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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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DOE OSTI2017

Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems

We propose optimal dimensionality reduction techniques for the solution of goal-oriented linear-Gaussian inverse problems, where the quantity of interest (QoI) is a function of the inversion parameters. These approximations are suitable for large-scale applications. In particular, we study the approximation of the posterior covariance of the QoI as a low-rank negative update of its prior covariance and prove optimality of this update with respect to the natural geodesic distance on the manifold of symmetric positive definite matrices. Assuming exact knowledge of the posterior mean of the QoI, the optimality results extend to optimality in distribution with respect to the Kullback--Leibler divergence and the Hellinger distance between the associated distributions. We also propose the approximation of the posterior mean of the QoI as a low-rank linear function of the data and prove optimality of this approximation with respect to a weighted Bayes risk. Both of these optimal approximations avoid the explicit computation of the full posterior distribution of the parameters and instead focus on directions that are well informed by the data and relevant to the QoI. These directions stem from a balance among all the components of the goal-oriented inverse problem: prior information, forward model, measurement noise, and ultimate goals. We illustrate the theory using a high-dimensional inverse problem in heat transfer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Deep Learning without Global Optimization by Random Fourier Neural Networks

Here we introduce a new training algorithm for deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov chain Monte Carlo sampling procedure to iteratively train network layers, avoiding global and gradient-based optimization while maintaining error control. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions, determined by network complexity. Additionally, it enables efficient learning of multiscale and high-frequency features, producing interpretable parameter distributions. Despite using sinusoidal basis functions, we do not observe Gibbs phenomena in approximating discontinuous target functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Intensity Distribution of the Three-Wave Diffraction from Dislocation Epitaxial Layers in the Reciprocal Space

The three-wave X-ray diffraction in strongly disordered epitaxial layers of GaN and ZnO is experimentally investigated. The charts of the intensity distribution in the reciprocal space are plotted in coordinates q{sub θ} and q{sub ϕ} for the most intensive three-wave combination (1010)/(1011) by means of subsequent θ- and ϕ-scanning. A nontrivial shape of the θ-sections of these contours at a distance from the ϕ center of reflection is revealed; it is different for different samples. For the θ-curves at the center of reflection, we observed a common peak that may be approximated by the Voigt function with a power-low decrease in the intensity at the wings; the decrease law (from–4.5 to–5.0) is found to be considerably greater than that for the similar curves of two-wave diffraction and not depending on the dislocation density and distribution in layers. In some films we observed a coarse-block structure; in addition, it follows from the distribution in the reciprocal space that these blocks are turned with respect to each other around a normal to the surface, which allows us to suggest the existence of low-angle boundaries between them, consisting exclusively of edge dislocations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Generation, dynamics, and correlations of the fission fragments' angular momenta

The generation of angular momentum in fissioning nuclei is not well understood. The predictions of different models disagree, particularly concerning the correlation between the fragments' angular momenta. In this article, a time-dependent collective Hamiltonian model is proposed to treat the generation of the angular momentum in the fission fragments due to the quantum uncertainty principle as well as the dynamics of the collective wave function during and after scission. The model is constructed in the framework of the frozen Hartree-Fock approximation using a Skyrme energy functional to extract deformations of the fission fragments as well as the interactions in a derived collective Hamiltonian. The fission reactions studied are $^{240}$Pu $\rightarrow$ $^{132}$Sn+$^{108}$Ru and $^{240}$Pu $\rightarrow$ $^{144}$Ba+$^{96}$Sr. The model can account for a large part of the angular momentum found in experimental data. The orientation of the angular momentum of each fragment is found to be mainly in the plane perpendicular to the fission axis, in agreement with the experiment. The magnitudes of the angular momenta in the two fragments are nearly uncorrelated, in agreement with the recent experimental data of Wilson et al., Nature (London) 590, 566 (2021). Some of the conclusions of the traditional collective vibration model are supported by the present model but some are not. Surprisingly, it is found that the angular momenta of the fragments are slightly correlated positively as in a wriggling mode. As a result, it is also found that the presence of an octupole deformation in a fragment can significantly increase the generated angular momentum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Robust Cross-correlation-based Measurement of Clump Sizes in Galaxies

Stars form in molecular complexes that are visible as giant clouds (∼10{sup 5−6} M{sub ⊙}) in nearby galaxies and as giant clumps (∼10{sup 8−9} M{sub ⊙}) in galaxies at redshifts z≈1–3. Theoretical inferences on the origin and evolution of these complexes often require robust measurements of their characteristic size, which is hard to measure at limited resolution and often ill-defined due to overlap and quasi-fractal substructure. We show that maximum and luminosity-weighted sizes of clumps seen in star formation maps (e.g., Hα) can be recovered statistically using the two-point correlation function (2PCF) if an approximate stellar surface density map is taken as the normalizing random field. After clarifying the link between Gaussian clumps and the 2PCF analytically, we design a method for measuring the diameters of Gaussian clumps with realistic quasi-fractal substructure. This method is tested using mock images of clumpy disk galaxies at different spatial resolutions and perturbed by Gaussian white noise. We find that the 2PCF can recover the input clump scale at ∼20% accuracy, as long as this scale is larger than the spatial resolution. We apply this method to the local spiral galaxy NGC 5194, as well as to three clumpy turbulent galaxies from the DYNAMO-HST sample. In both cases, our statistical measurements of Hα clump size agree with previous measurements and with the estimated Jeans lengths. However, the new measurements are free from subjective choices when fitting individual clumps.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

A Fast All-sky Radiation Model for Solar applications with Narrowband Irradiances on Tilted surfaces (FARMS-NIT): Part I. The clear-sky model

The solar energy industry often uses individual steps to empirically compute plane-of-array (POA) irradiance from horizontal irradiance and decompose it to narrow-wavelength bands. Conventional radiative transfer models designed for meteorological applications requires significant computing efforts in practice; however, they provide a physics-based solution of radiance and therefore are capable of computing spectral POA irradiances in a single step. In this study, we integrate the advantages of the current models and develop an innovative radiative transfer model, the Fast All-sky Radiation Model for Solar applications with Narrowband Irradiances on Tilted surfaces (FARMS-NIT), to efficiently compute irradiances on inclined photovoltaics (PV) panels for 2002 narrow-wavelength bands from 0.28 to 4.0 um. This study is reported in two parts. Part I presents the methodology and performance evaluation of the new model under clear-sky conditions. The Simple Model of the Atmospheric Radiative Transfer of Sunshine (SMARTS), which was designed to compute clear-sky irradiances, is employed to rapidly provide the optical properties of a given clear-sky atmosphere. The clear-sky radiances in the narrow-wavelength bands are computed by considering three paths of photon transmission and solving the radiative transfer equation with the single-scattering approximation. The Bi-directional Transmittance Distribution Function (BTDF) of aerosols is given by their single-scattering phase function with a correction using a two-stream approximation. The validation analysis confirms that FARMS-NIT has improved accuracy compared to TMYSPEC as evaluated by both surface observations and a state-of-the-art radiative transfer model. This model substantially improves computational efficiency compared to other radiative transfer models though it uses slightly more computing time than TMYSPEC. Part II of this study addresses the model in cloud-sky conditions and will be published as a companion paper.

14 SOLAR ENERGY↗
DOE OSTI2023

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler–Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to “physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Bayesian Monte Carlo Evaluation of Imperfect (n, 233 U) Data and Model

Conventional nuclear data evaluation methods using generalized linear least squares make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate to minimize the cost function (even for nonlinear models); the model (e.g., of neutron cross section) and experimental data (including covariance data) are without defect and prior PDFs of parameters and measured data are known perfectly. Neglect of covariance between model parameters and measured data in conventional evaluations contributes to imperfections. These assumptions are inherent to the generalized linear least squares minimization method commonly used for resolved resonance region neutron cross section evaluations but are often not justified due to the presence of non-normal PDFs, nonlinear models (e.g., R-matrix formalism), and inherent imperfections in data and models (e.g., imperfect covariance data). Here, these assumptions are removed in a mathematical framework of Bayes’ theorem, which is implemented using the Metropolis-Hastings Monte Carlo method. Most importantly, new parameters are introduced to parameterize discrepancies between the theoretical model and measured data to quantify judgement about discrepancies or imperfections in a reproducible manner. An evaluation of 233U in the eV region using the ENDF-B/VIII.0 library and transmission data (Guber et al.) is presented, and posterior parameters are compared to those obtained by conventional evaluation methods. This example illustrates the effects of removing the most harmful assumption: that of model-data perfection.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Conductive Ink with Circular Life Cycle for Printed Electronics

Electronic waste carries energetic costs and an environmental burden rivaling that of plastic waste due to the rarity and toxicity of the heavy-metal components. Recyclable conductive composites are introduced for printed circuits formulated with polycaprolactone (PCL), conductive fillers, and enzyme/protectant nanoclusters. Circuits can be printed with flexibility (breaking strain ≈80%) and conductivity (≈2.1 × 10 4 S m -1 ). These composites are degraded at the end of life by immersion in warm water with programmable latency. Approximately 94% of the functional fillers can be recycled and reused with similar device performance. The printed circuits remain functional and degradable after shelf storage for at least 7 months at room temperature and one month of continuous operation under electrical voltage. Here, the present studies provide composite design toward recyclable and easily disposable printed electronics for applications such as wearable electronics, biosensors, and soft robotics.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A simple finite element method for the Stokes equations

The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Effects of La Doping and Zn or O Vacancy on the Magnetic Property of ZnO

Research on the magnetic origin and mechanism of La-doped ZnO system has been controversial. To solve this problem, we studied the effects of La doping and Zn or O vacancy on the magnetic property of ZnO using geometry optimization and energy calculation on the basis of first-principle generalized gradient approximation method of density functional theory. The electronic structures and magnetic properties of undoped ZnO, La-doped ZnO system, and systems with coexisting La doping and Zn or O vacancies were calculated. Results showed that the systems of La-doped ZnO and the coexistence of La doping and O vacancy are nonmagnetic. In addition, the system of La replacing Zn and one Zn vacancy exhibits long-range orderly ferromagnetism, and the Curie temperature of the doping system can achieve room temperature. The magnetism source of the systems with La doping and Zn vacancy coexisting in ZnO demonstrates strong hybrid coupling electron exchange effects existing among Zn-4s, Zn-3p, O-2p, and La-5s orbits that are nearest to the Zn vacancy. The next nearest distance between doping and Zn vacancy leads to the lowest formation energy and highest stability under the same doping condition.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Effect of Fe Doping and Point Defects (V{sub O} and V{sub Sn}) on the Magnetic Properties of SnO{sub 2}

We investigated the effects of Fe doping and point defects (oxygen and tin vacancies, V{sub O} and V{sub Sn}, respectively) on the ferromagnetism of SnO{sub 2} through first-principles calculations by using generalized gradient approximation + U under density functional theory. Calculation results show that Fe-doped SnO{sub 2} with V{sub O} or V{sub Sn} exhibit long-range ordered ferromagnetism and Curie temperature above room temperature. The system has different magnetic properties with different doping modes, which are beneficial to the magnetic adjustment of dilute magnetic semiconductor (DMS). The double-exchange effects among the electrons of O–2p and Fe–3d states are the origin of ferromagnetism in Sn{sub 15}FeO{sub 31}. Similarly, ferromagnetism in Sn{sub 14}FeO{sub 32} is derived from the double-exchange effects among the electrons of O–2p and Fe–3d states. These effects are produced by hole carriers after complexes form by Fe doping and V{sub O} or V{sub Sn}. Simultaneously, Sn{sub 14}FeO{sub 32} shows a half-metallic behavior, thus resulting in 100% conduction hole polarizability, which is highly beneficial to DMSs as a hole-injection source. Moreover, results also show that the decreased distance between Fe and vacancies (V{sub O} or V{sub Sn}) lowers formation energy and thus increases the system stability.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A hybrid meshfree discretization to improve the numerical performance of peridynamic models

Efficient and accurate calculation of spatial integrals is of major interest in the numerical implementation of peridynamics (PD). The standard way to perform this calculation is a particle-based approach that discretizes the strong form of the PD governing equation. This approach has rapidly been adopted by the PD community since it offers some advantages. Additionally, it is computationally cheaper than other available schemes, can conveniently handle material separation, and effectively deals with nonlinear PD models. Nevertheless, PD models are still computationally very expensive compared with those based on the classical continuum mechanics theory, particularly for large-scale problems in three dimensions. This results from the nonlocal nature of the PD theory which leads to interactions of each node of a discretized body with multiple surrounding nodes. Here, we propose a new approach to significantly boost the numerical efficiency of PD models. We propose a discretization scheme that employs a simple collocation procedure and is truly meshfree; i.e., it does not depend on any background integration cells. In contrast to the standard scheme, the proposed scheme requires a much smaller set of neighboring nodes (keeping the same physical length scale) to achieve a specific accuracy and is thus computationally more efficient. Our new scheme is applicable to the case of linear PD models and within neighborhoods where the solution can be approximated by smooth basis functions. Therefore, to fully exploit the advantages of both the standard and the proposed schemes, a hybrid discretization is presented that combines both approaches within an adaptive framework. The high performance of the developed framework is illustrated by several numerical examples, including brittle fracture and corrosion problems in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2020

Particlization in fluid dynamical simulations of heavy-ion collisions: The IS3D module

The IS3D particlization module simulates the emission of hadrons from heavy-ion collisions via Monte-Carlo sampling of the Cooper–Frye formula which converts fluid dynamical information into local phase-space distributions for hadrons. The code package includes multiple choices for the non-equilibrium correction to these distribution functions: the 14-moment approximation, first-order Chapman–Enskog expansion, and two types of modified equilibrium distributions. This makes it possible to explore to what extent heavy-ion experimental data are sensitive to different choices for δf n , presently the main source of theoretical uncertainty in the particlization stage. Here, we validate our particle sampler with a high degree of precision by generating several million hadron emission events from a longitudinally boost-invariant hypersurface and comparing the event-averaged particle spectra and space–time distributions to the Cooper–Frye formula.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Stochastic scheduling of generating units with weekly energy storage: A hybrid decomposition approach

We propose a solution method for the large-scale stochastic unit commitment (SUC) problem with weekly-dispatched energy storage and significant weather-dependent stochastic generating capacity. Weekly storage facilities that mostly charge during weekends and discharge during weekdays require a weekly scheduling of generating units, which result in a large-scale optimization problem. This SUC problem is formulated as a two-stage stochastic model and we use the conditional value-at-risk as a risk measure. Using a Benders framework, the proposed solution method decomposes the problem into a mixed-integer linear master problem and linear and continuous subproblems. The master problem corresponds to the first-stage decisions throughout the week and includes all the commitment (binary) variables and their corresponding constraints. The subproblems correspond to the actual dispatch of the generating units on a weekly basis. Based on the success of column-and-constraint generation algorithms to solve robust optimization problems, we improve the low communication between the master problem and the subproblems in the standard Benders decomposition by adding primal variables and constraints from the subproblems to the master problem, which provides a better approximation of the recourse function. Furthermore, our computational experiments demonstrate the effectiveness of the proposed decomposition method using an instance of the South Carolina synthetic system with 90 generating units under 40 scenarios.

25 ENERGY STORAGE↗
DOE OSTI2021

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Double Diffusion Maps and their Latent Harmonics for scientific computations in latent space

In this work, we introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion Maps on those latent coordinates allows the approximation of the reduced dynamical models. This second round enables mapping the latent space coordinates back to the full ambient space (what is called lifting); it also enables the approximation of full state functions of interest in terms of the reduced coordinates. In our work, we develop and test three different reduced numerical simulation methodologies, either through pre-tabulation in the latent space and integration on the fly or by going back and forth between the ambient space and the latent space. The data-driven latent space simulation results, based on the three different approaches, are validated through (a) the latent space observation of the full simulation through the Nyström Extension formula, or through (b) lifting the reduced trajectory back to the full ambient space, via Latent Harmonics. Latent space modeling often involves additional regularization to favor certain properties of the space over others, and the mapping back to the ambient space is then constructed mostly independently from these properties; here, we use the same data-driven approach to construct the latent space and then map back to the ambient space.

97 MATHEMATICS AND COMPUTING↗