Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximation methods”

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 1,621 records · Page 90
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

DMC-ICE13 : Ambient and high pressure polymorphs of ice from diffusion Monte Carlo and density functional theory

Ice is one of the most important and interesting molecular crystals, exhibiting a rich and evolving phase diagram. Recent discoveries mean that there are now 20 distinct polymorphs; a structural diversity that arises from a delicate interplay of hydrogen bonding and van der Waals dispersion forces. This wealth of structures provides a stern test of electronic structure theories, with Density Functional Theory (DFT) often not able to accurately characterize the relative energies of the various ice polymorphs. Thanks to recent advances that enable the accurate and efficient treatment of molecular crystals with Diffusion Monte Carlo (DMC), we present here the DMC-ICE13 dataset; a dataset of lattice energies of 13 ice polymorphs. This dataset encompasses the full structural complexity found in the ambient and high-pressure molecular ice polymorphs, and when experimental reference energies are available, our DMC results deliver sub-chemical accuracy. Using this dataset, we then perform an extensive benchmark of a broad range of DFT functionals. Of the functionals considered, revPBE-D3 and RSCAN reproduce reference absolute lattice energies with the smallest error, while optB86b-vdW and SCAN+rVV10 have the best performance on the relative lattice energies. Our results suggest that a single functional achieving reliable performance for all phases is still missing, and that care is needed in the selection of the most appropriate functional for the desired application. The insights obtained here may also be relevant to liquid water and other hydrogen-bonded and dispersion-bonded molecular crystals.

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

Learning physics-based reduced-order models from data using nonlinear manifolds

Here we present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Quenching of highly rotationally excited HCl in collisions with He

We report rotational quenching cross sections and rate coefficients of HCl due to collisions with He. The close-coupling method and the coupled-states approximation are applied in quantum-mechanical scattering calculations of state-to-state cross sections for HCl with initial rotational levels up to j = 20 for kinetic energies from 10{sup –5} to 15,000 cm{sup –1}. State-to-state rate coefficients for temperatures between 0.1 and 3000 K are also presented. Comparison of the present rate coefficients with previous results reported in the literature for lowly excited rotational levels shows reasonable agreement. Small differences are attributed to the differences in the interaction potential energy surfaces. The uncertainty in the computed cross sections and rate coefficients is estimated by varying the potential well depth. Applications of current results to astrophysical systems are also briefly discussed.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2012

BAYESIAN ANGULAR POWER SPECTRUM ANALYSIS OF INTERFEROMETRIC DATA

We present a Bayesian angular power spectrum and signal map inference engine which can be adapted to interferometric observations of anisotropies in the cosmic microwave background (CMB), 21 cm emission line mapping of galactic brightness fluctuations, or 21 cm absorption line mapping of neutral hydrogen in the dark ages. The method uses Gibbs sampling to generate a sampled representation of the angular power spectrum posterior and the posterior of signal maps given a set of measured visibilities in the uv-plane. We use a mock interferometric CMB observation to demonstrate the validity of this method in the flat-sky approximation when adapted to take into account arbitrary coverage of the uv-plane, mode-mode correlations due to observations on a finite patch, and heteroschedastic visibility errors. The computational requirements scale as O(n{sub p} log n{sub p}) where n{sub p} measures the ratio of the size of the detector array to the inter-detector spacing, meaning that Gibbs sampling is a promising technique for meeting the data analysis requirements of future cosmology missions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

S 8 ring content in liquid sulfur determined from x-ray diffraction

The S 8 ring content in liquid sulfur has been determined from the 4.47 Å peak in the x-ray pair distribution function over the temperature range −55 °C –330 °C. This peak represents the characteristic 3rd and 4th nearest atom-atom distances across an S 8 -ring. Three procedures were used to calculate the S 8 -ring fraction; scaling to crystalline β-S, a linear combination fit and a direct integration method. All methods gave similar values, indicating that approximately one third of the S 8 -rings break up upon melting into a distribution of short chains with an average length of 5 ± 2 atoms. Our results contradict established models of low temperature sulfur that indicate below the λ-transition the liquid comprises almost entirely of S8-rings. In addition, we find the S 8 -ring fraction increases to 76 ± 10% at −30 °C in the supercooled liquid, and decreases to 23% ± 3% at 330 °C in the high temperature melt. First principle molecular dynamics calculations confirm the onset of dynamic ring distortion via broad bond angle distributions, associated with the interstitial region between the first and second peaks in the pair distribution function. Our results are consistent with the presence of a propensity of short chains in the low temperature liquid, that are required for the bond switching mechanism responsible for the polymerization process to occur at the λ-transition temperature, T λ .

lambda transition↗
DOE OSTI2019

Modeling the Kondo effect of a magnetic atom adsorbed on graphene

The Kondo effect due to a magnetic atom adsorbed on graphene is investigated using two theoretical approaches, including the non-equilibrium Green's function method within the slave-boson mean-field approximation and a newly developed tight-binding (TB) model with an effectively infinite Hubbard U term. Both methods reveal the presence of a Kondo peak in the local density of state (LDOS) of graphene near the Fermi level. A sharp Kondo peak is only observed in the odd-neighboring C sites of the C atom directly below the magnetic atom placed in top position. The peak intensity is found to decay quickly with respect to the distance between the C site and the magnetic atom. A theoretical model of scanning tunneling microscopy (STM) of graphene is presented as a means to identify the manifestation of the Kondo effect via direct topographic STM measurements. STM simulations show that in the proximity of the magnetic atom, only the C atoms of one sublattice are visible at low bias potential and thus a triangular lattice can be seen, in agreement with recent experiments. Further away from the magnetic atom, the Kondo effect dies down and eventually both sublattices are visible, leading to the recovery of the hexagonal lattice. Furthermore, this work not only provides a new TB method to study the Kondo effect in graphene, but also presents both scanning tunneling spectroscopy and microscopy fingerprints of the Kondo effect to facilitate its experimental verification.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Inelastic rate coefficients for collisions of C 4 H - with H 2

Carbon-chain anions were recently detected in the interstellar medium. These very reactive species are used as tracers of the physical and chemical conditions in a variety of astrophysical environments. However, the local thermodynamic equilibrium conditions are generally not fulfilled in these environments. Therefore, collisional as well as radiative rates are needed to accurately model the observed emission lines. We determine in this work the state-to-state rate coefficients of C 4 H- in collision with both ortho- and para-H 2 . A new ab initio 4D potential energy surface was computed using explicitly correlated coupled-cluster procedures. This surface was then employed to determine rotational excitation and de-excitation cross-sections and rate coefficients for the first 21 rotational levels (up to rotational level j 1 = 20) using the close-coupling method, while the coupled-state approximation was used to extend the calculations up to j 1 = 30. State-to-state rate coefficients were obtained for the temperature range 2–100K. The differences between the ortho- and para-H 2 rate coefficients are found to be small.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Electron impact excitation of molecular hydrogen

Here, we report the electron impact integrated and differential cross sections for excitation to the b 3 Σ$+\atop{u}$, a 3 Σ$+\atop{g}$, c 3 Π u , B 1 Σ$+\atop{u}$, E, F 1 Σ$+\atop{g}$, C 1 Π u , e 3 Σ$+\atop{u}$, h 3 Σ $+\atop{g}$, d 3 Π u , B'' 1 Σ$+\atop{u}$ , D 1 Π u , B'' 1 Σ$+\atop{u}$, and D' 1 Π u states of molecular hydrogen in the energy range from 10 to 300 eV. Total scattering and total ionization cross sections are also presented. The calculations have been performed by using the convergent close-coupling method within the fixed-nuclei approximation. Detailed convergence studies have been performed with respect to the size of the close-coupling expansion and a set of recommended cross sections has been produced. Significant differences with previous calculations are found. Agreement with experiment is mixed, ranging from excellent to poor depending on the transition and incident energies.

08 HYDROGEN↗
DOE OSTI2020

Radiative capture rates at deep defects from electronic structure calculations

We present a methodology to calculate radiative carrier capture coefficients at deep defects in semiconductors and insulators from first principles. Electronic structure and lattice relaxations are accurately described with hybrid density functional theory. Calculations of capture coefficients provide an additional validation of the accuracy of these functionals in dealing with localized defect states. We also discuss the validity of the Condon approximation, showing that even in the event of large lattice relaxations the approximation is accurate. We test the method on GaAs:VGa-TeAs and GaN:CN, for which reliable experiments are available, and demonstrate very good agreement with measured capture coefficients.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Effect of nuclear charge on laser-induced fusion enhancement in advanced fusion fuels

Here, based on the preliminary work done in a previous paper [Phys. Rev. C 105, 054001 (2022)], we investigate the effects of laser-induced fusion rate enhancements of different fusion fuels. In the aforementioned work, which considered $_{1}^{2}$H-$_{1}^{3}$H (D-T) and DHe 3 fusion, it was observed that a larger product of charge numbers of the fusion reactants leads to an increased laser-induced enhancement to the fusion cross section for static external electric fields. We investigate whether this trend persists for DT, DHe 3 , and pB 11 fusion for dynamical electric fields, using the semiclassical approaches of the Wentzel-Kramers-Brillouin method and the imaginary-time method, as well as the Kramers- Henneberger method, and the Volkoff-state approximation. We find that the fusion cross section of pB 11 indeed exhibits the largest relative enhancement for all laser parameters considered and may even surpass the cross section of DT and DHe 3 fusion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Examining the effect of nonlocality in ( d , n ) transfer reactions

In the last year we have been exploring the effect of the explicit inclusion of nonlocality in (d,p) reactions. The goal of this work is to extend previous studies to (d,n) reactions, which, although similar to (d,p), have specific properties that merit inspection. We apply our methods (both the distorted wave Born approximation and the adiabatic wave approximation) to (d; n) reactions on 16 O, 40 Ca, 48 Ca, 126 Sn, 132 Sn, and 208 Pb at 20 and 50 MeV. As a result, we look separately at the modifications introduced by nonlocality in the final bound and scattering states, as well as the consequences reflected on the differential angular distributions. The cross sections obtained when using nonlocality explicitly are significantly different than those using the local approximation, just as in (d,p). Due to the particular role of Coulomb in the bound state, often we found the effects of nonlocality to be larger in (d,n) than in (d,p). In conclusion, our results con rm the importance of including nonlocality explicitly in deuteron-induced reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Deep-inelastic and quasielastic electron scattering from A = 3 nuclei

We perform a combined analysis of inclusive electron scattering data from $A=3$ nuclei in the deep-inelastic and quasielastic scattering regions, using Monte Carlo analysis methods and the nuclear weak binding approximation to establish the range over which the data can be described within the same theoretical framework. Comparison with quasielastic $^3$He cross sections from SLAC and Jefferson Lab suggests that most features of the $x \gtrsim 1$ data can be reasonably well described in the impulse approximation with finite-$Q^2$ nuclear smearing functions for momentum transfers $Q^2 \gtrsim 1$~GeV$^2$. For the DIS region, we analyze the recent $^3$He to deuterium cross section ratio from the Jefferson Lab E03-103 experiment to explore the possible isospin dependence of the nuclear effects. We discuss the implications of this for the MARATHON experiment, and outline how a Bayesian analysis of $^3$He, $^3$H and deuterium data can robustly determine the free neutron structure function.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Hidden Mn magnetic-moment disorder and its influence on the physical properties of medium-entropy NiCoMn solid solution alloys

In this work, the ab initio Korringa-Kohn-Rostoker method combined with the coherent potential approximation (CPA) was employed to investigate the electronic, magnetic, and transport properties of medium-entropy face-centered-cubic (fcc) NiCoMn solid solution alloys. By comparing the CPA electronic structure with that from supercell calculations, we uncovered an unconventional CPA ground state, which correctly distinguishes two equally populated Mn CPA components—with large spin moments but opposite orientations. Using the spin spiral calculations, we further demonstrated that this ground state is most energetically favorable in the presence of spin noncollinearity, and no significant longitudinal spin fluctuation is observed, justifying the applicability of the Heisenberg model. The finite-temperature magnetism was further studied using different approximations based on the Heisenberg model, and we found the Mn moments to be fully disordered at low temperature due to a small net effective Weiss field on Mn. In addition, the magnetic effect on the electron scattering at finite temperatures was evaluated and compared with other scattering mechanisms. Since the magnetization-induced electron scattering is almost saturated in the ground state, (full) spin disorder only yields a small addition to the resistivity, whereas the thermal displacements increase it modestly. Finally, we elucidate the role of hydrostatic pressure on the magnetic and transport properties. In conclusion, these findings reflect the importance of the magnetic signatures on the physical properties of alloys, and they provide a window into magnetism-controlled electronic structure and energy dissipation.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Comparing Power Flow Approximations for Electricity Infrastructure Capacity Expansion Models with High Spatial Resolution

Future electricity system portfolios will require strategic transmission expansions for economically integrating regionally dependent, high-quality renewable resources. In this context, accurate representation of transmission flows in large-scale electricity infrastructure capacity expansion planning problems is important. This paper describes an approximate linearized power flow transmission modeling method for such expansion problems and demonstrates the impact on planning solutions using the National Renewable Energy Laboratory's Regional Energy Deployment System (ReEDS) model. Results are compared against a pipe flow transmission representation, which is used in a number of large-scale planning models. We show that national-scale generation and transmission expansion is not substantially influenced by the power flow methodology but that the pipe flow representation does underestimate required transmission capacity and total system costs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Radiative Lifetimes of the Energy Levels of Palladium-like Ions Pr XIV and Nd XV

Radiative lifetimes for the 4d{sup 9}4f, 4d{sup 9}5p, 4d{sup 9}5d, and 4d{sup 9}6s levels in the spectra of palladium-like ions Pr XIV and Nd XV are calculated in the electric-dipole approximation by the intermediate coupling semiempirical method with the use of experimental energy levels available in the literature. The radial integrals of transitions necessary for calculating absolute values of transition probabilities are obtained in the length form with Hartree–Fock functions.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

Crystal structures and luminescence properties of novel compounds K{sub 4}M{sub 2}[Al{sub 2}Si{sub 8}O{sub 24}] (M = Ce, Gd)

Two novel potassium rare earth silicates, obtained by hydrothermal synthesis, have been investigated by X-ray diffraction and described by the general formula K{sub 4}M{sub 2}[Al{sub 2}Si{sub 8}O{sub 24}] (M = Ce, Gd). The parameters of the monoclinic K{sub 4}Ce{sub 2}[Al{sub 2}Si{sub 8}O{sub 24}] and K{sub 4}Gd{sub 2}[Al{sub 2}Si{sub 8}O{sub 24}] cells are, respectively, as follows: a = 26.867(1), 26.6520(2) A; b = 7.4150(2), 7.2854(1) A; c = 14.910(1), 14.8182(1) A; {beta} = 123.52(1) Degree-Sign , 123.46(1) Degree-Sign ; and sp. gr. P2{sub 1}/n. The structures are solved by the charge flipping method and refined in the anisotropic approximation of thermal vibrations for atoms to R = 5.2 and 2.5%, respectively. The compounds under study are crystallized into a new structural type, which is based on two-level [Al{sub 2}Si{sub 8}O{sub 24}] layers, combined into a three-dimensional framework by columns of edge-sharing seven-vertex REE polyhedra. Potassium atoms are located in the framework channels. The spectral luminescence characteristics are determined. The luminescence bands are typical of Gd{sup 3+} and Ce{sup 3+} ions. Upon excitation by light with {lambda}{sub exc} = 246 nm, a band due to the {sup 2}D {yields} {sup 8}F{sub 5/2} transition with {lambda}{sub max} = 430 nm is observed in the spectrum of K{sub 4}Ce{sub 2}[Al{sub 2}Si{sub 8}O{sub 24}] and a band related to the {sup 6}P{sub 7/2} {yields} {sup 8}S{sub 7/2} transition with {lambda}{sub max} = 311 nm is observed in the spectrum of K{sub 4}Gd{sub 2}[Al{sub 2}Si{sub 8}O{sub 24}].

36 MATERIALS SCIENCE↗
DOE OSTI2012

Generation of displaced squeezed superpositions of coherent states

We study the method of generation of states that approximate superpositions of large-amplitude coherent states (SCSs) with high fidelity in free-traveling fields. Our approach is based on the representation of an arbitrary single-mode pure state, and SCSs in particular, in terms of displaced number states with an arbitrary displacement amplitude. The proposed optical scheme is based on alternation of photon additions and displacement operators (in the general case, N photon additions and N - 1 displacements are required) with a seed coherent state to generate both even and odd displaced squeezed SCSs regardless of the parity of the used photon additions. It is shown that the optical scheme studied is sensitive to the seed coherent state if the other parameters are unchanged. Output states can approximate either even squeezed SCS or odd SCS shifted relative to each other by some value. This allows constructing a local rotation operator, in particular, the Hadamard gate, which is a mainframe element for quantum computation with coherent states. We also show that three-photon additions with two intermediate displacement operators are sufficient to generate even displaced squeezed SCS with the amplitude 1.7 and fidelity more than 0.99. The effects deteriorating the quality of output states are considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗