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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Initial value problem in string-inspired nonlocal field theory

We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory. The Lorentz-covariant action is characterized by a parameter ξ 2 that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in ξ 2 reduces the action to a local two-derivative theory with a ξ 2 -dependent potential. This picture is supported by evidence that the redefinition maps the wildly oscillating rolling tachyon solutions of the nonlocal theory to conventional rolling in the new scalar potential. For general field configurations we exhibit an obstruction to a local Lorentz-covariant formulation, but we can still achieve a formulation local in time, as well as a light-cone formulation. These constructions provide an initial value formulation and a Hamiltonian. Their causality is consistent with a lack of superluminal behavior in the nonlocal theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Time-dependent density-functional-theory calculations of the nonlocal electron stopping range for inertial confinement fusion applications

Nonlocal electron transport is important for understanding laser-target coupling for laser-direct-drive (LDD) inertial confinement fusion (ICF) simulations. Current models for the nonlocal electron mean free path in radiation-hydrodynamic codes are based on plasma-physics models developed decades ago; improvements are needed to accurately predict the electron conduction in LDD simulations of ICF target implosions. Here we utilized time-dependent density functional theory (TD-DFT) to calculate the electron stopping power (SP) in the so-called conduction-zone plasmas of polystyrene in a wide range of densities and temperatures relevant to LDD. Compared with the modified Lee-More model, the TD-DFT calculations indicated a lower SP and a higher stopping range for nonlocal electrons. We fit these electron SP calculations to obtain a global analytical model for the electron stopping range as a function of plasma conditions and the nonlocal electron kinetic energy. This model was implemented in the one-dimensional radiation-hydrodynamic code LILAC to perform simulations of LDD ICF implosions, which are further compared with simulations by the standard modified Lee-More model. In conclusion, results from these integrated simulations are discussed in terms of the implications of this TD-DFT-based mean-free-path model to ICF simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions [minus appendix B]

A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a traditional geometric configuration for local partial differential equation problems is used in which a computational domain is subdivided into non-overlapping subdomains. In the nonlocal setting, this approach is substructuring-based in the sense that those subdomains interact with neighboring domains over interface regions having finite volume, in contrast to the local PDE setting in which interfaces are lower dimensional manifolds separating abutting subdomains Key results include the equivalence between the global, single-domain nonlocal problem and its multi-domain reformulation, both at the continuous and discrete levels. These results provide the rigorous foundation necessary for the development of efficient solution strategies for nonlocal domain-decomposition methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws

We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Machine-Learning of Nonlocal Kernels for Anomalous Subsurface Transport from Breakthrough Curves

Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport in various subsurface applications, their application is hindered by computational challenges. Simpler nonlocal models characterized by integrable kernels and finite interaction length represent a computationally feasible alternative to fractional models; yet, the informed choice of their kernel functions still remains an open problem. We propose a general data-driven framework for the discovery of optimal kernels on the basis of very small and sparse data sets in the context of anomalous subsurface transport. Using spatially sparse breakthrough curves recovered from fine-scale particle-density simulations, we learn the best coarse-scale nonlocal model using a nonlocal operator regression technique. Predictions of the breakthrough curves obtained using the optimal nonlocal model show good agreement with fine-scale simulation results even at locations and time intervals different from the ones used to train the kernel, confirming the excellent generalization properties of the proposed algorithm. A comparison with trained classical models and with black-box deep neural networks confirms the superiority of the predictive capability of the proposed model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Mathematical Foundations for Nonlocal Interface Problems: Multiscale Simulations of Heterogeneous Materials (Final LDRD Report)

Nonlocal models provide a much-needed predictive capability for important Sandia mission applications, ranging from fracture mechanics for nuclear components to subsurface flow for nuclear waste disposal, where traditional partial differential equations (PDEs) models fail to capture effects due to long-range forces at the microscale and mesoscale. However, utilization of this capability is seriously compromised by the lack of a rigorous nonlocal interface theory, required for both application and efficient solution of nonlocal models. To unlock the full potential of nonlocal modeling we developed a mathematically rigorous and physically consistent interface theory and demonstrate its scope in mission-relevant exemplar problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A multifidelity method for a nonlocal diffusion model

Nonlocal models feature a finite length scale, referred to as the horizon, such that points separated by a distance smaller than the horizon interact with each other. Such models have proven to be useful in a variety of settings. However, due to the reduced sparsity of discretizations, they are also generally computationally more expensive compared to their local differential equation counterparts. In this work, we introduce a multifidelity Monte Carlo method that combines the high-fidelity nonlocal model of interest with surrogate models that use coarser grids and/or smaller horizons and thus have lower fidelities and lower costs. Using the multifidelity method, the overall computational cost of uncertainty quantification is reduced without compromising accuracy. It is shown for a one-dimensional nonlocal diffusion example that speedups of up to two orders of magnitude can be achieved using the multifidelity method to estimate the expectation of an output of interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type

Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world engineering applications. Here, we present a domain decomposition solver that is inspired by substructuring methods for classical local equations. In numerical experiments involving finite element discretizations of scalar and vectorial nonlocal equations of integrable and fractional type, we observe improvements in solution time of up to 14.6x compared to commonly used solver strategies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Nonlocal Feature-Driven Exemplar-Based Approach for Image Inpainting

Here, we present a nonlocal variational image completion technique which admits simultaneous inpainting of multiple structures and textures in a unified framework. The recovery of geometric structures is achieved by using general convolution operators as a measure of behavior within an image. These are combined with a nonlocal exemplar-based approach to exploit the self-similarity of an image in the selected feature domains and to ensure the inpainting of textures. We also introduce an anisotropic patch distance metric to allow for better control of the feature selection within an image and present a nonlocal energy functional based on this metric. Finally, we derive an optimization algorithm for the proposed variational model and examine its validity experimentally with various test images.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport

We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation. Furthermore, we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s ∊ [0.5, 1). We also present an application of the advection-diffusion equation to anomalous transport of solutes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions

We develop and analyze an optimization-based method for the coupling of a static peridynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the solutions of the PD and classical equations, the objective is to minimize their mismatch on an overlap of the PD and classical domains, and the controls are virtual volume constraints and boundary conditions applied at the local-nonlocal interface. Our numerical tests performed on three-dimensional geometries illustrate the consistency and accuracy of our method, its numerical convergence, and its applicability to realistic engineering geometries. We demonstrate the coupling strategy as a means to reduce computational expense by confining the nonlocal model to a subdomain of interest, and as a means to transmit local (e.g., traction) boundary conditions applied at a surface to a nonlocal model in the bulk of the domain.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Nonlocal Metasurfaces with Lithographically Defined Vertical Symmetry Breaking

Nonlocal metasurfaces have garnered significant interest for applications that require customized and enhanced light–matter interactions in a flat form factor. These metasurfaces are distinctive for their ability to systematically control some of the fundamental properties of optical resonances by manipulating the in-plane symmetry of the lattice. Recent theoretical works have suggested that engineering the symmetry of a metasurface not just within the plane of the metasurface but also in the vertical or out-of-plane direction enables improved control of additional fundamental properties, especially chirality. However, standard nanofabrication processes cannot readily support elaborate vertical symmetry breaking such as nanostructure heights or slopes that deliberately vary across the footprint of a metasurface. Here, in this work, we experimentally demonstrate a scalable method to lithographically define the vertical symmetry of nonlocal metasurfaces by selectively eroding the etch mask during the etch process. Moreover, as the etch mask erosion rates depend on the in-plane size of individual nanostructures, we introduce and experimentally demonstrate a compatible design framework that enables versatile control over the properties of optical resonances. The results hold promise for chiral nonlocal metasurfaces with highly customized behavior.

metamaterial↗
DOE OSTI2022

Observation of nonlocal Josephson effect on double InAs nanowires

Short-range coherent coupling of two Josephson junctions (JJs) are predicted to generate a supercurrent in one JJ nonlocally modulated by the phase difference in the other. We report on observation of the nonlocal Josephson effect on double InAs nanowires as experimental evidence of the coherent coupling. We measure one JJ sharing one superconducting electrode with the other JJ and observe switching current oscillation as a control of the nonlocal phase difference. Our result will contribute to engineer novel superconducting phenomena with the short-range coherent coupling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Space-time dependent thermal conductivity in nonlocal thermal transport

Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier-type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. Here, this capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport, but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Valley pumping via edge states and the nonlocal valley Hall effect in two-dimensional semiconductors

Recent experiments have studied the temperature and gate voltage dependence of nonlocal transport in bilayer graphene, identifying features thought to be associated with the two-dimensional semiconductor's bulk intrinsic valley Hall effect. Here, we use both simple microscopic tight-binding ribbon models and phenomenological bulk transport equations to emphasize the impact of sample edges on the nonlocal voltage signals. We show that the nonlocal valley Hall response is sensitive to electronic structure details at the sample edges and that it is enhanced when the local longitudinal conductivity is larger near the sample edges than in the bulk. We discuss recent experiments in light of these findings and also discuss the close analogy between electron pumping between valleys near two-dimensional sample edges in the valley Hall effect and bulk pumping between valleys due to the chiral anomaly in three-dimensional topological semimetals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Perturbative treatment of nonlocal chiral interactions in auxiliary-field diffusion Monte Carlo calculations

Nuclear many-body systems, ranging from nuclei to neutron stars, are some of the most interesting physical phenomena in our universe, and quantum Monte Carlo (QMC) approaches are among the most accurate many-body methods currently available to study them. In recent decades, interactions derived from chiral effective field theory (EFT) have been widely adopted in the study of nuclear many-body systems. One drawback of the QMC approach is the requirement that the nuclear interactions need to be local, whereas chiral EFT interactions usually contain nonlocalities. In this work, we leverage the capability of computing second-order perturbative corrections to the ground-state energy in order to develop a self-consistent approach to including nonlocal operators in QMC calculations. In conclusion, we investigate both the deuteron and the neutron-matter equation of state in order to show the robustness of our technique and pave the way for future QMC calculations at higher orders in the EFT, where nonlocal operators cannot be avoided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Nonlocal chiral contributions to generalized parton distributions of the proton at nonzero skewness

We compute the one-loop contributions to spin-averaged generalized parton distributions (GPDs) in the proton from pseudoscalar mesons with intermediate octet and decuplet baryon states at nonzero skewness. Our framework is based on nonlocal covariant chiral effective theory, with ultraviolet divergences regularized by introducing a relativistic regulator derived consistently from the nonlocal Lagrangian. Using the splitting functions calculated from the nonlocal Lagrangian, we find the nonzero skewness GPDs from meson loops by convoluting with the phenomenological pion GPD and the generalized distribution amplitude, and verify that these satisfy the correct polynomiality properties. We also compute the lowest two moments of GPDs to quantify the meson loop effects on the Dirac, Pauli, and gravitational form factors of the proton.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Atwood effects on nonlocality of the scalar transport closure in Rayleigh-Taylor mixing

The importance of nonlocality is assessed in modeling mean scalar transport for turbulent Rayleigh-Taylor (RT) mixing at different Atwood numbers. Building on the two-dimensional incompressible work of Lavacot et al. [J. Fluid Mech. 985, A47 (2024)], the present work extends the macroscopic forcing method to variable density problems in three-dimensional space to measure moments of the generalized eddy diffusivity kernel in RT mixing for increasing Atwood numbers (𝐴 = 0.05, 0.3, 0.5, 0.8). It is found that as 𝐴 increases, (1) the eddy diffusivity moments become asymmetric and (2) the higher-order eddy diffusivity moments become larger relative to the leading-order diffusivity, indicating that nonlocality becomes more important at higher 𝐴. There is a particularly strong temporal nonlocality at higher 𝐴, suggesting stronger history effects. In conclusion, the implications of these findings for closure modeling for finite-Atwood RT are discussed.

general physics↗