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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Analytical Modeling of Metal Foam Composite Phase Change Materials (PCM) in Thermal Energy Storage Using Asymptotic Analysis

The use of phase change materials (PCMs) for thermal energy storage can release or absorb a significant amount of latent heat during the freezing or melting process, offering a higher energy storage density. One of the main drawbacks of PCMs is their low thermal conductivity, resulting in poor thermal performance. Recent research has attempted to enhance heat transfer and increase the thermal conductivity of PCMs, including the use of metal foams. However, modeling the metal foam composite PCM using conventional methods is computationally expensive. This paper proposes an asymptotic solution for a Stefan-like problem subject to a convective boundary for outward solidification in a hollow cylinder, capable of predicting the freeze-melt cycle of the metal foam composite PCM. Specifically, three temporal regimes and four spatial layers are considered in the asymptotic analysis for each phase change process. The thermal conductivity is calculated by a theoretical three-dimensional tetrakaidecahedron model, while other thermophysical properties are obtained using the method of volume averaging. The results are verified with numerical data and validated against experimental data in the literature. The presented analytical modeling framework could have the potential to be applied to other types of composite PCMs with considerably lower computational costs compared with conventional methods.

analytical model↗
DOE OSTI2023

Non-asymptotic analysis of ensemble Kalman updates: effective dimension and localization

Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in applications where generating each particle is costly. This paper develops a non-asymptotic analysis of ensemble Kalman updates, which rigorously explains why a small ensemble size suffices if the prior covariance has moderate effective dimension due to fast spectrum decay or approximate sparsity. Here, we present our theory in a unified framework, comparing everal implementations of ensemble Kalman updates that use perturbed observations, square root filtering and localization. As part of our analysis, we develop new dimension-free covariance estimation bounds for approximately sparse matrices that may be of independent interest.

Mathematics↗
DOE OSTI2022

Selected results from full-core hydrogen redistribution asymptotic analysis in YH-moderated heat-pipe cooled microreactor

Yttrium hydride is the main candidate for moderation of high temperature nuclear microreactors . This is due to its high thermal stability and relatively high hydrogen retention at temperatures exceeding 870 C. One of the main issues associated with the use of yttrium hydride is that, when exposed to temperature, stress, or concentration gradients, the hydrogen contained in the metallic matrix tends to redistribute and leak from the moderating elements, potentially leading to reactivity losses and power swings. This paper is focused on presenting selected results from the asymptotic hydrogen redistribution analysis performed on the Simplified Microreactor Benchmark Assessment (SiMBA) problem, a microreactor core conceptual design developed at INL. The analysis is based on full core analysis, relies uniquely on Bison to perform hydrogen redistribution calculations, and discusses the physical causes of the reactivity feedback. It was found that the feedback is negative, but it is one order of magnitude lower than the one found for the empire reactor unit-cell. This is due to the lower axial temperature gradient together with the effect of the reflector.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Droplet formation simulation using mixed finite elements

Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate the size of a droplet but fails to approximate the shape of the droplet. This is due to a highly nonlinear flow description near the point where the first pinch-off happens. A one-dimensional axisymmetric mathematical model was first developed by Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] using asymptotic analysis. This asymptotic approach to the Navier–Stokes equations leads to a universal scaling explaining the self-similar nature of the solution. Numerical models for the one-dimensional model were developed using the finite difference [Eggers and Dupont, “Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and finite element method [Ambravaneswaran et al., “Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops,” Phys. Fluids 14, 2606–2621 (2002)]. The focus of this study is to provide a robust computational model for one-dimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation. The code is verified using the Method of Manufactured Solutions and validated using previous experimental studies done by Zhang and Basaran [“An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184–1203 (1995)]. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinch-off phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Efficient phase-factor evaluation in quantum signal processing

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem. A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures. However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits. Existing methods require the use of variable precision arithmetic and can only be applied to polynomials of a relatively low degree. We present here an optimization-based method that can accurately compute the phase factors using standard double precision arithmetic operations. We demonstrate the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and quantum linear system problems. Furthermore, our numerical results show that the optimization algorithm can find phase factors to accurately approximate polynomials of a degree larger than 10000 with errors below 10 -12 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Gravitational memory and compact extra dimensions

Here we develop a general formalism for treating radiative degrees of freedom near $\mathscr{I}^+$ in theories with an arbitrary Ricci-flat internal space. These radiative modes are encoded in a generalized news tensor which decomposes into gravitational, electromagnetic, and scalar components. We find a preferred gauge which simplifies the asymptotic analysis of the full nonlinear Einstein equations and makes the asymptotic symmetry group transparent. This asymptotic symmetry group extends the Bondi–Metzner–Sachs (BMS) group to include angle-dependent isometries of the internal space. We apply this formalism to study memory effects, which are expected to be observed in future experiments, that arise from bursts of higher-dimensional gravitational radiation. We outline how measurements made by gravitational wave observatories might probe properties of the compact extra dimensions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Numerical validation of scaling laws for stratified turbulence

Recent theoretical progress using multiscale asymptotic analysis has revealed various possible regimes of stratified turbulence. Notably, buoyancy transport can either be dominated by advection or diffusion, depending on the effective Péclet number of the flow. Two types of asymptotic models have been proposed, which yield measurably different predictions for the characteristic vertical velocity and length scale of the turbulent eddies in both diffusive and non-diffusive regimes. The first, termed a ‘single-scale model’, is designed to describe flow structures having large horizontal and small vertical scales, while the second, termed a ‘multiscale model’, additionally incorporates flow features with small horizontal scales, and reduces to the single-scale model in their absence. By comparing predicted vertical velocity scaling laws with direct numerical simulation data, we show that the multiscale model correctly captures the properties of strongly stratified turbulence within regions dominated by small-scale isotropic motions, whose volume fraction decreases as the stratification increases. Meanwhile its single-scale reduction accurately describes the more orderly, layer-like, quiescent flow outside those regions.

Mechanics↗
DOE OSTI2021

Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: $\phi$ 3 QFT in 6 Dimensions

We analyze the asymptotically free massless scalar $\phi$ 3 quantum field theory in 6 dimensions, using resurgent asymptotic analysis to find the trans-series solutions which yield the non-perturbative completion of the divergent perturbative solutions to the Kreimer–Connes Hopf-algebraic Dyson–Schwinger equations for the anomalous dimension. This scalar conformal field theory is asymptotically free and has a real Lipatov instanton. In the Hopf-algebraic approach we find a trans-series having an intricate Borel singularity structure, with three distinct but resonant non-perturbative terms, each repeated in an infinite series. These expansions are in terms of the renormalized coupling. The resonant structure leads to powers of logarithmic terms at higher levels of the trans-series, analogous to logarithmic terms arising from interactions between instantons and anti-instantons, but arising from a purely perturbative formalism rather than from a semi-classical analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Quantum Hamilton-Jacobi theory, spectral path integrals, and exact WKB analysis

We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi (HJ) theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in quantum theory beyond approximation schemes. The canonical transformation enables one to set the new Hamiltonian to constant or zero, but keeps the information about solution in Hamilton’s characteristic function. To benefit from this in quantum theory, one must work with a formulation in which classical Hamiltonian is used. This uniquely points to phase space path integral. However, the main variable in HJ formalism is energy, not time. Thus, we are led to consider the Fourier transform of the path integral, the spectral path integral Z ˜ ( E ) . The evaluation of path integrals reduces to determining the quantum Hamilton characteristic functions (which can be achieved via an asymptotic analysis) and a discrete sum over the quantum period lattice, generalizing Gutzwiller’s sum. Published by the American Physical Society 2025

Türe, Mustafa (ORCID:0009000975968618)↗
DOE OSTI2021

Power spectrum and form factor in random diagonal matrices and integrable billiards

Triggered by a controversy surrounding a universal behavior of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral universality class, and examine how the power spectrum and the form factor get affected by two-sided truncations of RDM spectra. Having developed a nonperturbative description of both statistics, we perform their detailed asymptotic analysis to demonstrate explicitly how a traditional assumption (lying at the heart of the controversy) – that the power spectrum is merely determined by the spectral form factor – breaks down for truncated spectra. This observation has important consequences as we further argue that bounded quantum systems with integrable classical dynamics are described by heavily truncated rather than complete RDM spectra. High-precision numerical simulations of semicircular and irrational rectangular billiards lend independent support to these conclusions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

High dimensional binary classification under label shift: phase transition and regularization

Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of the label shift, e.g., balancing the training data. However, these methods often consider the underparametrized regime, where the sample size is much larger than the data dimension. The research under the overparametrized regime is very limited. Here, to bridge this gap, we propose a new asymptotic analysis of the Fisher Linear Discriminant classifier for binary classification with label shift. Specifically, we prove that there exists a phase transition phenomenon: Under certain overparametrized regime, the classifier trained using imbalanced data outperforms the counterpart with reduced balanced data. Moreover, we investigate the impact of regularization to the label shift: The aforementioned phase transition vanishes as the regularization becomes strong.

binary classification↗
DOE OSTI2026

A hybrid Monte Carlo-deterministic second moment method with efficient variance reduction

In this work, we present a hybrid method that combines Monte Carlo with deterministic finite element methods to solve a linear Boltzmann transport equation. Our hybrid method runs orders of magnitude faster than Monte Carlo, without sacrificing accuracy, for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material. We believe that this is the first demonstration of a hybrid Second Moment Method in more than one spatial dimension, the first to consider more than one material, and the first to use variance reduction. Our variance reduction approach arises from an asymptotic analysis in which we show that the magnitude of the scattering source grows without bound. We transform the problem to compute the deviation of the radiation intensity from isotropy. The magnitude of the source in the transformed problem is bounded, and the quality of the hybrid method solution is dramatically improved by a substantial reduction in the variance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. Here, a formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

MATEY: multiscale adaptive transformer models for spatiotemporal physical systems

Accurate representation of the multiscale features in spatiotemporal physical systems using vision transformer architectures requires extremely long, computationally prohibitive token sequences. To address this issue, we propose two novel adaptive tokenization schemes that dynamically adjust patch sizes based on local features: one ensures convergent behavior to uniform patch refinement, while the other offers better computational efficiency. Moreover, we present a set of spatiotemporal attention schemes, where the temporal or axial spatial dimensions are decoupled, to evaluate their baseline computational and data efficiencies and to determine whether adaptive tokenization can improve this performance. We assess the performance of the proposed multiscale adaptive model, MATEY, in a sequence of experiments. Compared to a full spatiotemporal attention scheme or a scheme that decouples only the temporal dimension, we find that fully decoupled axial attention is less efficient and expressive, requiring more training time and model parameters to achieve the same accuracy. The experiments on the adaptive tokenization schemes show that, compared to a uniformly refined model, the proposed schemes achieve comparable or improved accuracy at a much lower cost in the tested two-dimensional settings. While the asymptotic analysis suggests the potential for favorable scaling, empirical validation at substantially longer sequence lengths remains to be performed in future work. Finally, we demonstrate in two fine-tuning tasks featuring different physics that models pretrained on PDEBench data outperform the ones trained from scratch, especially in the low data regime with frozen attention.

adaptive tokenization↗
DOE OSTI2022

Precoder Design for Physical-Layer Security and Authentication in Massive MIMO UAV Communications

Supporting reliable and seamless wireless connectivity for unmanned aerial vehicles (UAVs) has recently become a critical requirement to enable various different use cases of UAVs. Due to their widespread deployment footprint, cellular networks can support beyond visual line of sight (BVLOS) communications for UAVs. In this paper, we consider cellular connected UAVs (C-UAVs) that are served by massive multiple input-multiple-output (MIMO) links to extend coverage range, while also improving physical layer security and authentication. Here, we consider Rician channel and propose a novel linear precoder design for transmitting data and artificial noise (AN). We derive the closed-form expression of the ergodic secrecy rate of CUAVs for both conventional and proposed precoder designs. In addition, we obtain the optimal power splitting factor that divides the power between data and AN by asymptotic analysis. Then, we apply the proposed precoder design in the fingerprint embedding authentication framework, where the goal is to minimize the probability of detection of the authentication tag at an eavesdropper. In simulation results, we show the superiority of the proposed precoder in both secrecy rate and the authentication probability considering moderate and large number of antenna massive MIMO scenarios.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

Risk-Adaptive Experimental Design for High-Consequence Systems: LDRD Final Report

Constructing accurate statistical models of critical system responses typically requires an enormous amount of data from physical experiments or numerical simulations. Unfortunately, data generation is often expensive and time consuming. To streamline the data generation process, optimal experimental design determines the 'best' allocation of experiments with respect to a criterion that measures the ability to estimate some important aspect of an assumed statistical model. While optimal design has a vast literature, few researchers have developed design paradigms targeting tail statistics, such as quantiles. In this project, we tailored and extended traditional design paradigms to target distribution tails. Our approach included (i) the development of new optimality criteria to shape the distribution of prediction variances, (ii) the development of novel risk-adapted surrogate models that provably overestimate certain statistics including the probability of exceeding a threshold, and (iii) the asymptotic analysis of regression approaches that target tail statistics such as superquantile regression. To accompany our theoretical contributions, we released implementations of our methods for surrogate modeling and design of experiments in two complementary open source software packages, the ROL/OED Toolkit and PyApprox.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Asymptotic hydrogen redistribution analysis in yttrium-hydride-moderated heat-pipe-cooled microreactors using DireWolf

Yttrium hydride (YH x ) is one of the materials being considered for moderating thermal and epithermal nuclear microreactors. One potential issue with YH x use is that the hydrogen redistributes in the hydride when thermal and concentration gradients are present. This hydrogen redistribution leads to spatial gradients in the hydrogen concentration, thus affecting neutron transport in the reactor. Here, by building upon observations in prior works, this paper aims to gain a better understanding of the reactivity feedback associated with such hydrogen redistributions. In particular, we wish to understand the sign (+/–) of the hydrogen redistribution neutronic feedback, its order of magnitude, and its underlying physical causes. To achieve this goal, the DireWolf multiphysics software driver was used to solve the coupled radiation transport, heat transfer, heat pipe two-phase flow, and hydrogen redistribution equations for the Simplified Microreactor Benchmark Assessment (SiMBA) problem, a full-core microreactor numerical benchmark developed at Idaho National Laboratory.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Neuromorphic Graph Algorithms

Graph algorithms enable myriad large-scale applications including cybersecurity, social network analysis, resource allocation, and routing. The scalability of current graph algorithm implementations on conventional computing architectures are hampered by the demise of Moore’s law. We present a theoretical framework for designing and assessing the performance of graph algorithms executing in networks of spiking artificial neurons. Although spiking neural networks (SNNs) are capable of general-purpose computation, few algorithmic results with rigorous asymptotic performance analysis are known. SNNs are exceptionally well-motivated practically, as neuromorphic computing systems with 100 million spiking neurons are available, and systems with a billion neurons are anticipated in the next few years. Beyond massive parallelism and scalability, neuromorphic computing systems offer energy consumption orders of magnitude lower than conventional high-performance computing systems. We employ our framework to design and analyze new spiking algorithms for shortest path and dynamic programming problems. Our neuromorphic algorithms are message-passing algorithms relying critically on data movement for computation. For fair and rigorous comparison with conventional algorithms and architectures, which is challenging but paramount, we develop new models of data-movement in conventional computing architectures. This allows us to prove polynomial-factor advantages, even when we assume a SNN consisting of a simple grid-like network of neurons. To the best of our knowledge, this is one of the first examples of a rigorous asymptotic computational advantage for neuromorphic computing.

97 MATHEMATICS AND COMPUTING↗