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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A chain stretch-based gradient-enhanced model for damage and fracture in elastomers

Similar to quasi-brittle materials, it has been recently shown that elastomers can exhibit a macroscopically diffuse damage zone that accompanies the fracture process. In this study, we introduce a stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm of the phase field method for fracture, where a sharp crack is numerically approximated in a diffuse manner. Capturing fracture localization and diffuse damage in our approach is achieved by considering nonlocal effects that encompass network topology, heterogeneity, and imperfections. These considerations motivate the use of a statistical damage function dependent upon the nonlocal deformation state. From this model, fracture toughness is realized as an output. While GED models have been classically utilized for damage modeling of structural engineering materials (e.g., concrete), they face challenges when trying to capture the cascade from damage to fracture, often leading to damage zone broadening (de Borst and Verhoosel, 2016). This deficiency contributed to the popularity of the phase-field method over the GED model for elastomers and other quasi-brittle materials. Other groups have proceeded with damage-based GED formulations that prove identical to the phase-field method (Lorentz et al., 2012), but these inherit the aforementioned limitations. To address this issue in a thermodynamically consistent framework, we implement two modeling features (a nonlocal driving force bound and a simple relaxation function) specifically designed to capture the evolution of a physically meaningful damage field and the simultaneous localization of fracture, thereby overcoming a longstanding obstacle in the development of these nonlocal strain- or stretch-based approaches. Here, we discuss several numerical examples to understand the features of the approach at the limit of incompressibility, and compare them to the phase-field method as a benchmark for the macroscopic response and fracture energy predictions.

Elastomers↗
DOE OSTI2026

Development and assessment of models for turbulent Rayleigh-Taylor mixing using the macroscopic forcing method

Reynolds-Averaged Navier Stokes (RANS) simulations are a popular method for designing ICF experiments, and accurate mixing models are crucial for these simulations to give good predictions. To this end, the present work seeks to demonstrate the Macroscopic Forcing Method (MFM) as a tool for both improving existing RANS models as well as assessing RANS model forms. First, MFM analysis from Lavacot et al. (Phys. Rev. Fluids, 2025) is used to develop the k–L–F model, an extension of the k–L model of Dimonte and Tipton (Phys. Fluids, 2006) that incorporates nonlocality through addition of a turbulent species flux transport equation. MFM is then applied to the k–L–F model along with the k–L and BHR–4 models to assess their forms and compare the model-implied eddy diffusivity moments to those measured from high-fidelity simulations. Furthermore, the analysis reveals that models incorporating nonlocality (k–L–F and BHR–4) match the high-fidelity simulation data better than purely local models (k–L), both in terms of mean fields and eddy diffusivity moments. However, all of the considered RANS models struggle to match temporal moments at high Atwood numbers, highlighting the importance of temporal nonlocality in these regimes and the need for additional improvement even among models incorporating nonlocality.

general physics↗
DOE OSTI2020

Analysis of Tempered Fractional Operators

Tempered fractional operators are useful in models for subsurface transport and diffusion due to their ability to capture anomalous diffusion: a behavior which the classical partial differential equation models cannot describe. We analyze tempered fractional operators within the nonlocal vector calculus framework in order to assimilate them to the rigorous mathematical structure developed for nonlocal models. First, we show they are special instances of generalized nonlocal operators in correspondence of a proper choice of nonlocal kernels. Then, we work towards showing tempered fractional operators are equivalent to truncated fractional operators. These truncated operators are useful because they are less computationally intensive than the tempered operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Analysis of Tempered Fractional Operators

Tempered fractional operators provide an improved predictive capability for modeling anomalous effects that cannot be captured by standard partial differential equations. These effects include subdiffusion and superdiffusion (i.e. the mean square displacement in a diffusion process is proportional to a fractional power of the time), that often occur in, e.g., geoscience and hydrology. We analyze tempered fractional operators within the nonlocal vector calculus framework in order to assimilate them to the rigorous mathematical structure developed for nonlocal models. First, we show they are special instances of generalized nonlocal operators by means of a proper choice of the nonlocal kernel. Then, we present a plan for showing tempered fractional operators are equivalent to truncated fractional operators. These truncated operators are useful because they are less computationally intensive than the tempered operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Dirichlet-type absorbing boundary conditions for peridynamic scalar waves in two-dimensional viscous media

Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that nonlocal operators are commonly associated with volume constrained boundary conditions. Moreover, application of Fourier and Laplace transforms, which are essential for the majority of available methods for ABCs, to nonlocal models is complicated. In this paper, we propose a simple method to construct accurate ABCs for peridynamic scalar wave-type problems in viscous media. The proposed ABCs are constructed in the time and space domains and are of Dirichlet type. Consequently, their implementation is relatively simple, since no derivatives of the wave field are required. The proposed ABCs are derived at the continuum level, from a semi-analytical solution of the exterior domain using harmonic exponential basis functions in space and time (plane-wave modes). The numerical implementation is done using a meshfree collocation approach employed within a boundary layer adjacent to the interior domain boundary. The modes satisfy the peridynamic numerical dispersion relation, resulting in a compatible solution of the interior region (near-field) with that of the exterior region (far-field). The accuracy and stability of the proposed ABCs are demonstrated with several numerical examples in two-dimensional unbounded domains.

42 ENGINEERING↗
DOE OSTI2022

A Realistic Theory of Quantum Measurement

Abstract We propose that the ontic understanding of quantum mechanics can be extended to a fully realistic theory that describes the evolution of the wavefunction at all times, including during a measurement. In such an approach the wave equation should reduce to the standard wave equation when there is no measurement, and describe state reduction when the system is measured. The general wave equation must be nonlinear and nonlocal, and we require it to be time-symmetric; consequently, this approach is not a new interpretation but a new theory. The wave equation is an integrodifferential equation (IDE). The time symmetry requirement leads to a retrocausal approach, in which the wave equation is solved subject to initial and final conditions to determine history at intermediate times. We propose that different outcomes from (apparently) identically prepared experiments may result from uncontrolled parameters; both the nonlocality and the retrocausality of the theory imply that Bell’s Theorem cannot rule out such “hidden variables.” Beginning with Hamilton’s principle, we demonstrate the construction of such a theory by replacing the action with a functional designed to give rise to a nonlinear, nonlocal IDE as the wave equation. This IDE reduces to the standard wave equation (a differential equation) in the absence of a measurement, but exhibits state reduction to a single eigenvalue when the system interacts with another system with the properties of a measurement apparatus. We demonstrate several desirable features of this theory; for other properties we indicate their plausibility and possible avenues to a proof.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quantum Computational Advantage with String Order Parameters of One-Dimensional Symmetry-Protected Topological Order

Nonlocal games with advantageous quantum strategies give arguably the most fundamental demonstration of the power of quantum resources over their classical counterparts. Recently, certain multiplayer generalizations of nonlocal games have been used to prove unconditional separations between limited computational complexity classes of shallow-depth circuits. Here, we show advantageous strategies for these nonlocal games for generic ground states of one-dimensional symmetry-protected topological orders (SPTOs), when a discrete invariant of a SPTO known as a twist phase is nontrivial and -1. Finally, our construction demonstrates that sufficiently large string order parameters of such SPTOs are indicative of globally constrained correlations useful for the unconditional computational separation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Coupling Approaches with Non-matching Grids for Classical Linear Elasticity and Bond-based Peridynamic Models in 1D

Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal grids usually require a finer resolution than local grids. In that case, it is often convenient to resort to interpolation operators so that models can exchange information in the overlap regions when nodes from the two grids do not coincide. This paper studies three existing coupling approaches, namely 1) a method that enforces matching displacements in an overlap region, 2) a variant that enforces a constraint on the stresses instead, and 3) a method that considers a variable horizon in the vicinity of the interfaces. Further, the effect of the interpolation order and of the grid ratio on the performance of the three coupling methods with non-matching grids is carefully studied on one-dimensional examples using polynomial manufactured solutions. The numerical results show that the degree of the interpolants should be chosen with care to avoid introducing additional modeling errors, or simply minimize these errors, in the coupling approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Surface Tension of Dielectric–Air Interfaces

Analytical and semianalytical expressions for the surface tension of dielectric–air interfaces are presented after considering local and nonlocal dielectric effects near interfaces. It is shown that the nonlocal effects of dielectrics are significant for highly polar dielectric fluids such as water. Far from the interface, nonlocal dielectric effects are shown to cause not only the oscillatory potential of the mean force but also a reversal of sign at intermediate distances.

42 ENGINEERING↗
DOE OSTI2022

Thermal transport modeling of laser-irradiated spheres

Thermal transport of uniformly laser-irradiated spheres of various materials is investigated computationally. One-dimensional simulations of low- to mid-Z materials (Be, Al, and Cu) are performed to evaluate the impact of nonlocal electron transport on experimental observables under laser intensities of relevance to direct-drive inertial confinement fusion. Here we compare thermal transport models of different levels of fidelity: flux-limited Spitzer–Harm diffusion, the Schurtz–Nicolai–Busquet (SNB) reduced-order nonlocal model, and a Fokker–Planck description. Spitzer–Harm diffusion with different flux-limiter factors are compared with different implementations of the SNB model in the HYDRA radiation hydrodynamics code. Under the conditions of interest, the peak heat flux in the thermal front with the SNB model shows good agreement with Fokker–Planck calculations, with the largest errors below 10% at 10 15 W/cm 2 laser intensity. From HYDRA-SNB simulations, two experimentally relevant effects are observed from nonlocal heat transport when compared to flux-limited Spitzer–Harm modeling: coronal temperatures are cooler due to reduced heat fluxes in the expanding plasma and (for mid-Z materials) x-ray emissions are enhanced due to preheating in the dense plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Fracton models from product codes

We explore a deep connection between fracton order and product codes. In particular, we propose and analyze conditions on classical seed codes which lead to fracton order in the resulting quantum product codes. Depending on the properties of the input codes, product codes can realize either Type-I or Type-II fracton models, in both nonlocal and local constructions. For the nonlocal case, we show that a recently proposed model of lineons on nonlocal graphs can be obtained as a hypergraph product code. Interestingly, constrained mobility in this model arises only from energy barriers associated with the graph. For the local case, we introduce a novel type of classical LDPC code defined on a planar aperiodic tiling. By considering the specific example of the pinwheel tiling, we demonstrate the systematic construction of local Type-I and Type-II fracton models as product codes. Our work establishes product codes as a natural setting for exploring fracton order.

Fractons↗
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 OSTI2024

Determination of short- and long-distance contributions in B 0 → K * 0 μ + μ − decays

An amplitude analysis of the B 0 → K * 0 μ + μ − decay is presented. The analysis is based on data collected by the LHCb experiment from proton-proton collisions at s = 7 , 8 and 13 TeV, corresponding to an integrated luminosity of 4.7 fb − 1 . For the first time, Wilson coefficients and nonlocal hadronic contributions are accessed directly from the unbinned data, where the latter are parametrized as a function of q 2 with a polynomial expansion. Wilson coefficients and nonlocal hadronic parameters are determined under two alternative hypotheses: the first relies on experimental information alone, while the second one includes information from theoretical predictions for the nonlocal contributions. Both models obtain similar results for the parameters of interest. The overall level of compatibility with the Standard Model is evaluated to be between 1.8 and 1.9 standard deviations when looking at the C 9 Wilson coefficient alone, and between 1.3 and 1.4 standard deviations when considering the full set of C 9 , C 10 , C 9 ′ and C 10 ′ Wilson coefficients. The ranges reflect the theoretical assumptions made in the analysis. © 2024 CERN, for the LHCb Collaboration 2024 CERN

Aaij, R. (ORCID:0000000305331952)↗
DOE OSTI2021

Fully kinetic simulations of strong steady-state collisional planar plasma shocks

We report on simulations of strong, steady-state collisional planar plasma shocks with fully kinetic ions and electrons, independently confirmed by two fully kinetic codes (an Eulerian continuum and a Lagrangian particle-in-cell). While kinetic electrons do not fundamentally change the shock structure as compared with fluid electrons, we find an appreciable rearrangement of the preheat layer, associated with nonlocal electron heat transport effects. The electron heat-flux profile qualitatively agrees between kinetic- and fluid-electron models, suggesting a certain level of “stiffness,” though substantial nonlocality is observed in the kinetic heat flux. We also find good agreement with nonlocal electron heat-flux closures proposed in the literature. Finally, in contrast to the classical hydrodynamic picture, we find a significant collapse in the “precursor” electric-field shock at the preheat layer leading edge, which correlates with the electron-temperature gradient relaxation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Localizing Transformations of the Galaxy-Galaxy Lensing Observable

Modern cosmological analyses of galaxy-galaxy lensing face a theoretical systematic effect arising from the nonlocality of the observed galaxy-galaxy lensing signal. Because the predicted tangential shear signal at a given separation depends on the physical modeling on all scales internal to that separation, systematic uncertainties in the modeling of nonlinear small scales are propagated outward to larger scales. Even in the absence of other limiting factors, this systematic effect alone can necessitate conservative small-scale cuts, resulting in significant losses of information in the tangential shear data vector. We develop a simple linear transformation of the standard galaxy-galaxy observable that removes this nonlocality, which ensures that the cosmological signal contained within the transformed observable is exclusively drawn from well-understood physical scales. This new observable, through its robustness against nonlocality, also enables a significant extension in the range of usable scales in galaxy-galaxy lensing compared to the standard approach in current cosmological analyses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Direct Measurement of the Return Current Instability in a Laser-Produced Plasma

Measurements were made of the return current instability growth rate, demonstrating its concurrence with nonlocal transport. Thomson scattering was used to measure a maximum growth rate of 5.1 × 10 9 Hz, which was 3 times less than classical Spitzer-Härm theory predicts. Here, the measured plasma conditions indicate the heat flux was nonlocal, and Vlasov–Fokker-Planck simulations that account for nonlocality reproduce the measured growth rates. Furthermore, the threshold for the return current instability was measured (δ T = 0.017 ± 0.002) to be in good agreement with previous theoretical models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Evaluating the Trustworthiness of Explainable Artificial Intelligence (XAI) Methods Applied to Regression Predictions of Arctic Sea Ice Motion

Abstract Recent advances in explainable artificial intelligence (XAI) methods show promise for understanding predictions made by machine learning (ML) models. XAI explains how the input features are relevant or important for the model predictions. We train linear regression (LR) and convolutional neural network (CNN) models to make 1-day predictions of sea ice velocity in the Arctic from inputs of present-day wind velocity and previous-day ice velocity and concentration. We apply XAI methods to the CNN and compare explanations to variance explained by LR. We confirm the feasibility of using a novel XAI method [i.e., global layerwise relevance propagation (LRP)] to understand ML model predictions of sea ice motion by comparing it to established techniques. We investigate a suite of linear, perturbation-based, and propagation-based XAI methods in both local and global forms. Outputs from different explainability methods are generally consistent in showing that wind speed is the input feature with the highest contribution to ML predictions of ice motion, and we discuss inconsistencies in the spatial variability of the explanations. Additionally, we show that the CNN relies on both linear and nonlinear relationships between the inputs and uses nonlocal information to make predictions. LRP shows that wind speed over land is highly relevant for predicting ice motion offshore. This provides a framework to show how knowledge of environmental variables (i.e., wind) on land could be useful for predicting other properties (i.e., sea ice velocity) elsewhere. Significance Statement Explainable artificial intelligence (XAI) is useful for understanding predictions made by machine learning models. Our research establishes trustability in a novel implementation of an explainable AI method known as layerwise relevance propagation for Earth science applications. To do this, we provide a comparative evaluation of a suite of explainable AI methods applied to machine learning models that make 1-day predictions of Arctic sea ice velocity. We use explainable AI outputs to understand how the input features are used by the machine learning to predict ice motion. Additionally, we show that a convolutional neural network uses nonlinear and nonlocal information in making its predictions. We take advantage of the nonlocality to investigate the extent to which knowledge of wind on land is useful for predicting sea ice velocity elsewhere.

Hoffman, Lauren [Scripps Institution of Oceanograp↗
DOE OSTI2020

On the Parameterization of Convective Downdrafts for Marine Stratocumulus Clouds

The role of nonlocal transport on the development and maintenance of marine stratocumulus (Sc) clouds in coarse-resolution models is investigated, with a special emphasis on the downdraft contribution. A new parameterization of cloud-top-triggered downdrafts is proposed and validated against large-eddy simulation (LES) for two Sc cases. The applied nonlocal mass-flux scheme is part of the stochastic multiplume eddy-diffusivity/mass-flux (EDMF) framework decomposing the turbulent transport into local and nonlocal contributions. The complementary local turbulent transport is represented with the Mellor–Yamada–Nakanishi–Niino (MYNN) scheme. This EDMF version has been implemented in the Weather Research and Forecasting (WRF) single-column model (SCM) and tested for three model versions: without mass flux, with updrafts only, and with both updrafts and downdrafts. In the LES, the downdraft and updraft contributions to the total heat and moisture transport are comparable and significant. The WRF SCM results show a good agreement between the parameterized downdraft turbulent transport and LES. While including updrafts greatly improves the modeling of Sc clouds over the simulation without mass flux, the addition of downdrafts is less significant, although it helps improve the moisture profile in the planetary boundary layer.

Wu, Elynn↗