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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.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Exact sum rules with approximate ground states

Electromagnetic and weak transitions tell us a great deal about the structure of atomic nuclei. Yet modeling transitions can be difficult: it is often easier to compute the ground state, if only as an approximation, than excited states. One alternative is through transition sum rules, in particular the non-energy-weighted and energy-weighted sum rules, which can be computed as expectation values of operators. We investigate by computing sum rules for a variety of nuclei, comparing the numerically exact full configuration-interaction shell model, as a reference, to Hartree-Fock, projected Hartree-Fock, and the nucleon pair approximation. Furthermore, these approximations yield reasonable agreement, which we explain by prior work on the systematics of transition moments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics

We present a simple analytic approximation for the covariance between pre-reconstruction galaxy power spectrum measurements and post-reconstruction two-point correlation functions. This cross-covariance is essential for joint analyses that combine full-shape clustering information with baryon acoustic oscillation (BAO) measurements, as commonly performed in modern spectroscopic surveys. Our model builds on the disconnected contribution to the covariance and accounts for the damping of correlations due to the BAO reconstruction process. We validate our analytic prescription against numerical simulations from the Dark Energy Spectroscopic Instrument (DESI), testing both idealized cubic geometries and realistic survey configurations including complex footprints and fiber assignment effects. Despite neglecting survey window functions in the analytic calculation, we find excellent agreement with simulation-based covariances and demonstrate that cosmological parameter constraints are virtually unchanged when using our approximation. Our results show that the pre-post cross-covariance is sufficiently small that even approximate treatments are adequate for cosmological inference, opening a pathway toward fully analytic covariance matrices for next-generation galaxy surveys.

baryon acoustic oscillations↗
DOE OSTI2020

Validity of the static-exchange approximation for inner-shell photoionization of polyatomic molecules

The simple single-channel static-exchange approximation completely ignores correlation between the continuum and molecular ion electrons. In molecular systems with symmetry equivalent atoms, the single-channel approximation can seriously fail in core ionization when using delocalized orbitals to represent the core hole states. We present cross sections and molecular frame photoelectron angular distributions with both localized and delocalized core orbitals in CF 4 F (1 s ) ionization. We show that only a full coupled-channel calculation can recover an accurate description of the physics of inner-shell photoionization when using delocalized orbitals, whereas nearly the same result can be obtained from independent single-channel static-exchange calculations when localized core orbitals are used. A grid-based variational method described here makes such single-channel calculations possible on larger systems without local-exchange approximations. Illustrative calculations on the core ionization of SF 6 are presented to illustrate the power of the grid-based method.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Loschmidt-echo approach to error estimation in Krylov-subspace approximation

The Krylov subspace method is a traditional approach to approximate quantum evolution, allowing us to treat systems with large Hilbert spaces. Despite its popularity, current bounds typically overestimate the error, which translates into more expensive simulation routines. Here, in this paper, we tackle this problem by realizing that the error can be understood as a Loschmidt echo in a one-dimensional (1D) noninteracting tight-binding Hamiltonian. We show that the different time regimes of the approximation can be understood using simple physical ideas. More importantly, we obtain computationally cheap error bounds that describe with high precision the actual error in the approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Modeling noise in global Mølmer-Sørensen interactions applied to quantum approximate optimization

Many-qubit Mølmer-Sørensen (MS) interactions applied to trapped ions offer unique capabilities for quantum information processing, with applications including quantum simulation and the quantum approximate optimization algorithm (QAOA). Here, we develop a physical model to describe many-qubit MS interactions under four sources of experimental noise: vibrational mode frequency fluctuations, laser power fluctuations, thermal initial vibrational states, and state preparation and measurement errors. The model parametrizes these errors from simple experimental measurements, without free parameters. Herein, we validate the model in comparison with experiments that implement sequences of MS interactions on two 171 Yb + ions. The model shows reasonable agreement after several MS interactions as quantified by the reduced chi-squared statistic $χ^{2}_{red}$≈2. As an application we examine MaxCut QAOA experiments on three and six ions. The experimental performance is quantified by approximation ratios that are 91% and 83% of the optimal theoretical values. Our model predicts $0.93^{+0.03}_{-0.02}$ and $0.95^{+0.04}_{-0.03}$, respectively, with disagreement in the latter value attributable to secondary noise sources beyond those considered in our analysis. With realistic experimental improvements to reduce measurement error and radial trap frequency variations, the model achieves approximation ratios that are 99% of the optimal. Incorporating these improvements into future experiments is expected to reveal new aspects of noise for future modeling and experimental improvements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Success and breakdown of the T-matrix approximation for phonon-disorder scattering

Here, we examine the validity of the widely used T-matrix approximation for treating phonon-disorder scattering by implementing an unfolding algorithm that allows simulation of disorder up to tens of millions of atoms. The T-matrix approximation breaks down for low-energy flexure phonons that play an important role in thermal transport in two-dimensional materials. Furthermore, insights are developed into the success of the T-matrix approximation in describing maximally mass disordered systems. To achieve this, the phonon unfolding formalism is generalized to describe mass disorder and strongly nonperturbative features of the spectrum are connected to the Boltzmann quasiparticle picture.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Formation energy puzzle in intermetallic alloys: Random phase approximation fails to predict accurate formation energies

We performed density functional calculations to estimate the formation energies of intermetallic alloys. We used two semilocal approximations, the generalized gradient approximation (GGA) by Perdew-Burke- Ernzerhof (PBE) and the strongly constrained and appropriately normed (SCAN) meta-GGA. In addition, we utilized two nonlocal DFT functionals, the hybrid HSE06, and the state-of-the-art random phase approximation (RPA). The nonlocal functionals such as HSE06 and RPA yield accurate formation energies of binary alloys with completely-filled d-band metals, where semilocal functionals underperform. The accuracy at the nonlocal functionals is greatly reduced when a partially-filled d-band metal is present in an alloy, while PBE-GGA outperforms in these cases. We show that the accurate prediction of formation energies by any DFT method depends on its ability to predict the accurate electronic properties, e.g., valence d-band contribution to the density of states (DOS). The SCAN meta-GGA often corrects the PBE-DOS, however, it does not provide accurate formation energies compared to PBE. This is assumed to be due to the lack of proper error cancellation that should be expected due to the similar bulk nature of both alloys and their constituents, which may improve with the modification of meta-GGA ingredients. RPA yields too negative formation energies of alloys with partially-filled d-band metals. RPA results can be corrected by restoring the exchange-correlation kernel, thereby improving the short-range electron-electron correlation in metallic densities.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Twisted bilayer graphene. I. Matrix elements, approximations, perturbation theory, and a k · p two-band model

We investigate the twisted bilayer graphene (TBG) model of Bistritzer and MacDonald (BM) [Bistritzer and MacDonald, Proc. Natl. Acad. Sci. 108, 12233 (2011)] to obtain an analytic understanding of its energetics and wave functions needed for many-body calculations. We provide an approximation scheme for the wave functions of the BM model, which first elucidates why the BM K M -point centered original calculation containing only four plane waves provides a good analytical value for the first magic angle (θ M ≈ 1°). The approximation scheme also elucidates why most of the many-body matrix elements in the Coulomb Hamiltonian projected to the active bands can be neglected. By applying our approximation scheme at the first magic angle to a Γ M -point centered model of six plane waves, we analytically understand the reason for the small Γ M -point gap between the active and passive bands in the isotropic limit w 0 = w 1 . Furthermore, we analytically calculate the group velocities of the passive bands in the isotropic limit, and show that they are almost doubly degenerate, even away from the Γ M point, where no symmetry forces them to be. Furthermore, moving away from the Γ M and K M points, we provide an explicit analytical perturbative understanding as to why the TBG bands are flat at the first magic angle, despite the first magic angle is defined by only requiring a vanishing K M -point Dirac velocity. We derive analytically a connected “magic manifold” w 1 = $2\sqrt{1 + w^{2}_{0}}$ $-\sqrt{2 + 3w^2_0}$, on which the bands remain extremely flat as w 0 is tuned between the isotropic (w 0 = w 1 ) and chiral (w 0 = 0) limits. We analytically show why going away from the isotropic limit by making w 0 less (but not larger) than w 1 increases the Γ M -point gap between the active and the passive bands. Finally, by perturbation theory, we provide an analytic Γ M point k ∙ p two-band model that reproduces the TBG band structure and eigenstates within a certain w 0 , w 1 parameter range. Further refinement of this model are discussed, which suggest a possible faithful representation of the TBG bands by a two-band Γ M point k ∙ p model in the full w 0 , w 1 parameter range.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Dynamical vertex approximation for many-electron systems with spontaneously broken SU(2) symmetry

We generalize the formalism of the dynamical vertex approximation (DΓA)—a diagrammatic extension of the dynamical mean-field theory (DMFT)—to treat magnetically ordered phases. To this aim, we start by concisely illustrating the many-electron formalism for performing ladder resummations of Feynman diagrams in systems with broken SU(2) symmetry associated to ferromagnetic (FM) or antiferromagnetic (AF) order. We then analyze the algorithmic simplifications introduced by taking the local approximation of the two-particle irreducible vertex functions in the Bethe-Salpeter equations, which defines the ladder implementation of DΓA for magnetic systems. The relation of this assumption with the DMFT limit of large coordination-number/high dimensions is explicitly discussed. As a last step, we derive the expression for the ladder DΓA self-energy in the FM- and AF-ordered phases of the Hubbard model. The physics emerging in the AF-ordered case is explicitly illustrated by means of approximated calculations based on a static mean-field input for DΓA equations. The results obtained capture fundamental aspects of both metallic and insulating ground states of two-dimensional antiferromagnets, providing a reliable compass for future, more extensive applications of our approach. Furthermore, possible routes to further develop diagrammatic-based treatments of magnetic phases in correlated electron systems are briefly outlined in the Conclusions.

2-dimensional systems↗
DOE OSTI2022

Generalized quasiharmonic approximation via space group irreducible derivatives

The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature-dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. In this work we formulate the generalized QHA, providing a practical algorithm for computing the strain state and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second-order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate our approach by evaluating the temperature and pressure dependence of select elastic constants and the thermal expansion in thoria (ThO 2 ) using density functional theory with three exchange-correlation functionals. The QHA results are compared to our measurements of the elastic constant tensor using time-domain Brillouin scattering and inelastic neutron scattering. Our irreducible derivative approach simplifies the implementation of the generalized QHA, which will facilitate reproducible, data-driven applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Power Flow Geometry and Approximation

Here, the power flow equations are important in numerous power systems problems of practical interest which consider alternating current power flow (ACPF) physics. Perhaps the most well studied being the alternating current optimal power flow problem (ACOPF), seeking to optimize the operation of an electric power system. Due to their non-linearity, problems which include the power flow equations are typically challenging, particularly in optimization. Interestingly, the set of solutions to the power flow equations forms a smooth manifold. As a result, differential geometry can be used to describe and analyze this set of equations. This approach has proven effective in several engineering applications (e.g., solving ACOPF and analyzing the solution space boundary). Central to the success of this approach is an understanding of the power flow manifold's geometry. In this work, we develop the geometric and topological properties of this manifold using concepts from differential geometry. After demonstrating the convenience of this manifold's representation as a function's graph, computational methods are emphasized: we develop retractions, error bounds for linear approximation, and formulas for evaluating the Riemannian metric (including associated objects such as geodesics and the curvature tensor). Scalar curvature and the second fundamental form play a new role in quantifying the quality of linear approximations, like the popular direct current approximation. All functions are implemented in Julia and available in an online repository. Proofs are included for completeness.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Fast increased fidelity samplers for approximate Bayesian Gaussian process regression

Gaussian processes (GPs) are common components in Bayesian non-parametric models having a rich methodological literature and strong theoretical grounding. The use of exact GPs in Bayesian models is limited to problems containing several thousand observations due to their prohibitive computational demands. We develop a posterior sampling algorithm using H-matrix approximations that scales at O(n log 2 n). We show that this approximation’s Kullback-Leibler divergence to the true posterior can be made arbitrarily small. Though multidimensional GPs could be used with our algorithm, d-dimensional surfaces are modeled as tensor products of univariate GPs to minimize the cost of matrix construction and maximize computational efficiency. We illustrate the performance of this fast increased fidelity approximate GP, FIFA-GP, using both simulated and non-synthetic data sets

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The use of subchondral bone topography to approximate the center of rotation of the elbow joint in dogs

Abstract Objectives The aim of this study was to compare the approximate center of rotation in normal and diseased elbows in dogs. Study design Cross‐sectional study Sample population Computer tomography scans of nine dogs with unilateral fragmented medial coronoid process (FMCP). Methods A board certified radiologist confirmed that each dog had unilateral FMCP, and a normal contralateral elbow. Digital 3D models of all elbow joints were uploaded into a surgical planning software package. Four axes approximating the center of rotation (COR) of elbow joints were generated using five geometric shapes based on subchondral topography of the humeral condyle radius and ulna. Images showing the locations where axes exited the medial and lateral cortex of the humeral condyle were captured and imported into a second software package, for measurement of distances between exit points and the origin of a system of axes. Results In normal joints 20/27 (74%) axes exited the medial cortex, and 25/27 (93%) axes exited the lateral cortex cranial and distal to the medial and lateral epicondyles, respectively. In diseased joints 22/27 (81%) axes exited medial cortex and 19/27 (70%) axes exited the lateral cortex, caudal and distal to the medial and lateral epicondyles, respectively. Conclusion Based on CT‐ derived geometry, the COR of elbow affected with FMCP was generally more caudal than normal. Clinical significance External landmarks approximating the location of the elbow COR are provided, and while not validated, may assist in planning, creation, and assessment of procedures for FMCP.

Berger, Chen↗
DOE OSTI2021

Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control

Herein, we present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional sub-spaces whose basis functions are realizations of a sequence of neural networks. Here, the finite-dimensional subspaces are then used to define a standard Galerkin approximation of the variational equation. This approach enjoys a number of advantages, including: the sequential nature of the algorithm offers a systematic approach to enhancing the accuracy of a given approximation; the sequential enhancements provide a useful indicator for the error that can be used as a criterion for terminating the sequential updates; the basic approach is largely oblivious to the nature of the partial differential equation under consideration; and, some basic theoretical results are presented regarding the convergence (or otherwise) of the method which are used to formulate basic guidelines for applying the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Extended Galerkin Neural Network Approximation of Singular Variational Problems with Error Control

We present extended Galerkin neural networks, a variational framework for approximating general boundary value problems (BVPs) with error control. The main contributions of this work are (1) a rigorous theory guiding the construction of new weighted least squares variational formulations suitable for use in neural network approximation of general BVPs, and (2) an “extended” feedforward network architecture which incorporates and is even capable of learning singular solution structures, thus greatly improving approximability of singular solutions. Furthermore, numerical results are presented for several problems, including steady Stokes flow around reentrant corners and in convex corners with Moffatt eddies in order to demonstrate efficacy of the method.

a posteriori error estimate↗
DOE OSTI2021

PLANC: Parallel Low-rank Approximation with Nonnegativity Constraints

In this work, we consider the problem of low-rank approximation of massive dense nonnegative tensor data, for example, to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting bottlenecks in both computation time and available memory. We propose a distributed-memory parallel computing solution to handle massive data sets, loading the input data across the memories of multiple nodes, and performing efficient and scalable parallel algorithms to compute the low-rank approximation. We present a software package called Parallel Low-rank Approximation with Nonnegativity Constraints, which implements our solution and allows for extension in terms of data (dense or sparse, matrices or tensors of any order), algorithm (e.g., from multiplicative updating techniques to alternating direction method of multipliers), and architecture (we exploit GPUs to accelerate the computation in this work). We describe our parallel distributions and algorithms, which are careful to avoid unnecessary communication and computation, show how to extend the software to include new algorithms and/or constraints, and report efficiency and scalability results for both synthetic and real-world data sets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Visualization of Multi-Fidelity Approximations of Stochastic Economic Dispatch

As renewable energy generation deployment increases, the operation of electrical grids becomes more complex. Economic dispatch is part of a grid operator's regular decision process where the amount of energy to generate is determined based on the number of available generators and the actual level of energy demand. Renewable generators are inherently stochastic due to the chaotic nature of weather patterns, and thus, real-time decisions of economic dispatch become increasingly complex. Modeling efforts to assist in these decisions in the highest fidelity typically take hours to days to solve on leadership-class computers; too long for the 5-minute operational time-frame demanded of operators. Alternatively, multi-fidelity approximations can be used to predict generation levels quickly and with sufficient accuracy to be used for real-time operations. We have developed a visualization tool to demonstrate the utility of multi-fidelity approximations by displaying contextual results of economic dispatch approximations, comparisons across fidelity levels of generation levels and possible failures to meet demand, and meta-data on the modeling setup.

interactive visualization↗
DOE OSTI2023

Parameter Transfer for Quantum Approximate Optimization of Weighted MaxCut

Finding high-quality parameters is a central obstacle to using the quantum approximate optimization algorithm (QAOA). Previous work partially addresses this issue for QAOA on unweighted MaxCut problems by leveraging similarities in the objective landscape among different problem instances. However, we show that the more general weighted MaxCut problem has significantly modified objective landscapes, with a proliferation of poor local optima. Our main contribution is a simple rescaling scheme that overcomes these deleterious effects of weights. Here we show that for a given QAOA depth, a single “typical” vector of QAOA parameters can be successfully transferred to weighted MaxCut instances. This transfer leads to a median decrease in the approximation ratio of only 2.0 percentage points relative to a considerably more expensive direct optimization on a dataset of 34,701 instances with up to 20 nodes and multiple weight distributions. This decrease can be reduced to 1.2 percentage points at the cost of only 10 additional QAOA circuit evaluations with parameters sampled from a pretrained metadistribution, or the transferred parameters can be used as a starting point for a single local optimization run to obtain approximation ratios equivalent to those achieved by exhaustive optimization in 96.35% of our cases.

97 MATHEMATICS AND COMPUTING↗