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Results for “PROLATE SPHEROID FUNCTION”

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 NTRS1985

Optimal frequency domain textural edge detection filter

An optimal frequency domain textural edge detection filter is developed and its performance evaluated. For the given model and filter bandwidth, the filter maximizes the amount of output image energy placed within a specified resolution interval centered on the textural edge. Filter derivation is based on relating textural edge detection to tonal edge detection via the complex low-pass equivalent representation of narrowband bandpass signals and systems. The filter is specified in terms of the prolate spheroidal wave functions translated in frequency. Performance is evaluated using the asymptotic approximation version of the filter. This evaluation demonstrates satisfactory filter performance for ideal and nonideal textures. In addition, the filter can be adjusted to detect textural edges in noisy images at the expense of edge resolution.

Townsend, J. K.↗
NASA NTRS1999

A Comparative Study of Interferometric Regridding Algorithms

THe paper discusses regridding options: (1) The problem of interpolating data that is not sampled on a uniform grid, that is noisy, and contains gaps is a difficult problem. (2) Several interpolation algorithms have been implemented: (a) Nearest neighbor - Fast and easy but shows some artifacts in shaded relief images. (b) Simplical interpolator - uses plane going through three points containing point where interpolation is required. Reasonably fast and accurate. (c) Convolutional - uses a windowed Gaussian approximating the optimal prolate spheroidal weighting function for a specified bandwidth. (d) First or second order surface fitting - Uses the height data centered in a box about a given point and does a weighted least squares surface fit.

Hensley, Scott↗
NASA NTRS2020

An Overview of the Null-Field Method. II: Convergence and Numerical Stability

In this paper we provide an analysis of the convergence and numerical stability of the null-field method with discrete sources. We show that (i) if the null-field scheme is numerically stable then we can decide whether or not convergence can be achieved; (ii) if the null-field scheme is numerically unstable then we cannot draw any conclusion about the convergence issue; and (iii) the numerical stability is closely related to the property of a tangential system of radiating discrete sources to form a Riesz basis. Our numerical analysis indicates that for prolate spheroids and localized vector spherical wave functions, the null-field scheme is numerically unstable (this system of vector functions does not form a Riesz basis), while for distributed vector spherical wave functions, the numerical instability is not so pronounced (this system of discrete sources almost possesses the property of being a Riesz basis). We also describe an analytical method for computing the surface integrals in the framework of the conventional null-field method with localized vector spherical wave functions which increases the stability of the numerical scheme.

Null-field method↗
NASA NTRS1990

Trigonometric Polynomials For Estimation Of Spectra

Orthogonal sets of trigonometric polynomials used as suboptimal substitutes for discrete prolate-spheroidal "windows" of Thomson method of estimation of spectra. As used here, "windows" denotes weighting functions used in sampling time series to obtain their power spectra within specified frequency bands. Simplified windows designed to require less computation than do discrete prolate-spheroidal windows, albeit at price of some loss of accuracy.

Greenhall, Charles A.↗
DOE OSTI2020

Cuboidal Liquid Crystal Phases Under Multiaxial Geometrical Frustration.

Cuboidal liquid crystal phases - the so-called blue phases - consist of a network of topological defects arranged into a cubic symmetry. They exhibit striking optical properties, including Bragg reflection in the visible range and fast response times. Confining surfaces can interfere with the packing of such a network, leading to structures that have not been explored before. In this work, a Landau-de Gennes free energy formalism for the tensor alignment field Q is used to investigate the behavior of chiral liquid crystals under non-isotropic confinement. The underlying free energy functional is solved by relying on a Monte Carlo method that facilitates efficient exploration of configuration space. The results of simulations are expressed in terms of phase diagrams as a function of chirality and temperature for three families of spheroids: oblate, spherical, and prolate. Upon deformation, blue phases adapt and transform to accommodate the geometrical constraints, thereby resulting in a wider range of thermal stability. For oblate spheroids, confinement interferes with the development of a full blue phase structure, resulting on a combination of half skyrmions. For prolate spheroids, the blue phases are hybridized and exhibit features of blue phases I and II. More generally, it is shown that mechanical deformation provides an effective means to control, manipulate and stabilize blue phases and cholesterics confined in tactoids.

Palacio-Betancur, Viviana↗
DOE OSTI2024

Theoretical Assessment of the Transition Between Electron Emission Mechanisms for Nonplanar Diodes

Theoretically and computationally describing the operation of nanodiodes requires characterizing the transitions between multiple electron emission mechanisms for nanodiodes with complicated geometries. This motivates our development of techniques to determine when simplified theories for individual mechanisms suffice compared to more complete, but more computationally expensive, models. Leveraging recent theories that define a canonical gap distance to translate planar theory to nonplanar diodes, we derive the conditions for the transitions among thermal emission, field emission, and space-charge-limited current density (SCLCD) in vacuum and with collisions for non-Cartesian coordinate systems, including spherical, cylindrical, and prolate spheroidal coordinate systems. Particle-in-cell (PIC) simulations of the current density as a function of applied voltage for a tip-to-plate geometry in vacuum agreed qualitatively with the asymptotes for thermal emission at low voltage and SCLCD at higher voltage using the canonical gap distance. As a result, this demonstrates the utility of this approach for guiding system design and suggests future extensions to save simulation time for more realistic geometries that are more computationally expensive.

Conformal mapping↗
NASA NTRS1993

A C-band backscatter model for lake ice in Alaska

ERS-1 SAR imagery of lake ice growing on shallow tundra lakes in northern Alaska shows interesting radar backscatter variations. Based on the analysis of ice cores from these lakes, a multi-layer backscatter model comprised of the following elements has been developed: (1) specular air-ice; ice-water and ice-frozen soil boundaries; (2) an ice layer of variable thickness; (3) ice sub-layers with air inclusions of variable density, size and shape including spheres, prolate spheroids, and cylinders of finite length. Preliminary model results confirm that backscatter is a sensitive function of greater reflectivity than from an ice-frozen soil interface. The model has also been tested using bubble data derived from ice cores in April 1992. The modelled backscatter is compared with backscatter derived from ERS-1 SAR images obtained at the same time as the fieldwork.

Wakabayashi, H.↗
NASA NTRS1979

Light scattering properties of spheroidal particles

In the present paper, the light scattering characteristics of spheroidal particles are evaluated within the framework of a scattering theory developed for a homogeneous isotropic spheroid. This approach is shown to be well suited for computing the scattering quantities of spheroidal particles of fairly large sizes (up to a size parameter of 30). The effects of particle size, shape, index of refraction, and orientation on the scattering efficiency factors and the scattering intensity functions are studied and interpreted physically. It is shown that, in the case of oblique incidence, the scattering properties of a long slender prolate spheroid resemble those of an infinitely long circular cylinder.

Asano, S.↗
NASA NTRS1926

Inertia Factors of Ellipsoids for Use in Airship Design

This report is based on a study made by the writer as a member of the Special Committee on Design of Army Semirigid Airship RS-1 appointed by the National Advisory Committee for Aeronautics. The increasing interest in airships has made the problem of the potential flow of a fluid about an ellipsoid of considerable practical importance. In 1833 George Green, in discussing the effect of the surrounding medium upon the period of a pendulum, derived three elliptic integrals, in terms of which practically all the characteristics of this type of motion can be expressed. The theory of this type of motion is very fully given by Horace Lamb in his "Hydrodynamics," and applications to the theory of airships by many other writers. Tables of the inertia coefficients derived from these integrals are available for the most important special cases. These tables are adequate for most purposes, but occasionally it is desirable to know the values of these integrals in other cases where tabulated values are not available. For this reason it seems worth while to assemble a collection of formulae which would enable them to be computed directly from standard tables of elliptic integrals, circular and hyperbolic functions and logarithms without the need of intermediate transformations. Some of the formulae for special cases (elliptic cylinder, prolate spheroid, oblate spheroid, etc.) have been published before, but the general forms and some special cases have not been found in previous publications. (author)

Tuckerman, L. B.↗
NASA NTRS1992

Wall functions for the kappa-epsilon turbulence model in generalized nonorthogonal curvilinear coordinates

A k-epsilon turbulence model suitable for compressible flow, including the new wall function formulation, has been incorporated into an existing compressible Reynolds-averaged Navier-Stokes code, F3D. The low Reynolds number k-epsilon model of Chien (1982) was added for comparison with the present method. A number of features were added to the F3D code including improved far-field boundary conditions and viscous terms in the streamwise direction. A series of computations of increasing complexity was run to test the effectiveness of the new formulation. Flow over a flat plate was computed by using both orthogonal and nonorthogonal grids, and the friction coefficients and velocity profiles compared with a semi-empirical equation. Flow over a body of revolution at zero angle of attack was then computed to test the method's ability to handle flow over a curved surface. Friction coefficients and velocity profiles were compared to test data. All models gave good results on a relatively fine grid, but only the wall function formulation was effective with coarser grids. Finally, in order to demonstrate the method's ability to handle complex flow fields, separated flow over a prolate spheroid at angle of attack was computed, and results were compared to test data. The results were also compared to a k-epsilon model by Kim and Patel (1991), in which one equation model patched in at the wall was employed. Both models gave reasonable solutions, but improvement is required for accurate prediction of friction coefficients in the separated regions.

Sondak, D. L.↗
DOE OSTI2022

Slepians.jl

Slepians.jl is a package that solves the concentration problem of Slepian, Landau and Pollak, numerically. Loosely speaking, we find a function that is both finite in extent and has a Fourier transform which lies in a certain domain. In a single dimension, with discrete sampling, the discrete prolate spheroidal sequences solve this optimization problem.

HALEY, CHARLOTTE ANNA LISA↗
NASA NTRS1995

Morphology, near-infrared luminosity, and mass of the Galactic bulge from COBE DIRBE observations

Near-infrared images of the Galactic bulge at 1.25, 2.2, 3.5, and 4.9 microns obtained by the Diffuse Infrared Background Experiment (DIRBE) onboard the Cosmic Background Explorer (COBE) satellite are used to characterize its morphology and to determine its infrared luminosity and mass. Earlier analysis of the DIRBE observations (Weiland et al. 1994) provided supporting evidence for the claim made by Blitz & Spergel (1991) that the bulge is bar-shaped with its near end in the first Galactic quadrant. Adopting various triaxial analytical functions to represent the volume emissivity of the source, we confirm the barlike nature of the bulge and show that triaxial Gaussian-type functions provide a better fit to the data than other classes of functions, including an axisymmetric spheroid. The introduction of a `boxy' geometry, such as the one used by Kent, Dame, & Fazio (1991) improves the fit to the data. Our results show that the bar is rotated in the plane with its near side in the first Galactic quadrant creating an angle of 20 deg +/- 10 deg between its major axis and the line of sight to the Galactic center. Typical axis ratios of the bar are (1:0.33 +/- 0.11:0.23 +/- 0.08), resembling the geometry of prolate spheroids. There is no statistically significant evidence for an out-of-plane tilt of the bar at 2.2 microns, and marginal evidence for a tilt of approximately equal 2 deg at 4.9 microns. The introduction of a roll around the intrinsic major axis of the bulge improves the `boxy' appearance of some functions. A simple integration of the observed projected intensity of the bulge gives a bulge luminosity of 1.2 x 10(exp 9), 4.1 x 10(exp 8), 2.3 x 10(exp 8), and 4.3 x 10(exp 7) solar luminosity, respectively, at 1.25, 2.2, 3.5, and 4.9 microns wavelength for a Galactocentric distance of 8.5 kpc. The 2.2 microns luminosity function of the bulge population in the direction of Baade's window yields a bolometric luminosity of L(sub bol) = 5.3 x 10(exp 9) solar luminosity. Stellar evolutionary models relate this luminosity to the number of main-sequence progenitor stars that currently populate the red giant branch. Combined with the recent determination of the main-sequence turnoff mass for the bulge by the Hubble Space Telescope (Holtzman et al. 1993) we derive a photometrically determined bulge mass of approximately equal to 1.3 x 10(exp 10) solar mass for a Salpeter initial mass function extended down to 0.1 solar mass.

Dwek, E.↗
NASA NTRS1997

Particle Scattering in the Resonance Regime: Full-Wave Solution for Axisymmetric Particles with Large Aspect Ratios

Reliable descriptions of the optical properties of clouds and aerosols are essential for studies of radiative transfer in planetary atmospheres. The scattering algorithms provide accurate estimates of these properties for spherical particles with a wide range of sizes and refractive indices, but these methods are not valid for non-spherical particles (e.g., ice crystals, mineral dust, and smoke). Even though a host of methods exist for deriving the optical properties of nonspherical particles that are very small or very large compared with the wavelength, only a few methods are valid in the resonance regime, where the particle dimensions are comparable with the wavelength. Most such methods are not ideal for particles with sharp edges or large axial ratios. We explore the utility of an integral equation approach for deriving the single-scattering optical properties of axisymmetric particles with large axial ratios. The accuracy of this technique is shown for spheres of increasing size parameters and an ensemble of randomly oriented prolate spheroids of size parameter equal to 10.079368. In this last case our results are compared with published results obtained with the T-matrix approach. Next we derive cross sections, single-scattering albedos, and phase functions for cylinders, disks, and spheroids of ice with dimensions extending from the Rayleigh to the geometric optics regime. Compared with those for a standard surface integral equation method, the storage requirement and the computer time needed by this method are reduced, thus making it attractive for generating databases to be used in multiple-scattering calculations. Our results show that water ice disks and cylinders are more strongly absorbing than equivalent volume spheres at most infrared wavelengths. The geometry of these particles also affects the angular dependence of the scattering. Disks and columns with maximum linear dimensions larger than the wavelength scatter much more radiation in the forward and backward directions and much less radiation at intermediate phase angles than equivalent volume spheres.

Zuffada, Cinzia↗