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Results for “SPECTRAL THEORY”

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
NASA NTRS1972

Stability conditions derived from spectral theory - Discrete systems with periodic feedback.

By use of the spectral theory of linear operators, necessary and sufficient conditions are derived for the stability of a class of discrete time feedback systems with a periodically time-varying feedback gain. These conditions involve a Nyquist plot for an equivalent time-invariant system which may be determined from the frequency response function of the system under consideration. In the special case of a scalar-input scalar-output system, these conditions may be given in a particularly simple form.

Davis, J. H.↗
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 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↗
NASA NTRS2018

An Interplay between Photons, Canopy Structure, and Recollision Probability: A Review of the Spectral Invariants Theory of 3D Canopy Radiative Transfer Processes

Earth observations collected by remote sensors provide unique information to our ever-growing knowledge of the terrestrial biosphere. Yet, retrieving information from remote sensing data requires sophisticated processing and demands a better understanding of the underlying physics. This paper reviews research efforts that lead to the developments of the stochastic radiative transfer equation (RTE) and the spectral invariants theory. The former simplifies the characteristics of canopy structures with a pair-correlation function so that the 3D information can be succinctly packed into a 1D equation. The latter indicates that the interactions between photons and canopy elements converge to certain invariant patterns quantifiable by a few wavelength independent parameters, which satisfy the law of energy conservation. By revealing the connections between plant structural characteristics and photon recollision probability, these developments significantly advance our understanding of the transportation of radiation within vegetation canopies. They enable a novel physically-based algorithm to simulate the “hot-spot” phenomenon of canopy bidirectional reflectance while conserving energy, a challenge known to the classic radiative transfer models. Therefore, these theoretical developments have a far-reaching influence in optical remote sensing of the biosphere.

vegetation remote sensing; stochastic radiative tr↗
NASA NTRS1973

An analysis of the unified and scalar additivity theories of spectral line broadening

The qualities of the unified and scalar theories proposed by various authors for describing the static and dynamic characteristics of a radiation perturber interaction are discussed. The regions of validity of these theories and the properties of the approximations applied by them are considered. New derivation procedures are proposed for the unified and scalar additivity theories of line broadening. These procedures do not require the use of an elaborate projection operator, of Green's function techniques in contrast to previous methods.

Smith, E. W.↗
NASA NTRS1978

Two-stream theory of spectral reflectance of snow

Spectral reflectance of snow under diffuse illumination is studied using the two-stream approximation of the radiative transfer equation. The scattering and absorption within the snowcover due to the randomly distributed ice grains are characterized by the single scattering albedo and anisotropic phase function. Geometric optics calculations are used to relate the scattering and absorption parameters to grain size and density of snow. Analytical expressions for the intensity within the snowpack and the asymptotic flux extinction coefficient are also obtained. Good agreement is shown between the theory and available experimental data on visible and near-infrared reflectance and asymptotic flux extinction coefficient. The theory also may be used to explain the observed effect of aging on the snow reflectance.

Choudhury, B. J.↗
NASA NTRS1978

Theory of spectral radiance of pollutants at sea

Remote measurement of soluble pollutants that change the color of the water in the sea is reported. The sensor is a spectral radiometer that flies over the polluted area and compares its spectral radiance to that of surrounding clean seawater. A quantitative analysis of the concentration of pollutants using the measured radiance of the sea compared to laboratory measurements of reflection and transmission spectra of the pollutants is presented. The quantities involved are defined and means for measuring them are described. The equations for remote sensing with a low-flying aircraft, in which case the absorption and radiance of intervening air is negligible are derived. High-flying aircraft and satellites, in which case the radiance of intervening air is the major problem are applied.

Source record↗
NASA NTRS1979

Theory of spectral radiance of pollutants at sea, volume 1

Remote measurement of pollutants dumped in the sea, not oil slicks, but soluble pollutants that change the color of the water, is addressed. The sensor is a spectral radiometer that flies over the polluted area and compares its spectral radiance (color) to that of surrounding clean seawater. The goal is to infer the concentration of pollutants using the measured radiance of the sea compared to laboratory measurements of reflection and transmission spectra of the pollutants. The subject is treated in three steps: (1) the quantities involved are defined and means for measuring them are described; (2) the equations for remote sensing with a low-flying aircraft are derived, in which wase the absorption and radiance of intervening air is negligible; and (3) high-flying aircraft and satellites are applied, in which case the radiance of intervening air is the major problem.

Source record↗
NASA NTRS1995

Intermittent turbulence in solar wind from the south polar hole

The magnetic fields measured by the Ulysses spacecraft are used to study solar wind turbulence in the fast solar wind from the south polar hole. The spacecraft was at about 46 deg south latitude and 3.9 AU. For a magnetic field with a Gaussian distribution the power spectrum (second-order structure function) is sufficient to completely characterize the turbulence. However, the actual distribution is non-Gaussian so that the effects of intermittency must be taken into account. The observed spectral exponents include effects of intermittency and cannot be directly compared with the standard second-order spectral theories such as the Kolmogorov and Kraichnan theories. To permit a better comparison of the observations with the theoretical models, we study the structure characteristics of the data. We find the exponents of the second-order structure functions (power spectra) and the higher-order normalized structure functions for the components of the magnetic fields. We show that these sets of exponents can be approximately described by two basic numbers: the spectral exponent and the intermittency exponent. The intermittency exponent characterizes correlation properties of the energy cascade from large to small scales. Before comparing the observations to the theoretically expected values, a reduction must be made to the observed spectral exponent. The amount of the reduction depends on both the intermittency exponent and the model of the energy cascade assumed in the turbulence theory. We reduce the measured spectral indices according to a simple model for Alfven turbulence that is described here. We then compare our reduced spectral indices with second-order spectral theory. The reduced spectral indices for the period range of 1 min to about a half hour are remarkably constant and in good agreement with the value of 3/2. Thus our treatment is self-consistent. Our tentative conclusion is that the high-frequency turbulence appears to agree with the model of random-phased Alfven waves. This tentative conclusion must be tested by further theoretical and observational work.

Ruzmaikin, A. A.↗
NASA NTRS1993

Spectral mixing models of S-Type asteroids

This paper presents the results of an attempt to determine S-Type asteroid mineralogies with the use of Hapke theory spectral mixing modelling. Previous attempts to understand the spectral variations present in this single class of asteroids have concentrated on spectral parameters such as absorption band center wavelengths, band area ratios, and geometric albedos. The procedure taken here is to utilize the Hapke spectral reflectance model to calculate single scatter albedo as a function of wavelength for a suite of candidate end-member materials. These materials are then mixed linearly in single scatter albedo space, and the mixture is converted, assuming intimate particle mixing, back to reflectance for the spectrum matching routine. A total of 39 S-Type asteroids selected from the Bell et al. survey have been matched with mixture model spectra.

Clark, Beth E.↗
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↗