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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 19 records
All sourcesNASA NTRSDOE OSTI
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 OSTI2020

Experimental Validation of Calorimetric Electron Capture Spectral Theory with 193 Pt

Using microcalorimeters, a high statistics, high-resolution calorimetric spectrum of electron capture in 163 Ho can be used to determine the neutrino mass. The spectral shape can be calculated from first principles with various assumptions and approximations. To determine the validity of these choices, the theoretical calculations must be compared to data from multiple isotopes. In this work, new calorimetric data for a 193 Pt-in-Pt absorber measured with a transition edge sensor are presented and compared to theoretical calculations and values from the literature.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Introduction to spectral line shape theory

Spectral line-shape models are an important part of understanding high-energy-density (HED) plasmas. Models are needed for calculating opacity of materials and can serve as diagnostics for astrophysical and laboratory plasmas. However, much of the literature on line shapes is directed toward specialists. This perspective makes it difficult for non-specialists to enter the field. We have two broad goals with this topical review. First, we aim to give information so that others in HED physics may better understand the current field. Additionally, this first goal may help guide future experiments to test different aspects of the theory. Second, we provide an introduction for those who might be interested in line-shape theory, and enough materials to be able to navigate the field and the literature. We give a high-level overview of line broadening process, as well as dive into the formalism, available methods, and approximations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Combining geometric-optical and spectral invariants theories for modeling canopy fluorescence anisotropy

The spectral invariants theory ( p -theory) has received much attention in the field of quantitative remote sensing over the past few decades and has been adopted for modeling of canopy solar-induced chlorophyll fluorescence (SIF). However, the spectral invariant properties (SIP) in simple analytical formulae have not been applied for modeling canopy fluorescence anisotropy primarily because they are parameterized in terms of leaf total scattering, which precludes the differentiation between forward and backward leaf SIF emissions. In this study, we have developed the canopy-SIP SIF model by combining geometric-optical (GO) theory to account for asymmetric leaf SIF forward and backward emissions at the first-order scattering and by modeling multiple scattering based on the p-theory, thus avoiding the dependence on radiative transfer models. The applicability of the model simulations especially over 3D heterogeneous canopies was improved by incorporating canopy structure through multi-angular clumping index, and by modeling single scattering from the four components of the scene in view according to the GO approach. The results show good consistency with both the state-of-the-art SIF models and multi-angular field SIF observations over grass and chickpea canopies. Further, the coefficient of determination (R²) between the simulated SIF and field measurements was 0.75 (red) and 0.74 (far-red) for chickpea, and 0.65 (both red and far-red) for grass. The average relative error was approximately 3% for 1D homogeneous scenes when comparing the canopy-SIP SIF model simulations to the SCOPE model simulations, and around 4% for the 3D heterogeneous scene when comparing to the LESS model simulations. The results indicate that the proposed approach for separating asymmetric leaf SIF emissions is a robust way to keep a balance between satisfactory simulation accuracy and efficiency. Model simulations suggest that neglecting the leaf SIF asymmetry can lead to an underestimation of canopy red SIF by 6.3% to 42.6% for various leaf biochemical and canopy structural parameters. This study presents a simple but efficient analytical approach for canopy fluorescence modeling, with potential for large-scale canopy fluorescence simulations.

3D heterogeneous structure↗
DOE OSTI2021

Understanding Discrete Fracture Networks Through Spectral Graph Theory

Discrete Fracture Network models (DFNs) are used to simulate fluid flow and particle transport through fracture networks in low permeability rock. Understanding these processes are essential in many subsurface applications, such as environmental restoration of contaminated fractured media, CO 2 sequestration, detection of low-level nuclear tests, and hydrocarbon extraction. Compared with other models, DFNs allow for incorporation of a wider range of network characteristics but have substantially greater computation cost. These networks can be represented with graphs, allowing the use of graph theory tools to study the networks. I used Python to simulate flow and transport on a range of DFNs and analyzed these networks using methods from network analysis and spectral graph theory. My purpose was to find ways to gain insight about flow and transport on DFNs using these graph representations, bypassing the computationally intensive meshing typically required. My work is still in progress, but I have discovered several interesting trends and patterns that I believe could be useful towards my goal. If I am able to bring these results to fruition, they will aid subsurface geologists in extracting flow and transport information about fracture networks more efficiently.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Discrete Green’s functions and spectral graph theory for computationally efficient thermal modeling

Here, this work concerns solutions of the heat equation with the spectral graph method, for which the temperature is defined at discrete points in the domain and the spatial relationship among the points is described by a graph. The heat equation on the graph is solved using matrix techniques involving the eigenvectors and eigenvalues of the Laplacian matrix. The spectral graph approach precludes the computationally intensive meshing and numerous time-integration steps of the finite element method. In the present work, the spectral graph method is extended to include heat loss at the boundaries with a generalized boundary condition, and physics-based edge weights are introduced which simplify the calibration process. From this approach a discrete Green’s function is defined which allows for solutions under a variety of heating conditions including: space-varying initial conditions; time-and-space varying internal heating; and, time-and-space-varying heating at boundaries of type 1 (Dirichlet), type 2 (Neumann) and type 3 (Robin). Results are provided for benchmark heat transfer problems in one spatial dimension and in three spatial dimensions, and verification is provided by comparison with exact analytical solutions and finite difference solutions. The spectral graph method converges within 0.4% error of the analytical solution. The practical utility of the approach is demonstrated by thermal simulation of a multilayer additive manufacturing process. The spectral graph results are compared to experimentally-obtained temperature data for two metal parts, with error less than 5% of the experimental measurements, with computation time less than one minute on a desktop computer.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A radiative transfer model for solar induced fluorescence using spectral invariants theory

Solar Induced chlorophyll Fluorescence (SIF) shows promise as an approach for estimating gross primary production (GPP) remotely. However, sun-target-sensor geometry and within-canopy absorption of SIF can alter the relationship between measured SIF and GPP, because sensors can only retrieve some unknown fraction of the total emitted SIF. Radiative transfer models that allow for variation in canopy structure and sensor angles are therefore needed to properly interpret SIF measurements. Spectral invariants allow decoupling of the wavelength-independent canopy structure and the wavelength-dependent leaf and soil spectrum in the radiative transfer process. Here we develop a simple analytical Fluorescence Radiative Transfer model based on Escape and Recollision probability (FluorRTER) to investigate the impact of canopy structure and sun-target-sensor geometry on SIF emissions. SIF simulations using the FluorRTER model agreed well the one-dimensional Soil-Canopy Observation of Photochemistry and Energy balance (SCOPE) model and the three-dimensional Fluorescence model with Weighted Photon Spread (FluorWPS) model. The fractional vegetation cover (FVC) and clumping effect have a large influence the SIF emission of 3D discontinuous canopies. For a moderate solar zenith angle (30°) and a clumped canopy (FVC?=?0.6), the difference between the directional observed SIF of a 3D discontinuous canopy and a 1D homogeneous canopy was as large as 43.2% and 38.4% for Photosystem I?+?II fluorescence at 685?nm and at 740?nm, respectively. By bridging the gap between observed SIF and total emitted SIF over 3D heterogeneous vegetation canopies, the FluorRTER model can assist with the angular normalization of SIF measurements and enable the more robust interpretation of how variations in SIF from directional and hemispherical in-situ, airborne and satellite observations relate to leaf and whole-canopy physiological processes.

Zeng, Yelu↗
DOE OSTI2021

Harmonic analysis of 2d CFT partition functions

We apply the theory of harmonic analysis on the fundamental domain of SL(2, Z) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space H/SL(2, Z), and of target space moduli space O(c, c; Z)\O(c, c; R)/O(c)×O(c). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS 3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Right-handed neutrinos and U(1) X symmetry-breaking

In [1] we proposed a model for Heterotic F-theory duality with Wilson line symmetry-breaking and a 4 + 1 split of the F-theory spectral divisor. One goal of this note is to call attention to the existence of right-handed neutrinos in our F-theory model. As pointed out in section 4 of [2] such existence may be evidence for the U(1) X -symmetry that remains after the Higgsing of E 8 via E 8 $\Rightarrow$ SU(5) gauge ⊕ [SU(4) ⊕ U(1) X ] Higgs occasioned by the 4 + 1 split of the spectral divisor. In addition, as a result of the $\mathbb{Z}$ 2 -action that supports the Wilson line we argue that the U(1) X -symmetry is, in fact, broken to $\mathbb{Z}$ 2 -matter parity. Finally we identify co-dimension 3 singularities which determine Yukawa couplings for the MSSM matter fields.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Classifying photonic topology using the spectral localizer and numerical K -theory

Recently, the spectral localizer framework has emerged as an efficient approach for classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous definitions for concepts such as topological solitons and topological dynamics, where a system’s occupation induces a local change in its topology due to nonlinearity. For systems embedded in radiative environments that do not possess a shared bulk spectral gap, this framework enables the identification of local topology and shows that local topological protection is preserved despite the lack of a common gap. However, as the spectral localizer framework is rooted in the mathematics of C*-algebras, and not vector bundles, understanding and using this framework requires developing intuition for a somewhat different set of underlying concepts than those that appear in traditional approaches for classifying material topology. In this tutorial, we introduce the spectral localizer framework from a ground-up perspective and provide physically motivated arguments for understanding its local topological markers and associated local measure of topological protection. In doing so, we provide numerous examples of the framework’s application to a variety of topological classes, including crystalline and higher-order topology. We then show how Maxwell’s equations can be reformulated to be compatible with the spectral localizer framework, including the possibility of radiative boundary conditions. To aid in this introduction, we also provide a physics-oriented introduction to multi-operator pseudospectral methods and numerical K-theory, two mathematical concepts that form the foundation for the spectral localizer framework. Finally, we provide some mathematically oriented comments on the C*-algebraic origins of this framework, including a discussion of real C*-algebras and graded C*-algebras that are necessary for incorporating physical symmetries. Looking forward, we hope that this tutorial will serve as an approachable starting point for learning the foundations of the spectral localizer framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Temporally-consistent koopman autoencoders for forecasting dynamical systems

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the Temporally-Consistent Koopman Autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE’s superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Symmetries and spectral statistics in chaotic conformal field theories

We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic properties of the spectrum from those which are a consequence of Virasoro symmetry and modular invariance. We argue that random matrix universality in the near-extremal limit is an independent feature of each spin sector separately; this is a non-trivial statement because the exact spectrum is fully determined by only the spectrum of spin zero primaries and those of a single non-zero spin (“spectral determinacy”). We then describe an argument analogous to the one leading to Cardy’s formula for the averaged density of states, but in our case applying it to spectral correlations: assuming statistical universalities in the near-extremal spectrum in all spin sectors, we find similar random matrix universality in a large spin regime far from extremality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Theory of Photoluminescence Spectral Line Shapes of Semiconductor Nanocrystals

Single-molecule photoluminescence (PL) spectroscopy of semiconductor nanocrystals (NCs) reveals the nature of exciton–phonon interactions in NCs. Understanding the homogeneous spectral line shapes and their temperature dependence remains an open problem. Here, we develop an atomistic model to describe the PL spectrum of NCs, accounting for excitonic effects, phonon dispersion relations, and exciton–phonon couplings. We validate our model using single-NC measurements on CdSe/CdS NCs from T = 4 to 290 K, and we find that the slightly asymmetric main peak at low temperatures is comprised of a narrow zero-phonon line (ZPL) and acoustic phonon sidebands. Furthermore, we identify the specific phonon modes that give rise to the optical phonon sidebands. At temperatures above 200 K, the spectral line width shows a stronger dependence upon the temperature, which we demonstrate to be correlated with higher order exciton–phonon couplings. We also identify the line width dependence upon reorganization energy, NC core sizes, and shell thicknesses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Spectral Constraints on Theories of Colored Particles and Gravity

In this Letter, we consider effective field theories for light fields transforming under the fundamental or adjoint representation of a continuous group. Assuming tree-level completions, we demonstrate that, in the presence of gravity, crossing symmetry combined with twice-subtracted sum rules leads to constraints on the irreducible representations that the ultraviolet degrees of freedom must populate. A spectrum is allowed only if its low energy projection contains the graviton pole. Beautifully, the graviton pole is the anchor of our argument, not an obstruction.

Effective field theory↗
DOE OSTI2022

Towards Ab-Initio Simulations of Crystalline Defects at the Exascale Using Spectral Quadrature Density Functional Theory

Defects in crystalline solids play a crucial role in determining properties of materials at the nano, meso- and macroscales, such as the coalescence of vacancies at the nanoscale to form voids and prismatic dislocation loops or diffusion and segregation of solutes to nucleate precipitates, phase transitions in magnetic materials via disorder and doping. First principles Density Functional Theory (DFT) simulations can provide a detailed understanding of these phenomena. However, the number of atoms needed to correctly simulate these systems is often beyond the reach of many widely used DFT codes. The aim of this article is to discuss recent advances in first principles modeling of crystal defects using the spectral quadrature method. The spectral quadrature method is linear scaling with respect to the number of atoms, permits spatial coarse-graining, and is capable of simulating non-periodic systems embedded in a bulk environment, which allows the application of appropriate boundary conditions for simulations of crystalline defects. In this article, we discuss the state-of-the-art in ab-initio modeling of large metallic systems of the order of several thousand atoms that are suitable for utilizing exascale computing resourses.

36 MATERIALS SCIENCE↗