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Saturated packing is a random packing state of particles widely applied in investigating the physicochemical properties of granular materials. Optimizing particle shape to maximize packing density is a crucial challenge in saturated packing research. The known optimal three-dimensional shape is an ellipsoid with a saturated packing density of 0.437 72(51). In this work, we generate saturated packings of three-dimensional asymmetric shapes, including spherocylinders, cones, and tetrahedra, via the random sequential adsorption algorithm and investigate their packing properties. Results show that the optimal shape of asymmetric spherocylinders gives the maximum density of 0.4338(9), while cones achieve a higher value of 0.4398(10). Interestingly, tetrahedra exhibit two distinct optimal shapes with significantly high densities of 0.4789(19) and 0.4769(18), which surpass all previous results in saturated packing. The study of adsorption kinetics reveals that the two optimal shapes of tetrahedra demonstrate notably higher degrees of freedom and faster growth rates of the particle number. The analysis of packing structures via the density pair-correlation function shows that the two optimal shapes of tetrahedra possess faster transitions from local to global packing densities. [ABSTRACT FROM AUTHOR]

ABSTRACT This study investigates discharge phenomena in suspended droplets using needle–needle electrodes. By employing ultrasonic suspension technology for noncontact droplet suspension and high‐speed cameras for capturing time‐resolved discharge images, the study examines the impact of droplets on discharge characteristics and morphology. Results show that droplets alter the electric field distribution, affecting discharge paths. Low‐conductivity droplets hinder discharge, causing deflection or changes in the discharge channel, whereas high‐conductivity droplets act as suspended electrodes, facilitating discharge channel formation, reducing breakdown voltage and shortening the establishment time. Droplets transition from ellipsoid to flat and back during discharge, with high‐conductivity droplets potentially undergoing liquid explosion. These findings are crucial for designing high‐voltage equipment in liquid‐contaminated environments. [ABSTRACT FROM AUTHOR]

With the development of high-performance computing technology, the number of scientific publications regarding computational modelling of applications with the Discrete Element Method/Modelling (DEM) approaches in agricultural engineering has risen in the past decades. Many granular materials, e.g. grains, fruits and soils in agricultural engineering are processed, and thus a better understanding of these granular media with DEM is of great significance in design and optimization of tools and process in agricultural engineering. In this review, the theory and background of DEM have been introduced. Some improved contact models discussed in the literature for accurately predicting the contact force between two interacting particles have been compared. Accurate approximation of irregular particle shapes is of great importance in DEM simulations to model real particles in agricultural engineering. New algorithms to approximate irregular particle shapes, e.g. overlapping multi-sphere approach, ellipsoid, etc., have been summarized. Some remarkable engineering applications of the improved numerical models developed and implemented in DEM are discussed. Finally, potential applications of DEM and some suggested further works are addressed in the last section of this review. [ABSTRACT FROM AUTHOR]

Introduction: Cortinariaceae, which belongs to the Agaricales order, is a globally recognized family, known for its high species diversity. Methods: Eight internal transcribed spacer (ITS) and nuclear large ribosomal subunit (LSU) sequences were newly generated, and phylogenetic analyses were performed by combining ITS and LSU datasets. Four species were identified as forming four independent lineages with robust support in phylogenies based on both datasets. Results: These new species in the taxa, Cortinarius gansuensis, Cortinarius tricholomoidus, Cortinarius vinoso-griseum, and Phlegmacium subcalyptratum from Northwestern China are described and illustrated based on morphological and molecular evidence. Cortinarius gansuensis is characterized by a convex and brownish vinaceous pileus, generative hyphae with clamp connections, and ellipsoid basidiospores (8.5-10.6 µm × 5.4-6.8 µm); Cortinarius tricholomoidus is characterized by a broadly umbonate and snuff brown pileus, generative hyphae with clamp connections, and broadly ellipsoid to subglobose basidiospores (7.4-8.5 µm × 6.2-7.3 µm); Cortinarius vinoso-griseum is characterized by a violaceous gray pileus, generative hyphae with clamp connections, and smaller basidiospores (7.5-9.7 µm × 5.6-7.8 µm); and Phlegmacium subcalyptratum is characterized by a small and apricot-orange pileus, generative hyphae with clamp connections, and fusiform basidiospores (10.0-12.7 µm × 5.6-6.8 µm). Discussion: Full descriptions, illustrations, and results of phylogenetic analyses of the four species along with discussions on related species are provided. [ABSTRACT FROM AUTHOR]

The formula for the area of a rhumb polygon, a polygon whose edges are rhumb lines on an ellipsoid of revolution, is derived and a method is given for computing the area accurately. This paper also points out that standard methods for computing rhumb lines give inaccurate results for nearly east- or west-going lines; this problem is remedied by the systematic use of divided differences. [ABSTRACT FROM AUTHOR]

Apollonius defined the circle as the set of points that have a given ratio μ of distances from two given points, where the ratio is not equal to one. In a more general sense, consider two 0-symmetric, bounded, convex bodies K and K ′ , which define two norms. Their unit balls are K and K ′ . The surface of Apollonius is defined as the set of points equidistant from the centres of bodies K and K ′ with respect to the aforementioned norms. In this paper we demonstrate that the surface of Apollonius of two ellipsoids is a quadratic surface. We also examine the circumstances under which this surface becomes a sphere. [ABSTRACT FROM AUTHOR]

Wet Age-related Macular Degeneration (wet AMD) is a common ophthalmic disease that significantly impacts patients' vision. Optical coherence tomography (OCT) examination has been widely utilized for diagnosing, treating, and monitoring wet AMD due to its cost-effectiveness, non-invasiveness, and repeatability, positioning it as the most valuable tool for diagnosis and tracking. OCT can provide clear visualization of retinal layers and precise segmentation of lesion areas, facilitating the identification and quantitative analysis of abnormalities. However, the lack of high-quality datasets for assessing wet AMD has impeded the advancement of related algorithms. To address this issue, we have curated a comprehensive wet AMD OCT Segmentation Dataset (AMD-SD), comprising 3049 B-scan images from 138 patients, each annotated with five segmentation labels: subretinal fluid, intraretinal fluid, ellipsoid zone continuity, subretinal hyperreflective material, and pigment epithelial detachment. This dataset presents a valuable opportunity to investigate the accuracy and reliability of various segmentation algorithms for wet AMD, offering essential data support for developing AI-assisted clinical applications targeting wet AMD. [ABSTRACT FROM AUTHOR]

Concentrated solar power (CSP) technology relies on thermal energy storage to extend operating hours, making the selection of heat storage media crucial for system efficiency. Bauxite powder, known for its availability and high-temperature stability, emerges as a potential alternative to conventional materials in CSP systems. This study employed the discrete element method to investigate the influence of particle shape on the packing and heat transfer characteristics of non-spherical particles. The research focused on assessing the impact of particle sphericity by comparing spherical particles with non-spherical shapes, including ellipsoids and cylinders, and exploring the effect of varying the aspect ratio (AR) of the cylindrical particles. Particle sphericity significantly influenced packing morphology, with the cylindrical particles exhibiting distinct structural patterns that were absent in the ellipsoidal particles, and strongly affected heat transfer, as observed in the average temperature variations within the packed bed over time. The cylinders with higher aspect ratios demonstrated enhanced heat transfer rates, driven by the increased contact area and coordination numbers, despite their predominant misalignment with the heat flux direction. These insights are valuable for optimizing thermal energy storage media in CSP systems. [ABSTRACT FROM AUTHOR]

ABSTRACT This article considers the trajectory tracking problem of automated guided vehicles with unknown‐but‐bounded noises and proposes a set‐membership filtering (SMF) based model predictive control strategy. A 2‐DOF vehicle model is first established with considering the unknown‐but‐bounded process and measurement noises. Then, a trajectory tracking control scheme is proposed which consists of two parts, that is, a set‐membership observer and a model predictive controller. The proposed set‐membership observer is able to deal with the unknown‐but‐bounded noises and obtain the state estimation ellipsoid for the considered automated guided vehicle. Further, the designed model predictive controller utilizes the estimated ellipsoid to compute the control sequence. Finally, simulation results demonstrate the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

A feasibility study on the compensation of 3D mispositioning errors of the probe occurring in the characterization of a long antenna, via a non-redundant (NR) near to far-field (NTFF) transformation with helicoidal scan, is conducted in this article. Such types of errors can result from imperfections in the rail driving the linear motion of the probe and from an imprecise synchronization of the linear and rotational movements of the probe and the antenna when drawing the scan helix. To correct them, an approach, which proceeds through two steps, is proposed. The former step uses a technique called cylindo rical wave (CW) correction for compensating the phase of the near-field (NF) samples, which, owing to the rail imperfections, result in not being acquired over the measurement cylinder surface. The latter exploits an iterative scheme to restore the samples at the sampling points required by the adopted NR representation along the scan helix from those obtained by applying the CW correction technique and impaired by 2D mispositioning errors. The so compensated NF samples are then effectively recovered via a 2D optimal sampling interpolation (OSI) scheme to accurately obtain the input data required to carry out the standard cylindrical NTFF transformation. The OSI representation is determined here by assuming a long antenna under test as enclosed in a prolate ellipsoid or cylinder ending into two hemispheres (cigar) in order to make, depending on the particular geometry of the considered antenna, the representation effectively non-redundant. The reported numerical simulation results show the capability of the proposed approach to compensate even severe 3D mispositioning errors, thus enabling its usage in a real measurement scenario. [ABSTRACT FROM AUTHOR]

The translational diffusivity of covalent open‐[60]fullerene dimers in an organic solvent was found to be well describable by a prolate ellipsoid model while a monomeric open‐[60]fullerene behaves like a sphere model. The water association dynamics were examined for two open‐[60]fullerene dimers, showing a higher water affinity for the sp3‐linked dimer relative to sp2‐linked dimer owing to an effective orbital–orbital overlap identified by π(fullerene)→σ*(H2O) interactions as suggested by theoretical calculations. [ABSTRACT FROM AUTHOR]

In this paper we consider shape optimization problems for sets of prescribed mass, where the driving energy functional is nonlocal and anisotropic. More precisely, we deal with the case of attractive/repulsive interactions in two and three dimensions, where the attraction is quadratic and the repulsion is given by an anisotropic variant of the Coulomb potential. Under the sole assumption of strict positivity of the Fourier transform of the interaction potential, we show the existence of a threshold value for the mass above which the minimizer is an ellipsoid, and below which the minimizer does not exist. If, instead, the Fourier transform of the interaction potential is only non-negative, we show the emergence of a dichotomy: either there exists a threshold value for the mass as in the case above, or the minimizer is an ellipsoid for any positive value of the mass. [ABSTRACT FROM AUTHOR]

This paper examines the impact of two tandem configurations of ellipsoids on laminar flow using numerical methods. The first configuration features an ellipsoid in a prolate orientation, while the other employs a prolate ellipsoid tilted at a 45° angle relative to the vertical axis. The study investigates inter-ellipsoid distances ranging from one ellipsoid diameter (1D) to eight diameters (8D) from the ellipsoids' centers and different Reynolds numbers (100, 200, 300, and 400). The presented results focus on hydrodynamic forces, wake symmetry, and wake patterns for different scenarios. The findings reveal that when an angle is present in the ellipsoid, the drag forces between the front and rear ellipsoids tend to approach at smaller separations compared to the prolate orientation case. In these cases, flow separation is asymmetric in the x–y plane but becomes symmetric in the x–z plane at larger ellipsoid spacings. Additionally, the detachment zones are analyzed concerning the angle and Reynolds number. It is observed that up to a distance of approximately 4D, the wake of the front ellipsoid significantly influences the recirculation and hydrodynamics of the rear ellipsoid. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of making inferences about a common mean vector from several independent multivariate normal populations with unknown and unequal dispersion matrices. We propose an unbiased estimator of the common mean vector, along with its asymptotic estimated variance, which can be used to test hypotheses and construct confidence ellipsoids, both of which are valid for large samples. Additionally, we discuss an approximate method based on generalized p-values. The paper also presents exact test procedures and methods for constructing exact confidence sets for the common mean vector, with a comparison of the local power of these exact tests. The performance of the proposed methods is demonstrated through a simulation study and an application to data from the Current Population Survey (CPS) Annual Social and Economic (ASEC) Supplement 2021 conducted by the U.S. Census Bureau for the Bureau of Labor Statistics. [ABSTRACT FROM AUTHOR]

Power systems are naturally prone to numerous uncertainties. Power system functioning is inherently unpredictable, which makes the networks susceptible to instability. Rotor-angle instability is a critical problem that, if not effectively resolved, may result in a series of failures and perhaps cause blackouts (collapse). The issue of state feedback sliding mode control (SMC) for the excitation system is addressed in this work. Control is decentralized by splitting the global system into several subsystems. The effect of the rest of the system on a particular subsystem is considered a disturbance. The next step is to build the state feedback controller with the disturbance attenuation level in mind to guarantee the asymptotic stability of the closed-loop system. The algorithm for SMC design is introduced. It is predicated on choosing the sliding surface correctly using the invariant ellipsoid approach. According to the control architecture, the system motion in the sliding mode is guaranteed to only be minorly affected by mismatched disturbances in power systems. Furthermore, the proposed controllers are expressed in terms of Linear Matrix Inequalities (LMIs) using the Lyapunov theory. Lastly, an IEEE test system is used to illustrate how successful the suggested approach is. [ABSTRACT FROM AUTHOR]

In the present study, two new species of Pholiota (Strophariaceae) viz. Pholiota fasciculata and Pholiota himalayensis belonging to subgenus Flammuloides are described based on morphological characteristics and molecular phylogenetic analyses. The specimens were collected during the macrofungal expedition in different areas of Darjeeling Hills in the monsoon season 2019–2022. Pholiota fasciculata is characterized by its brightly coloured fruit bodies when young, prominent umbo at maturity, viscid when moist, ellipsoid to ovoid basidiospores with minute and inconspicuous germ pore, fusiform-lageniform pleurocystidia, some crystalline cap covering the apex and bundled cheilocystidia which cannot be separated easily. Pholiota himalayensis is characterized by having viscid fruit bodies, basidiospores with inconspicuous germ pore, pleurocystidia projecting prominently and similar in shape to cheilocystidia. [ABSTRACT FROM AUTHOR]

Despite having 20/20 vision, a 17-year-old Emirati female presented with central visual changes in her left eye. These changes were attributed to a dull foveal reflex with pigmentary alterations. Retinal pigment epithelium (RPE) mottling at the macula level, attenuating the ellipsoid zone, and a hyper-reflective line connecting the RPE to the outer nuclear layer was observed through spectral domain optical coherence tomography (SD-OCT) of the left eye. In the presence of negative results from laboratory evaluations, the patient was started on oral prednisolone. The medication induced an increased reflectivity of the inner layers on SD-OCT, which turned into a full-thickness macular retinitis with vitreous inflammation, causing a visual decrease to 20/80. A vitreous tap confirmed a positive result for HSV-1, and the patient was prescribed oral valacyclovir 3 g. This treatment led to a resolution of the retinitis and a restoration of the patient's vision to 20/25. [ABSTRACT FROM AUTHOR]

In order to improve the precision of plane coordinate conversion between different datum, a fourparameter coordinate conversion method which calculated the approximate parameters of coordinate system first was adopted. The main steps of the method are as follows: Firstly, by studying the Gaussian projection deformation and the principle of compensating coordinate system, the linear correlation between the height of the projection surface and the length deformation of the coordinate transformation control point was analyzed. Then, combined with the influence of Gaussian projection on the angular projection deformation, the coordinate transformation model with scale parameters and rotation parameters was determined to reduce the linear projection deformation difference between control points, such as the four-parameter and sevenparameter transformation model. Secondly, by analyzing the influence of ellipsoid type on the projection deformation difference between coordinate transformation control points, a method which calculating the approximate parameters of different ellipsoid coordinates was proposed to reduce the Gaussian projection nonlinear deformation difference. The research results show that, the effect of ellipsoid type on the nonlinear projection deformation of coordinates is submillimeter. When the coordinate system parameters of different datum are approximately the same, the inner and outer coincidence accuracy of the coordinate transformation of four parameters and seven parameters can reach millimeter level. An engineering example shows that the precision of coordinate transformation can be improved by one order of magnitude by the four-parameter coordinate conversion method which calculates the approximate parameters of coordinate system first. [ABSTRACT FROM AUTHOR]

The exact formulae for calculating the demagnetizing factors of a general ellipsoid along the three main axes a ≥ b ≥ c have been long known. According to these formulae, the demagnetizing factors depend only on the axial ratios b/a and c/a. Although the calculation of the demagnetizing factors is a straightforward task, the calculation itself is not a simple one. Therefore, tabular and graphical representations of these demagnetizing factor data have also been presented which can then be used for approximating the demagnetizing factors of a rectangular ferromagnetic slab with the same axial ratios. It turned out in our recent study, however, that, in some ranges of axial ratios (e.g., for very small c/a values), the available tables and graphs do not provide sufficient resolution for obtaining the demagnetizing factors with reasonable accuracy. It was decided to calculate these missing values, and they are presented here in both tabular and graphical form by giving instructions for how to obtain conveniently further interpolated data. In addition, the previous and current demagnetizing factor data have been replotted and fitted to a polynomial function with high accuracy. The functional form of these fitting polynomials is presented in a table for the whole range of the axial ratios b/a and c/a. By graphically displaying these functions, one can obtain, in a relatively simple manner, the demagnetizing factors of a general ellipsoid with known axial ratios without the need to directly calculate through the exact formulae. This may be helpful in obtaining a quick estimate for the demagnetizing factors of any rectangular ferromagnetic slab of interest. [ABSTRACT FROM AUTHOR]

Let (M2n+1, θ) be a compact strictly pseudoconvex real hypersurfaces equipped with the pseudohermitian structure θ, and λ1 be the first positive eigenvalue of sub-Laplacian ∆b on (M2n+1, θ). In this paper, we will give the upper bound of λ1 under certain conditions that “Re∆b (ρj + ρ¯j ) (2∆˜ ρρj + |∂ρ|² ρn −1ρkρjk) ≤ 0 (for some j)” or “ρj ¯k = δjk” holds, and apply these results to the ellipsoids furthermore. [ABSTRACT FROM AUTHOR]

We revisit the following nonlinear Schrödinger equation - ε 2 Δ u + V (x) u = u p , u > 0 , u ∈ H 1 (R N) , where ε > 0 is a small parameter, N ≥ 2 and 1 < p < 2 ∗ - 1 . It is known that the Morse index gives a strong qualitative information on the solutions, such as non-degeneracy, uniqueness, symmetries, singularities as well as classifying solutions. Here we compute the Morse index of positive k-peak solutions to above problem when the critical points of V(x) are non-isolated and degenerate. We also give a specific formula for the Morse index of k-peak solutions when the critical point set of V(x) is a low-dimensional ellipsoid. Our main difficulty comes from the non-uniform degeneracy of potential V(x). Our results generalize Grossi and Servadei's work (Ann Math Pura Appl 186: 433–453, (2007)) to very degenerate (non-admissible) potentials and show that the structure of potentials highly affects the properties of concentrated solutions. [ABSTRACT FROM AUTHOR]

In this current work, a sequential extended Kalman filter (EKF) algorithm is proposed to solve the quandary of regional accuracy disparity for time difference of arrival (TDOA) positioning in passive radar. The proposed approach entails merging the complete set of active radar observation data with the TDOA data of passive radar in a serial fashion, followed by the deployment of the EKF algorithm for the purpose of filtering. The simulation results show that the proposed data fusion method effectively solves the regional accuracy imbalance problem caused by the fuzzy area and no solution area of the TDOA positioning solution through the conflation of the precision merits of active and passive radar, and improves the overall target detection accuracy. [ABSTRACT FROM AUTHOR]

Purpose: To evaluate optical-coherence-tomography (OCT)-morphological and clinical parameters three years after primary rhegmatogenous retinal detachment (RRD) repair surgery and the role of postoperative foveal bulge sign. Methods: Of the 32 initially enrolled patients with primary RRD 20 (14 fovea-on, 6 fovea-off) completed this prospective study. Preoperatively and 3 years after surgery best corrected visual acuity (BCVA) and OCT including macula status, central retinal thickness (CRT), central choroidal thickness (CCT), thickness of each single retinal layer, integrity of cone-interdigitation-zone (CIZ) and ellipsoid zone (EZ), and presence of foveal bulge were evaluated. Results: Preoperatively fovea-off RRD patients show significantly thinner CCT, inner nuclear layer (INL) and inner plexiform layer (IPL) compared to fovea-on RRD patients, whereas only IPL and INL were significantly thicker compared to the fellow eye. Three years after surgery this thickening recovered. Final BCVA did not differ statistically significantly between fovea-off and fovea-on patients, no difference in CIZ-integrity or presence of foveal bulge was observed. Presence of foveal bulge at 3 years showed significantly better final BCVA and was associated with intact preoperative CIZ-integrity and postoperative EZ- and CIZ-integrity. The preoperative fovea status showed no correlation to the postoperative presence of foveal bulge. Conclusion: Three years after RRD repair retinal layers show similar thickness. The presence of foveal bulge is associated with better final BCVA. Sufficient pre- and postoperative CIZ-integrity as well as postoperative CIZ-integrity seem to be strongly associated with the restoration of foveal bulge. No correlation was found with the preoperative macular status or BCVA. Plain Language Summary: We analyzed long-term optical-coherence-tomography changes after rhegmatogenous retinal detachment repair. Three years after rhegmatogenous retinal detachment repair retinal layers show similar thickness and visual acuity did not differ between fovea off and fovea on patients. The restoration of foveal bulge sign was the most important factor for good postoperative visual acuity. Integrity of specific retinal layers, such as the ellipsoid zone and cone-interdigitation-zone, seems to be strongly associated with the restoration of the foveal bulge. [ABSTRACT FROM AUTHOR]

The present study describes a new record of Coniolepiotaspongodes from India. Coniolepiotaspongodes is a monotypic taxon of the genus Coniolepiota and is characterized by a white to purplish white pileus; stipe with powdery coverings; free lamellae with smooth margins appearing cream to pale yellowish in colour; pungent odour; ellipsoid to oblong basidiospores measuring 4.0–6.0 × 2.5–4.1 µm; irregular cylindrical squamules cells on the pileus and stipe surface. A comprehensive morphological description, photographs, and molecular sequence-based phylogenetic analyses of the present collections are provided. [ABSTRACT FROM AUTHOR]

We analyze the transverse electro-optic (EO) effect in an arbitrary direction in LiNbO3 (LN) and LiTaO3 (LT) crystals based on the Fresnel index ellipsoid theory. A set of analytical formulas for calculating the birefringence in any direction in a crystal of the lowest symmetry is first deduced. The maximum magnitudes of the transverse EO effect appear along the directions that are turned out from the optic axis on the angles θm (φ = 30°, 150° or 270°) or 180°− θm (φ = 90°, 210° or 330°), the angles θm of congruent LN and LT crystals are 36° and 59.5°, respectively. For experimental verification, the (yzw)θm cut congruent LN and LT crystals were prepared. The half-wave voltage (HWV) of the (yzw)36° cut LN crystals is half that of the x-cut LN crystals and is only 30% that of the z-cut LN crystals, and the HWV of the (yzw)59.5° cut LT crystals is 7% higher than that of the x-cut LT crystals, the experimental results agree well with the theoretical analysis. The crystals with the optimized cell geometries are more practical because of the low HWV and lower sensitivity of birefringence to temperature. [ABSTRACT FROM AUTHOR]

Generalized Abel equations have been employed in the recent literature to invert Radon transforms which arise in a number of important imaging applications, including Compton Scatter Tomography (CST), Ultrasound Reflection Tomography (URT), and X-ray CT. In this paper, we present novel injectivity results and inversion methods for generalized Abel operators. We apply our theory to a new Radon transform, R j , of interest in URT, which integrates a square integrable function of compact support, 푓, over ellipsoid and hyperboloid surfaces with centers on a plane. Using our newly established theory on generalized Abel equations, we show that R j is injective and provide an inversion method based on Neumann series. In addition, using algebraic methods, we present image phantom reconstructions from R j ⁢ f data with added pseudo-random noise. [ABSTRACT FROM AUTHOR]

We theoretically study the polarization of plasmonic fields in a hybrid nanosystem composed of three different metallic nano ellipsoid and a semiconductor quantum dot. The components of the hybrid nanosystem interact with three electromagnetic fields and one another via dipole-dipole interactions. We derive the density matrix equations at a steady state for the description of the optical properties of the hybrid nanosystem. The polarization of the plasmonic fields induced on the prolate, spherical, and oblate nano ellipsoid is calculated. We find that the polarization of the plasmonic fields depends on the number of the metallic nanoparticles (ellipsoid), the depolarization factor of the metallic nano ellipsoid, the direction of the plasmonic field, and the metallic nano ellipsoid parameters of the hybrid nanosystem. The phenomena of electromagnetically induced transparency (EIT) and electromagnetically induced transparency with amplification (EITA) are obtained in this work. [ABSTRACT FROM AUTHOR]

A new species of Chlorophytum is described and illustrated in this article. Morphological, root anatomical, pollen and molecular features were compared with its allied species C. laxum R.Br. which has apiculate anther, lanceolate bract, 16–18 nerved flat leaf and ellipsoid pollen with contrast to obtuse anther, ovate bract, 11–13 nerved conduplicate leaf and ovoid pollen. The molecular features complement the differences. [ABSTRACT FROM AUTHOR]

Besides amplitude variation, phase variation of seismic wave is also an important carrier of geological information at the fault slip interface. To analyze the seismic propagation through the fault slip interface, which is assumed to be a flat, horizontal and imperfectly welded contact (nonwelded) interface between two different tilted anisotropic (TTI) media, we derived the analytical formulae for amplitude and phase variations of reflected and transmitted seismic waves with longitudinal wave (qP), the slow and fast waves (qS and SH) generated simultaneously. The derived formulae could satisfy the fracture model, in which the symmetry axis planes of the upper and lower media coincide. Also, we provided the exact and approximate methods for velocities and polarizations as well as the reflected and transmitted angles based on the slowness ellipsoid. Moreover, weakly anisotropic parameters are taken into consideration by the approximate amplitude (AVO) and phase formulae of qP and qS. The approximations also clearly show the effect of anisotropic parameters on the amplitude and phase change. The derived results show that the compliance parameters affect the phase change rather than amplitude, while anisotropic parameters affect both. The numerical model shows that with respect to the incident P-wave, the phase change of the reflected qP wave is more significant than the other generating waves due to the linear slip boundary; the coefficients could be used to determine the fracture dip and strike; the frequency hardly affects the real part of the coefficient, while the imaginary part of the coefficient. Moreover, the derived formulae for phase change will contribute to the seismic inversion with the formulae for amplitude variation simultaneously. [ABSTRACT FROM AUTHOR]

The emergence of 3D Gaussian splatting (3DGS) has greatly accelerated rendering in novel view synthesis. Unlike neural implicit representations like neural radiance fields (NeRFs) that represent a 3D scene with position and viewpoint-conditioned neural networks, 3D Gaussian splatting utilizes a set of Gaussian ellipsoids to model the scene so that efficient rendering can be accomplished by rasterizing Gaussian ellipsoids into images. Apart from fast rendering, the explicit representation of 3D Gaussian splatting also facilitates downstream tasks like dynamic reconstruction, geometry editing, and physical simulation. Considering the rapid changes and growing number of works in this field, we present a literature review of recent 3D Gaussian splatting methods, which can be roughly classified by functionality into 3D reconstruction, 3D editing, and other downstream applications. Traditional point-based rendering methods and the rendering formulation of 3D Gaussian splatting are also covered to aid understanding of this technique. This survey aims to help beginners to quickly get started in this field and to provide experienced researchers with a comprehensive overview, aiming to stimulate future development of the 3D Gaussian splatting representation. [ABSTRACT FROM AUTHOR]

The NVH (Noise, Vibration, and Harshness) characteristics of micro-motors used in vehicles directly affect the comfort of drivers and passengers. However, various factors influence the motor's structural parameters, leading to uncertainties in its NVH performance. To improve the motor's NVH characteristics, we propose a method for optimizing the structural parameters of automotive micro-motors under uncertain conditions. This method uses the motor's maximum magnetic flux as a constraint and aims to reduce vibration at the commutation frequency. Firstly, we introduce the Pareto ellipsoid parameter method, which converts the uncertainty problem into a deterministic one, enabling the use of traditional optimization methods. To increase efficiency and reduce computational cost, we employed a data-driven method that uses the one-dimensional Inception module as the foundational model, replacing both numerical models and physical experiments. Simultaneously, the module's underlying architecture was improved, increasing the surrogate model's accuracy. Additionally, we propose an improved NSGA-III (Non-dominated Sorting Genetic Algorithm III) method that utilizes adaptive reference point updating, dividing the optimization process into exploration and refinement phases based on population matching error. Comparative experiments with traditional models demonstrate that this method enhances the overall quality of the solution set, effectively addresses parameter uncertainties in practical engineering scenarios, and significantly improves the vibration characteristics of the motor. [ABSTRACT FROM AUTHOR]

The problem of particle clogging in a conveying pipeline in thin-phase pneumatic transportation is essentially the effect of the particle-deposition mechanism in gas–solid two-phase flow. This paper presents a particle-deposition model of gas–solid two-phase flow based on the ellipsoid hypothesis, and a fast-calculation method of material particle-deposition efficiency in industry based on the tabular-assigned drag-correction coefficient of the particle ellipsoid-shape parameter A r and incoming flow angle ϕ. A simulation comparison of spherical particles under the same pneumatic transport conditions and experimental verification based on the self-built particle deposition system are given. The validity of the model and the accuracy of the algorithm are verified. This provides a feasible simulation and experimental scheme for the research of pneumatic-conveying technology in the industrial field. [ABSTRACT FROM AUTHOR]

A zone control algorithm is proposed that considers both economic performance indicators and control performance indicators. Unlike classic set point control, zone control expands the control target into a convex set. In this study, an ellipsoid is used as the control target, and the advantages of the ellipsoid target are explained in terms of overall stability and computational load. After defining the distance measurement function and appropriate terminal constraints, an objective function that considers both control performance and optimization performance is constructed. A theoretical analysis shows that the proposed control algorithm satisfies the Lyapunov stability criterion. The superiority of the ellipsoid control target in handling complex multivariable control tasks is also demonstrated. This method has significant potential value in practical industrial applications, helping to unleash the potential control performance and economic benefits of zone control systems. Finally, the feasibility and stability of the algorithm are verified through a typical chemical process simulation. [ABSTRACT FROM AUTHOR]

This study evaluates the existing design methods of Geosynthetic-Reinforced Load Transfer Platform for Pile-Supported Embankments (GLTP-PSE) through comprehensive 3D Finite Element (FE) analyses. It scrutinizes the assumed arching mechanisms, methodologies, design criteria (arching height, maximum strain, differential settlement, and T in geosynthetics), and overall performance of these methods. The 3D FE analysis results and measurements from two case studies were compared with six established GLTP-PSE design methods based on the four design criteria. Key findings include the identification of a progressive concentrated ellipsoid as the developed soil arching formation, with arching height dependent on the embankment equivalent height (including embankment and traffic load), pile spacing, maximum strain along the geosynthetics, and the number of geosynthetic layers. The load distribution on geosynthetic reinforcement was observed to align more closely with a non-linear inverse triangle. These insights led to recommendations for updating existing design methods, enhancing the accuracy and reliability of GLTP-PSE designs. The study's outcomes contribute significantly to advancing and refining GLTP-PSE design practices by providing a deeper understanding of soil arching mechanisms and the performance of geosynthetic reinforcements. • Comparison of 3D FE analysis results and measurements from two case studies with six design methods with four criteria. • Identification of a progressive concentrated ellipsoid as the developed soil arching formation. • Arching height was found to be dependent on embankment equivalent, pile spacing, geosynthetics, and the geosynthetic layers. • Load distribution on geosynthetic reinforcement observed to align more closely with a non-linear inverse triangle. • Contribution to GLTP-PSE design practices by providing understanding of soil arching mechanisms and geosynthetic performance. [ABSTRACT FROM AUTHOR]

This document explores the impact of particle shape on the behavior of granular materials. The authors reference previous studies and present their own experimental results to evaluate the relationship between particle shape and critical state. They find that granular soils with rounded particles have lower and less steep critical state lines compared to soils with angular particles. The authors also discuss the effect of particle shape on instability triggering and highlight inconsistencies in simulation results. The study emphasizes the importance of considering particle shape in determining the mechanical behavior of granular materials. [Extracted from the article]

Existing empirical relations used to predict the porosity of gravel beds are mainly derived from laboratory-generated sediment beds with random grain packing. However, such relations could not adequately describe beds with non-random grain arrangements that occur widely in fluvial deposits. In this work, the effect of grain imbrication on gravel-bed porosity has been quantified using beds with variable strengths of imbrication generated by flume experiments. Mono-sized ellipsoids with specific shapes were used in experiments to remove particle size and sorting effects on porosity. Random bed packings were generated by settling of ellipsoids in still water whilst imbricated beds generated under flowing water. Beds were frozen using liquid nitrogen before extraction. A new relatively simple and time-saving workflow was developed to measure the orientation of particles and quantify the degree of grain imbrication in frozen beds from X-ray Computed Tomography images. Beds with the strongest grain fabric display a ca. 0.03 absolute reduction of porosity value on average (8–10% relative reduction) compared to that of random packing for undisturbed beds. Further, results were obtained for beds deposited under still-water conditions subject to disturbance by shaking, to mimic the potential effect of vibrations from currents, waves or other sources in the environment. A reduction in bed porosity of ca. 0.014–0.018 (ca. 5% relative reduction) is observed between beds with the strongest grain fabric and those with random packing that had undergone shaking after deposition. Hence, a significant proportion (> 50%) of the porosity loss observed for imbricated beds may be attributable to tighter packing due to turbulence-related vibrations from the flow. The small decrease in porosity value despite the formation of strong imbrication is considered to be due to the limited improvement in grain organization, as the results show that the flat shape of the ellipsoids and the uniformity of their size promote the formation of a stacking structure under gravity, leading to a similarly highly ordered grain organization in random packings compared to the imbricated packings. [ABSTRACT FROM AUTHOR]

The realization of high interconnect densities for three-dimensional integration demands development of new wafer-to-wafer bonding approaches. Recently introduced Cu-to-Cu wafer-to-wafer hybrid bonding schemes overcome scaling limitations, but like other Cu-based interconnect structures, they are prone to electromigration. Migration and growth of voids, induced by electromigration and mechanical stress, cause Cu-to-Cu hybrid bonds to fail. A comprehensive modeling approach is required to fully understand the complex dynamics of voids with their influencing factors, such as current density, temperature, and mechanical stress. In this work, we utilize such a modeling approach to perform studies of void migration through Cu-to-Cu hybrid bonds. The calculated velocities of the evolving void surface fully correspond to the experimentally observed behavior of voids migrating from the lower pad to the upper diffusion barrier of the upper pad, where they cause electrical failure. The migration velocity of a void in the upper pad is 20% higher than the migration velocity of a void in the bottom pad. Unbalance of the normal velocity distribution at the void surface leads to the transformation of the originally ellipsoid void into a teardrop shape. The simulations provide full insight in the impact of layout geometry, material properties, and operating conditions on void dynamics. In addition, the results enable targeted adjustments of the influencing factors to inhibit void migration and growth in order to delay or to fully prevent Cu-to-Cu hybrid bond failure. [ABSTRACT FROM AUTHOR]

Trajectory-based methods that propagate classical nuclei on multiple quantum electronic states are often used to simulate nonadiabatic processes in the condensed phase. A long-standing problem of these methods is their lack of detailed balance, meaning that they do not conserve the equilibrium distribution. In this article, we investigate ideas for restoring detailed balance in mixed quantum–classical systems by tailoring the previously proposed spin-mapping approach to thermal equilibrium. We find that adapting the spin magnitude can recover the correct long-time populations but is insufficient to conserve the full equilibrium distribution. The latter can however be achieved by a more flexible mapping of the spin onto an ellipsoid, which is constructed to fulfill detailed balance for arbitrary potentials. This ellipsoid approach solves the problem of negative populations that has plagued previous mapping approaches and can therefore be applied also to strongly asymmetric and anharmonic systems. Because it conserves the thermal distribution, the method can also exploit efficient sampling schemes used in standard molecular dynamics, which drastically reduces the number of trajectories needed for convergence. The dynamics does however still have mean-field character, as is observed most clearly by evaluating reaction rates in the golden-rule limit. This implies that although the ellipsoid mapping provides a rigorous framework, further work is required to find an accurate classical-trajectory approximation that captures more properties of the true quantum dynamics. [ABSTRACT FROM AUTHOR]

Macular Telangiectasia Type 2 (MacTel) is a chronic, progressive disease of the central retina characterized by vascular and neurodegenerative changes. As there is currently no treatment for non-neovascular MacTel, there is a dearth for biomarkers identifying eyes with an increased risk for disease progression for patient counseling and clinical trial recruitment. Eyes were classified to be stable or progressive, defined by the fundus photography-based grading system by Gass and Blodi. First, structural differences between these two groups were assessed, employing optical coherence tomography (OCT) and OCT-angiography. Univariate regression analyses revealed evidence towards a lower superficial retinal layer (SRL) vessel density (VD), skeleton density (SD) and deep retinal layer (DRL) SD in progressing compared to stable eyes (p = 0.05, p = 0.05, p = 0.07). Second, a multivariable predictive model was employed to examine the predictive value of structural and functional parameters for disease progression. Baseline best corrected visual acuity (BCVA) and SRL SD are prognostic for disease progression (p < 0.001, p = 0.05). The presence of ellipsoid zone (EZ) loss is prognostic for future central retinal thickness (p < 0.01). We propose SRL SD, BCVA, and EZ loss as prognostic biomarkers and as possible outcome measures in future interventional studies in MacTel. [ABSTRACT FROM AUTHOR]

My model, it has three layers, Three layers is nematic. And had it just two layers, it would be a smectic. We study a reduced model of smectic formation in two dimensions where the particles occupy three equally spaced layers. The role of particle geometry comes in through the interactions between particles on the central layer and those above and below. The system is understood to be a perfect smectic when the central layer is empty, and nematic when all three are equally occupied. It is possible to compute the free energies of these states exactly. We find that the free energy of the nematic can only exceed that of the perfect smectic if the particle tips are sufficiently wide. While not an indication of a true smectic transition, this mirrors the fact that ellipsoids do not make a smectic but sphero-cylinders do. [ABSTRACT FROM AUTHOR]

Context. The morphology of open clusters plays a major role in the study of their dynamic evolution. The study of their morphological coherence, namely, the three-dimensional (3D) difference between the inner and outer morphologies of open clusters, allows us to obtain a better understanding of the morphological evolution of open clusters. Aims. We aim to investigate the morphological coherence of 132 open clusters with up to 1 kpc from the Sun in the three-dimensional (3D) space within the heliocentric cartesian coordinate frame. The 132 open clusters have a 3D core-shell structure and conform to the ellipsoidal model, with all of them coming from a catalog of publicly available clusters in the literature. Methods. We employed the ellipsoid fitting method to delineate the 3D spatial structure of the sample clusters, while using the morphological dislocation (MD) defined in our previous work and the ellipticity ratio (ER) of the clusters' inner and outer structures to characterize the morphological coherence of the sample clusters. Results. The results show an inverse correlation between the ER of the sample clusters and the number of their members, indicating that sample clusters with a much more elliptical external morphology than internal shape generally tend to host a large number of members. Meanwhile, a slight shrinking of the MD of the sample clusters with their members' number may shed light on the significant role of the gravitational binding of the sample clusters in maintaining their morphological stability. Moreover, there are no correlations between the MD and ER of the sample clusters and their age. They are also not significantly correlated with the X-axis, the Y-axis, their orbital eccentricities, and the radial and vertical forces on them. However, the ER of the sample clusters displays some fluctuations in the distributions between it and the above covariates, implying that the morphologies of the sample clusters are sensitive to the external environment if sample effects are not taken into account. Finally, the analysis of the 3D spatial shapes of sample clusters with a small ER or a large ER demonstrates that the number of members lays an important foundation for forming a dense internal system for sample clusters. At the same time, the MD of the sample clusters can serve well as an indicator of their morphological stability, which is built upon a certain amount of member stars. Conclusions. We present a new insight into the morphological coherence of open clusters, attributed to the combination of their gravitational binding capacity and external environmental perturbations. [ABSTRACT FROM AUTHOR]

[Display omitted] Transition metal phosphides have been demonstrated to be promising non-noble catalysts for water splitting, yet their electrocatalytic performance is impeded by unfavorable free energies of adsorbed intermediates. The achievement of nanoscale modulation in morphology and electronic states is imperative for enhancing their intrinsic electrocatalytic activity. Herein, we propose a strategy to expedite the water splitting process over NiCoP/FeNiCoP hollow ellipsoids by modulating the electronic structure and d-band center. These unique phosphorus (P) vacancies-rich ellipsoids are synthesized through an ion-exchange reaction between uniform NiCo-nanoprisms and K 3 [Fe(CN) 6 ], followed by NaH 2 PO 2 -assisted phosphorization under N 2 atmosphere. Various characterizations reveals that the titled catalyst possesses high specific surface area, abundant porosity, and accessible inner surfaces, all of which are beneficial for efficient mass transfer and gas diffusion. Moreover, density functional theory (DFT) calculations further confirms that the NiCoP/FeNiCoP heterojunction associated with P vacancies regulate the electronic structures of d-electrons and p-electrons of Co and P atoms, respectively, resulting in a higher desorption efficiency of adsorbed H* intermediates with a lower energy barrier for water splitting. Due to the aforementioned advantages, the resultant NiCoP/FeNiCoP hollow ellipsoids exhibit remarkably low overpotentials of 45 and 266 mV for hydrogen and oxygen evolution reaction to achieve the current densities of 10 and 50 mA cm−2, respectively. This work not only reports the synthesis of a hollow double-shell structure of NiCoP/FeNiCoP but also introduces a novel strategy for constructing a multifunctional electrocatalyst for water splitting. [ABSTRACT FROM AUTHOR]

While the collective dynamics of spherical active Brownian particles is relatively well understood by now, the much more complex dynamics of nonspherical active particles still raises interesting open questions. Previous work has shown that the dynamics of rod-like or ellipsoidal active particles can differ significantly from that of spherical ones. Here, we obtain the full state diagram of active Brownian ellipsoids in two spatial dimensions without hydrodynamic interactions depending on the Péclet number and packing density via computer simulations. The system is found to exhibit a rich state behavior that includes cluster formation, local polar order, polar flocks, and disordered states. Moreover, we obtain numerical results and an analytical representation for the pair-distribution function of active ellipsoids. This function provides useful quantitative insights into the collective behavior of active particles with lower symmetry and has potential applications in the development of predictive theoretical models. The authors study the collective behavior of ellipsoidal active particles, which is richer and less understood than that of their spherical counterparts. They find a variety of states such as cluster formation, local polar order, polar flocks, and disordered states, and obtain an analytical expression for the pair-distribution function, which allows a quantitative characterization of the system's state. [ABSTRACT FROM AUTHOR]

Due to the difficulty of accurately predicting system reliability for many engineering structures, bounds on system reliability have received increasing attention. By dealing with structural uncertain parameters with an ellipsoid model, a linear programming-based non-probabilistic reliability bounds method is proposed in this paper for series systems. In this research, a linear programming model is first established, and then several strategies are proposed to simplify the model by removing zero design variables. Three numerical examples are presented to demonstrate the feasibility and validity of the proposed method. [ABSTRACT FROM AUTHOR]

The problem of equilibrium figures of two liquid masses in a state of tidal mutual capture is posed and solved. The condition of complete synchronous (orbital plus spin) rotation is satisfied in the system, and both bodies have the same masses and congruent ellipsoidal surfaces. For each figure, besides its own gravity and centrifugal forces, the attraction from the second body is taken into account in the tidal approximation. The spatial form of equilibrium figures as triaxial ellipsoids is found by an analytical and numerical method. The spin rotation of ellipsoidal equilibrium figures is established to occur not around small axes, as is usually assumed, but around the middle axes of the ellipsoids. This method is used to study the binary asteroid (190166) 2005 UP156, which approximately satisfies the initial conditions of the problem. The study showed that with the parameters known today, the system of two asteroids (190166) 2005 UP156 is nonequilibrium. [ABSTRACT FROM AUTHOR]

The present study focuses on controller design for high-order fully actuated systems that experience input saturation and are affected by bounded disturbances, such as nonlinear uncertainties and time-varying unknown parameters. A saturated adaptive controller is developed via the fully actuated system approach and the Lyapunov stability theory to achieve output control and reject disturbances. The disturbances are treated as an extended state and then estimated by introducing an extended state observer. An adaptive variable is used to handle the estimation error between the actual and estimated values of the disturbances. An auxiliary system is designed to mitigate the saturation effect. Lyapunov's direct method verifies that the estimation error, the tracking error, the adaptive state, and the auxiliary system state will eventually stabilise within a bounded ellipsoid. An illustration of spacecraft attitude control demonstrates the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

Our objective is to construct a model of the velocity ellipsoid and the retrieved Solar velocity for two programs of ultra-cool L dwarfs with 49 points (UCDs 49) and 39 points (UCDs 39) within 85◦ ≥ b ≥ -85◦. Firstly, we calculated the velocity dispersion (σ1, σ2, σ3; km s-1) ratios (σ2/σ1 = 0.78 ± 0.06; UCDs 49 &0.79 ± 0.05; UCDs 39) and (σ3/σ1 = 0.41 ± 0.04; UCDs 49 & 0.51 ± 0.03; UCDs 39), the vertex longitude (l2) which has often differed significantly from zero in many analyses (i.e., l2 = -0◦8967; UCDs 49 & -0.4454; UCDs 39). Here, we have computed the Solar velocity (S⊙; km s-1) as (32.13±0.18; UCDs 49 & 21.73± 0.22) and the other Solar elements (lA, bA). Finally, we have computed Oort's constants (A,B; km s-1 kpc1) and the angular velocities for UCDs 49 and UCDs 39 programs where their numerical values are in the same manner. [ABSTRACT FROM AUTHOR]

High-quality, 3D-shaped, SiO2 colloidal photonic crystals (ellipsoids, hyperboloids, and others) were fabricated by self-assembly. They possess a quadratic surface and are wide-angle-independent, direction-dependent, diffractive reflection crystals. Their size varies between 1 and 5 mm and can be achieved as mechanical-resistant, free-standing, thick (hundreds of ordered layers) objects. High-quality, 3D-shaped, polystyrene inverse-opal photonic superstructures (highly similar to diatom frustules) were synthesized by using an inside infiltration method as wide-angle-independent, reflective diffraction objects. They possess multiple reflection bands given by their special architecture (a torus on the top of an ellipsoid) and by their different sized holes (384 nm and 264 nm). Our hanging-drop self-assembly approach uses setups which deform the shape of an ordinary spherical drop; thus, the colloidal self-assembly takes place on a non-axisymmetric liquid/air interface. The deformed drop surface is a kind of topological interface which changes its shape in time, remaining as a quality template for the self-assembly process. Three-dimensional-shaped colloidal photonic crystals might be used as devices for future spectrophotometers, aspheric or freeform diffracting mirrors, or metasurfaces for experiments regarding space-time curvature analogy. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fast and accurate method for approximating the Minkowski sum of two rotational ellipsoids with a superellipsoid. The Minkowski sum is used in a variety of applications such as robot motion planning and particle flow simulation requiring collision detection. Many of them are computed based on Minkowski sum, whose accuracy and processing time depend on how the mesh is created. We approximate Minkowski sum with a superellipsoid function. The superellipsoid has various shapes with the value of the exponents, and the computation of the parameters including the exponents is an algebraic computation with the time complexity O (1) . As a result, approximation error is small and computation is fast in all combinations of rotational ellipsoids. In addition, collision is quickly detected by solving the inequality of superellipsoid. [ABSTRACT FROM AUTHOR]