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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Does a meteor's "color" reflect its composition?

Astronomers sometimes use color – the relative brightness of an object seen through two different color filter – as a proxy for other quantities. For instance, a star’s color indicates its temperature because stellar spectra vary in a predictable way.Meteor spectra are dominated by emission lines and reducing them to a “color” is not as straightforward.We combine meteor spectra from the literature with standard Bessel filter functions to test whether color measurements can probe a meteor’s spectral type.

Althea Valkyrie Moorhead↗
NASA NTRS1984

A method for computing the kernel of the downwash integral equation for arbitrary complex frequencies

For the design of active controls to stabilize flight vehicles, which requires the use of unsteady aerodynamics that are valid for arbitrary complex frequencies, algorithms are derived for evaluating the nonelementary part of the kernel of the integral equation that relates unsteady pressure to downwash. This part of the kernel is separated into an infinite limit integral that is evaluated using Bessel and Struve functions and into a finite limit integral that is expanded in series and integrated termwise in closed form. The developed series expansions gave reliable answers for all complex reduced frequencies and executed faster than exponential approximations for many pressure stations.

Desmarais, R. N.↗
DOE OSTI2016

Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers

We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and conductivity) with uniaxial anisotropy. Analytical expressions are obtained based on the spectral representation of the tensor Green's function based on cylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxial media. Due to the poor scaling of these eigenfunctions for extreme arguments and/or orders, direct numerical evaluation of such expressions can produce numerical instability, i.e., underflow, overflow, and/or round-off errors under finite precision arithmetic. To circumvent these problems, we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain, to yield a robust algorithm for all parameter ranges. Numerical results are presented to illustrate the robustness of the formulation including cases of practical interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Generalized Bessel–Struve Operator and Its Properties

We define the generalized Bessel–Struve operator in the space of functions analytic in an arbitrary domain. The conditions of equivalence of the generalized Bessel–Struve operator to the operator of second derivative are investigated. We also describe the commutant of the generalized Bessel–Struve operator and establish its hypercyclicity and chaotic nature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Short and medium range structure in elastic deformation of metallic and covalent glasses

Here, we present a concise methodology to analyze structural response to the applied stress in amorphous solids, including metallic glasses (MG), glassy selenium, silica and polycarbonate, using high energy x-ray diffraction and atomic pair distribution function (PDF) analysis. To assess the structural anisotropy induced by applied axial stress, diffraction data were expanded into spherical harmonics. Using Bessel transformation, components of the structure function were converted into isotropic and anisotropic PDFs. The PDFs were compared to the expected model behavior for ideal elastic deformation to separate homogeneous affine strain from local non-affine strains. In metallic glass the range of non-affine deformation is limited to the nearest neighbor shell, suggesting local strain relaxation under stress that occurs even in the elastic regime. Beyond the second atomic shell strain is uniform. However, in glassy silica, polycarbonate and selenium strong local bonding inhibits local displacements and strain in short range order is accommodated by rotation of local units. Interestingly, beyond a molecular unit, deformation in covalent systems is similar to MG, and response of the medium range order scales with the macroscopic stress.

glassy structure↗
DOE OSTI2018

Noncollinear Acousto-Optic Filtering of Polychromatic Bessel Light Beams in Uniaxial Crystals

We have studied the features of noncollinear acousto-optic filtering of quasi-nondiffracting Bessel light beams in uniaxial crystals. We have obtained coupled wave equations for the vector amplitudes of an incident ordinary (o-type) Bessel beam and an extraordinary (e-type) diffracted beam for different modes. We have found an expression for the diffraction efficiency as a function of the parameters of interacting ordinary and extraordinary Bessel beams, and also as a function of the values of the overlap integrals. Using the overlap integral method, we have shown that regardless of the mode order for the Bessel light beam, under transverse phase matching conditions for ordinary and extraordinary diffracted Bessel beams in the optical spectral range 0.4–1.1 μm we can achieve a filter transmission bandwidth of ~0.6 nm in paratellurite crystals .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

The elimination of short and intermediate period terms from the problem of a high altitude earth satellite

The Delaunay-Similar elements of Scheifele (1976) are applied to the problem of an earth satellite that is perturbed by the sun, moon, and J2. All three effects are assumed to be the same order of magnitude. Since the external body terms depend explicitly on time, the time element appears as an additional angle variable. Also, the eccentric anomaly is used as a noncanonical auxiliary variable. A solution to the first Von Zeipel equation allows simultaneous elimination of short- and intermediate-period terms. The canonical transformation to mean elements is defined by a generating function that is a series involving Bessel coefficients.

Graf, O. F., Jr.↗
DOE OSTI2024

Galaxy bispectrum in the spherical Fourier-Bessel basis

The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on large scales. In this work we develop a formalism for the bispectrum in the spherical Fourier-Bessel (SFB) basis—a natural basis for computing correlation functions on the curved sky, as it diagonalizes the Laplacian operator in spherical coordinates. Working in the SFB basis allows for line-of-sight effects such as redshift space distortions and GR to be accounted for exactly, i.e., without having to resort to perturbative expansions to go beyond the plane-parallel approximation. Only analytic results for the SFB bispectrum exist in the literature given the intensive computations needed. We numerically calculate the SFB bispectrum for the first time, enabled by a few techniques: We implement a template decomposition of the redshift-space kernel Z 2 into Legendre polynomials, and separately treat the PNG and velocity-divergence terms. We derive an identity to integrate a product of three spherical harmonics connected by a Dirac delta function as a simple sum and use it to investigate the limit of a homogeneous and isotropic Universe. Furthermore, we present a formalism for convolving the signal with separable window functions and use a toy spherically symmetric window to demonstrate the computation and give insights into the properties of the observed bispectrum signal. While our implementation remains computationally challenging, it is a step toward a feasible full extraction of information on large scales via a SFB bispectrum analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Frequency-Bessel Transform Method for Effective Imaging of Higher-Mode Rayleigh Dispersion Curves From Ambient Seismic Noise Data

It has been widely recognized that the cross-correlation function of ambient seismic noise data recorded at two stations approximates to the part of Greens function between two stations. Therefore, the cross-correlation function should include higher modes, aside from the fundamental mode. However, the problem of measuring or extracting overtones from ambient seismic noise data remains. In this paper, we propose the frequency-Bessel transform method (F-J method) for extracting the dispersion curves of higher modes from ambient seismic noise data. We then assess the validity, accuracy, and applicability of the F-J method by conducting extensive numerical simulations and processing the observed ambient seismic noise data of the USArray. As demonstrated in this study, the F-J method is a convenient, practical, and accurate method for extracting the dispersion curves of multimodes from ambient seismic noise data and therefore has significant potentiality in the field of ambient seismic noise tomography.

58 GEOSCIENCES↗
DOE OSTI2016

Light-sheet microscopy by confocal line scanning of dual-Bessel beams

Here, we have developed a light-sheet microscope that uses confocal scanning of dual-Bessel beams for illumination. A digital micromirror device (DMD) is placed in the intermediate image plane of the objective used to collect fluorescence and is programmed with two lines of pixels in the “on” state such that the DMD functions as a spatial filter to reject the out-of-focus background generated by the side-lobes of the Bessel beams. The optical sectioning and out-of-focus background rejection capabilities of this microscope were demonstrated by imaging of fluorescently stained actin in human A431 cells. The dual-Bessel beam system enables twice as many photons to be detected per imaging scan, which is useful for low light applications (e.g., single-molecule localization) or imaging at high speed with a superior signal to noise. While demonstrated for two Bessel beams, this approach is scalable to a larger number of beams.

confocal microscopy↗
DOE OSTI2018

Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality

We prove tail triviality of determinantal point processes μ on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for Sine{sub 2},Airy{sub 2},Bessel{sub 2}, and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1983

The effects of digitizing rate and phase distortion errors on the shock response spectrum

Some of the methods used for acquisition and digitization of high-frequency transients in the analysis of pyrotechnic events, such as explosive bolts for spacecraft separation, are discussed with respect to the reduction of errors in the computed shock response spectrum. Equations are given for maximum error as a function of the sampling rate, phase distortion, and slew rate, and the effects of the characteristics of the filter used are analyzed. A filter is noted to exhibit good passband amplitude, phase response, and response to a step function is a compromise between the flat passband of the elliptic filter and the phase response of the Bessel filter; it is suggested that it be used with a sampling rate of 10f (5 percent).

Wise, J. H.↗
DOE OSTI2023

Adaptive methods of generating complex light arrays

Structured light arrays of various shapes have been a cornerstone in optical science, driven by the complexities of precise and adaptable generation. This study introduces an approach using a spatial light modulator (SLM) as a generator for these arrays. By projecting a holographic mask onto the SLM, it functions simultaneously as an optical convolution device, focusing mechanism, and structured light beam mask. Our approach offers unmatched versatility, allowing for the experimental fabrication of traditional beam arrays like azimuthal Laguerre–Gaussian (LG), Bessel–Gaussian (BG), and Hermite–Gauss (HG) in the far-field. Notably, it has enabled a method of generating Ince–Gauss (IG) and LG radial mode beam arrays using a convolution solution. Our system provides exceptional control over array periodicity and intensity distribution, bypassing the Talbot self-imaging phenomenon seen in traditional setups. We provide an in-depth theoretical discussion, supported by empirical evidence, of our far-field results. This method has vast potential for applications in optical communication, data processing, and multi-particle manipulation. It paves the way for rapid generation of structured light with high spatial frequencies and complex shapes, promising transformative advances in these domains.

Optics↗
NASA NTRS1979

Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms

Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.

Ikhabisimov, D. K.↗
DOE OSTI2018

Beyond the plane-parallel approximation for redshift surveys

Redshift -space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modelling of clustering observables, leading to what are frequently called 'wide-angle effects'. We study these effects analytically, computing their signature in the clustering of the multipoles in configuration and Fourier space. We take into account both physical wide-angle contributions as well as the terms generated by the galaxy selection function. Similar considerations also affect the way power spectrum estimators are constructed. We quantify in an analytical way the biases that enter and clarify the relation between what we measure and the underlying theoretical modelling. The presence of an angular window function is also discussed. Motivated by this analysis, we present new estimators for the three dimensional Cartesian power spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel coefficients. In conclusion, we show how the latter have several interesting properties, allowing in particular a clear separation between angular and radial modes.

79 ASTRONOMY AND ASTROPHYSICS↗