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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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DOE OSTI2011

Local and Nonlocal Parallel Heat Transport in General Magnetic Fields

A novel approach for the study of parallel transport in magnetized plasmas is presented. The method avoids numerical pollution issues of grid-based formulations and applies to integrable and chaotic magnetic fields with local or nonlocal parallel closures. In weakly chaotic fields, the method gives the fractal structure of the devil's staircase radial temperature profile. In fully chaotic fields, the temperature exhibits self-similar spatiotemporal evolution with a stretched-exponential scaling function for local closures and an algebraically decaying one for nonlocal closures. It is shown that, for both closures, the effective radial heat transport is incompatible with the quasilinear diffusion model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

A Review of Local-to-Nonlocal Coupling Methods in Nonlocal Diffusion and Nonlocal Mechanics

Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. This allows to consolidate the accuracy of nonlocal models with the computational expediency of their local counterparts, while often simultaneously removing nonlocal modeling issues such as surface effects. The number and variety of proposed LtN coupling approaches have significantly grown in recent years, yet the field of LtN coupling continues to grow and still has open challenges. This review provides an overview of the state of the art of LtN coupling in the context of nonlocal diffusion and nonlocal mechanics, specifically peridynamics. Furthermore, we present a classification of LtN coupling methods and discuss common features and challenges. The goal of this review is not to provide a preferred way to address LtN coupling but to present a broad perspective of the field, which would serve as guidance for practitioners in the selection of appropriate LtN coupling methods based on the characteristics and needs of the problem under consideration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Nonlocal elastic metasurfaces: Enabling broadband wave control via intentional nonlocality

While elastic metasurfaces offer a remarkable and very effective approach to the subwavelength control of stress waves, their use in practical applications is severely hindered by intrinsically narrow band performance. In applications to electromagnetic and photonic metamaterials, some success in extending the operating dynamic range was obtained by using nonlocality. However, while electronic properties in natural materials can show significant nonlocal effects, even at the macroscales, in mechanics, nonlocality is a higher-order effect that becomes appreciable only at the microscales. This study introduces the concept of intentional nonlocality as a fundamental mechanism to design passive elastic metasurfaces capable of an exceptionally broadband operating range. The nonlocal behavior is achieved by exploiting nonlocal forces, conceptually akin to long-range interactions in nonlocal material microstructures, between subsets of resonant unit cells forming the metasurface. These long-range forces are obtained via carefully crafted flexible elements, whose specific geometry and local dynamics are designed to create remarkably complex transfer functions between multiple units. The resulting nonlocal coupling forces enable achieving phase-gradient profiles that are functions of the wavenumber of the incident wave. The identification of relevant design parameters and the assessment of their impact on performance are explored via a combination of semianalytical and numerical models. The nonlocal metasurface concept is tested, both numerically and experimentally, by embedding a total-internal-reflection design in a thin-plate waveguide. Results confirm the feasibility of the intentionally nonlocal design concept and its ability to achieve a fully passive and broadband wave control.

36 MATERIALS SCIENCE↗
DOE OSTI2020

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius $\delta$ goes to zero, and to the fractional Laplacian as $\delta$ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We also provide theoretical convergence rates with respect to $\delta$ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, $\delta$ and $\alpha$, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order $\alpha(y)$, which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as $\delta$. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(γ), which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Application-level benchmarking of quantum computers using nonlocal game strategies

In a nonlocal game, two noncommunicating players cooperate to convince a referee that they possess a strategy that does not violate the rules of the game. Quantum strategies allow players to optimally win some games by performing joint measurements on a shared entangled state, but computing these strategies can be challenging. We present a variational quantum algorithm to compute quantum strategies for nonlocal games by encoding the rules of a nonlocal game into a Hamiltonian. We show how this algorithm can generate a short-depth optimal quantum strategy for a graph coloring game with a quantum advantage. This quantum strategy is then evaluated on fourteen different quantum hardware platforms to demonstrate its utility as a benchmark. Finally, we discuss potential sources of errors that can explain the observed decreased performance of the executed task and derive an expression for the number of samples required to accurately estimate the win rate in the presence of noise.

nonlocal games↗
DOE OSTI2020

A Unified Theory of Fractional Nonlocal and Weighted Nonlocal Vector Calculus

Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green's identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fractional vector calculus have been put forward. Some have been studied rigorously and in depth, while others have been introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green's identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. The proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

New solutions of coupled nonlocal NLS and coupled nonlocal mKdV equations

In this study, we provide several novel solutions of the coupled Ablowitz–Musslimani (AM) version of the nonlocal nonlinear Schrödinger (NLS) equation and the coupled nonlocal modified Korteweg–de Vries (mKdV) equation. In each case we compare and contrast the corresponding solutions of the relevant coupled local equations. Further, we provide new solutions of the coupled local NLS and coupled local mKdV equations which are not the solutions of the corresponding nonlocal equations. We also show that the nonlocal coupled (as well as uncoupled) mKdV equations have hidden Galilean invariance and admit novel solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

On nonlocal problems with Neumann boundary conditions: scaling and convergence for nonlocal operators and solutions

Formulations of Neumann-type boundary conditions for boundary value problems in the nonlocal framework are beset with difficulties, some related to the choice of a proper scaling. Here we identify a space-dependent scaling for a nonlocal Neumann operator, for which we prove linear in δ (δ being the radius for the support for the kernel) convergence of the Neumann operator and $\mathcal{O}$(δ 2 ) convergence of solutions to their classical counterparts. The pointwise-like convergence of the nonlocal normal operator is cast as a new type of two-scale operator-point convergence, which we call condensated convergence . The results hold for general integrable kernels, a setting which is favored in numerical simulations. We support this analysis with numerical convergence studies using a piecewise linear discontinuous Galerkin discretization and show an $\mathcal{O}$(δ 2 ) rate of convergence of solutions, also exhibiting an $\mathcal{O}$(h 2 ) convergence, where h is the mesh size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Use of the rVV10 Nonlocal Correlation Functional in the B97M-V Density Functional: Defining B97M-rV and Related Functionals [On the Use of the rVV10 Nonlocal Correlation Functional in the B97M-V Density Functional: Defining B97M-rV and Related Functionals]

The VV10 and rVV10 nonlocal correlation functionals are consistently implemented and assessed, with the goal of determining if the rVV10 nonlocal correlation functional can replace the VV10 nonlocal correlation functional in the recently developed B97M-V density functional, to give the B97M-rV density functional. Along the way, four density functionals are simultaneously tested: VV10, rVV10, B97M-V, and B97M-rV. An initial assessment is carried out across the S22 data set, and the short-range damping variable, b, is varied for all four density functionals in order to determine the sensitivity of the functionals to the empirical parameter. The results of this test indicate that a value of b = 6 (fortuitously the same as that in B97M-V) is suitable for B97M-rV. The functionals are then compared across an extensive database of interaction energies, and it is demonstrated that B97M-rV either matches or outperforms B97M-V for all of the tests considered. Finally, the optimization of b across the S22 data set is extended to two range-separated hybrid density functionals, ωB97X-V and ωB97M-V, and a value of b = 6.2 is recommended for both ωB97X-rV and ωB97M-rV.

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

The charge-asymmetric nonlocally determined local-electric (CANDLE) solvation model

Many important applications of electronic structure methods involve molecules or solid surfaces in a solvent medium. Since explicit treatment of the solvent in such methods is usually not practical, calculations often employ continuum solvation models to approximate the effect of the solvent. Previous solvation models either involve a parametrization based on atomic radii, which limits the class of applicable solutes, or based on solute electron density, which is more general but less accurate, especially for charged systems. We develop an accurate and general solvation model that includes a cavity that is a nonlocal functional of both solute electron density and potential, local dielectric response on this nonlocally determined cavity, and nonlocal approximations to the cavity-formation and dispersion energies. The dependence of the cavity on the solute potential enables an explicit treatment of the solvent charge asymmetry. With four parameters per solvent, this “CANDLE” model simultaneously reproduces solvation energies of large datasets of neutral molecules, cations, and anions with a mean absolute error of 1.8 kcal/mol in water and 3.0 kcal/mol in acetonitrile.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Nonlocal Gravity and Structure in the Universe

The observed acceleration of the Universe can be explained by modifying general relativity. One such attempt is the nonlocal model of Deser and Woodard. Here we fix the background cosmology using results from the Planck satellite and examine the predictions of nonlocal gravity for the evolution of structure in the universe, confronting the model with three tests: gravitational lensing, redshift space distortions, and the estimator of gravity $E_G$. Current data favor general relativity (GR) over nonlocal gravity: fixing primordial cosmology with the best fit parameters from Planck leads to weak lensing results favoring GR by 5.9 sigma; redshift space distortions measurements of the growth rate preferring GR by 7.8 sigma; and the single measurement of $E_G$ favoring GR, but by less than 1-sigma. The significance holds up even after the parameters are allowed to vary within Planck limits. The larger lesson is that a successful modified gravity model will likely have to suppress the growth of structure compared to general relativity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Adaptive nonlocal means filtering based on local noise level for CT denoising

Purpose: To develop and evaluate an image-domain noise reduction method based on a modified nonlocal means (NLM) algorithm that is adaptive to local noise level of CT images and to implement this method in a time frame consistent with clinical workflow. Methods: A computationally efficient technique for local noise estimation directly from CT images was developed. A forward projection, based on a 2D fan-beam approximation, was used to generate the projection data, with a noise model incorporating the effects of the bowtie filter and automatic exposure control. The noise propagation from projection data to images was analytically derived. The analytical noise map was validated using repeated scans of a phantom. A 3D NLM denoising algorithm was modified to adapt its denoising strength locally based on this noise map. The performance of this adaptive NLM filter was evaluated in phantom studies in terms of in-plane and cross-plane high-contrast spatial resolution, noise power spectrum (NPS), subjective low-contrast spatial resolution using the American College of Radiology (ACR) accreditation phantom, and objective low-contrast spatial resolution using a channelized Hotelling model observer (CHO). Graphical processing units (GPU) implementation of this noise map calculation and the adaptive NLM filtering were developed to meet demands of clinical workflow. Adaptive NLM was piloted on lower dose scans in clinical practice. Results: The local noise level estimation matches the noise distribution determined from multiple repetitive scans of a phantom, demonstrated by small variations in the ratio map between the analytical noise map and the one calculated from repeated scans. The phantom studies demonstrated that the adaptive NLM filter can reduce noise substantially without degrading the high-contrast spatial resolution, as illustrated by modulation transfer function and slice sensitivity profile results. The NPS results show that adaptive NLM denoising preserves the shape and peak frequency of the noise power spectrum better than commercial smoothing kernels, and indicate that the spatial resolution at low contrast levels is not significantly degraded. Both the subjective evaluation using the ACR phantom and the objective evaluation on a low-contrast detection task using a CHO model observer demonstrate an improvement on low-contrast performance. The GPU implementation can process and transfer 300 slice images within 5 min. On patient data, the adaptive NLM algorithm provides more effective denoising of CT data throughout a volume than standard NLM, and may allow significant lowering of radiation dose. After a two week pilot study of lower dose CT urography and CT enterography exams, both GI and GU radiology groups elected to proceed with permanent implementation of adaptive NLM in their GI and GU CT practices. Conclusions: This work describes and validates a computationally efficient technique for noise map estimation directly from CT images, and an adaptive NLM filtering based on this noise map, on phantom and patient data. Both the noise map calculation and the adaptive NLM filtering can be performed in times that allow integration with clinical workflow. The adaptive NLM algorithm provides effective denoising of CT data throughout a volume, and may allow significant lowering of radiation dose.

62 RADIOLOGY AND NUCLEAR MEDICINE↗