Ellipsoidal Surface Research Articles

Does plastic anisotropy affect the thermo-mechanical coupling in steel?

The Taylor-Quinney coefficient (TQC) quantifies the ratio of thermal to plastic work in a (dynamically) deforming specimen. Its importance lies in the determination of the material self-heating under shock which might influence the properties of the materials. Most work to date is based on isotropically deforming specimens, so that the determined global quantities exhibit no spatial variation or anisotropy. Even the few existing works on anisotropic material were carried out using an average stress-strain relation, eliminating spatial dependency.This study presents experimental and numerical results for Wire and Arc Additive Manufacturing (WAAM) 316 L stainless specimens that deform from a standard initial cylindrical shape into well-defined ellipsoids upon impact as in the case of an anisotropic material. The measured thermal evolutions across the major and the minor axes of the ellipsoid are quite different, which might suggest that each direction possesses its own TQC when average plastic work is used. Numerical modeling allows for determining the local stress and strains on the ellipsoid's surface. Using this data, our measurements show that the TQC is not affected by the orientation of the measurements. In other words, and in contrast to previous works, despite plastic anisotropy, the TQC remains isotropic.

Fermi Surface and Superconducting Properties of α-IrSn4, α-RhSn4, IrGe4, and RhGe4 with Trigonal Chiral Structure

We grew single crystals of α-IrSn4 and α-RhSn4 using the Sn-self flux method and those of IrGe4 using the Czochralski method in a tetra-arc furnace, together with polycrystals of RhGe4 under pressure. The obtained single crystals were found to be an enantiopure of the trigonal chiral structures with space groups P3121 (No. 152) or P3221 (No. 154), depending on the samples. Namely, one ingot belongs to P3121 and another ingot belongs to P3221. Single crystalline samples were of high quality, with residual resistivity ρ0 = 0.052 µΩ·cm and residual resistivity ratio RRR = 1250 in α-IrSn4. We confirmed bulk-superconductivity in IrGe4 and RhGe4 from the measurements of the specific heat. The present four compounds are uncompensated metals because the valence electrons are odd in number. The corresponding transverse magnetoresistance indicated saturated behaviors in high magnetic fields, while non-saturated behaviors were observed in the configuration with current \(J\parallel [11\bar{2}0]\) and magnetic field \(H\parallel [\bar{1}100]\), suggesting the existence of open orbits along the [0001] direction. To clarify the Fermi surfaces of these compounds, we conducted de Haas–van Alphen experiments, which showed that the main Fermi surface is a flat ellipsoidal Fermi surface with many arms and is split into two Fermi surfaces, reflecting the noncentrosymmetric (chiral) structure.

Aspherical, sphero-cylindrical, toroidal, and ellipsoidal surfaces for designing astigmatic spectacle lenses with axis orientation

In this paper, formulas for aspherical, sphero-cylindrical, toroidal, and ellipsoidal surfaces with astigmatic axes are derived. Based on this, four types of curved surfaces were designed to correct astigmatism with axis, and, subsequently, the lenses were simulated, fabricated, and measured. A total of ten spectacle lenses in two groups were designed. Those in the first group used identical optical parameters. The spherical and cylindrical powers and maximum and minimum edge thicknesses of aspherical, sphero-cylindrical, and ellipsoidal surfaces were compared. The results indicated that the power of the lens constructed using the toroidal surface was more accurate than those of the other three lenses. Moreover, the minimum edge thickness of the toroidal surface was 1.2%, 4.98%, and 4.87% lower than those of the aspherical, sphero-cylindrical, and ellipsoidal surfaces, respectively. The powers and edge thicknesses of toroidal surfaces with different diopters were compared in the second group. The minimum and maximum edge thicknesses were observed to be reduced by 8.97% and 6.05%, respectively, corresponding to the conic constants obtained via ray tracing. The conclusion will be significant for clinical ophthalmology and optical design for the patients with astigmatism.

Necessary conditions for existence of an additional integral in the problem on motion of a solid body with a fixed point in the flow of particles bounded by an ellipsoid revolution surface

Рассматривается задача о движении в свободном молекулярном потоке частиц твердого тела с неподвижной точкой, ограниченного поверхностью эллипсоида вращения. Получены необходимые условия существования в этом случае дополнительного аналитического первого интеграла, независимого с интегралом энергии.

Abrasive slurry jet machining system using polyurethane@silica core-shell particles for internal surfaces of axisymmetric x-ray mirrors.

Abrasive machining has been used for inner surface processing of various hollow components. In this study, we applied an in-air fluid jet as a precision machining method for the inner surface of an axisymmetric x-ray mirror whose inner diameter was less than 10mm. We employed an abrasive with a polyurethane@silica core-shell structure, which has a low density of about 1.2 g/cm3 and a relatively large particle size of about 15 µm. By using this abrasive, a practical removal rate and a smooth machined surface were simultaneously obtained. We performed figure corrections for an axisymmetric mirror and improved the circumferential figure accuracy to a sub-10nm root mean square level. To evaluate the machining performance in the longitudinal direction of the ellipsoidal surface, we also performed periodic figure fabrication on the inner surface of a 114 mm-long nickel ellipsoidal mirror. X-ray ptychography, an optical phase retrieval method, was also employed as a three-dimensional figure measurement technique of the mirror. The wavefield of the x-ray beam focused by the processed ellipsoidal mirror was observed with the ptychographic system at SPring-8, a synchrotron radiation facility. The retrieval calculations for the wavefront error confirmed that a sinusoidal waveform with a period of 12mm was fabricated on the mirror surface. These experimental results suggest that a nanoscale figure fabrication cycle for the inner surface consisting of jet machining and wavefront measurement has been successfully constructed. We expect this technique to be utilized in the fabrication of error-free optical mirrors and various parts having hollow shapes.

Stadiums based on curvilinear geometry: Approximation of the ellipsoid offset surface

Abstract This article provides an effective method of determining the coordinates of points and the angles for various surfaces approximating the ellipsoid surface. The stands of the stadium (with a capacity of up to 82,000 seats) with rows shaped by ellipse arcs were designed (in accordance with the European Standard EN 13200-1). An algorithm was proposed to determine the optimal height of the ring steps (with the guarantee of unobstructed vision of the entire playing field from each seat of the stands). The second algorithm ensures a comfortable space in each individual seating place in the stands (deviation of the depth of the row generated by ellipse arcs did not exceed 0.000009 m at any place of the stands). This article encourages readers to program DXF files (read in the AutoCAD system) to streamline design work.

Light scattering by media consisting of Maxwell 3-foci concave particles in the geometrical optics approximation

We study light scattering by non-spherical Maxwell particles and media consisting of them using computer simulations. The particle shapes are defined by a generalization of the concept 3-foci ellipses introduced by J. C. Maxwell. We modify them for the 3-D case by replacing the distances between the foci and current points on the ellipsoid surface by their logarithms. This makes it possible to describe 3-D ellipsoids that have partially concave surfaces. We carry out simulations within the framework of geometrical optics based on reflection and refraction of 108 rays and calculate phase curves of the nonzero elements of the Mueller matrix. This enables us to clarify the origin of the characteristics of the phase curves, i.e., which scattering order is responsible for the curve features. It is shown that equality M12 = M21 and M34 = –M43 that are valid for isolated particles are broken by the interactions with neighboring particles. It is also shown that the opposition effect of such particulate surfaces is mainly formed by components having one or more internal reflections within particles.

Strain-induced control of radiative heat transfer between nanoparticles in a plasmonic cavity

Graphene enables the versatile modulation and significant enhancement of their optical properties by external strains, which plays a pivotal role in various applications, such as active thermal modulation. In this work, we investigate the near-field radiative heat transfer (NFRHT) between two nanoparticles mediated by a strain-induced plasmonic cavity consisting of the two parallel graphene sheets (GSs) under external mechanical strain. By adjusting the strain modulus, the ellipsoidal surface plasmon polaritons supported by strain-induced graphene are found to significantly impact the NFRHT between nanoparticles. The integral and interlayer twist can synergistically manipulate the reflection properties of the cavity, allowing the anisotropic coupling of nanoparticles with the cavity in different directions. Under large strain modulus and suitable twisted angles, the NFRHT can be enhanced up to 5 orders of magnitude. In addition, the chemical potential of graphene can be tuned to provide additional ways to modulate the heat transfer between nanoparticles. These findings may open up promising avenues for highly efficient thermal management, thermal communication, and energy harvesting.

Improved chord method for the direct and inverse problems of the distances and azimuths on the reference ellipsoid

Through transformation from geocentric to topocentric space rectangular coordinate system and taking advantage of the plain geometrical relationships from the chord between two points on the ellipsoidal surface, the problems of the distances and azimuths on the reference ellipsoid can be converted to several elementary equations and corresponding corrective terms. Based on this, an improved chord method has been proposed in the article. Numeric experiments have validated that the new algorithm can be effective for arbitrary distances. Moreover, the solution can also be operational without singularity in the polar or equatorial regions, in the situations where the difference in longitude is 180°, and in other special cases. And with suitable corrections, the improved method can be prospectively applied to other problems of distances and azimuths with corresponding precision.

The shape of aroma: Measuring and modeling citrus oil gland distribution

Societal Impact StatementCitrus are intrinsically connected to human health and culture, preventing human diseases like scurvy and inspiring sacred rituals. Citrus fruits come in a stunning number of different sizes and shapes, ranging from small clementines to oversized pummelos, and fruits display a vast diversity of flavors and aromas. These qualities are key in both traditional and modern medicine and in the production of cleaning and perfume products. By quantifying and modeling overall fruit shape and oil gland distribution, we can gain further insight into citrus development and the impacts of domestication and improvement on multiple characteristics of the fruit.Summary Citrus come in diverse sizes and shapes, and play a key role in world culture and economy. Citrus oil glands in particular contain essential oils which include plant secondary metabolites associated with flavor and aroma. Capturing and analyzing nuanced information behind the citrus fruit shape and its oil gland distribution provide a morphology‐driven path to further our insight into phenotype–genotype interactions. We investigated the shape of citrus fruit of 51 accessions based on 3D X‐ray computed tomography (CT) scan reconstructions. Accessions include members of the three ancestral citrus species as well as related genera, and several interspecific hybrids. We digitally separate and compare the size of fruit endocarp, mesocarp, exocarp, and oil gland tissue. Based on the centers of the oil glands, overall fruit shape is approximated with an ellipsoid. Possible oil gland distributions on this ellipsoid surface are explored using directional statistics. There is a strong allometry along fruit tissues; that is, we observe a strong linear relationship between the logarithmic volume of any pair of major tissues. This suggests that the relative growth of fruit tissues with respect to each other follows a power law. We also observe that on average, glands distance themselves from their nearest neighbor following a square root relationship, which suggests normal diffusion dynamics at play. The observed allometry and square root models point to the existence of biophysical developmental constraints that govern novel relationships between fruit dimensions from both evolutionary and breeding perspectives. Understanding these biophysical interactions prompts an exciting research path on fruit development and breeding.

NURBS Surface-Altering Optimization for Identifying Critical Slip Surfaces in 3D Slopes

The evaluation of slope stability of a three-dimensional slope requires identifying the critical slip surface with the minimum factor of safety, which is a complex optimization problem. Failure to identify the critical slip surface can lead to unconservative conclusions about the stability of a slope. This paper proposes a novel 3D surface-altering optimization method, which iteratively alters the geometry of a 3D slip surface to find the critical slip surface representing the minimum factor of safety in a slope. The geometry of the slip surface is defined via nonuniform rational basis spline (NURBS) curves formed over a plan grid of control points. The proposed method includes a series of five subroutines that apply various forms of transformations to the control points. These subroutines include minimization problems, which determine the optimal transformation parameters for minimizing the obtained factor of safety of the resulting slip surfaces. Given that any geometrically defined slip surface can be approximated using an equivalent series of NURBS control points, the proposed method can be used in efforts to further reduce the global factor of safety first obtained via conventional search methods, such as those involving spherical or ellipsoidal slip surfaces. To demonstrate its effectiveness, the proposed method was applied to further optimize the critical ellipsoidal slip surfaces reported in some numerical examples. Comparing the results with those limited to ellipsoidal slip surfaces, the proposed method was consistently able to identify slip surfaces with significantly lower factors of safety. The postaltered slip surfaces also matched closely with finite element shear strength reduction results. As such, the proposed method is effective in searching for critical slip surfaces and can be used as a final step in the critical surface searching routine.

Model anisotropic materials with ellipsoidal wave surfaces and their application to determination of elastic constants by acoustical methods

A new class of elastic materials with orthorhombic symmetry is introduced. For such materials, group velocity surfaces of quasi-longitudinal waves have ellipsoidal shapes. Relations between elastic constants that guaranty ellipsoidal shapes of the group velocity surfaces are indicated. The model materials are used for approximate determination of effective elastic constants of heterogeneous materials by acoustical methods. Examples of reconstruction of elastic constants from acoustical data are presented, and possible errors of the reconstructions are discussed.

ABB Robotic Laser Doppler Anemometry Measurements With RobotStudio® With An Open Wind Channel And An Ellipsoid

Laser Doppler anemometry is a state-of-the-art non-invasive experimental flow measurement technique. Traditionally used linear traversing units can only change the position of the measurement probe, but cannot change the orientation of the probe. A six degrees of freedom robot can simplify and fasten up the pose planning and measurement process real-offline. A developed LDA software plug-in for RobotStudio is used to real-offline plan and perform flow measurements in an open wind channel (flow rate = 300 m³/h) with an ellipsoid (diameter y=z = 140 mm and x = 40 mm). In 25 mm, 20 mm, 15 mm, 10 mm, 5 mm and 2 mm orthogonal distance of the ellipsoid surface the tangential velocity component is determined. Accuracy and repeatability of the robot-LDA system is found and compared to the traditional linear traversing system. Results show a positive velocity gradient towards the axis of the wind channel with a velocity range of 4.4 – 20.3 m/s. At 25 mm distance the tangential velocity is in the range of 4.4 – 12.5 m/s, at 20 mm 7.6 – 17.5 m/s, at 15 mm 12.1 – 19.7 m/s, at 10 mm 16.5 – 20.1 m/s, at 5 mm 19.0 – 20.2 m/s and at 2 mm 18.3 – 20.3 m/s. In positive y and negative z-direction, a reduction of the tangential velocity component is found in all measurements. At a distance of 25 mm, the measurement surface is slightly outside to the wind channel inlet (diameter = 80 mm). The closer the measurement surface is at the wind channel axis, the higher is the wind channel axial component. Robot-LDA average accuracy of 13 µm and repeatability of 10 µm is in the range of the linear traversing unit where the accuracy is 20 µm and the repeatability is 6 µm. The robot-LDA measurement system is an alternative to the existing linear-LDA with the advantages of real-offline robot path planning for arbitrary surfaces requiring six degrees of freedom probe placement.

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.

Predicting transition from selective withdrawal to entrainment in two-fluid stratified systems.

Selective withdrawal is a desired phenomenon in transferring oil from large caverns in the U.S. Strategic Petroleum Reserve (SPR), because entrainment of oil at the time during withdrawal poses a risk of contaminating the environment. Motivated to understand selective withdrawal in an SPR-like orientation, we performed experiments in order to investigate the critical submergence depth as a function of critical flow rate. For the experiments, a tube was positioned through a liquid-liquid interface that draws the lower liquid upward, avoiding entrainment of the upper fluid. Analysis of the normal stress balance across the interface produced a Weber number, utilizing dynamic pressure scaling, that predicted the transition to entrainment. Additionally, an inviscid flow analysis was performed assuming an ellipsoidal control volume surface that produced a linear relationship between the Weber number and the scaled critical submergence depth. This analytical model was validated using the experimental data, resulting in a robust model for predicting transition from selective withdrawal to entrainment.

Observation of ultracold atomic bubbles in orbital microgravity.

Substantial leaps in the understanding of quantum systems have been driven by exploring geometry, topology, dimensionality and interactions in ultracold atomic ensembles1-6. A system where atoms evolve while confined on an ellipsoidal surface represents a heretofore unexplored geometry and topology. Realizing an ultracold bubble-potentially Bose-Einstein condensed-relates to areas of interest including quantized-vortex flow constrained to a closed surface topology, collective modes and self-interference via bubble expansion7-17. Large ultracold bubbles, created by inflating smaller condensates, directly tie into Hubble-analogue expansion physics18-20. Here we report observations from the NASA Cold Atom Lab21 facility onboard the International Space Station of bubbles of ultracold atoms created using a radiofrequency-dressing protocol. We observe bubble configurations of varying size and initial temperature, and explore bubble thermodynamics, demonstrating substantial cooling associated with inflation. We achieve partial coverings of bubble traps greater than one millimetre in size with ultracold films of inferred few-micrometre thickness, and we observe the dynamics of shell structures projected into free-evolving harmonic confinement. The observations are among the first measurements made with ultracold atoms in space, using perpetual freefall to explore quantum systems that are prohibitively difficult to create on Earth. This work heralds future studies (in orbital microgravity) of the Bose-Einstein condensed bubble, the character of its excitations and the role of topology in its evolution.

Multi-Kinects fusion for full-body tracking in virtual reality-aided assembly simulation

Skeleton tracking based on multiple Kinects data fusion has been proved to have better accuracy and robustness than single Kinect. However, previous works did not consider the inconsistency of tracking accuracy in the tracking field of Kinect and the self-occlusion of human body in assembly operation, which are of vital importance to the fusion performance of the multiple Kinects data in assembly task simulation. In this work, we developed a multi-Kinect fusion algorithm to achieve robust full-body tracking in virtual reality (VR)-aided assembly simulation. Two reliability functions are first applied to evaluate the tracking confidences reflecting the impacts of the position-related error and the self-occlusion error on the tracked skeletons. Then, the tracking skeletons from multiple Kinects are fused based on weighted arithmetic average and generalized covariance intersection. To evaluate the tracking confidence, the ellipsoidal surface fitting was used to model the tracking accuracy distribution of Kinect, and the relations between the user-Kinect crossing angles and the influences of the self-occlusion on the tracking of different parts of body were studied. On the basis, the two reliability functions were developed. We implemented a prototype system leveraging six Kinects and applied the distributed computing in the system to improve the computing efficiency. Experiment results showed that the proposed algorithm has superior fusion performance compared to the peer works.

СПОСОБ ВЫЧИСЛЕНИЯ АНОМАЛИЙ СИЛЫ ТЯЖЕСТИ ОТНОСИТЕЛЬНО КВАЗИГЕОИДА

A method for calculating gravity anomalies relative to a quasigeoid is described. The following formulas are given: reduction of values of the normal gravity from the ellipsoid surface to the quasigeoid surface; calculation of the conditional density of rocks of the Bouger plate; calculation of gravity anomalies relative to the quasigeoid. An example of comparison of the Bouguer gravities and anomalies relative to a quasi-geoid is given; it shows the advantages of the latter for the geological interpretation of gravity survey data.

Study on the friction performance of textured surface on water hydraulic motor piston pair

In order to explore the effects of textured surfaces on the friction performance of a low-speed and high-torque water hydraulic motor, the textured surface was designed on the friction pair. A transient simulation, a gap-flow-field simulation analysis, and a wear experiment were carried out according to the actual working conditions of piston pair. The results showed that the connect surface with ellipsoidal pits could improve the stability of the lubricating water film between the contact surfaces by improving the stress distribution on the surface of the piston pair, and reduce the abrasive wear by reducing the fall of matrix material. The experimental results showed that about 62.6% of the wear loss reduction could be reached using the ellipsoidal pit surface, and the wear loss mainly happened in the edge of pits. Therefore, it is a great reason for reasonable design of textured pits surface to improve the surface friction performance of piston pair under working condition.

Wavefront shaping system of tiny optical path difference based on off-axis ellipsoidal surface

Wavefront shaping system of tiny optical path difference based on off-axis ellipsoidal surface