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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Shape matters: The case for Ellipsoids and Ellipsoidal Water

We describe the shape potentials used for the van der Waals interactions between soft-ellipsoids used to coarse-grain molecular moieties in our Metropolis Monte-Carlo simulation software. The morphologies resulting from different expressions for these van der Waals interaction potentials are discussed for the case of a prolate spheroid system with a strong dipole at the ellipsoid center. We also show that the calculation of ellipsoids is, at worst, only about fivefold more expensive computationally when compared to a simple Lennard- Jones sphere. Finally, as an application of the ellipsoidal shape we parametrize water from the original SPC water model and observe – just through the difference in shape alone – a significant improvement of the O-O radial distribution function when compared to experimental data.

Tillack, Andreas↗
DOE OSTI2021

How Snow Aggregate Ellipsoid Shape and Orientation Variability Affects Fall Speed and Self-Aggregation Rates

Snow aggregate shapes and orientations have long been known to exhibit substantial variability. Despite this observed variability, most weather and climate prediction models use fixed power-law functions that deterministically map particle size to mass and fall speed. As such, integrated quantities like precipitation and self-aggregation rates currently ignore nonlinear effects resulting from variation in shape and orientation for aggregates of the same size. This study therefore develops an analytic framework that couples an empirically based bivariate distribution of ellipsoid shapes to classical hydrodynamic theory so as to capture an appropriate dispersion of masses, projected areas, and fall speeds for an assumed size distribution. For a fixed aggregate size, shape variations produce approximately ±0.13 m s -1 standard deviation of fall speed which increases the mass flux fall speed dispersion by more than 100% over traditional microphysics models. This increased fall speed dispersion results predominantly from shape-induced mass dispersion whereas orientation and drag dispersion play a lesser role. Shape variations can increase mass- and reflectivity-weighted fall speeds by up to 60% of traditional models whereas self-aggregation rates can increase by a factor of 100 for very small slope parameters. This implies that aggregate shape variations effectively forestall the theorized onset of fall speed distribution narrowing and subsequent quenching of the aggregation process. As a result, it is likely that secondary ice formation is necessary to prevent an ever decreasing slope parameter. The mathematical theory presented in this study is used to develop simple correction factors for snow forecast and climate models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Poisson Equation for a (General) Homogeneous d-Dimensional Ellipsoid with Applications to Beam Envelope Tracking

This note describes the solution of the free-space Poisson equation in the interior of a $d$-dimensional homogeneous ellipsoid, and the associated space charge fields. An explicit formula (\ref{Sformula}) is provided that relates the $d\times d$ matrix describing the space charge (quadratic) potential to the $d\times d$ covariance matrix of the ellipsoid. For the cases $d=2$ and $d=3$, this result is used to determine the linear map corresponding to a space charge kick, that may be used to push the beam $6\times 6$ covariance matrix during envelope tracking. The treatment of upright ellipsoids for $d=2$ and $d=3$ is well-represented in the literature. However, the approach taken here emphasizes a general ellipsoid with arbitrary correlations in any dimension. The Appendix provides a general solution of the free-space Poisson equation in dimension $d$ for a source distribution with ellipsoidal symmetry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Anisotropy effects on the kinetics of colloidal crystallization and melting: comparison of spheres and ellipsoids

We use alternating current (AC) electric field assisted self-assembly to produce two-dimensional, millimeter scale arrays of ellipsoidal colloids and study the kinetics of their phase reconfiguration by means of confocal microscopy, light scattering, and computer simulation. We find that the kinetics of orientational and positional ordering can be manipulated by changing the shape of the colloids: ellipsoids with aspect ratio 2.0 melt into disordered structures 5.7 times faster compared to spheres. On the other hand, ellipsoids self-assemble into ordered crystals at a similar rate to spheres. Confocal microscopy is used to directly visualize defects in the self-assembled structures. Small-angle light scattering (SALS) quantifies the light diffraction response, which is sensitive to the kinetics of positional and orientational ordering in the self-assembled anisotropic structures. We find three different light diffraction patterns: a phase with high orientational order (with chain-like structure in real space), a phase with high positional and orientational order (characteristic of a close-packed structure), and a phase that is disordered in position but with intermediate orientational order. The large influence of aspect ratio on the kinetics of the positionally and orientationally ordered phase is explored through simulation; it is found that the number of particle degrees of freedom controls the difference between the melting rates of the ellipsoids and spheres. This research contributes to the understanding of reconfiguration kinetics and optical properties of colloidal crystals produced from anisotropic colloids.

36 MATERIALS SCIENCE↗
DOE OSTI2018

An Ellipsoidal Model for Small Multilayer Particles

This paper presents an ellipsoidal model that is constructed for small layered nonspherical particles and methods for constructing “effective” multilayer ellipsoids, the light-scattering properties of which would be close to the corresponding properties of original particles. In the case of axisymmetric particles, prolate or oblate spheroids (ellipsoids of revolution) are implied. Numerical calculations of the polarizability and scattering cross sections of small layered nonspherical particles, including nonconfocal (similar) spheroids, Chebyshev particles, and pseudospheroids, are performed by different approximate and rigorous methods. Approximate approaches involve the use of an ellipsoidal model, in which the polarizability of a layered particle is determined in two ways. In the first case, the polarizability is calculated in the approximation of confocal spheroids, while, in the second case, it is sought as a linear combination of the polarizabilities of embedded spheroids proportionally to the volumes of layers. Among rigorous methods, the extended boundary conditions method and the generalized separation of variables method are applied. On the basis of a comparison of the results obtained with rigorous and approximate approaches, their drawbacks and advantages are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and how this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A 3D DLM/FD method for simulating the motion of spheres and ellipsoids under creeping flow conditions

We present in this article a novel distributed Lagrange multiplier/fictitious domain (DLM/FD) method for simulating fluid-particle interaction in three-dimensional (3D) Stokes flow. The methodology is validated by comparing the numerical results for a neutrally buoyant particle, of either spherical or prolate shape, with the associated Jeffrey's solutions for a simple shear flow. The results concerning two balls, interacting under creeping flow conditions in a bounded shear flow, are consistent with those available in the literature. We will discuss also the interactions of two balls in a bounded shear flow, when these balls are very close initially. For a prolate ellipsoid rotating in a shear flow under the sole effect of the particle inertia, shear plane tumbling is stable, while log-rolling is unstable. For two prolate ellipsoids interacting in a bounded shear flow, the results are similar to those for two balls if the major axes are initially orthogonal to the shear plane (a result not at all surprising considering that the intersections of the ellipsoids with the shear pane are circular).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Spherical nematic shells with a prolate ellipsoidal core

We report that liquid crystal shells have attracted considerable attention in recent years. In such systems, a combination of confinement and curvature generates topological defect structures that do not exist in the bulk. Past studies, however, have largely focused on perfectly spherical shells, and little attention has been devoted to the impact of core geometry on the configuration and arrangement of topological defects. In this work, a microfluidic glass capillary device is used to encapsulate spherical and prolate ellipsoidal particles in nematic liquid crystal (LC) droplets dispersed in aqueous media. Our experimental studies show that, when trapped inside a radial LC droplet, spherical particles with both homeotropic and planar anchoring are highly localized at the droplet's center. While the radial configuration of the LC droplets is not altered by a homeotropic particle, polystyrene particles with strong planar anchoring disturb the radial ordering, leading to a twisted structure. Experiments indicate that off-center particle positions can also arise, in which defects are displaced towards the vicinity of the droplet's surface. In contrast, when prolate ellipsoidal particles are encapsulated in a thick radial LC shell, the minimum free energy corresponds to configurations where the particle is positioned at the droplet center. Lastly, in this case, defects arise at the two ends of the prolate ellipsoid, where the curvature of the particle is maximal, leading to the formation of peculiar hybrid and twisted structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Ellipsoidal Fitting Methodology for Defect Clusters in Gallium Arsenide

In assessing the initial spatial distribution of defects from neutron or heavy ion irradiation, it is useful to have a reliable, automated, and fast-running tool to evaluate characteristic metrics such as the number of sub-clusters or the overall cluster volume. The latter metric, for instance, can be utilized to estimate a reference neutron fluence level at which inter-cluster interaction effects begin to become significant. This paper details a methodology to fit an arbitrarily complex defect map with a set of ellipsoids (one per identified sub-cluster) in which the constituent defects of a sub-cluster are determined using fuzzy degree-of-membership analysis. Specifically, a parameterized model is developed for point defects in gallium arsenide. Cluster volume calculations based on the model are compared against convex hull and single- ellipsoid representations. Results show that the parameterized sub-cluster model begins to deviate from the two reference models at a recoil energy of about 100 keV in GaAs, with the convex hull and single-ellipsoid representations increasingly overestimating the volume thereafter.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

The orbital nature of 81 ellipsoidal red giant binaries in the large magellanic cloud

In this paper, we collect a sample of 81 ellipsoidal red giant binaries in the Large Magellanic Cloud (LMC), and we study their orbital natures individually and statistically. The sample contains 59 systems with circular orbits and 22 systems with eccentric orbits. We derive orbital solutions using the 2010 version of the Wilson–Devinney code. The sample is selection-bias corrected, and the orbital parameter distributions are compared to model predictions for the LMC and to observations in the solar vicinity. The masses of the red giant primaries are found to range from about 0.6 to 9 M{sub ⊙} with a peak at around 1.5 M{sub ⊙}, in agreement with studies of the star formation history of the LMC, which find a burst of star formation beginning around 4 Gyr ago. The observed distribution of mass ratios q=m{sub 2}/m{sub 1} is more consistent with the flat q distribution derived for the solar vicinity by Raghavan et al. than it is with the solar vicinity q distribution derived by Duquennoy and Mayor. There is no evidence for an excess number of systems with equal mass components. We find that about 20% of the ellipsoidal binaries have eccentric orbits, twice the fraction estimated by Soszynski et al. Our eccentricity evolution test shows that the existence of eccentric ellipsoidal red giant binaries on the upper parts of the red giant branch (RGB) can only be explained if tidal circularization rates are ∼1/100 the rates given by the usual theory of tidal dissipation in convective stars.

79 ASTRONOMY AND ASTROPHYSICS↗
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↗
DOE OSTI2017

Retroreflection of Optical Radiation from Ellipsoidal-Porous Surfaces

The retroreflection of optical radiation from surfaces with roughness in the form of ellipsoidal pores and two-level roughness in the form of convex ellipsoids with elliptical-porous surfaces is studied using the ROKS-RG Monte-Carlo method software in the geometrical-optics approximation. The dependence of the retroreflection phase function on the parameters of bodies that simulates the rough surface is analyzed. It is shown that the angular dependence of the retroreflection from porous rough surfaces with arbitrarily oriented pores and the aspect ratio higher than unity is a pronounced peak with concave sides at all incidence angles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗