Ellipsoidal Research Articles

An Ellipsoidal Focused Ultrasound Transducer for Extend-Focus Photoacoustic Microscopy

Limited by spherical focused ultrasound transducer (SUT) with a high acoustic numerical aperture, photoacoustic microscopy (PAM) suffers a rapidly degrading sensitivity and lateral resolution as increased depth. In this study, an ellipsoidal focused ultrasound transducer (EUT) was developed to address the above restriction via providing high sensitivity and lateral resolution over a large depth of field (DOF). To fabricate the EUT, the piezoelectric element was laminated onto a curved steel surface for self-focusing (the ellipsoidal continuous-focus geometry was employed instead of the spherical single-focus one). Additionally, phantoms and in vivo animal experiments were performed by an extend-focus PAM equipped with EUT to characterize its performance. The EUT involved over 30 MHz center frequency and -6 dB bandwidth of 124% with a resolution-invariant focal depth of 1.39 mm, more than 3 times the DOF of the SUT. The in vivo imaging results demonstrated that the EUT was capable of extending the focal depth to get rid of the restriction of the visual field, while the DOF of the SUT was limited by the nature of spherical geometry. The EUT markedly enhances the image quality at different imaging depths, which has great potential for promoting the biomedical development of in vivo rapid-noninvasive PAM.

3D Morphology of Open Clusters in the Solar Neighborhood with Gaia EDR 3: Its Relation to Cluster Dynamics

Abstract We analyze the 3D morphology and kinematics of 13 open clusters (OCs) located within 500 pc of the Sun, using Gaia EDR 3 and kinematic data from the literature. Members of OCs are identified using the unsupervised machine-learning method StarGO, using five parameters (X, Y, Z, ). The OC sample covers an age range of 25 Myr to 2.65 Gyr. We correct the asymmetric distance distribution that is due to parallax error using Bayesian inversion. The uncertainty in the corrected distance for a cluster at 500 pc is 3.0–6.3 pc, depending on the intrinsic spatial distribution of its members. We determine the 3D morphology of the OCs in our sample and fit the spatial distribution of stars within the tidal radius in each cluster with an ellipsoid model. The shapes of the OCs are well described with oblate spheroids (NGC 2547, NGC 2516, NGC 2451A, NGC 2451B, and NGC 2232), prolate spheroids (IC 2602, IC 4665, NGC 2422, Blanco 1, and Coma Berenices), or triaxial ellipsoids (IC 2391, NGC 6633, and NGC 6774). The semimajor axis of the fitted ellipsoid is parallel to the Galactic plane for most clusters. Elongated filament-like substructures are detected in three young clusters (NGC 2232, NGC 2547, and NGC 2451B), while tidal-tail-like substructures (tidal tails) are found in older clusters (NGC 2516, NGC 6633, NGC 6774, Blanco 1, and Coma Berenices). Most clusters may be supervirial and expanding. N-body models of rapid gas expulsion with a star formation efficiency of ≈1/3 are consistent with clusters more massive than 250 M ⊙, while clusters less massive than 250 M ⊙ tend to agree with adiabatic gas expulsion models. Only five OCs (NGC 2422, NGC 6633, NGC 6774, Blanco 1, and Coma Berenices) show clear signs of mass segregation.

Striatibotrys neoeucylindrosporus sp. nov., a Stachybotrys-like fungus from North America.

Two isolates from Canada and the USA (UAMH 7122 and UAMH 7211, respectively) previously identified as Stachybotrys eucylindrosporus were studied by morphology and six-locus phylogeny (cmdA, ITS, LSU, rpb2, tef1α and tub2). UAMH 7122 and UAMH 7211 are morphologically related but phylogenetically distinct from Striatibotrys eucylindrosporus (≡Stachybotrys eucylindrosporus) and Str. rhabdosporus. Hence, UAMH 7122 and UAMH 7211 are described as a new species, Striatibotrys neoeucylindrosporus sp. nov. with UAMH 7211 as the holotype. The characters of this species include some phialides proliferating by holoblastic extension of phialides and conidia clavate, subcylindrical or cylindrical ellipsoid, or dumbbell-shaped, dark brown to olivaceous grey when mature, longitudinally striate, 10.3-12.3×3-3.8 µm. A key to the species of Striatibotrys is provided.

Impact of shape: DNS of sediment transport with non-spherical particles

Abstract

Volume properties and some characterizations of ellipsoids in En+1

Volume properties and some characterizations of ellipsoids in En+1

Single-cell mechanical analysis and tension quantification via electrodeformation relaxation.

The mechanical behavior and cortical tension of single cells are analyzed using electrodeformation relaxation. Four types of cells, namely, MCF-10A, MCF-7, MDA-MB-231, and GBM, are studied, with pulse durations ranging from 0.01 to 10s. Mechanical response in the long-pulse regime is characterized by a power-law behavior, consistent with soft glassy rheology resulting from unbinding events within the cortex network. In the subsecond short-pulse regime, a single timescale well describes the process and indicates the naive tensioned (prestressed) state of the cortex with minimal force-induced alteration. A mathematical model is employed and the simple ellipsoidal geometry allows for use of an analytical solution to extract the cortical tension. At the shortest pulse of 0.01s, tensions for all four cell types are on the order of 10^{-2} N/m.

Hailstone Shapes

AbstractHailstone growth results in a variety of hailstone shapes. These shapes hold implications for modeling of hail processes, hailstone fall behaviors including fall speeds, and remote sensing signatures of hail. This study is an in-depth analysis of natural hailstone shapes, using a large dataset of hailstones collected in the field over a 6-yr period. These data come from manual measurements with digital calipers and three-dimensional infrared laser scans. Hailstones tend to have an ellipsoidal geometry with minor-to-major axis ratios ranging from 0.4 to 0.8, and intermediate-to-major axis ratios between 0.8 and 1.0. These suggest hailstones are better represented as triaxial ellipsoids as opposed to spheres or spheroids, which is commonly assumed. The laser scans allow for precise sphericity measurements, for the first time. Hailstones become increasingly nonspherical with increasing maximum dimension, with a typical range of sphericity values of 0.57 to 0.99. These sphericity values were used to estimate the drag coefficient, which was found to have a typical range of 0.5 to over 0.9. Hailstone maximum dimension tends to be 20%–50% larger than the equivalent-volume spherical diameter. As a step toward understanding and quantifying hailstone shapes, this study may aid in better parameterizations of hail in models and remote sensing hail detection and sizing algorithms.

Performance of a solution of the direct geodetic problem by Taylor series of Cartesian coordinates

Abstract The direct geodetic problem is regarded on the biaxial and triaxial ellipsoid. A known solution method suitable for low eccentricities, which uses differential equations in Cartesian coordinates and Taylor series expansions of these coordinates, is advanced in view of its practical application. According to previous works, this approach has the advantages that no singularities occur in the determination of the coordinates, its mathematical formulation is simple and it is not computationally intensive. The formulas of the solution method are simplified in the present contribution. A test of this method using an extensive test data set on a biaxial earth ellipsoid shows its accuracy and practicability for distances of any length. Based on the convergence behavior of the series of the test data set, a truncation criterion for the series expansions is compiled taking into account accuracy requirements of the coordinates. Furthermore, a procedure is shown which controls the truncation of the series expansions by accuracy requirements of the direction to be determined in the direct problem. The conducted tests demonstrate the correct functioning of the methods for the series truncation. However, the considered solution method turns out to be significantly slower than another current method for biaxial ellipsoids, which makes it more relevant for triaxial ellipsoids.

A New Record of Epicoccum draconis Isolated from the Soil in Korea

A fungal isolate US-18-11 was isolated from the soil in Uiseong, Korea. The mycelium growth measured after 7 days of incubation at 22℃ on malt extract agar (MEA) and oatmeal agar (OA) media was 42-43 mm and 41-44 mm in diameter, respectively. The fungal colony formed white to dull green aerial mycelia that were floccose with regular margins and olivaceous black with leaden gray patches on the reverse side. The conidia were hyaline to brown in color, ellipsoidal to ovoid, guttulate, abundant, globose, solitary, or confluent measuring 3.2-7.2×1.1-2.3 μm. A BLAST search of the large subunit (LSU), internal transcribed spacer (ITS) region, second largest subunit of DNA-directed RNA polymerase II (RPB2) and β-tubulin (TUB2) gene sequences revealed that the isolate US-18-11 has similarities of 99, 100, 97, and 99% with those of Epicoccum draconis CBS 186.83, respectively. A neighbor-joining phylogenetic tree constructed based on the concatenated dataset of above-mentioned sequences showed that isolate US-18-11 clustered with Epicoccum draconis CBS 186.83 in the same clade. Based on the results of morphological, cultural, and phylogenetic analysis, the isolate US-18-11 was identical to the previously described E. draconis CBS 186.83. To our knowledge, this is the first report of E. draconis in Korea.

Direct and Indirect Estimation of the Variance–Covariance Matrix of the Parameters of a Fitted Ellipse and a Triaxial Ellipsoid

AbstractThis work deals with the estimation of the variance–covariance matrix of the parameters of a fitted ellipse and an ellipsoid by a direct and an indirect procedure. In the direct approach, t...

Quadratic Element Integration of Approximated First Order Polarization Tensor for Sphere

Polarization tensor is an object-specific property in order to indicate its shape, size and also the material used. This information is beneficial to determine between used and unused material underground for example. In this paper, we describe an accurate and easy-implemented method based on numerical integration in order to compute the first order polarization tensor. We proposed an alternative method to deal with boundary integral equation of first order polarization tensor which is quadratic element numerical integration. This method uses standard three points Gaussian quadrature in order to generate the singular integral operator matrix of polarization tensor. Different values of object’s conductivity are used in order to study the behavior of the polarization tensor. The validation of the results was based on the exact solution provided for sphere and ellipsoid geometry by previous researcher. Moreover, numerical computation showed that the quadratic element integration generates more accurate numerical results for the approximated first order polarization tensor and better in its convergence. The numerical results are illustrated in graphical form in order to show the validity of the proposed scheme.

Studying and simulation of ellipsoidal contact models for application in AFM nano manipulation

Four contact models including Hertz, Jamari, Jeng-Wang and Weng-Tang-Zhou-Zhu were considered. To verify the results of contact mechanics, the indentation depth has been compared with spherical geometry. According to the obtained results, by comparing the spherical and elliptical geometries, the indentation depth for spherical geometry is higher than for the ellipsoidal geometry, due to the existence of eccentricity in elliptical contact models which does not exist in spherical geometry. Among the models, the Jeng-Wang and Weng-Tang-Zhou-Zhu are models that are based on the contact of a particle with the substrate. Based on the existing experimental work, Jeng-Wang is the most suitable model for being applied in particle-substrate contact point. The Hertz model has been developed from crowned cylinder equations in order to be implemented for ellipsoidal geometry, moreover the Jamari model investigates two ellipses in contact with each other. By comparing Jeng-Wang and Weng-Tang-Zhou-Zhu models it is obvious that Jeng-Wang has the highest indentation depth while for the Weng-Tang-Zhou-Zhu model it is the lowest. These trends happen for two contact points. Also four materials are compared, among which graphite and chromium have the highest and the lowest indentation depths, respectively. Finally based on the obtained results Jeng-Wang and Jamari are the most suitable contact models that can be implemented in the manipulation of ellipsoidal nanoparticles.

Toughening mechanisms of the elytra of the diabolical ironclad beetle.

Joining dissimilar materials such as plastics and metals in engineered structures remains a challenge1. Mechanical fastening, conventional welding and adhesive bonding are examples of techniques currently used for this purpose, but each of these methods presents its own set of problems2 such as formation of stress concentrators or degradation under environmental exposure, reducing strength and causing premature failure. In the biological tissues of numerous animal and plant species, efficient strategies have evolved to synthesize, construct and integrate composites that have exceptional mechanical properties3. One impressive example is found in the exoskeletal forewings (elytra) of the diabolical ironclad beetle, Phloeodes diabolicus. Lacking the ability to fly away from predators, this desert insect has extremely impact-resistant and crush-resistant elytra, produced by complex and graded interfaces. Here, using advanced microscopy, spectroscopy and in situ mechanical testing, we identify multiscale architectural designs within the exoskeleton of this beetle, and examine the resulting mechanical response and toughening mechanisms. We highlight a series of interdigitated sutures, the ellipsoidal geometry and laminated microstructure of which provide mechanical interlocking and toughening at critical strains, while avoiding catastrophic failure. These observations could be applied in developing tough, impact- and crush-resistant materials for joining dissimilar materials. We demonstrate this by creating interlocking sutures from biomimetic composites that show a considerable increase in toughness compared with a frequently used engineering joint.

Reference frame and map projection for irregular shaped celestial bodies

Abstract. Recent advancements of technology resulted in greater knowledge of the Solar System and the need for mapping small celestial bodies significantly increased. However, creating a good map of such small objects is a big challenge for the cartographer: they are usually irregular shaped, the usual reference frames like the ellipsoid of revolution is inappropriate for their approximation.A method is presented to develop best-fitting irregular surfaces of revolution that can approximate any irregular celestial body. (Fig. 1.) Then a simple equal-area map projection is calculated to map this reference frame onto a plane. The shape of the resulting map in this projection resembles the shape of the original celestial body.The usefulness of the method is demonstrated on the example of the comet 67P/Churyumov-Gerasimenko. This comet has a highly irregular shape, which is hard to map. Previously used map projections for this comet include the simple cylindrical, which greatly distorts the surface and cannot depict the depressions of the object. Other maps used the combination of two triaxial ellipsoids as the reference frame, and the gained mapping had low distortion but at the expense of showing the tiny surface divided into 11 maps in different complicated map projections (Nyrtsov et. al., 2018). On the other hand, our mapping displays the comet in one single map with moderate distortion and the shape of the map frame suggests the original shape of the celestial body (Fig. 2. and 3.).

Asteroid lightcurve inversion with Bayesian inference

Context.We assess statistical inversion of asteroid rotation periods, pole orientations, shapes, and phase curve parameters from photometric lightcurve observations, here sparse data from the ESAGaiaspace mission (Data Release 2) or dense and sparse data from ground-based observing programs.Aims.Assuming general convex shapes, we develop inverse methods for characterizing the Bayesian a posteriori probability density of the parameters (unknowns). We consider both random and systematic uncertainties (errors) in the observations, and assign weights to the observations with the help of Bayesian a priori probability densities.Methods.For general convex shapes comprising large numbers of parameters, we developed a Markov-chain Monte Carlo sampler (MCMC) with a novel proposal probability density function based on the simulation of virtual observations giving rise to virtual least-squares solutions. We utilized these least-squares solutions to construct a proposal probability density for MCMC sampling. For inverse methods involving triaxial ellipsoids, we update the uncertainty model for the observations.Results.We demonstrate the utilization of the inverse methods for three asteroids withGaiaphotometry from Data Release 2: (21) Lutetia, (26) Proserpina, and (585) Bilkis. First, we validated the convex inverse methods using the combined ground-based andGaiadata for Lutetia, arriving at rotation and shape models in agreement with those derived with the help of Rosetta space mission data. Second, we applied the convex inverse methods to Proserpina and Bilkis, illustrating the potential of theGaiaphotometry for setting constraints on asteroid light scattering as a function of the phase angle (the Sun-object-observer angle). Third, with the help of triaxial ellipsoid inversion as applied toGaiaphotometry only, we provide additional proof that the absoluteGaiaphotometry alone can yield meaningful photometric slope parameters. Fourth, for (585) Bilkis, we report, with 1-σuncertainties, a refined rotation period of (8.5750559 ± 0.0000026) h, pole longitude of 320.6° ± 1.2°, pole latitude of − 25.6° ± 1.7°, and the first shape model and its uncertainties from convex inversion.Conclusions.We conclude that the inverse methods provide realistic uncertainty estimators for the lightcurve inversion problem and that theGaiaphotometry can provide an asteroid taxonomy based on the phase curves.

Oscillations of Hypermassive Compact Stars with Gravitational Radiation and Viscosity

Abstract Binary neutron star mergers, such as the multimessenger GW170817 event, may produce hypermassive compact objects that are supported against collapse by the internal circulation of the fluid within the star. We compute their unstable modes of oscillations driven by gravitational-wave radiation and shear viscosity, modeling them as triaxial Riemann ellipsoids. We work in a perturbative regime, where the gravitational radiation-reaction force is taken into account at 2.5-post-Newtonian order and find unstable modes with dissipation timescales ≳1 ms that are relevant to the transient state of a hypermassive remnant of a merger. We show that the secular instabilities are dominated by gravitational-wave radiation. If the shear viscosity is included, it can increase the growth times or even stabilize the unstable modes, but it must have values several orders of magnitude larger than predicted for cold neutron stars.

Zero Temperature Coefficient behavior for Ellipsoidal MOSFET

The zero temperature coefficient (ZTC) is investigated by three-dimensional numerical simulations in the Metal-Oxide-Semiconductor (MOS) Field Effect Transistor (MOSFET) with the ellipsoidal (EM) and conventional rectangular gate geometries (CM), considering the same channel widths (W), gate areas (Ag) and bias condition (BC). In this work an improved simple model which predicts the ZTC point taking into account only the mobility degradation factor (c) and threshold voltage (Vth) parameters as function of temperature is proposed in the linear and saturation operation regions. The analysis takes into account the temperature variations of the threshold voltage and the mobility degradation factor. Although simple, the model predictions present a good agreement with the numerical simulations results.

Selectively Enhancing Solar Scattering for Direct Radiative Cooling through Control of Polymer Nanofiber Morphology.

Radiative cooling can alleviate urban heat island effects and passively improve personal thermal comfort. Among many emerging approaches, infrared (IR) transparent films and fabrics are promising because they can allow objects to directly radiate heat through bands of atmospheric transparency while blocking solar heating. However, achieving high solar reflectance while maintaining IR transmittance using scalable nanostructured materials requires control over the shape and size distribution of the nanoscale building blocks. Here, we investigate the scattering and transmission properties of electrospun polyacrylonitrile (PAN) nanofibers that feature spherical, ellipsoidal, and cylindrical morphologies. We find that nanofibers that have ellipsoidal beads exhibit the most efficient solar scattering, mainly due to the additive dielectric resonances of the ellipsoidal and cylindrical geometries, as confirmed through electromagnetic simulations. This favorable scattering decreases the amount of material needed to reach above 95% solar reflectance, which, in turn, enables high infrared transmittance (>70%) despite PAN's intrinsic IR absorption. We further show that these PAN nanofibers (nanoPAN) can enable cooling of surfaces with relatively low solar reflectance, which is demonstrated by covering a reference blackbody surface with beaded nanoPAN. During peak solar hours, this configuration lowers the temperature of the black surface by approximately 50 °C and is able to achieve as low as 3 °C below the ambient air temperature. More broadly, our demonstration using PAN, which is not as IR transparent as more commonly used polyethylene, provides a method for utilizing lower purity materials in radiative cooling.

Estimation of elastic seismic demands in TU structures using interactive relations between shear and torsion

The code static eccentricity model for elastic torsional design of structures has two critical shortcomings: (1) the negation of the inertial torsional moment at the center of mass (CM), particularly for torsionally-unbalanced (TU) building structures, and (2) the confusion caused by the discrepancy in the definition of the design eccentricity in codes and the resistance eccentricity commonly used by engineers such as in FEMA454. To overcome these shortcomings, using the resistance eccentricity model that can accommodate the inertial torsional moment at the CM, interactive relations between shear and torsion are proposed as follows: (1) elastic responses of structures at instants of peak edge-frame drifts are given as functions of resistance eccentricity, and (2) elastic hysteretic relationships between shear and torsion in forces and deformations are bounded by ellipsoids constructed using two adjacent dominant modes. Comparison of demands estimated using these two interactive relations with those from shake-table tests of two TU building structures (a 1:5-scale five-story reinforced concrete (RC) building model and a 1:12-scale 17-story RC building model) under the service level earthquake (SLE) show that these relations match experimental results of models reasonably well. Concepts proposed in this study enable engineers to not only visualize the overall picture of torsional behavior including the relationship between shear and torsion with the range of forces and deformations, but also pinpoint easily the information about critical responses of structures such as the maximum edge-frame drifts and the corresponding shear force and torsion moment with the eccentricity.

Modeling transit and reflected light curves for non-spherical exoplanets

Newton was the first to provide a mathematical framework to describe the oblateness of the Earth, a framework later expended by Maclaurin, Jacobi, and Poincaré and applied to other astronomical objects. In the Solar System, the Jacobi triaxial ellipsoid has successfully described the shape of Haumea and Chariklo, while Ceres appears to be an oblate spheroid of the Maclaurin type. Beyond the Solar System, new exoplanets are being discovered almost daily showing vastly different characteristics (e.g. mass, temperature, eccentricity, radius, orbital period). Recently, Kepler-427b was shown to be a moderately oblate spheroid, and it is possible to imagine that certain exoplanets could be triaxial ellipsoids. Considering the wealth of data now available from the current and past missions whose aim is to hunt for new extra-solar systems, it has become vital to broaden the range of parameters to be estimated for a single exoplanet. In this paper, we present a new algorithm to model variations in transit light curves induced by ellipsoidal exoplanets, which will be ultimately released to the community as a MATLAB-based package. Most variations happen during the ingress and egress phase of the transit. Combining several transits can lead to the detection of oblateness by measuring the precession of the obliquity angle of the exoplanet over time. For the first time, we also model reflected light curves for ellipsoidal exoplanets.