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DOE OSTI2025

An end-to-end deep learning method for solving nonlocal Allen–Cahn and Cahn–Hilliard phase-field models

Here, we propose an efficient end-to-end deep learning method for solving nonlocal Allen–Cahn (AC) and Cahn–Hilliard (CH) phase-field models. One motivation for this effort emanates from the fact that discretized partial differential equation-based AC or CH phase-field models result in diffuse interfaces between phases, with the only recourse for remediation is to severely refine the spatial grids in the vicinity of the true moving sharp interface whose width is determined by a grid-independent parameter that is substantially larger than the local grid size. In this work, we introduce non-mass conserving nonlocal AC or CH phase-field models with regular, logarithmic, or obstacle double-well potentials. Because of non-locality, some of these models feature totally sharp interfaces separating phases. The discretization of such models can lead to a transition between phases whose width is only a single grid cell wide. Another motivation is to use deep learning approaches to ameliorate the otherwise high cost of solving discretized nonlocal phase-field models. To this end, loss functions of the customized neural networks are defined using the residual of the fully discrete approximations of the AC or CH models, which results from applying a Fourier collocation method and a temporal semi-implicit approximation. To address the long-range interactions in the models, we tailor the architecture of the neural network by incorporating a nonlocal kernel as an input channel to the neural network model. We then provide the results of extensive computational experiments to illustrate the accuracy, predictive capabilities, and cost reductions of the proposed method.

42 ENGINEERING↗

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

Holographic map for cosmological horizons

Here, we propose a holographic map between Einstein gravity coupled to matter in a de Sitter background and large N quantum mechanics of a system of spins. Holography maps a spin model with a finite-dimensional Hilbert space defined on a version of the stretched horizon into bulk gravitational dynamics. The full Hamiltonian of the spin model contains a nonlocal piece which generates chaotic dynamics, widely conjectured to be a necessary part of quantum gravity, and a local piece which recovers the perturbative spectrum in the bulk.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Considering nonlocality in the optical potentials within eikonal models

Background: For its simplicity, the eikonal method is the tool of choice to analyze nuclear reactions at high energies (E > 100 MeV/nucleon), including knockout reactions. However, so far, the effective interactions used in this method are assumed to be fully local. Purpose: Given the recent studies on nonlocal optical potentials, in this work we assess whether nonlocality in the optical potentials is expected to impact reactions at high energies and then explore different avenues for extending the eikonal method to include nonlocal interactions. Method: We compare angular distributions obtained for nonlocal interactions (using the exact R-matrix approach for elastic scattering and the adiabatic distorted wave approximation for transfer) with those obtained using their local-equivalent interactions. Results: Our results show that transfer observables are significantly impacted by nonlocality in the high-energy regime. Because knockout reactions are dominated by stripping (transfer to inelastic channels), nonlocality is expected to have a large effect on knockout observables too. Three approaches are explored for extending the eikonal method to nonlocal interactions, including an iterative method and a perturbation theory. Conclusions: None of the derived extensions of the eikonal model provide a good description of elastic scattering. Here, this paper suggests that nonlocality removes the formal simplicity associated with the eikonal model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Nonlocal effects on thermal transport in hydrodynamic simulations of unmagnetized MagLIF-relevant gaspipes on NIF

We present simulations of heat flow relevant to gaspipe experiments on the National Ignition Facility to investigate kinetic effects on transport phenomena. D 2 and neopentane (C 5 H 12 ) filled targets are used to study the laser preheat stage of a MagLIF scheme where an axial magnetic field is sometimes applied to the target. Simulations were done with the radiation-MHD code HYDRA with a collision-dominated fluid model and the SNB nonlocal electron thermal conduction model. Using the SNB model to evolve the electron temperature increased the heat front propagation of neopentane gas targets compared to a local model by limiting radial heat flow. This increases electron temperature near the axis, which decreases laser absorption. We find that the effect of heat flow models on temperature profiles and laser propagation is modest. Beyond the SNB model, we utilize HYDRA to initialize plasma conditions for the Vlasov–Fokker–Planck K2 code. We run K2 until a quasi-steady state is reached and examine the impact of kinetic effects on heat transport. Although axial heat flow is well predicted by fluid models, the fluid model consistently overpredicts radial heat flow up to 150% in regions with the largest temperature gradient of D 2 filled gaspipes. On the other hand, the SNB nonlocal electron conduction model is found to be adequate for capturing kinetic heat flow in gaspipes.

Lau, Ryan Y. [Univ. of Colorado, Boulder, CO (Unit↗

DOE OSTI2026

Code for the manuscript "Lagrangian Attention Tensor Networks for Velocity Gradient Statistical Mode

We disclose a python/pytorch implementation of the physics-informed machine learning algorithm described in "Lagrangian Attention Tensor Networks for Velocity Gradient Statistical Modeling", LA-UR-24-30678. Direct numerical simulation (DNS) of ubiquitous turbulence phenomena is computationally infeasible for realistic flows. As a result, reduced modeling for turbulent flows aim to reduce the number of resolved scales while retaining accurate representations of the small-scale physics. The dynamics of the velocity gradient tensor (VGT) is a key ingredient in reduced or subgrid turbulence models. The evolution equation for the VGT involves nonlocal terms, requiring closure modeling. This implementation of the novel methodology of Lagrangian Attention Tensor Networks (LATN), utilizes a structured representation of the history of the VGT to inform a physics-informed machine learning algorithm. This addition of structured memory terms is shown to outperform previous models when trained and evaluated on DNS data.

Livescu, Daniel [LANL]↗

DOE OSTI2021

An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture

Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. Herein, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whose a priori unknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for a number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.

42 ENGINEERING↗

NASA NTRS1993

Sounding rocket observation of a hot atomic oxygen geocorona

A sounding rocket measurement of the ultraviolet, atomic oxygen dayglow reveals an excess of emission compared to standard thermospheric model calculations at exospheric altitudes. We explore two explanations for this discrepancy: a breakdown of the radiative transfer model due to nonlocal thermal equilibrium (non-LTE) conditions above the exobase and a hot atomic oxygen geocorona. In particular, the effects of non-LTE on the 3P2, 1, 0 sublevel populations are modeled, and a hot O component in the upper thermosphere and lower exosphere is added to investigate the effects on the modeled emissions. For both cases, the data are reanalyzed and compared with the results using a standard LTE model. A hot O geocorona having a peak density of 10(exp 6)/cc at 550 km and a temperature of 4000 K is consistent with the data and appears to be the most reasonable explanation of the high-altitude enhanced emissions observed in the data.

Cotton, Daniel M.↗

DOE OSTI2023

Impact of solvation on the GW quasiparticle spectra of molecules

First-principles calculations for electrochemistry require accurate treatment of both electronic structure and solvation. The perturbative GW approximation starting from density functional theory (DFT) calculations accurately models materials systems with varying dimensionality. Continuum solvation models enable efficient treatment of solvation effects in DFT calculations, but their applications with beyond-DFT electronic structure methods such as GW have been limited. Here, we introduce the frequency-dependent liquid polarizability from a nonlocal continuum solvation model in the screened Coulomb interaction of full-frequency GW calculations with a solvated DFT starting point. In this study, we show that the liquid screening contributions substantially reduce the HOMO–LUMO gap of molecules by 3–5 eV, while solvent effects on the DFT starting point negligibly impact the GW gap. The resulting framework facilitates the simultaneous electronic and solvation accuracy needed for first-principles electrochemistry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1980

The discovery of an O subdwarf in the globular cluster NGC 6712

Spectral data for C49 in the globular cluster NGC 6712 are examined with reference to evolutionary models for low-mass stars that are contracting into white dwarfs. The spectrum of this star is found to be almost identical to that of the first sdO star found in a globular cluster, star A in NGC 6397. Analysis of the spectral data using nonlocal thermodynamic equilibrium models gives surface parameters T not less than 50,000 K, log g = 5.5 plus or minus 0.5, and N(He)/N(H) approximately equal to 0.1. The results are consistent with the models considered.

Remillard, R. A.↗

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 OSTI2024

Full wave modeling of radio-frequency beams in tokamaks in the electron cyclotron frequency range

Simulation of full wave, without paraxial approximation, high-resolution solution of wave equations in frequency domain in the electron cyclotron resonance (ECR) frequency range for realistic Tokamak plasma parameters became possible by using recently formulated hybrid iterative algorithm [Svidzinski et al., Phys. Plasmas 25, 082509 (2018)] for numerically solving discretized wave equations. This approach combines time evolution and iterative relaxation techniques into iteration cycles. This algorithm is implemented in 2D code FullWave, solving wave equations in Tokamaks in cold and hot plasma models, and it has been tested in 3D full wave iterative RF beams simulation tool, which is presently being developed to model 3D ECRH RF beams in fusion devices using dynamic grid adaptation. The results of 2D full wave modeling, assuming specified toroidal mode number, of ECRH RF beams in DIII-D plasma, performed in the cold and hot plasma models for outboard and top launch scenarios using FullWave are presented. Nonlocal hot plasma response model, based on accurate numerical solution of linearized Vlasov equation, is used to model beam propagation and absorption in the 2nd electron cyclotron harmonic region. Demonstration of capability of the hybrid iterative algorithm to model ECRH RF beams in 3D is made by simulating a substantial part of realistic beam in DIII-D, launched from outboard side of the machine. All relevant physics of RF beam propagation, most of which is not captured in paraxial approximation, such as beam's divergence, interference between the X and O modes in the beam, X-O mode conversion, beam splitting into the X and O mode beams, transformation of beam's cross section, and absorption at the 2nd electron cyclotron harmonic, is captured in the simulations. A numerical technique to find an optimal beam polarization at the launcher to launch a nearly pure X or O mode beam in plasma is developed and tested.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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 OSTI2023

New determination of the branching ratio of the structure dependent radiative K + → e + ν e γ

The branching ratio of the structure dependent (SD) radiative K + → e + ν e γ decay relative to that of the K + → e + ν e (γ) decay including the internal bremsstrahlung (IB) process (K e2 (γ) ) has been measured in the J-PARC E36 experiment using plastic scintillator/lead sandwich detectors, in contrast to the previous E36 measurement, which used a CsI(Tl) calorimeter. In the analysis, the effect of IB was also taken into account in the SD radiative decay as $K$$^{SD}_{e2γ(γ)}$. By combining the new data with the previous E36 result after revision for the IB correction for $K$$^{SD}_{e2γ(γ)}$, a new value Br($K$$^{SD}_{e2γ(γ)}$)/Br(Ke 2(γ) ) = 1.20 ± 0.07 has e2γ(γ) e2γ(γ) been determined. This is consistent with a recent lattice QCD calculation, but larger than the expectation of Chiral Perturbation Theory (ChPT) at order O(p 4 ) and the previous KLOE value. Using the method to relate form factor and branching ratio described in the KLOE paper, the present result is also consistent with the form factor prediction based on a gauged nonlocal chiral quark model, but larger than that from ChPT at order O(p 6 ).

79 ASTRONOMY AND ASTROPHYSICS↗

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 OSTI2023

Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm

Directed self-assembly (DSA) of block copolymers (BCPs) is one of the most promising developments in the cost-effective production of nanoscale devices. The process makes use of the natural tendency for BCP melts to form nanoscale structures upon phase separation. The phase separation can be directed through the use of chemically patterned substrates to promote the formation of morphologies that are essential to the production of semiconductor devices. Moreover, the design of substrate pattern can be formulated as an optimization problem for which we seek optimal substrate designs that effectively produce given target morphologies. In this paper, we adopt a phase field model given by a nonlocal Cahn–Hilliard partial differential equation (PDE) based on the minimization of the Ohta–Kawasaki free energy, and present an efficient PDE-constrained optimization framework for the optimal design problem. The design variables are the locations of circular- or strip-shaped guiding posts that are used to model the substrate chemical pattern. To solve the ensuing optimization problem, we propose a variant of an inexact Newton conjugate gradient algorithm tailored to this problem. Additionally, we demonstrate the effectiveness of our computational strategy on numerical examples that span a range of target morphologies. Owing to our second-order optimizer and fast state solver, the numerical results demonstrate five orders of magnitude reduction in computational cost over previous work. The efficiency of our framework and the fast convergence of our optimization algorithm enable us to rapidly solve the optimal design problem in not only two, but also three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.

36 MATERIALS SCIENCE↗

DOE OSTI2020

New Grids of Pure-hydrogen White Dwarf NLTE Model Atmospheres and the HST/STIS Flux Calibration

Nonlocal thermodynamic equilibrium (NLTE) calculations of hot white dwarf (WD) model atmospheres are the cornerstone of modern flux calibrations for the Hubble Space Telescope and for the CALSPEC database. These theoretical spectral energy distributions (SEDs) provide the relative flux versus wavelength, and only the absolute flux level remains to be set by reconciling the measured absolute flux of Vega in the visible with the Midcourse Space Experiment values for Sirius in the mid-IR. The most recent SEDs calculated by the tlusty and tmap NLTE model atmosphere codes for the primary WDs G191-B2B, GD 153, and GD 71 show improved agreement to 1% from 1500 Å to 30 μm, in comparison to the previous 1% consistency only from 2000 Å to 5 μm. These new NLTE models of hot WDs now provide consistent flux standards from the far UV to the mid-IR.

79 ASTRONOMY AND ASTROPHYSICS↗