ordinate-Method Radiative Transfer in Scattering and Emitting Layered Media: An Update of DISORT

This update reports a state-of-the-art discrete ordinate algorithm for monochromatic unpolarized radiative transfer in non-isothermal, vertically inhomogeneous, but horizontally homogeneous media. The physical processes included are Planckian thermal emission, scattering with arbitrary phase function, absorption, and surface bidirectional reflection. The system may be driven by parallel or isotropic diffuse radiation incident at the top boundary, as well as by internal thermal sources and thermal emission from the boundaries. Radiances, fluxes, and mean intensities are returned at user-specified angles and levels. DISORT has enjoyed considerable popularity in the atmospheric science and other communities since its introduction in 1988. Several new DISORT features are described in this update: intensity correction algorithms designed to compensate for the 8-M forward-peak scaling and obtain accurate intensities even in low orders of approximation; a more general surface bidirectional reflection option; and an exponential-linear approximation of the Planck function allowing more accurate solutions in the presence of large temperature gradients. DISORT has been designed to be an exemplar of good scientific software as well as a program of intrinsic utility. An extraordinary effort has been made to make it numerically well-conditioned, error-resistant, and user-friendly, and to take advantage of robust existing software tools. A thorough test suite is provided to verify the program both against published results, and for consistency where there are no published results. This careful attention to software design has been just as important in DISORT's popularity as its powerful algorithmic content.

Tsay, Si-Chee↗

DOE OSTI2021

Measurements of dihadron correlations relative to the event plane in Au+Au collisions at $\sqrt{s_{NN}} =200$ GeV*

Dihadron azimuthal correlations containing a high transverse momentum ($ p_{T} $) trigger particle are sensitive to the properties of the nuclear medium created at RHIC through the strong interactions occurring between the traversing parton and the medium, i.e. jet-quenching. Previous measurements revealed a strong modification to dihadron azimuthal correlations in Au+Au collisions with respect to p+p and d+Au collisions. The modification increases with the collision centrality, suggesting a path-length or energy density dependence to the jet-quenching effect. This paper reports STAR measurements of dihadron azimuthal correlations in mid-central (20%-60%) Au+Au collisions at $ \sqrt{s_{\rm{NN}}} = 200 $ GeV as a function of the trigger particle's azimuthal angle relative to the event plane, $ \phi_{s} = | \phi_{t}- \psi_{{\rm{EP}}}| $. The azimuthal correlation is studied as a function of both the trigger and associated particle $ p_{T} $. The subtractions of the combinatorial background and anisotropic flow, assuming Zero Yield At Minimum (ZYAM), are described. The correlation results are first discussed with subtraction of the even harmonic (elliptic and quadrangular) flow backgrounds. The away-side correlation is strongly modified, and the modification varies with $ \phi_{s} $, with a double-peak structure for out-of-plane trigger particles. The near-side ridge (long range pseudo-rapidity $ \Delta\eta $ correlation) appears to drop with increasing $ \phi_{s} $ while the jet-like component remains approximately constant. The correlation functions are further studied with the subtraction of odd harmonic triangular flow background arising from fluctuations. It is found that the triangular flow, while responsible for the majority of the amplitudes, is not sufficient to explain the $ \phi_{s} $-dependence of the ridge or the away-side double-peak structure. The dropping ridge with $ \phi_{s} $ could be attributed to a $ \phi_{s} $-dependent elliptic anisotropy; however, the physics mechanism of the ridge remains an open question. Even with a $ \phi_{s} $-dependent elliptic flow, the away-side correlation structure is robust. These results, with extensive systematic studies of the dihadron correlations as a function of $ \phi_{s} $, trigger and associated particle $ p_{T} $, and the pseudo-rapidity range $ \Delta\eta $, should provide stringent inputs to help understand the underlying physics mechanisms of jet-medium interactions in high energy nuclear collisions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. Here, we show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

42 ENGINEERING↗

DOE OSTI2023

Probing reaction channels via reinforcement learning

Abstract Chemical reactions are dynamical processes involving the correlated reorganization of atomic configurations, driving the conversion of an initial reactant into a result product. By virtue of the metastability of both the reactants and products, chemical reactions are rare events, proceeding fleetingly. Reaction pathways can be modelled probabilistically by using the notion of reactive density in the phase space of the molecular system. Such density is related to a function known as the committor function, which describes the likelihood of a configuration evolving to one of the nearby metastable regions. In theory, the committor function can be obtained by solving the backward Kolmogorov equation (BKE), which is a partial differential equation (PDE) defined in the full dimensional phase space. However, using traditional methods to solve this problem is not practical for high dimensional systems. In this work, we propose a reinforcement learning based method to identify important configurations that connect reactant and product states along chemical reaction paths. By shooting multiple trajectories from these configurations, we can generate an ensemble of states that concentrate on the transition path ensemble. This configuration ensemble can be effectively employed in a neural network-based PDE solver to obtain an approximation solution of a restricted BKE, even when the dimension of the problem is very high. The resulting solution provides an approximation for the committor function that encodes mechanistic information for the reaction, paving a new way for understanding of complex chemical reactions and evaluation of reaction rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1986

Unimolecular diffusion-mediated reactions with a nonrandom time-modulated absorbing barrier

A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.

Bashford, D.↗

DOE OSTI2018

Solution of the Problem of Free Vibrations of a Nonthin Orthotropic Shallow Shell of Variable Thickness in the Refined Statement

We consider the problem of investigation of the spectrum of natural vibrations of a nonthin orthotropic shallow shell variable in two coordinate directions of thickness in the nonclassical statement. The approach to the solution of the obtained two-dimensional boundary-value problem is based on its reduction (by the method of spline-approximation of the unknown functions along one coordinate direction) to the one-dimensional problem with its subsequent solution. We study different cases of boundary conditions imposed on the contours of the shell. We also perform the comparison and analysis of the natural frequencies and modes of vibrations of orthotropic shells of constant and variable thickness.

42 ENGINEERING↗

DOE OSTI2024

Approaching periodic systems in ensemble density functional theory via finite one-dimensional models

Ensemble density functional theory (EDFT) is a generalization of ground-state DFT, which is based on an exact formal theory of finite collections of a system's ground and excited states. EDFT in various forms has been shown to improve the accuracy of calculated energy level differences in isolated model systems, atoms, and molecules, but it is not yet clear how EDFT could be used to calculate band gaps for periodic systems. We extend the application of EDFT toward periodic systems by estimating the thermodynamic limit with increasingly large finite one-dimensional 'particle in a box' systems, which approach the uniform electron gas (UEG). Using ensemble-generalized Hartree and local spin density approximation exchange-correlation functionals, we find that corrections go to zero in the infinite limit, as expected for a metallic system. However, there is a correction to the effective mass, with results comparable to other calculations on 1D, 2D, and 3D UEGs, which indicates promise for non-trivial results from EDFT on periodic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Lineshape theory of pigment-protein complexes: How the finite relaxation time of nuclei influences the exciton relaxation-induced lifetime broadening

In pigment-protein complexes, often the excited states are partially delocalized and the exciton-vibrational coupling in the basis of delocalized states contains large diagonal and small off-diagonal elements. This inequality may be used to introduce potential energy surfaces (PESs) of exciton states and to treat the inter-PES coupling in Markov and secular approximations. The resulting lineshape function consists of a Lorentzian peak that is broadened by the finite lifetime of the exciton states caused by the inter-PES coupling and a vibrational sideband that results from the mutual displacement of the excitonic PESs with respect to that of the ground state. So far analytical expressions have been derived that relate the exciton relaxation-induced lifetime broadening to the Redfield [T. Renger and R. A. Marcus, J. Chem. Phys. 116, 9997 (2002)] or modified Redfield [M. Schröder, U. Kleinekathöfer, and M. Schreiber, J. Chem. Phys. 124, 084903 (2006)] rate constants of exciton relaxation, assuming that intra-PES nuclear relaxation is fast compared to inter-PES transfer. Here, we go beyond this approximation and provide an analytical expression, termed Non-equilibrium Modified Redfield (NeMoR) theory, for the lifetime broadening that takes into account the finite nuclear relaxation time. In an application of the theory to molecular dimers, we find that, for a widely used experimental spectral density of the exciton-vibrational coupling of pigment-protein complexes, the NeMoR spectrum at low-temperatures (T < 150 K) is better approximated by Redfield than by modified Redfield theory. At room temperature, the lifetime broadening obtained with Redfield theory underestimates the NeMoR broadening, whereas modified Redfield theory overestimates it by a similar amount. A fortuitous error compensation in Redfield theory is found to explain the good performance of this theory at low temperatures. Since steady state spectra of PPCs are often measured at low temperatures, Redfield theory still provides a numerically efficient alternative to NeMoR theory. At higher temperatures, we suggest to use NeMoR theory, because it has the same numerical costs as modified Redfield theory, but is more accurate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Machine-learning Kohn–Sham potential from dynamics in time-dependent Kohn–Sham systems

Abstract The construction of a better exchange-correlation potential in time-dependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculations and provide more accurate predictions of the properties of many-electron systems. Here, we propose a machine learning method to develop the energy functional and the Kohn–Sham potential of a time-dependent Kohn–Sham (TDKS) system is proposed. The method is based on the dynamics of the Kohn–Sham system and does not require any data on the exact Kohn–Sham potential for training the model. We demonstrate the results of our method with a 1D harmonic oscillator example and a 1D two-electron example. We show that the machine-learned Kohn–Sham potential matches the exact Kohn–Sham potential in the absence of memory effect. Our method can still capture the dynamics of the Kohn–Sham system in the presence of memory effects. The machine learning method developed in this article provides insight into making better approximations of the energy functional and the Kohn–Sham potential in the TDKS system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Galaxy and Mass Assembly (GAMA): Exploring the WISE Web in G12

We present an analysis of the mid-infrared Wide-field Infrared Survey Explorer (WISE) sources seen within the equatorial GAMA G12 field, located in the North Galactic Cap. Our motivation is to study and characterize the behavior of WISE source populations in anticipation of the deep multiwavelength surveys that will define the next decade, with the principal science goal of mapping the 3D large-scale structures and determining the global physical attributes of the host galaxies. In combination with cosmological redshifts, we identify galaxies from their WISE W1 (3.4 μm) resolved emission, and we also perform a star-galaxy separation using apparent magnitude, colors, and statistical modeling of star counts. The resulting galaxy catalog has ≃590,000 sources in 60 deg{sup 2}, reaching a W1 5σ depth of 31 μJy. At the faint end, where redshifts are not available, we employ a luminosity function analysis to show that approximately 27% of all WISE extragalactic sources to a limit of 17.5 mag (31 μJy) are at high redshift, z>1. The spatial distribution is investigated using two-point correlation functions and a 3D source density characterization at 5 Mpc and 20 Mpc scales. For angular distributions, we find that brighter and more massive sources are strongly clustered relative to fainter sources with lower mass; likewise, based on WISE colors, spheroidal galaxies have the strongest clustering, while late-type disk galaxies have the lowest clustering amplitudes. In three dimensions, we find a number of distinct groupings, often bridged by filaments and superstructures. Using special visualization tools, we map these structures, exploring how clustering may play a role with stellar mass and galaxy type.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Quantum Monte Carlo analysis of a charge ordered insulating antiferromagnet: The Ti 4 O 7 Magneli phase

The Magneli phase Ti 4 O 7 is an important transition metal oxide with a wide range of applications because of its interplay between charge, spin, and lattice degrees of freedom. At low temperatures, it has non-trivial magnetic states very close in energy, driven by electronic exchange and correlation interactions. We have examined three low- lying states, one ferromagnetic and two antiferromagnetic, and calculated their energies as well as Ti spin moment distributions using highly accurate Quantum Monte Carlo methods. We compare our results to those obtained from density functional theory- based methods that include approximate corrections for exchange and correlation. Our results confirm the nature of the states and their ordering in energy, as compared with density-functional theory methods. However, the energy differences and spin distributions differ. Here, a detailed analysis suggests that non-local exchange-correlation functionals, in addition to other approximations such as LDA+U to account for correlations, are needed to simultaneously obtain better estimates for spin moments, distributions, energy differences and energy gaps.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Pressure induced magnetic phase transition in RhFe{sub 3}N and IrFe{sub 3}N: An ab-initio study

The structural, electronic, elastic and magnetic properties of RhFe{sub 3}N and IrFe{sub 3}N are investigated using ab-initio calculations based on density functional theory as implemented in VASP code within the gradient generalized approximation. The non-spin polarized and spin polarized calculations are performed for these nitrides at normal and high pressures. It is found that these ternary nitrides are stable in ferromagnetic state at normal pressure. The lattice constant and bulk modulus values are calculated. The electronic structure reveals that these nitrides are metallic at normal pressure. The calculated elastic constants indicate that they are mechanically stable at ambient pressure. Ferromagnetic to nonmagnetic phase transition is observed in RhFe{sub 3}N and IrFe{sub 3}N at high pressure. Ferromagnetism is quenched in these nitrides at high pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

Fractional charge and spin errors in self-consistent Green’s function theory

We examine fractional charge and spin errors in self-consistent Green’s function theory within a second-order approximation (GF2). For GF2, it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Møller-Plesset (MP2) theory for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end, we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently minimal many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Furthermore, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗