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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Derivation of closed-form ellipsoidal X-ray mirror shapes from Fermat's principle

Ellipsoidal and plane-elliptical surfaces are widely used as reflective, point-to-point focusing elements in many optical systems, including X-ray optics. Here the classical optical path function approach of Fermat is applied to derive a closed-form expression for these surfaces that are uniquely described by the object and image distances and the angle of incidence at a point on a mirror surface. A compact description facilitates design, modeling, fabrication, and testing to arbitrary accuracy. Congruent surfaces in two useful coordinate systems — a system centered on the ellipsoid's axes of symmetry and a mirror-centered or `vertex' system with the surface tangent to the xy plane at the mirror's center — are presented. Expressions for the local slope and radii of curvature are derived from the result, and the first several terms of the Maclauren series expansion are provided about the mirror center.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Bifurcation of equilibrium positions for ellipsoidal particles in inertial shear flows between two walls

We conducted a systematic numerical investigation of spherical, prolate and oblate particles in an inertial shear flow between two parallel walls, using smoothed particle hydrodynamics (SPH). It was previously shown that above a critical Reynolds number, spherical particles experience a supercritical pitchfork bifurcation of the equilibrium position in shear flow between two parallel walls, namely that the central equilibrium position becomes unstable, leading to the emergence of two new off-centre stable positions (Foxet al.,J. Fluid Mech., vol. 915, 2021). This phenomenon was unexpected given the symmetry of the system. In addition to confirming this finding, we found, surprisingly, that ellipsoidal particles can also return to the centre position from the off-centre positions when the particle Reynolds number is further increased, while spherical particles become unstable under this increased Reynolds number. By utilizing both SPH and the finite element method for flow visualization, we explained the underlining mechanism of this reverse of bifurcation by altered streamwise vorticity and symmetry breaking of pressure. Furthermore, we expanded our investigation to include asymmetric particles, a novel aspect that had not been previously modelled, and we observed similar trends in particle dynamics for both symmetric and asymmetric ellipsoidal particles. While further validation through laboratory experiments is necessary, our research paves the road for development of new focusing and separation methods for shaped particles.

Mechanics↗
DOE OSTI2020

Quantifying patterns in optical micrographs of one- and two-dimensional ellipsoidal particle assemblies

Current developments in colloidal science include the assembly of anisotropic colloids with broad geometric diversity. As the complexity of particle assemblies increases, the need for ubiquitous algorithms that quantitatively analyze images of the assemblies to deliver key information such as quantification of crystal structures becomes more urgent. This contribution describes algorithms capable of image analysis for classifying colloidal structures based on abstracted interparticle relationship information and quantitatively analyzing the abundance of each structure in mixed pattern assemblies. The algorithm parameters can be adjusted, allowing for the algorithms to be adapted for different image analyses. Three different ellipsoidal particle assembly images are presented to demonstrate the effectiveness of the algorithms: a one-dimensional (1D) particle chain assembly and two two-dimensional (2D) polymorphic crystals each consisting of assemblies of two distinct plane symmetry groups. Angle relationships between neighbouring particles are calculated and neighbour counts of each particle are determined. Combining these two parameters as rules for classification criteria allows for the labeling and quantification of each particle into a defined symmetry class within an assembly. The algorithms provide a labelled image comprising classification results and particle counts of each defined class. For multiple images or individual frames from a video, the script can be looped to achieve automatic processing. The yielded classification data allow for more in-depth image analysis of mixed pattern particle assemblies. Finally, we envision that these algorithms will have utility in quantitative analysis of images comprising ellipsoidal colloidal materials, nanoparticles, or biological matter.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Proof-of-concept of a neutron time-of-flight ellipsoidal detector

The time-resolved measurement of neutrons emitted from nuclear implosions at inertial confinement fusion facilities is used to characterize the fusing plasma. Several significant quantities are routinely measured by neutron time-of-flight (nToF) detectors in these experiments. Current nToF detectors use scintillators as well as solid-state Cherenkov radiators. The latter has an inherently faster time response and can provide a co-registered γ-ray measurement as well as improved precision in the bulk hot-spot velocity. This work discusses a nToF ellipsoidal detector that also utilizes a solid-state Cherenkov radiator. The detector has the potential to achieve a fast instrument response function allowing for characterization of the γ-ray burn history as well as the ability to field the detector closer to the fusion source. Proof-of-concept testing of the nToF ellipsoidal detector has been conducted at the National Ignition Facility using commercial optics. A time-resolved neutron signal has been measured from the diagnostic. Preliminary simulations corroborate the results.

Jeet, J. (ORCID:0000000291091563)↗
DOE OSTI2021

High tide: a systematic search for ellipsoidal variables in ASAS-SN

ABSTRACT The majority of non-merging stellar mass black holes are discovered by observing high energy emission from accretion processes. Here, we pursue the large, but still mostly unstudied population of non-interacting black holes and neutron stars by searching for the tidally induced ellipsoidal variability of their stellar companions. We start from a sample of about 200 000 rotational variables, semiregular variables, and eclipsing binary stars from the All-Sky Automated Survey for Supernovae. We use a χ2 ratio test followed by visual inspection to identify 369 candidates for ellipsoidal variability. We also discuss how to combine the amplitude of the variability with mass and radius estimates for observed stars to calculate a minimum companion mass, identifying the most promising candidates for high mass companions.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1975

The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion

The problem of an anisotropic ellipsoidal inclusion which undergoes a stress-free transformation strain (in the sense of J. D. Eshelby) is considered, and the following theorem is proved: if an ellipsoidal region in an infinite anisotropic linear elastic medium undergoes, in the absence of its surroundings, a stress-free transformation strain which is a polynomial of degree M in given position coordinates, then the final stress and strain state in the transformed inclusion, when constrained by its surroundings, is also a polynomial of degree M in those position coordinates.

Asaro, R. J.↗
NASA NTRS1978

Narrow zone heating by a new radiation focusing technique - Toroidal ellipsoid furnace

The paper describes the design of a toroidal ellipsoid furnace for narrow zone heating of materials in sealed transparent ampoules. The heater is a toroid flattened to an elliptical cross section like a partially inflated inner tube resting on a horizontal surface. The foci of the ellipsoid are two concentric rings. The outer focus is occupied by a heater wire, and the inner focus is arranged to fall on the surface of the cylindrical ingot within its transparent capsule. One advantage of the new furnace is that the wire heater closely approximates the ideal shape, lying along an extended line focus, as opposed to the elusive point source of the Costello furnace. Also, the ingot is heated uniformly around its circumference.

Davidson, M. C.↗
NASA NTRS1981

Radiative transfer theory for active remote sensing of a layer of small ellipsoidal scatterers

The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.

Tsang, L.↗
NASA NTRS1954

Variation of Local Liquid-Water Concentration About and Ellipsoid of Fineness Ratio 5 Moving in a Droplet Field

Trajectories of water droplets about an ellipsoid of revolution with a fineness ratio of 5 (which often approximates the shape of an aircraft fuselage or missile) were computed with the aid of a differential analyzer. Analyses of these trajectories indicate that the local concentration of liquid water at various points about an ellipsoid in flight through a droplet field varies considerably and under some conditions may be several times the free-stream concentration. Curves of the local concentration factor as a function of spatial position were obtained and are presented in terms of dimensionless parameters Re(sub 0) (free-stream Reynolds number) and K (inertia), which contain flight and atmospheric conditions. These curves show that the local concentration factor at any point is very sensitive to change in the dimensionless parameters Re(sub 0) and K. These data indicate that the expected local concentration factors should be considered when choosing the location of, or when determining antiicing heat requirements for, water- or ice-sensitive devices that protrude into the stream from an aircraft fuselage or missile. Similarly, the concentration factor should be considered when choosing the location on an aircraft of instruments that measure liquid-water content or droplet-size distribution in the atmosphere.

Dorsch, Robert G.↗
NASA NTRS1955

Variation of Local Liquid-Water Concentration About an Ellipsoid of Fineness Ratio 10 Moving in a Droplet Field

Trajectories of water droplets about an ellipsoid of revolution with a fineness ratio of 10 (10 percent thick) in flight through a droplet field were computed with the aid of a differential analyzer. Analyses of these trajectories indicate that the local concentration of liquid water at various points about an ellipsoid varies considerably and under some conditions may be several times the free-stream concentration. Curves of the local concentration factor as a function of spatial position were obtained and are presented in terms of dimensionless parameters that describe flight and atmospheric conditions. The data indicate that the expected local concentration factors should be considered when choosing the location of devices that protrude into the stream from aircraft fuselages or missiles, or when determining antiicing heat requirements for the protection of these devices.

Brun, Rinaldo J.↗
NASA NTRS1981

Ellipsoidal corrections for geoid undulation computations using gravity anomalies in a cap

Ellipsoidal correction terms have been derived for geoid undulation computations when the Stokes equation using gravity anomalies in a cap is combined with potential coefficient information. The correction terms are long wavelength and depend on the cap size in which its gravity anomalies are given. Using the regular Stokes equation, the maximum correction for a cap size of 20 deg is -33 cm, which reduces to -27 cm when the Stokes function is modified by subtracting the value of the Stokes function at the cap radius. Ellipsoidal correction terms were also derived for the well-known Marsh/Chang geoids. When no gravity was used, the correction could reach 101 cm, while for a cap size of 20 deg the maximum correction was -45 cm. Global correction maps are given for a number of different cases. For work requiring accurate geoid computations these correction terms should be applied.

Rapp, R. H.↗
NASA NTRS1982

Fundamental aspects in quantitative ultrasonic determination of fracture toughness: The scattering of a single ellipsoidal inhomogeneity

The scattering of a single ellipsoidal inhomogeneity is studied via an eigenstrain approach. The displacement field is given in terms of volume integrals that involve eigenstrains that are related to mismatch in mass density and that in elastic moduli. The governing equations for these unknown eigenstrains are derived. Agreement with other approaches for the scattering problem is shown. The formulation is general and both the inhomogeneity and the host medium can be anisotrophic. The axisymmetric scattering of an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the scattered displacement field, the differential and total cross sections are formally given in series expansions for the case of uniformly distributed eigenstrains.

Fu, L. S. W.↗
NASA NTRS1982

Volume integrals of ellipsoids associated with the inhomogeneous Helmholtz equation

Problems of wave phenomena in the fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the inhomogeneous Helmholtz equation, for an ellipsoidal region. By using appropriate Taylor series expansions and the multinomial theorem, these volume integrals are obtained in series form for regions r greater than r-prime and r less than r-prime, where r and r-prime are the distances from the origin to the point of observation and the source. Derivatives of these integrals are easily evaluated. When the wavenumber approaches zero the results reduce directly to the potentials of ellipsoids of variable densities.

Fu, L. S.↗
NASA NTRS1983

The determination of the elastodynamic fields of an ellipsoidal inhomogeneity

The determination of the elastodynamic fields of an ellipsoidal inhomogeneity is studied in detail via the eigenstrain approach. A complete formulation and a treatment of both types of eigenstrains for equivalence between the inhomogeneity problem and the inclusion problem are given. This approach is shown to be mathematically identical to other approaches such as the direct volume integral formulation. Expanding the eigenstrains and applied strains in the polynomial form in the position vector and satisfying the equivalence conditions at every point, the governing simultaneous algebraic equations for the unknown coefficients in the eigenstrain expansion are derived. The elastodynamic field outside an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the induced displacement field, as well as the differential and total cross sections are formally given in series expansion form for the case of uniformly distributed eigenstrains.

Fu, L. S.↗
NASA NTRS1985

Improved Ellipsoidal Radiation Furnace

Spherical reflector around heat source increases efficiency and minimizes power requirements. Furnace consists of ellipsoid with point heat source, at one focus and sample heated at other focus. Spherical reflector with circular slit surrounds heat source. All radiation not passing through circular slit in spherical reflector reflected back to lamp. Radiation passing through spherical slit focused by ellipsoid surface onto sample. Arrangement uses heat efficiently, reduces waste heat generation and permits full view of specimen.

Ethridge, E. C.↗
NASA NTRS1985

Ellipsoidal Balloon Antenna

Direct-broadcast ellipsoidal antenna 40 percent smaller than spherical reflector. Balloon antenna has feedpoint on surface of ellipsoid outside balloon, simplifying balloon deployment and feed support. Dielectric shrouds used locally to adjust shape of balloon and maintain feed distance at its optimum value.

Cramer, P. W.↗
NASA NTRS1985

Ellipsoidal geometry in asteroid thermal models - The standard radiometric model

The major consequences of ellipsoidal geometry in an othewise standard radiometric model for asteroids are explored. It is shown that for small deviations from spherical shape a spherical model of the same projected area gives a reasonable aproximation to the thermal flux from an ellipsoidal body. It is suggested that large departures from spherical shape require that some correction be made for geometry. Systematic differences in the radii of asteroids derived radiometrically at 10 and 20 microns may result partly from nonspherical geometry. It is also suggested that extrapolations of the rotational variation of thermal flux from a nonspherical body based solely on the change in cross-sectional area are in error.

Brown, R. H.↗