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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Improving modular bootstrap bounds with integrality

We propose methods that efficiently impose integrality — i.e., the condition that the coefficients of characters in the partition function must be integers — into numerical modular bootstrap. We demonstrate the method with a number of examples where it can be used to strengthen modular bootstrap results. First, we show that, with a mild extra assumption, imposing integrality improves the bound on the maximal allowed gap in dimensions of operators in theories with a U(1) c symmetry at c = 3, and reduces it to the value saturated by the SU(4) 1 WZW model point of c = 3 Narain lattices moduli space. Second, we show that our method can be used to eliminate all but a discrete set of points saturating the bound from previous Virasoro modular bootstrap results. Finally, when central charge is close to 1, we can slightly improve the upper bound on the scaling dimension gap.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Glow Discharge Boronization and Real-Time Boronization Using an Impurity Powder Dropper in LHD

In the Large Helical Device (LHD), boronization is utilized for wall conditioning, employing two distinct methods: glow discharge using diborane gas and the injection of boron powder into the plasma via an impurity powder dropper (IPD). Glow discharge boronization is conducted after maintenance when the vacuum vessel is exposed to air and just before the start of an experimental campaign. In contrast, real-time boronization using the IPD is performed during discharges. The distribution of boron on plasma-facing components was assessed through long-term material probes in the case of glow discharge and through numerical simulations for the IPD method. Results indicated non-uniform boron distributions in both cases. The impact of these boronization techniques on impurity levels and the lifetime of their effects were also examined. Both methods effectively reduced oxygen and iron in the plasma, with the iron impurities originating from the first wall. For glow discharge boronization, the reduction in oxygen levels persisted until the end of the experimental campaign, whereas the reduction in iron levels only lasted a few days. In the case of boron injection during long pulse discharges exceeding 200 s, the suppression of oxygen and iron was observed. The effect on iron quickly diminished within several seconds after the injection ended, whereas the effect on oxygen lasted more than 100 s. The difference in the lifetimes of the boronization effects is further discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Numerical simulations of three-dimensional ion crystal dynamics in a Penning trap using the fast multipole method

We simulate the dynamics, including laser cooling, of three-dimensional (3-D) ion crystals confined in a Penning trap using a newly developed molecular dynamics-like code. The numerical integration of the ions’ equations of motion is accelerated using the fast multipole method to calculate the Coulomb interaction between ions, which allows us to efficiently study large ion crystals with thousands of ions. In particular, we show that the simulation time scales linearly with ion number, rather than with the square of the ion number. By treating the ions’ absorption of photons as a Poisson process, we simulate individual photon scattering events to study laser cooling of 3-D ellipsoidal ion crystals. Initial simulations suggest that these crystals can be efficiently cooled to ultracold temperatures, aided by the mixing of the easily cooled axial motional modes with the low frequency planar modes. In our simulations of a spherical crystal of 1000 ions, the planar kinetic energy is cooled to several millikelvin in a few milliseconds while the axial kinetic energy and total potential energy are cooled even further. This suggests that 3-D ion crystals could be well suited as platforms for future quantum science experiments.

Zaris, John (ORCID:0009000196476323)↗
DOE OSTI2025

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

Here, this work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A modern concept of Lagrangian hydrodynamics

Here, we offer a modern interpretation of Lagrangian hydrodynamics as employed in Lagrangian simulations of compressible fluid flow. Our main result is to show that artificial viscosity, traditionally viewed as a numerical artifice to control unphysical oscillations in flows with shocks, actually represents a physical process and is necessary to derive accurate simulations in any compressible flow. We begin by reviewing the origins of two numerical devices, artificial viscosity and finite-volume methods. We proceed to construct a mathematical (PDE) model that incorporates those numerics and in which a new length scale, the observer, arises representing the discretization. Associated with that length scale, there are new inviscid fluxes that are the artificial viscosity as first formulated by Richtmyer and an artificial heat flux postulated by Noh but typically not included in Lagrangian codes. We discuss the connection of our results to bivelocity hydrodynamics. We conclude with some speculation as to the direction of future developments in multidimensional Lagrangian codes as computers get faster and have larger memories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Absorbing boundary conditions in material point method adopting perfectly matched layer theory

This study focuses on solving the numerical challenges of imposing absorbing boundary conditions for dynamic simulations in the material point method (MPM). To attenuate elastic waves leaving the computational domain, the current work integrates the Perfectly Matched Layer (PML) theory into the implicit MPM framework. The proposed approach introduces absorbing particles surrounding the computational domain that efficiently absorb outgoing waves and reduce reflections, allowing for accurate modeling of wave propagation and its further impact on geotechnical slope stability analysis. The study also includes several benchmark tests to validate the effectiveness of the proposed method, such as several types of impulse loading and symmetric and asymmetric base shaking. The conducted numerical tests also demonstrate the ability to handle large deformation problems, including the failure of elasto-plastic soils under gravity and dynamic excitations. The findings extend the capability of MPM in simulating continuous analysis of earthquake-induced landslides, from shaking to failure.

58 GEOSCIENCES↗
DOE OSTI2025

Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections

Subspace projection methods utilizing perturbative corrections have been proposed for computing the lowest few eigenvalues and corresponding eigenvectors of large Hamiltonian matrices. In this paper, we build upon these methods and introduce the term Subspace Projection with Perturbative Corrections (SPPC) method to refer to this approach. We tailor the SPPC for nuclear many-body Hamiltonians represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). We use the hierarchical structure of the NCSM Hamiltonian to partition the Hamiltonian as the sum of two matrices. The first matrix corresponds to the Hamiltonian represented in a small configuration space, whereas the second is viewed as the perturbation to the first matrix. Eigenvalues and eigenvectors of the first matrix can be computed efficiently. Because of the split, perturbative corrections to the eigenvectors of the first matrix can be obtained efficiently from the solutions of a sequence of linear systems of equations defined in the small configuration space. These correction vectors can be combined with the approximate eigenvectors of the first matrix to construct a subspace from which more accurate approximations of the desired eigenpairs can be obtained. We show by numerical examples that the SPPC method can be more efficient than conventional iterative methods for solving large-scale eigenvalue problems such as the Lanczos, block Lanczos and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The method can also be combined with other methods to avoid convergence stagnation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Score-based deterministic density sampling

We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density π given only its score ∇ log π. Our method approximates the Wasserstein gradient flow on KL($f_t$∥π) by learning the time-varying score ∇ log $f_t$ on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A randomized sketching trust-region secant method for low-memory dynamic optimization

The numerical solution of dynamic optimization problems is often limited by the memory required to store the state trajectory, which is used to evaluate the objective function and its derivatives. Recently, [R. Muthukumar et al., SIAM Journal on Optimization 31(2), pp. 1242–1275 (2021)] introduced a trust-region method for dynamic optimization that employs randomized sketching to compress the state trajectory, resulting in inexact derivative computations. By adaptively learning the sketch rank, the trust-region algorithm achieves rigorous convergence guarantees. Here, we extend this approach to use secant Hessian approximations. Due to the randomness introduced by the sketch, the traditional secant update formulae can produce poor Hessian approximations. In particular, the difference of two gradients, computed from two different sketches, may be inconsistent. To overcome this, we employ a sketched approximation of the Hessian application, in lieu of computing the gradient difference. We numerically demonstrate the improved stability of this approach on an example from PDE-constrained optimization.

dynamic optimization↗
DOE OSTI2026

Coulomb corrections for the nonflip and spin-flip electromagnetic 𝑝 ↑⁢ 𝐴 amplitudes

It is demonstrated that, within the eikonal approach, the Coulomb corrections to the elastic electromagnetic nonflip and spin-flip proton-nucleus amplitudes are identical when the two amplitudes share the same exponential form factors. This result allows Coulomb corrections to be computed numerically, and with high precision, for both electromagnetic and hadronic elastic 𝑝 ↑⁢ 𝐴 amplitudes in the massless-photon limit, including the effects of soft magnetic photon exchange. The method relies on analytical expressions and numerical integrations over a finite impact-parameter range with nonsingular integrands, providing a practical and systematically controlled framework for phenomenological applications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

A Finite Difference informed Random Walk solver for simulating radiation defect evolution in polycrystalline structures with strongly inhomogeneous diffusivity

Diffusivity of species and defects on grain boundaries is usually several orders of magnitude larger than that inside grains. Such strongly inhomogeneous diffusivity requires prohibitively high computational demands for modeling microstructural evolution. Here, this paper presents a highly-efficient numerical solver, combining the Finite Difference method and Random Walk model, designed for accurately modeling strongly inhomogeneous diffusion within polycrystalline structures. The proposed solver, termed Finite Difference informed Random Walk (FDiRW), integrates a customized Finite Difference (cFD) scheme tailored for fast diffusion along thin grain boundaries represented by a single-layer of nodes. Numerical experiments demonstrate that the FDiRW solver achieves an impressive efficiency gain of 1560x compared to traditional Finite Difference methods while maintaining accuracy, making it feasible for personal computer machines to handle diffusional systems with strongly inhomogeneous diffusivity across static polycrystalline microstructures. The model has been successfully applied to simulate radiation defect evolution, showcasing its scalability to engineering scales in both length and time dimensions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Out-of-time-ordered-correlators for the pure inverted quartic oscillator: classical chaos meets quantum stability

Out-of-time-ordered-correlators (OTOCs) have been suggested as a means to diagnose chaotic behavior in quantum mechanical systems. Recently, it was found that OTOCs display exponential growth for the inverted quantum harmonic oscillator, mirroring the fact that this system is classically and quantum mechanically unstable. In this work, I study OTOCs for the inverted anharmonic (pure quartic) oscillator in quantum mechanics, finding only oscillatory behavior despite the classically unstable nature of the system. For higher temperature, OTOCs seem to exhibit saturation consistent with a value of –2< x 2 > T < p 2 > T at late times. I provide analytic evidence from the spectral zeta-function and the WKB method as well as direct numerical solutions of the Schrödinger equation that the inverted quartic oscillator possesses a real and positive energy eigenspectrum, and normalizable wave-functions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A Particle Method for the Multispecies Landau Equation

Abstract The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as electrons and ions. Recently, a structure preserving deterministic particle method (Carrillo et al. in J. Comput. Phys. 7:100066, 2020) has been developed for the single species spatially homogeneous Landau equation. This method relies on a regularization of the Landau collision operator so that an approximate solution, which is a linear combination of Dirac delta distributions, is well-defined. Based on a weak form of the regularized Landau equation, the time dependent locations of the Dirac delta functions satisfy a system of ordinary differential equations. In this work, we extend this particle method to the multispecies case, and examine its conservation of mass, momentum, and energy, and decay of entropy properties. We show that the equilibrium distribution of the regularized multispecies Landau equation is a Maxwellian distribution, and state a critical condition on the regularization parameters that guarantees a species independent equilibrium temperature. A convergence study comparing an exact multispecies Bobylev-Krook-Wu (BKW) solution to the particle solution shows approximately 2nd order accuracy. Important physical properties such as conservation, decay of entropy, and equilibrium distribution of the particle method are demonstrated with several numerical examples.

Mathematics↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations

The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution bounds and limiting for the Euler equations through the kinetic representation provided by the Boltzmann equation, which allows for extending limiters designed for linear advection directly to the Euler equations. Given an arbitrary set of solution values to compute bounds over (e.g., numerical stencil) and a desired linear advection limiter, the proposed approach yields an analytic expression for the admissible region of particle distribution function values, which may be numerically integrated to yield a set of bounds for the density, momentum, and total energy. Further, these solution bounds are shown to preserve positivity of density/pressure/internal energy and, when paired with a limiting technique, can robustly resolve strong discontinuities while recovering high-order accuracy in smooth regions without any ad hoc corrections (e.g., relaxing the bounds). This approach is demonstrated in the context of an explicit unstructured high-order discontinuous Galerkin/flux reconstruction scheme for a variety of difficult problems in gas dynamics, including cases with extreme shocks and shock-vortex interactions. Furthermore, this work presents a foundation for limiting techniques for more complex macroscopic governing equations that can be derived from an underlying kinetic representation for which admissible solution bounds are not well-understood.

42 ENGINEERING↗
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
DOE OSTI2026

Neural entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws

We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined numerical discretization. While recent neural network architectures have successfully integrated classical numerical principles into learned models, most rely on prior knowledge of the governing equations or assume a fixed discretization. Our approach removes this dependency by embedding entropy-stable design principles into the learning process itself, enabling the discovery of physically consistent dynamics in a fully data-driven setting. By jointly learning both the flux function and a corresponding entropy, NESCFN promotes conservation and entropy dissipation, which is critical for long-term stability and fidelity in the system of hyperbolic conservation laws. Furthermore, numerical results demonstrate that the method achieves stability and conservation over extended time horizons and accurately captures shock propagation speeds, even without oracle access to future-time solution profiles in the training data.

Conservative flux form↗
DOE OSTI2025

Quantum entropy as a harbinger of factorizability

Deeply inelastic scattering (DIS) is a powerful probe for investigating the QCD structure of hadronic matter and testing the standard model (SM). DIS can be described through QCD factorization theorems which separate contributions to the scattering interaction arising from disparate scales — e.g ., with nonperturbative matrix elements associated with long distances and a perturbative hard scattering kernel applying to short-distance parton-level interactions. The fundamental underpinnings of factorization may be recast in the quantum-theoretic terms of entanglement, (de)coherence, and system localization in a fashion which sheds complementary light on the dynamics at work in DIS from QCD bound states. In this Letter, we propose and quantitatively test such a quantum-information theoretic approach for dissecting factorization in DIS and its domain of validity; we employ metrics associated with quantum entanglement such as a differential quantum entropy and associated Kullback-Leibler (KL) divergences in numerical tests. We deploy these methods on an archetypal quark-spectator model of the proton, for which we monitor quantum decoherence in DIS as underlying model parameters are varied. On this basis, we demonstrate quantitatively how factorization-breaking effects may be imprinted on quantum entropies in a kinematic regime where leading-twist factorization increasingly receives large corrections from finite- Q 2 effects; our findings suggest potential applications of quantum simulation to QCD systems and their interactions.

Deep inelastic scattering↗