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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Nonlinear Alfvén wave dynamics in plasmas

Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Delay-induced stochastic bifurcations in a bistable system under white noise

In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A modified approach for simulating electronically nonadiabatic dynamics via the generalized quantum master equation

We present a modified approach for simulating electronically nonadiabatic dynamics based on the Nakajima-Zwanzig generalized quantum master equation (GQME). The modified approach utilizes the fact that the Nakajima-Zwanzig formalism does not require casting the overall Hamiltonian in system-bath form, which is arguably neither natural nor convenient in the case of the Hamiltonian that governs nonadiabatic dynamics. Within the modified approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density operator is fully captured by a memory kernel super-operator. A methodology for calculating the memory kernel from projection-free inputs is developed. Simulating the electronic dynamics via the modified approach, with a memory kernel obtained using exact or approximate methods, can be more cost effective and/or lead to more accurate results than direct application of those methods. The modified approach is compared to previously proposed GQME-based approaches, and its robustness and accuracy are demonstrated on a benchmark spin-boson model with a memory kernel which is calculated within the Ehrenfest method.

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

Nonlocal suppression of Biermann battery magnetic-field generation for arbitrary atomic numbers and magnetization

The Biermann battery term of magnetohydrodynamics (MHD) generates a magnetic field where electron density gradients and electron temperature gradients are perpendicular to one another. Kinetic simulations and experiments have shown that the rate of magnetic-field generation is lower than Biermann when the electron mean free path becomes comparable to or greater than the temperature gradient scale length, known as the nonlocal regime. We investigate the nonlocal suppression of the Biermann term using simplified Fokker–Planck simulations covering a wide range of parameters. We provide the first fit for nonlocal Biermann suppression that has physically accurate behavior for small and large values of a suitable nonlocality parameter, valid for an arbitrary atomic number, and that includes the effect of magnetization on nonlocality. Lastly, the fit is intended to provide an approximate method to account for reduced magnetic-field generation in MHD codes and theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Quantum utility in simulating the real-time dynamics of the Fermi–Hubbard model using superconducting quantum computers

The Fermi–Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi–Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi–Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi–Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Lastly, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Analysis of reaction schemes using maximum rates of constituent steps

Significance The design of active and selective catalysts is essential for a wide range of industrial applications and societal issues. A fundamental approach is to identify the key elementary steps and to elucidate the predicted reaction kinetics for potential reaction mechanisms. We present a methodology to analyze analytically the performance of catalytic reaction schemes by calculation of the maximum rates of the constituent steps. This proposed methodology can be used to identify the important transition states and adsorbed species, such that more detailed calculations can be carried out for these species, whereas more approximate methods can be used for the remaining species, thereby substantially reducing the computational time required to elucidate how catalyst performance is controlled by the fundamental surface chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

LONG-LIVED CHAOTIC ORBITAL EVOLUTION OF EXOPLANETS IN MEAN MOTION RESONANCES WITH MUTUAL INCLINATIONS

We present N-body simulations of resonant planets with inclined orbits that show chaotically evolving eccentricities and inclinations that can persist for at least 10 Gyr. A wide range of behavior is possible, from fast, low amplitude variations to systems in which eccentricities reach 0.9999 and inclinations 179.°9. While the orbital elements evolve chaotically, at least one resonant argument always librates. We show that the HD 73526, HD 45364, and HD 60532 systems may be in chaotically evolving resonances. Chaotic evolution is apparent in the 2:1, 3:1, and 3:2 resonances, and for planetary masses from lunar- to Jupiter-mass. In some cases, orbital disruption occurs after several gigayears, implying the mechanism is not rigorously stable, just long-lived relative to the main sequence lifetimes of solar-type stars. Planet-planet scattering appears to yield planets in inclined resonances that evolve chaotically in about 0.5% of cases. These results suggest that (1) approximate methods for identifying unstable orbital architectures may have limited applicability, (2) the observed close-in exoplanets may be produced during epochs of high eccentricit induced by inclined resonances, (3) those exoplanets' orbital planes may be misaligned with the host star's spin axis, (4) systems with resonances may be systematically younger than those without, (5) the distribution of period ratios of adjacent planets detected via transit may be skewed due to inclined resonances, and (6) potentially habitable planets may have dramatically different climatic evolution than Earth. The Gaia spacecraft is capable of discovering giant planets in these types of orbits.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The journey from forensic to predictive materials science using density functional theory

Approximate methods for electronic structure, implemented in sophisticated computer codes and married to ever-more powerful computing platforms, have become invaluable in chemistry and materials science. The maturing and consolidation of quantum chemistry codes since the 1980s, based upon explicitly correlated electronic wave functions, has made them a staple of modern molecular chemistry. Here, the impact of first principles electronic structure in physics and materials science had lagged owing to the extra formal and computational demands of bulk calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Production of alternate realizations of DESI fiber assignment for unbiased clustering measurement in data and simulations

A critical requirement of spectroscopic large scale structure analyses is correcting for selection of which galaxies to observe from an isotropic target list. This selection is often limited by the hardware used to perform the survey which will impose angular constraints of simultaneously observable targets, requiring multiple passes to observe all of them. In SDSS this manifested solely as the collision of physical fibers and plugs placed in plates. In DESI, there is the additional constraint of the robotic positioner which controls each fiber being limited to a finite patrol radius. A number of approximate methods have previously been proposed to correct the galaxy clustering statistics for these effects, but these generally fail on small scales. To accurately correct the clustering we need to upweight pairs of galaxies based on the inverse probability that those pairs would be observed (Bianchi & Percival 2017). This paper details an implementation of that method to correct the Dark Energy Spectroscopic Instrument (DESI) survey for incompleteness. To calculate the required probabilities, we need a set of alternate realizations of DESI where we vary the relative priority of otherwise identical targets. These realizations take the form of alternate Merged Target Ledgers (AMTL), the files that link DESI observations and targets. We present the method used to generate these alternate realizations and how they are tracked forward in time using the real observational record and hardware status, propagating the survey as though the alternate orderings had been adopted. We detail the first applications of this method to the DESI One-Percent Survey (SV3) and the DESI year 1 data. We include evaluations of the pipeline outputs, estimation of survey completeness from this and other methods, and validation of the method using mock galaxy catalogs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains

Here, this work focuses on weighted Lagrange interpolation on an unbounded domain and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are a nested sequence of points defined on a compact subset of the real line and can be extended to unbounded domains with the introduction of a weight function w:R → [0,1]. Due to a simple recursive formulation in one dimension, such abscissas provide a foundation for high-dimensional approximation methods such as sparse grid collocation, deterministic least squares and compressed sensing. Just as in the unweighted case of interpolation on a compact domain, we use results from potential theory to prove that the Lebesgue constant for the Leja points grows subexponentially with the number of interpolation nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The completed SDSS-IV extended baryon oscillation spectroscopic survey: pairwise-inverse probability and angular correction for fibre collisions in clustering measurements

ABSTRACT The completed extended Baryon Oscillation Spectroscopic Survey (eBOSS) catalogues contain redshifts of 344 080 quasars at 0.8 < z < 2.2, 174 816 luminous red galaxies between 0.6 < z < 1.0, and 173 736 emission-line galaxies over 0.6 < z < 1.1 in order to constrain the expansion history of the Universe and the growth rate of structure through clustering measurements. Mechanical limitations of the fibre-fed spectrograph on the Sloan telescope prevent two fibres being placed closer than 62 arcsec in a single pass of the instrument. These ‘fibre collisions’ strongly correlate with the intrinsic clustering of targets and can bias measurements of the two-point correlation function resulting in a systematic error on the inferred values of the cosmological parameters. We combine the new techniques of pairwise-inverse probability and the angular upweighting (PIP+ANG) to correct the clustering measurements for the effect of fibre collisions. Using mock catalogues, we show that our corrections provide unbiased measurements, within data precision, of both the projected $\rm {\mathit{ w}_p}\left(\mathit{ r}_p\right)$ and the redshift-space multipole ξ(ℓ = 0, 2, 4)(s) correlation functions down to $0.1\, h^{-1}{\rm Mpc}$, regardless of the tracer type. We apply the corrections to the eBOSS DR16 catalogues. We find that, on scales $s\gtrsim 20\, h^{-1}{\rm Mpc}$ for ξℓ, as used to make baryon acoustic oscillation and large-scale redshift-space distortion measurements, approximate methods such as nearest-neighbour upweighting are sufficiently accurate given the statistical errors of the data. Using the PIP method, for the first time for a spectroscopic program of the Sloan Digital Sky Survey, we are able to successfully access the one-halo term in the clustering measurements down to $\sim 0.1\, h^{-1}{\rm Mpc}$ scales. Our results will therefore allow studies that use the small-scale clustering to strengthen the constraints on both cosmological parameters and the halo occupation distribution models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Glauber-theory analysis of nuclear reactions on a 12 C target with variational Monte Carlo wave functions

The application of Glauber theory has been playing an increasingly important role with the study of unstable or exotic nuclei. Its adaptation to medium and high-energy nucleus-nucleus collisions is severely limited because one has to evaluate the matrix elements of multiple-scattering operators. The extraction of physical observables has been done using ‘approximate’ Glauber theory whose validity is hard to evaluate. Here, we perform a full calculation of the matrix elements using Monte Carlo integration and analyze the elastic differential cross sections and the total reaction cross sections for p+¹²C, ⁴,⁶He+¹²C, and ¹²C+¹²C collisions. We use the variational Monte Carlo wave functions for ⁴,⁶He and ¹²C obtained by using realistic two- and three-nucleon potentials. We demonstrate the performance of the Glauber-theory calculations by comparing with available experimental data. We further discuss the accuracy of the conventional approximate methods in the light of the cumulant expansion for Glauber’s phase-shift function.

Horiuchi, W. [Osaka Metropolitan University (Japan↗
DOE OSTI2025

Bias-hardened estimators of patchy screening profiles

Detecting anisotropic screening of the cosmic microwave background (CMB) holds the promise of revealing the distribution of gas in the Universe, characterizing the complex processes of galaxy formation and feedback, and studying the epoch of reionization. Estimators for inhomogeneous screening, including some recently proposed small-scale (stacked) estimators, are quadratic or higher order in the CMB temperature or polarization fields and are therefore subject to contamination from CMB lensing. We review the origin of this lensing bias and show that, when stacking on unWISE galaxies, the expected lensing bias dominates the signal if left unmitigated. Hardening techniques that null the lensing bias have been proposed for standard quadratic estimators, whereas only approximate methods have been proposed for stacked estimators. In conclusion, we review these techniques and apply the former to stacked estimators, presenting several strategies (including the optimal strategy) to null lensing contamination when stacking on any large-scale structure tracer.

Cosmic microwave background↗
DOE OSTI2020

Capturing multireference excited states by constrained-density-functional theory

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

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Cumulant methods for electron-phonon problems. I. Perturbative expansions

Here in this work, we investigate the ability of the cumulant expansion (CE) to capture one-particle spectral information in electron-phonon coupled systems at both zero and finite temperatures. In particular, we present a comprehensive study of the second- and fourth-order CEs for the one-dimensional Holstein model as compared with numerically exact methods. We investigate both finite sized systems as well as the approach to the thermodynamic limit, drawing distinctions, and connections between the behavior of systems in and away from the thermodynamic limit that enable a greater understanding of the ability of the CE to capture real-frequency information across the full range of wave vectors. We find that for zero electronic momentum, the spectral function is well described by the second-order CE at low and high temperatures. However, for nonzero electronic momenta, the CE is only accurate at high temperature. We analyze the fourth-order cumulant and find that while it improves the description of the short-time dynamics encoded in the one-particle Green's function, it can introduce divergences in the time domain as well as unphysical negative spectral weight in the spectral function. When well-behaved, the fourth-order CE does provide notable accurate corrections to the second-order CE. Finally, we use our results to comment on the use of the CE as a tool for calculating transport behavior in the realistic ab initio modeling of materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Cumulant methods for electron-phonon problems. II. The self-consistent cumulant expansion

Here in this paper we present a self-consistent cumulant expansion (SC-CE) and investigate its accuracy for the one-dimensional Holstein model with and without phonon dispersion. We show that for finite lattice sizes, the numerical integration of the SC-CE equations becomes unstable at long times. This defect is partially ameliorated when studying systems in the thermodynamic limit, enabling the demonstration that the SC-CE corrects many deficits of the standard perturbative CE in the (nondispersive) Holstein model. The natural phonon damping that arises in the more realistic dispersed Holstein model renders the SC-CE stable, allowing for a complete assessment of the method. Here, we find that self-consistency dramatically corrects many of the failures found in the perturbative CE, but also introduces some unphysical features. Finally, we comment on the potential use of SC-CE as a tool for calculating Green's functions in generic many-body problems.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Nonequilibrium DMFT + CPA for correlated disordered systems

We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean-field theory and the equilibrium coherent potential approximation methods to the nonequilibrium many-body formalism, using the Kadanoff-Baym-Keldysh complex time contour, for the dynamics of interacting disordered systems away from equilibrium. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We further apply the nonequilibrium solution to the interaction quench problem for an isolated disordered system. Here, the interaction is abruptly changed from zero (noninteracting system) to another constant (finite) value at which it is subsequently kept. We observe via the time dependence of the potential, kinetic, and total energies the effect of disorder on the relaxation of the system as a function of final interaction strength. Finally, the real-time approach has the potential to shed light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Experimental study of the low-lying negative-parity states in 11 Be using the 12 B( d , 3 He) 11 Be reaction

In this work, low-lying negative-parity states in 11 Be having dominant p-wave neutron configurations were studied using the 12 B(d, 3 He) 11 Be proton-removal reaction in inverse kinematics. The 1/2 $\overset{-}{1}$ state at 0.32 MeV, the 3/2 $\overset{-}{1}$ state at 2.56 MeV and one or both of the states including the 5/2 $\overset{-}{1}$ level at 3.89 MeV and the 3/2 $\overset{-}{2}$ level at 3.96 MeV were populated in the present reaction. Spectroscopic factors were determined from the differential cross sections using a distorted wave Born approximation method. The p-wave proton removal strengths were well described by the shell model calculations while the Nilsson model calculation underestimates the spectroscopic factors for the higher excited states. Results from both variational Monte Carlo and no-core shell model calculations were also compared with the experimental observations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗