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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A splice method for local-to–nonlocal coupling of weak forms

Here, we propose a method to couple local and nonlocal diffusion models. By inheriting desirable properties such as patch tests, asymptotic compatibility and unintrusiveness from related splice and optimization-based coupling schemes, it enables the use of weak (or variational) formulations, is computationally efficient and straightforward to implement. We prove well-posedness of the coupling scheme and demonstrate its properties and effectiveness in a variety of numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. In this work, we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets. Firstly, we develop a novel coarse-graining method, to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets. Inspired by the weighted essentially non-oscillatory (WENO) scheme, the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil, then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities. Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion. In the first phase, we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties. Then, in the second phase, the material damage criterion is learnt as a smoothed step function from the data with fractures. As a result, a peridynamics surrogate is obtained. As a continuum model, our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training, and hence allows for substantial reductions in computational cost compared with MD. We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene. Our tests show that the proposed data-driven model is robust and generalizable, in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Peridynamic neural operators: A data-driven nonlocal constitutive model for complex material responses

Neural operators, which can act as implicit solution operators of hidden governing equations, have recently become popular tools for learning the responses of complex real-world physical systems. Nevertheless, most neural operator applications have thus far been data-driven and neglect the intrinsic preservation of fundamental physical laws in data. Here, in this work, we introduce a novel integral neural operator architecture called the Peridynamic Neural Operator (PNO) that learns a nonlocal constitutive law from data. This neural operator provides a forward model in the form of state-based peridynamics, with objectivity and momentum balance laws automatically guaranteed. As applications, we demonstrate the expressivity and efficacy of our model in learning complex material behaviors from both synthetic and experimental data sets. We also compare the performances with baseline models that use predefined constitutive laws. We show that, owing to its ability to capture complex responses, our learned neural operator achieves improved accuracy and efficiency. Moreover, by preserving the essential physical laws within the neural network architecture, the PNO is robust in treating noisy data. The method shows generalizability to different domain configurations, external loadings, and discretizations.

42 ENGINEERING↗
DOE OSTI2022

Data–driven and constrained optimization of semi–local exchange and nonlocal correlation functionals for materials and surface chemistry

Reliable predictions of surface chemical reaction energetics require an accurate description of both chemisorption and physisorption. Herein, we present an empirical approach to simultaneously optimize semi-local exchange and nonlocal correlation of a density functional approximation to improve these energetics. A combination of reference data for solid bulk, surface, and gas-phase chemistry and physical exchange-correlation model constraints leads to the VCML-rVV10 exchange-correlation functional. Owing to the variety of training data, the applicability of VCML-rVV10 extends beyond surface chemistry simulations. It provides optimized gas phase reaction energetics and an accurate description of bulk lattice constants and elastic properties.

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

Data-driven nonlocal model for fragmentation in the crushing of solids

A technique is proposed for reproducing particle size distributions in three-dimensional simulations of the crushing and comminution of solid materials. The method is designed to produce realistic distributions over a wide range of loading conditions, especially for small fragments. In contrast to most existing methods, the new model does not explicitly treat the small-scale process of fracture. Instead, it uses measured fragment distributions from laboratory tests as the basic material property that is incorporated into the algorithm, providing a data-driven approach. The algorithm is implemented within a nonlocal peridynamic solver, which simulates the underlying continuum mechanics and contact interactions between fragments after they are formed. Finally, the technique is illustrated in reproducing fragmentation data from drop weight testing on sandstone samples.

58 GEOSCIENCES↗
DOE OSTI2025

Field redefinitions can be nonlocal

We revisit the lore establishing the allowed space of field redefinitions and show that there are essentially no restrictions. Our conclusions hold to all orders in perturbation theory and for any dispersion relation. Field redefinitions can be nonlocal, symmetry breaking, or in certain cases have explicit dependence on spacetime. We address field redefinitions that can be resummed into the propagator, which demonstrates how to perform perturbative calculations away from the minimum in field space. Field redefinitions are used to derive higher-order Schwinger-Dyson equations, which imply multiparticle soft theorems. Non-standard field redefinitions are showcased using both relativistic and nonrelativistic examples.

effective field theories↗
DOE OSTI2023

Peridynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet-type absorbing boundary conditions

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. So our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.

42 ENGINEERING↗
DOE OSTI2023

Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials

Ductile materials, such as metal alloys, can undergo substantial deformation before failure. Additionally, these materials are usually of polycrystalline composition and exhibit strongly anisotropic behavior at small length scales. Previously developed fast Fourier transform (FFT)-based models can model ductile fracture of isotropic materials or the elastic–plastic behavior of anisotropic polycrystalline materials; however, there remains a need to couple both capabilities. This work extends a large-strain FFT-based crystal plasticity model to simulate ductile fracture of polycrystalline materials. In this work, a triaxiality-based continuum damage mechanics (CDM) formulation is incorporated into a large-strain elasto-viscoplastic FFT (LS-EVPFFT) framework. The CDM formulation is augmented with an integral-based nonlocal regularization approach that correctly handles gas-phase material necessary to model unconstrained surfaces. To validate the damage-enabled LS-EVPFFT framework, mesoscale copper tensile coupons were machined using microwire electrical discharge machining and experimentally characterized using electron backscatter diffraction. In-situ optical digital image correlation was performed during uniaxial testing to provide a side-by-side comparison of the experimental and computational strain fields and stress–strain responses. The damage-enabled LS-EVPFFT framework can simulate the complete macroscopic stress–strain response of ductile polycrystals to failure. The model reproduces necking behavior that qualitatively agrees with experimental observations. By leveraging the relatively low computational cost of the damage-enabled LS-EVPFFT framework, the framework presented here allows the ductile fracture response of 3D polycrystalline materials to be tractably predicted.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The Influence of Nonlocal Metal–Dielectric Environments on Physical and Chemical Processes

Plasmonic nanolayers and laminar metallic/dielectric multilayers were originally developed for optical cloaking applications and lensing applications that could potentially image objects whose size was below the diffraction limit. These assemblies were initially formed from gold or silver nanorods grown within an alumina mesh. However, more recently, assemblies with similar properties have also been prepared by sequential thin-layer deposition of alternating layers of gold and magnesium fluoride (MgF 2 ). These metal/dielectric composite materials enable control of the dielectric constant in the directions perpendicular to the layers and balance the real and imaginary dielectric constants of the assembly such that the speed and the amplitude of the waves traveling through the assembly are not attenuated. In this Account, we will also focus on a few of the applications ranging from surface wetting to fluorescence quenching to enhancement of photochemical reactions. First, we will share an introduction to processes used to create these materials, which are combinations of low refractive index metals and transparent higher index materials arranged in a scalable repeating fashion. Two fabrication methods were employed: an electrochemical deposition of Ag nanorods into an anodized alumina matrix which produced materials with an anisotropic negative refractive index material within the plane of the film and lamellar metal/dielectric layers in which the negative index perpendicular to the growth direction. These alternating layers of plasmonic metals and dielectric materials were ultimately chosen to prepare films for further testing, because of their relative ease of fabrication. We will continue with a discussion of a few of the applications of both of these nonlocal dielectric composite materials including more specialized plasmonic, composite, and hyperbolic metamaterials including fluorescence quenching, photochemical reactions, and surface wetting. In each of these applications, the unique response caused by the enhancement of the electric field and the interface between hyperbolic materials and plasmonic materials as they interact photophysically with their near neighbors is presented. In each of the applications, the enhanced electric field extends from the composite substrate layer to interact with its near neighbors and beyond. Furthermore, the presence of this extended interaction can be observed in the form of decreased emission lifetime, enhancement of photochemical reaction rates, and changes in the surface energies measured by contact angle goniometry. In this Account, all of these situations will be addressed. Finally, we will conclude with a summary and vision for the future as well as a discussion of the unique challenges and opportunities available as research active faculty at an HBCU.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Nonlocal Effect of Percolated Particle Networks on Viscoelasticity of Polymer–Filler Nanocomposites: A Mesoscale Simulation Study

With nanoparticles (NPs) as fillers, polymer nanocomposites (PNCs) usually exhibit enhanced mechanical properties. However, a direct connection between the microscopic structural relaxation and macroscopic mechanical properties of PNCs remains to be established. To investigate the micro-to-macro connection, we develop a mesoscale model, in which the NPbridging polymer chains are represented by a dynamic bonded interaction between NPs, and the bulk polymer matrix is implicitly modeled by overdamped Langevin dynamics. Extensive equilibrium simulations are performed to quantify the microscopic dynamics of model PNCs. Systematic analyses of modified Rouse dynamics, dynamic structure factor, and relaxation modulus uncover that the microscopic relaxation dynamics of PNCs are significantly decelerated across different length scales because of nonlocal effects of percolated particle networks a phenomenon that has not been adequately captured in prior simulation studies. We find that NPvolume- fraction and NP-bonding-energy barrier are the two critical variables that affect bulk viscoelasticity the most. The proposed mesoscale model is versatile and provides a powerful framework for studying structure−property relations of different PNCs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Giant Enhancement of Four-Wave Mixing by Doubly Zone-Folded Nonlocal Metasurfaces

Resonant optical metasurfaces hold promise for enhancing nonlinear optical signals and manipulating their fundamental properties. However, they rarely excel at amplifying signals from nonlinear processes with two incident pump beams, such as four-wave mixing (FWM) or sum-frequency generation. Frequency-mixing experiments impose challenging requirements for metasurface design due to the need to support multiple optical resonances with compatible field profiles at specified resonant wavelengths, often across a substantial spectral separation. Here, in this work, we introduce nonlocal ‘quadromer’ metasurfaces containing four nanostructures per unit cell as the key to unlocking configurable, multiresonant metasurfaces that enhance frequency-mixing processes. As a proof of concept, we experimentally demonstrate enhanced FWM using quadromer metasurfaces made of silicon and silicon-rich silicon nitride. The results are relevant for applications such as imaging of infrared light upconverted into the visible spectrum and the generation of quantum light via spontaneous FWM.

four-wave mixing↗
DOE OSTI2020

Nonlocal Coulomb interaction and spin-freezing crossover as a route to valence-skipping charge order

Abstract Multiorbital systems away from global half-filling host intriguing physical properties promoted by Hund’s coupling. Despite increasing awareness of this regime dubbed Hund’s metal, effect of nonlocal interaction is still elusive. Here we study a three-orbital model with 1/3 filling (two electrons per site) including the intersite Coulomb interaction ( V ). Using the G W plus extended dynamical mean-field theory, the valence-skipping charge order transition is shown to be driven by V . Most interestingly, the instability to this transition is significantly enhanced in the spin-freezing crossover regime, thereby lowering the critical V to the formation of charge order. This behavior is found to be closely related to the population profile of the atomic multiplet states in the spin-freezing regime. In this regime, maximum spin states are dominant in each total charge subspace with substantial amount of one- and three-electron occupations, which leads to almost equal population of one- and the maximum spin three-electron state. Our finding unveils another feature of the Hund’s metal and has potential implications for the broad range of multiorbital systems as well as the recently discovered charge order in iron pnictides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Analytic insights into nonlocal energy transport. III. steady state Fokker Planck theory in spherical and planar geometry

This paper develops an approximate steady state Fokker Planck theory for energetic electron transport in a spherical laser fusion target. First, we apply the theory to only a small population of electrons, which is specified at the outset. Then, one determines the nonlocal electron energy flux of these electrons at a particular position. These energetic electrons may either come from the tail of the thermal distribution function or be generated by an instability. This paper develops two approximate methods of solution, which we call the “characteristic method” and “sparse eigenfunction.” The former works only in planar geometry and the latter in both planar and spherical geometry. Comparison of the two methods in planar geometry shows that even though the approximations are very different, they give about the same result, increasing their credibility. For the example we have chosen, spherical effects are not important for electrons from the tail of the distribution function but may well be for instability generated electrons, which have much higher energy. Comparing planar to spherical, one finds an additional spherical barrier protecting the fuel. It turns out that the associated fuel preheat a Fokker Planck model predicts is considerably less than that predicted by the Krook models as developed at both NRL and other places.

Manheimer, Wallace (ORCID:0000000163342591)↗
DOE OSTI2025

Nonlocal, diamagnetic electromagnetic effects in magnetically insulated transmission lines

We identify the time-dependent physics responsible for the critical reduction of current losses in magnetically insulated transmission lines (MITLs) due to uninsulated space charge-limited currents of electrons emitted by field stress. A drive current of sufficiently short pulse length introduces a strong enough time dependence that steady-state results alone become inadequate for the complete understanding of current losses. The time-dependent physics can be described as a nonlocal, diamagnetic electromagnetic response of space charge limited currents. As the pulse length is increased or equivalently, the MITL length reduced, these time-dependent effects diminish and current losses converge to those predicted by the well-known Child–Langmuir law in the external (vacuum) fields. We present a simple one-dimensional (1D) model that encapsulates the essence of this physics. We find excellent agreement with 2D particle-in-cell simulations for two MITL geometries, Cartesian parallel plate and azimuthally symmetric straight coaxial. Based on the 1D model, we explore various scaling dependencies of MITL losses with relevant parameters, e.g., peak current, pulse length, geometrical dimensions, etc. We propose an improved physics model of magnetic insulation in the form of a Hull curve, which could also help improve predictions of current losses by common circuit element codes, such as BERTHA. Finally, we describe how to calculate the temperature rise due to electron impact within the 1D model.

Computer simulation↗
DOE OSTI2025

Toward an improved nonlocal thermodynamic equilibrium model for more predictive simulations of ignition scale hohlraums

Recently, nonlocal thermodynamic equilibrium (NLTE) modeling has been identified as the primary reason for discrepant predictions of the peak neutron production time in indirectly driven inertial confinement fusion (ICF) platforms. It has also been observed that predictions of collisional excitation rates differ by as much as 50% from measurements. Theoretical uncertainties in dielectronic recombination rates have also been posited as possibly contributing to errors in NLTE predictions. This work examines the impact of multipliers on collisional excitation and dielectronic recombination rates on simulations of a directly driven gold sphere and an indirect drive ICF implosion. It is found that multipliers on the collisional excitation rates have a strong impact on radiant intensity and electron temperature and a weaker impact on ionization state, whereas multipliers on dielectronic recombinations rates strongly impact ionization state with a smaller impact on radiant intensity and electron temperature. A self-consistent NLTE model which places multipliers on differing transitions, as motivated by experimental measurements and more detailed atomic physics predictions, improves agreement but does not completely eliminate discrepancies with measurements of the radiant intensity within the 2–4 keV spectral range.

Farmer, W. A. [Lawrence Livermore National Laborat↗
DOE OSTI2026

Comment on “Nonlocal nucleon matrix elements in the rest frame”

In a recent paper, “Nonlocal nucleon matrix elements in the rest frame” [1], it was observed that the next-to-leading order calculations of the renormalization factor can describe, to a few percent accuracy, the logarithm of the lattice quantum chromodynamics (QCD) rest frame matrix elements with separations up to distances of 0.6 fm on multiple lattice spacings. We argue that perturbative QCD breaks down at such a distance scale after resumming the associated large logarithms, while the Ansatz used in the analysis there is not justified in perturbation theory. Besides, we explain the observation in Ref. [1] and demonstrate that the Ansatz fails to describe the data for 𝑧 > 0.3 fm, showing an opposite trend. Finally, although Ref. [1] proposes multiplying the Ansatz by a Gaussian correction model, which is shown to reduce the discrepancy with the data, this does not legitimize the use of perturbative QCD at such distance scales.

Lattice QCD↗
DOE OSTI2021

Twisted symmetric trilayer graphene: Single-particle and many-body Hamiltonians and hidden nonlocal symmetries of trilayer moiré systems with and without displacement field

Here, we derive the Hamiltonian for trilayer moiré systems with the Coulomb interaction projected onto the bands near the charge neutrality point. Motivated by the latest experimental results, we focus on the twisted symmetric trilayer graphene (TSTG) with a mirror symmetry with respect to the middle layer. We provide a full symmetry analysis of the noninteracting Hamiltonian with a perpendicular displacement field coupling the band structure made otherwise of the twisted bilayer graphene (TBG) and the high-velocity Dirac fermions, and we identify a hidden nonlocal symmetry of the problem. In the presence of this displacement field, we construct an approximate single-particle model, akin to the tripod model for TBG, capturing the essence of noninteracting TSTG. We also derive more quantitative perturbation schemes for the low-energy physics of TSTG with displacement field, obtaining the corresponding eigenstates. This allows us to obtain the Coulomb interaction Hamiltonian projected in the active band TSTG wave functions and derive the full many-body Hamiltonian of the system. We also provide an efficient parametrization of the interacting Hamiltonian. Finally, we show that the discrete symmetries at the single-particle level promote the U (2) × U (2) spin-valley symmetry to enlarged symmetry groups of the interacting problem under different limits. The interacting part of the Hamiltonian exhibits a large U (4) × U (4) × U (4) × U (4) symmetry in the chiral limit. Moreover, by identifying a symmetry which we dub spatial many-body charge conjugation, we show that the physics of TSTG is symmetric around charge neutrality.

2-dimensional systems↗