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Journal articles on the topic 'Ellipsoidal analysis'

Author: Grafiati

Published: 25 May 2024

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1

Møller, J. "Stereological analysis of particles of varying ellipsoidal shape." Journal of Applied Probability 25, no. 2 (June 1988): 322–35. http://dx.doi.org/10.2307/3214440.

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Stereological analysis of d-dimensional particles of ellipsoidal shape based on lower-dimensional sections through the particles is discussed. It is proved that the non-void intersections between three parallel hyperplanes and an ellipsoid uniquely determine the ellipsoid, and based on this fact we may reconstruct ellipsoids from sectional information. Combining this reconstruction with a new sampling procedure we obtain a useful tool for non-parametric stereological analysis of particle aggregates of ellipsoids. Finally, parametric models for ellipsoids which are mathematically convenient for the present set up are introduced and discussed.

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2

Møller, J. "Stereological analysis of particles of varying ellipsoidal shape." Journal of Applied Probability 25, no. 02 (June 1988): 322–35. http://dx.doi.org/10.1017/s0021900200040961.

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Stereological analysis of d-dimensional particles of ellipsoidal shape based on lower-dimensional sections through the particles is discussed. It is proved that the non-void intersections between three parallel hyperplanes and an ellipsoid uniquely determine the ellipsoid, and based on this fact we may reconstruct ellipsoids from sectional information. Combining this reconstruction with a new sampling procedure we obtain a useful tool for non-parametric stereological analysis of particle aggregates of ellipsoids. Finally, parametric models for ellipsoids which are mathematically convenient for the present set up are introduced and discussed.

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3

Giapalaki, S. N., and F. Kariotou. "The complete ellipsoidal shell-model in EEG imaging." Abstract and Applied Analysis 2006 (2006): 1–18. http://dx.doi.org/10.1155/aaa/2006/57429.

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This work provides the solution of the direct Electroencephalography (EEG) problem for the complete ellipsoidal shell-model of the human head. The model involves four confocal ellipsoids that represent the successive interfaces between the brain tissue, the cerebrospinal fluid, the skull, and the skin characterized by different conductivities. The electric excitation of the brain is due to an equivalent electric dipole, which is located within the inner ellipsoid. The proposed model is considered to be physically complete, since the effect of the substance surrounding the brain is taken into account. The direct EEG problem consists in finding the electric potential inside each conductive space, as well as at the nonconductive exterior space. The solution of this multitransmission problem is given analytically in terms of elliptic integrals and ellipsoidal harmonics, in such way that makes clear the effect that each shell has on the next one and outside of the head. It is remarkable that the dependence on the observation point is not affected by the presence of the conductive shells. Reduction to simpler ellipsoidal models and to the corresponding spherical models is included.

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4

Ross, C. T. F., and N. Rotherhamn. "Collapse of Inverted Hemi-Ellipsoidal Shell Domes Under Uniform Pressure." Journal of Ship Research 36, no. 04 (December 1, 1992): 378–86. http://dx.doi.org/10.5957/jsr.1992.36.4.378.

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Nine hemi-ellipsoidal shell domes were tested to destruction, under uniform pressure acting on their concave surfaces. The shell domes varied from flat oblate hemi-ellipsoids to long prolate hemi-ellipsoids. The experimentally obtained collapse pressures showed that the flat oblate hemi-ellipsoidal domes and the long prolate hemi-ellipsoidal domes were stronger than the hemi-spherical and near hemi-spherical domes. The theoretical analysis was based on the finite-element method, and it showed that the theoretically obtained stresses were, in general, larger in magnitude than the experimentally obtained stresses.

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5

Gureeva, Natalya, Anatoliy Nikolaev, and Mikhail Klochkov. "Continuos Parameterization of the Median Surface of an Ellipsoidal Shell and Its Geometric Parameters." Mathematical Physics and Computer Simulation, no. 1 (March 2020): 5–12. http://dx.doi.org/10.15688/mpcm.jvolsu.2020.1.1.

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When analyzing the stress-strain state of thin-walled structural elements that have the shape of an ellipsoid, it becomes necessary to calculate the geometric characteristics of the ellipsoidal surface. When using the canonical ellipsoid equation, regions of uncertainty appear in the Cartesian coordinate system at the intersection points of the ellipsoid surface with the horizontal coordinate plane. To exclude these areas of uncertainty, we propose an expression of the radius vector of an ellipsoidal surface whose projections are functions of two parametric representations in mutually perpendicular planes. One of the planes is the vertical plane XOZ, and the other plane is the plane perpendicular to the axis O at the point with the x coordinate. The parameter T of the ellipse obtained from the intersection of the ellipsoid with the XOZ plane was chosen as the argument of the first parametric function. The argument of the second parametric function t is the parameter of an ellipse formed as a result of the intersection of an ellipsoidal surface with a plane perpendicular to the abscissa axis at a distance of x from the origin. The proposed representation of the ellipsoidal surface allowed us to exclude uncertainties at the intersection points of the ellipsoid with the HOWE coordinate plane. By differentiating the proposed radius-vector expression at an arbitrary point on an ellipsoidal surface, we obtain relations for the basis vectors of an arbitrary point and their derivatives represented by components in the same local basis. These relations are necessary for the development of algorithms for numerical analysis of deformation processes of engineering structures that have ellipsoidal surfaces.

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6

Chong, Shuai, Lili Huang, Junchao Cao, and Xiaoyang Lu. "The optimization design of the triangular mesh of the lamella ellipsoid reticulated shell and the comparative analysis of its static performance." E3S Web of Conferences 165 (2020): 06054. http://dx.doi.org/10.1051/e3sconf/202016506054.

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Using the traditional geometric principle and ANSYS software Parametric Design Language (APDL), the optimization method is given for the triangular shell mesh of lamella ellipsoid. The mechanical properties of two types of ellipsoidal reticulated shells, optimized isosceles shell (OIS) and traditional shell (TS), are analyzed by comparison with ANSYS software. The results show that the ellipsoidal reticulated shell composed of an optimized isosceles triangle mesh has better mechanical performance and is widely used in engineering.

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7

Ziggah, Y. Y., I. Yakubu, and B. Kumi-Boateng. "Analysis of Methods for Ellipsoidal Height Estimation – The Case of a Local Geodetic Reference Network." Ghana Mining Journal 16, no. 2 (December 20, 2016): 1–9. http://dx.doi.org/10.4314/gm.v16i2.1.

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Ghana’s local geodetic reference network is based on the War Office 1926 ellipsoid with data in latitude, longitude and orthometric height without the existence of ellipsoidal height. This situation makes it difficult to apply the standard forward transformation equation for direct conversion of curvilinear geodetic coordinates to its associated cartesian coordinates (X, Y, Z) in the Ghana local geodetic reference network. In order to overcome such a challenge, researchers resort to various techniques to obtain the ellipsoidal height for a local geodetic network. Therefore, this paper evaluates, compares, and discusses different methods for estimating ellipsoidal height for a local geodetic network. The investigated methods are the Abridged Molodensky transformation model, Earth Gravitational Model, and the Orthometric Height approach. To evaluate these methods, their estimated local ellipsoidal height values were implemented in the seven-parameter similarity transformation model of Bursa-Wolf. The performance of each of the methods was assessed based on statistical indicators of Mean Square Error (MSE), Mean Absolute Error (MAE), Horizontal Position Error (HE) and Standard Deviation (SD). The statistical findings revealed that, the Abridged Molodensky model produced more reliable transformation results compared with the other methods. It can be concluded that for Ghana’s local geodetic network, the most practicable method for estimating ellipsoidal height is the Abridged Molodensky transformation model. Keywords: Abridged Molodensky Model, Earth Gravitational Model, Orthometric Height, Geodetic Network

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8

Phan-Thien, N., T. Tran-Cong, and M. Ramia. "A boundary-element analysis of flagellar propulsion." Journal of Fluid Mechanics 184 (November 1987): 533–49. http://dx.doi.org/10.1017/s0022112087003008.

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The swimming of a flagellar micro-organism by the propagation of helical waves along its flagellum is analysed by a boundary-element method. The method is not restricted to any particular geometry of the organism nor does it assume a specific wave motion for the flagellum. However, only results for an organism with a spherical or ellipsoidal cell body and a helically beating flagellum are presented here.With regard to the flagellum, it is concluded that the optimum helical wave (amplitude α and wavenumber k) has αk ≈ 1 (pitch angle of 45°) and that for the optimum flagellar length L/A = 10 (L being the flagellar length, A being the radius of the assumed spherical cell body) the optimum number of wavelengths Nλ is about 1.5. Furthermore there appears to be no optimal value for the flagellar radius a, with the thinner flagella being favoured. These conclusions show excellent quantitative agreement with those of slender-body theory.For the case of an ellipsoidal cell body, the optimum aspect ratios B/A and C/A of the ellipsoid are about 0.7 and 0.3 respectively; A, B and C are the principal radii of the ellipsoid. These and all of the above conclusions show good qualitative agreement with experimental observations of efficiently swimming micro-organisms.

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9

Kariotou, Fotini. "Electroencephalography in ellipsoidal geometry." Journal of Mathematical Analysis and Applications 290, no. 1 (February 2004): 324–42. http://dx.doi.org/10.1016/j.jmaa.2003.09.066.

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10

Lu, Xiao Yang, Jing Xin, Ran An, Jin Ming Liu, Lei Wang, and Feng Cheng Liu. "Ellipsoid Reticulated Shell of Parametric Design and Analysis of Mechanical Characteristics." Applied Mechanics and Materials 716-717 (December 2014): 682–85. http://dx.doi.org/10.4028/www.scientific.net/amm.716-717.682.

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By using the parametric design language APDL, developed ellipsoidal reticulated shell parametric macros, only enter the long axis S1, short axis S2, high vector F, scale factor t, ring symmetric region shares Kn, radial nodes turns Nx, to generate the desired lattice shell; comparative analysis of 30 kinds of scheme through two types of single-shell ellipsoid reticulated shell with different rise span ratio force, studied its stress characteristics, providing a theoretical reference for designing and engineering ellipsoid reticulated shell application.

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Vidal, Jérémie, and David Cébron. "Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits." Journal of Fluid Mechanics 833 (November 6, 2017): 469–511. http://dx.doi.org/10.1017/jfm.2017.689.

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We consider the hydrodynamic stability of homogeneous, incompressible and rotating ellipsoidal fluid masses. The latter are the simplest models of fluid celestial bodies with internal rotation and subjected to tidal forces. The classical problem is the stability of Roche–Riemann ellipsoids moving on circular Kepler orbits. However, previous stability studies have to be reassessed. Indeed, they only consider global perturbations of large wavelength or local perturbations of short wavelength. Moreover many planets and stars undergo orbital motions on eccentric Kepler orbits, implying time-dependent ellipsoidal semi-axes. This time dependence has never been taken into account in hydrodynamic stability studies. In this work we overcome these stringent assumptions. We extend the hydrodynamic stability analysis of rotating ellipsoids to the case of eccentric orbits. We have developed two open-source and versatile numerical codes to perform global and local inviscid stability analyses. They give sufficient conditions for instability. The global method, based on an exact and closed Galerkin basis, handles rigorously global ellipsoidal perturbations of unprecedented complexity. Tidally driven and libration-driven elliptical instabilities are first recovered and unified within a single framework. Then we show that new global fluid instabilities can be triggered in ellipsoids by tidal effects due to eccentric Kepler orbits. Their existence is confirmed by a local analysis and direct numerical simulations of the fully nonlinear and viscous problem. Thus a non-zero orbital eccentricity may have a strong destabilising effect in celestial fluid bodies, which may lead to space-filling turbulence in most of the parameters range.

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12

Chevillard, Laurent, and Charles Meneveau. "Orientation dynamics of small, triaxial–ellipsoidal particles in isotropic turbulence." Journal of Fluid Mechanics 737 (November 27, 2013): 571–96. http://dx.doi.org/10.1017/jfm.2013.580.

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AbstractThe orientation dynamics of small anisotropic tracer particles in turbulent flows is studied using direct numerical simulation (DNS) and results are compared with Lagrangian stochastic models. Generalizing earlier analysis for axisymmetric ellipsoidal particles (Parsa et al., Phys. Rev. Lett., vol. 109, 2012, 134501), we measure the orientation statistics and rotation rates of general, triaxial–ellipsoidal tracer particles using Lagrangian tracking in DNS of isotropic turbulence. Triaxial ellipsoids that are very long in one direction, very thin in another and of intermediate size in the third direction exhibit reduced rotation rates that are similar to those of rods in the ellipsoid’s longest direction, while exhibiting increased rotation rates that are similar to those of axisymmetric discs in the thinnest direction. DNS results differ significantly from the case when the particle orientations are assumed to be statistically independent from the velocity gradient tensor. They are also different from predictions of a Gaussian process for the velocity gradient tensor, which does not provide realistic preferred vorticity–strain-rate tensor alignments. DNS results are also compared with a stochastic model for the velocity gradient tensor based on the recent fluid deformation approximation (RFDA). Unlike the Gaussian model, the stochastic model accurately predicts the reduction in rotation rate in the longest direction of triaxial ellipsoids since this direction aligns with the flow’s vorticity, with its rotation perpendicular to the vorticity being reduced. For disc-like particles, or in directions perpendicular to the longest direction in triaxial particles, the model predicts noticeably smaller rotation rates than those observed in DNS, a behaviour that can be understood based on the probability of vorticity orientation with the most contracting strain-rate eigendirection in the model.

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13

Gao, Jun Shan, Jin Wang, and Ke Wang. "Analysis of Defect Magnetic Flux Leakage Field Based on Dipole." Applied Mechanics and Materials 274 (January 2013): 592–95. http://dx.doi.org/10.4028/www.scientific.net/amm.274.592.

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This paper makes an exhaustive analysis to common defect magnetic leakage field based on dipole theory, obtaining the analytical expression of some common injury shapes and exploiting distribution curves of the magnetic field intensity by MATLAB software, and based on this a new scheme is proposed to simulate various injuries using an ellipsoid tables defect model, and finally confirms the superiority of ellipsoidal model in analysis of defect leakage field by comparison.

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14

Kurzhanski, A. B., and A. I. Mesyats. "Optimal control of ellipsoidal motions." Differential Equations 48, no. 11 (November 2012): 1502–9. http://dx.doi.org/10.1134/s0012266112110080.

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15

Krivoshapko, S. N. "Research on General and Axisymmetric Ellipsoidal Shells Used as Domes, Pressure Vessels, and Tanks." Applied Mechanics Reviews 60, no. 6 (November 1, 2007): 336–55. http://dx.doi.org/10.1115/1.2806278.

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The principal advances in the design and construction, as well as the static, vibrational, and buckling analysis of thin-walled structures and buildings in the shape of general and axisymmetric ellipsoidal shells are summarized in this review. These shells are particularly useful as internally pressurized vessels or as heads and bottoms of cylindrical tanks and vessels. Reinforced concrete and structural steel domes of buildings, air-supported rubber-fabric shells, and underwater pressure vessels are also made in the form of ellipsoidal, shells. Knowing the geometry of ellipsoids, one can solve various problems in physics, optics, and so on. Basic results of theoretical and experimental investigations of the stress-strain state, buckling, and natural and forced vibrations contained in 209 references are presented in the review. The influence of temperature on the stress-strain state of the shells in question is also discussed. Some parts of the review are also devoted to an analysis of the literature on the stress-strain state of ellipsoidal and torispherical heads of pressure vessels with openings.

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Poluektov, Serhii, Natalia Bezugla, Kinga Kurowska-Wilczyńska, and Mikhail Bezuglyi. "INFORMATION SYSTEM FOR MULTI-VECTOR RAYTRACING IN ELLIPSOIDAL REFLECTORS." Bulletin of Kyiv Polytechnic Institute. Series Instrument Making, no. 65(1) (June 30, 2023): 19–28. http://dx.doi.org/10.20535/1970.65(1).2023.283215.

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Due to two focuses, ellipsoidal reflectors are unique reflective optical elements that allow conjugate imaging in two focal planes within their inner cavity. Such reflectors are used in various devices, such as lens telescopes, to achieve high resolution. They have found applications in microscope optical systems to increase the depth of field. They are used in scientific instruments, such as laser systems, to ensure the laser beam's high accuracy and stability. Despite their advantages, the non-spherical shape of ellipsoidal reflectors also introduces drawbacks in the form of errors arising from raytracing on the side surface. It complicates aberration analysis and necessitates specialized software for multi-vector ray tracing. Considering the deviations in the coordinates of the intersections between rays and the second focal plane allows for optimizing the reflector design to achieve maximum efficiency. Therefore, this work aims to enhance the efficiency of the aberration analysis of ellipsoidal reflectors by developing principles and informational tools for multi-vector ray tracing. The article presents the results of developing an information system for multi-vector analysis in ellipsoidal reflectors. The developed multi-vector algorithm enables selecting tracing modes, tuning launch parameters, and setting the step size for launching rays. The specialized software features for single- and multi-vector raytracing in an ellipsoidal reflector are presented. The side surface of the ellipsoid is the object under study. The software provides the capability to realize different methods of multi-vector ray tracing, such as radius-based, diameter-based, and partial radius-based, for different types of tasks, thereby expanding the possibilities for visualizing the simulation results. Based on the multi-vector aberration analysis of the side surface of the ellipsoidal reflector, the center coordinates and root mean square deviations were obtained for different reflection acts when changing the zenith angle of tracing. The influence of zenith angles on coordinate variations was assessed, which can be realized in selecting parameters for ellipsoidal reflectors and designing the optical system of photometers for various purposes. It can also aid in developing additional means to compensate for aberrations or modify the reflector's side surface shape.

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Liu, Ling, and Jianqiao Li. "Dynamic Deformation and Perforation of Ellipsoidal Thin Shell Impacted by Flat-Nose Projectile." Materials 15, no. 12 (June 10, 2022): 4124. http://dx.doi.org/10.3390/ma15124124.

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Experimental and theoretical studies were carried out on the dynamic deformation and penetration response characteristics of metal ellipsoidal thin curved shells under impact loads. The deformation characteristics of the impacted ellipsoid shell was investigated via the use of a light gas gun to carry out impact loading experiments at different speeds. Ten cases of experiments were conducted with the impact velocities distributed between 25.69 m/s and 118.97 m/s. Stereo digital image correlation (3D-DIC) technology was applied to capture the dynamic deformation and penetration process of the impacted shell. The recovered shells were measured, and the deformation characteristics were analyzed, along with the dynamic evolution, as observed through 3D-DIC analysis. Based on the experimental results, the displacement mode was summarized and the displacement distribution of the locally impacted ellipsoid shell was proposed. The governing equations were derived for the dynamic deformation and penetration of the impacted ellipsoid shell by means of the Lagrange equation. The proposed theoretical model was verified based on the experimental results. Finally, the influence of the curvature distribution on the impact resistance of ellipsoidal shells is discussed. The results indicated that the proposed theoretical model was effective in analyzing the large deformation and the penetration speed. Stretching the axial length of the ellipsoid shell in the impact direction improved its resistance to penetration. Stretching the axial length of the ellipsoid shell perpendicular to the impact direction improved its resistance to deformation, but reduced its resistance to penetration. Maintaining the triaxial ratio and appropriately reducing the size of the ellipsoidal shell improved its resistance to both deformation and penetration. The above research provides a reference for the analysis of the impact resistance of thin-walled curved shell structures in engineering.

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Grimes, David Robert, and Frederick J. Currell. "Oxygen diffusion in ellipsoidal tumour spheroids." Journal of The Royal Society Interface 15, no. 145 (August 2018): 20180256. http://dx.doi.org/10.1098/rsif.2018.0256.

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Oxygen plays a central role in cellular metabolism, in both healthy and tumour tissue. The presence and concentration of molecular oxygen in tumours has a substantial effect on both radiotherapy response and tumour evolution, and as a result the oxygen micro-environment is an area of intense research interest. Multi-cellular tumour spheroids closely mimic real avascular tumours, and in particular they exhibit physiologically relevant heterogeneous oxygen distribution. This property has made them a vital part of in vitro experimentation. For ideal spheroids, their heterogeneous oxygen distributions can be predicted from theory, allowing determination of cellular oxygen consumption rate (OCR) and anoxic extent. However, experimental tumour spheroids often depart markedly from perfect sphericity. There has been little consideration of this reality. To date, the question of how far an ellipsoid can diverge from perfect sphericity before spherical assumptions break down remains unanswered. In this work, we derive equations governing oxygen distribution (and, more generally, nutrient and drug distribution) in both prolate and oblate tumour ellipsoids, and quantify the theoretical limits of the assumption that the spheroid is a perfect sphere. Results of this analysis yield new methods for quantifying OCR in ellipsoidal spheroids, and how this can be applied to markedly increase experimental throughput and quality.

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Yeh, Chun Lang. "Chemical Reaction and Fluid Flow in a Carbon Monoxide Boiler(II) Chemical Reaction Analysis." Advanced Materials Research 581-582 (October 2012): 19–26. http://dx.doi.org/10.4028/www.scientific.net/amr.581-582.19.

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Performance of a CO boiler has a detrimental influence on the operation and production of related industries. In this paper, the reacting flow in a Carbon Monoxide boiler is investigated. The influence of insertion of an ellipsoidal cone is discussed. It is found that insertion of an ellipsoidal cone can lower the temperature in the DeNOx section. There is a larger skin friction coefficient with a larger ellipsoidal cone angle. It is also found that NOx formation in the DeNOx section can be alleviated by insertion of an ellipsoidal cone.

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Ma, Hai Bo, Quan Yuan, Yan Qiu Zhu, and Xin Ye. "The Nonlinear Analysis of the Biopresthetic Heart Valve." Applied Mechanics and Materials 71-78 (July 2011): 3438–42. http://dx.doi.org/10.4028/www.scientific.net/amm.71-78.3438.

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In order to improve long-term durability of bioprosthetic heart valve, we take the spherical,paraboloidal,cylindrical and the ellipsoidal leaflets for nonlinear analysis and the material is orthotropic.The experimental results of the finite element nonlinear analysis show that when the leaflets with the material orthotropic is closed,the deformation of the symmetric edge is larger than else. The stress distribution of the cylindrical, spherical, paraboloidal and ellipsoidal valve leaflets is quite different. The ellipsoidal valve leaflets have more advantages than the cylindrical, spherical, paraboloidal valve leaflets.This work is very helpful to manufacture reasonable shaped valvular leaflets and to prolong the lifetime of the bioprosthetic heart valve.

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Chernousko, F. L. "Ellipsoidal state estimation for dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (November 2005): 872–79. http://dx.doi.org/10.1016/j.na.2005.01.009.

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Dassios, George, Foteini Kariotou, and Panayiotis Vafeas. "Invariant vector harmonics. The ellipsoidal case." Journal of Mathematical Analysis and Applications 405, no. 2 (September 2013): 652–60. http://dx.doi.org/10.1016/j.jmaa.2013.03.015.

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Yuan, Quan, Xin Ye, Hai Bo Ma, Hua Cong, and Xu Huang. "Nonlinear Analysis of Bioprosthetic Heart Valves under Dynamic Loading." Applied Mechanics and Materials 152-154 (January 2012): 732–36. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.732.

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In order to investigate the effect of material nonlinearity on the dynamic behavior of bioprosthetic heart valve, we establish the spherical, cylindrical and ellipsoidal leaflets models with the material model of Mooney-Rivlin. The mechanical behavior of bioprosthetic valve leaflet during diastolic phase is analyzed. The finite element analysis results show that the stress distributions of the ellipsoidal and spherical valve leaflets are comparatively reasonable. The ellipsoidal and spherical valve leaflets have the following advantages over the cylindrical leaflet valve, lower peak von-Mises stress, smaller stress concentration area, and relatively uniform stress distribution. This work is very helpful to manufacture reasonable shaped valvular leaflets，thus to prolong the lifetime of the bioprosthetic heart valve.

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Duan, Chenyang, Shijie Zhang, Yafei Zhao, and Xianren Kong. "Robust Control Allocation among Overactuated Spacecraft Thrusters under Ellipsoidal Uncertainty." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/950127.

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Spacecrafts with overactuated and redundant thrusters can work normally once some of them are out of work, which improves the reliability of spacecraft in orbit. In this way, the desired command of controller needs to be dynamically allocated among thrusters. Considering that uncertain factors may appear in forms of dynamics, installation errors, thrust deviations, or failures, this paper proposes a robust control allocation under ellipsoidal uncertainty. This method uses the uncertainty ellipsoid set to describe the uncertainty of the thrusters firstly and establish the thrust allocation robust reference model and then transforms it into a cone optimization model which can be solved as an optimized problem. Finally, this paper adopts the interior-point method for solving the optimization problem. In this way, difficulties of solving the problem caused by parameter uncertainties are avoided effectively. Finally, we take satellite rendezvous and docking as simulation scenarios; it is verified that the cumulative distribution error and maximum error can be reduced by more than 15% when the random error of control efficiency matrix is 5%–20%; also, precision of thruster allocation is improved.

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FUJIWARA, Masaya, Tetsurou HIRANO, Yusuke FURUSE, and Masato ISHIKAWA. "Dynamic motion analysis of ellipsoidal rolling robot." Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2016 (2016): 2P1–06b1. http://dx.doi.org/10.1299/jsmermd.2016.2p1-06b1.

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Kurzhanski, A. B., and P. Varaiya. "Ellipsoidal techniques for reachability analysis: internal approximation." Systems & Control Letters 41, no. 3 (October 2000): 201–11. http://dx.doi.org/10.1016/s0167-6911(00)00059-1.

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Carvalho, J. A., and D. Bastos-Netto. "Weight Analysis of Thin-Walled Ellipsoidal Shells." Journal of Pressure Vessel Technology 112, no. 2 (May 1, 1990): 187–89. http://dx.doi.org/10.1115/1.2928608.

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Braatz, Richard D., and Oscar D. Crisalle. "Robustness analysis for systems with ellipsoidal uncertainty." International Journal of Robust and Nonlinear Control 8, no. 13 (November 1998): 1113–17. http://dx.doi.org/10.1002/(sici)1099-1239(1998110)8:13<1113::aid-rnc375>3.0.co;2-b.

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FEDORCHUK, A. "Analysis of erypsoidal heights errors based on GNSS-leveling results." Modern achievements of geodesic science and industry 41, no. I (April 1, 2021): 37–45. http://dx.doi.org/10.33841/1819-1339-1-41-37-45.

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Research the influence of errors on the measurement results is always an urgent task. Analysis of such values makes it possible to assess the nature of the change and the magnitude of the impact of errors for their further consideration or compensation, or minimization. In this paper, the errors in determining ellipsoidal heights from GNSS observations are considered. In determining the ellipsoidal heights, this method can achieve an accuracy of 1–2 cm in static mode (Static) and 2–4 cm in real time mode (RTK). Thus, the accuracy of the chosen mode of observations will indicate the initial limits of the ellipsoidal heights errors influence, and the factors that arise directly during observations and data processing will determine the extent to which these errors will change relative to the initial limits. The purpose of this work is to analyze the errors of ellipsoidal heights based on the results of GNSS-leveling obtained in the static and RTK modes. Method. The study used GNSS-leveling data at 17 points (wall and soil benchmarks) of leveling lines of I–II classes, which are located within a radius of 15 km from the permanent station SULP of the Lviv Polytechnic National University. Observations were performed in static mode (4-hour) and RTK (8–10 measurements). Points are divided into three categories (5–6 points): 1) statics on wall benchmarks; 2) real-time mode on wall benchmarks; 3) static mode on soil benchmarks. By combining methods and categories, four GNSS networks were formed, including 11, 11, 12 and 17 points. Results. For each category, the percentages within which the errors of ellipsoidal heights change in static observation mode and real-time mode using the GNSS leveling method are presented. On the basis of the received information it is established that for the first case errors of ellipsoidal heights on the average change within ± 43 %, for the second ± 36 %, and for the third ± 14 %. The analysis of statistical characteristics for each category shows that the standard deviation of the static mode data is 2 % and 19 %, and the RTK mode – 12 %, respectively. Scientific novelty and practical significance. The nature of the change in the error limits of the ellipsoidal heights determination gives an idea of what accuracy should be expected when performing GNSS-leveling depending on the mode of observation. Such data play an important role in solving scientific and applied problems by GNSS leveling, such as the constructions of new leveling networks or monitoring the height points of existing networks.

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Zuccaro, G., I. Elishakoff, and A. Baratta. "Antioptimization of earthquake exitation and response." Mathematical Problems in Engineering 4, no. 1 (1998): 1–19. http://dx.doi.org/10.1155/s1024123x98000696.

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The paper presents a novel approach to predict the response of earthquake-excited structures. The earthquake excitation is expanded in terms of series of deterministic functions. The coefficients of the series are represented as a point inN-dimensional space. Each available ccelerogram at a certain site is then represented as a point in the above space, modeling the available fragmentary historical data. The minimum volume ellipsoid, containing all points, is constructed. The ellipsoidal models of uncertainty, pertinent to earthquake excitation, are developed. The maximum response of a structure, subjected to the earthquake excitation, within ellipsoidal modeling of the latter, is determined. This procedure of determining least favorable response was termed in the literature (Elishakoff, 1991) as an antioptimization. It appears that under inherent uncertainty of earthquake excitation, antioptimization analysis is a viable alternative to stochastic approach.

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Ye, Xin, Quan Yuan, Hua Cong, Hai Bo Ma, and Dong Liang Wei. "Dynamic Analysis of Three Types of Bioprosthetic Heart Valves." Applied Mechanics and Materials 71-78 (July 2011): 2683–88. http://dx.doi.org/10.4028/www.scientific.net/amm.71-78.2683.

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This paper constructs three types of bioprosthetic valve leaflets’ parametric model via computer aided design, a series of accurate parameters of the bioproshtetic heart valve, such as radius of the sutural ring, height of the supporting stent and inclination of the supporting stent, are determined. Numerical simulation is used to determine the effect of different shape designs on the mechanical performance of the bioprosthetic valve leaflet. The dynamic behavior of the valve during diastolic phase is analyzed. The finite element analysis results show the stress distribution of the ellipsoidal and spherical valve leaflets are comparatively reasonable. The ellipsoidal and spherical valve leaflets have the following advantages over the cylindrical leaflet valve, lower peak von-Mises stress, smaller stress concentration area, and relatively uniform stress distribution. The ellipsoidal and spherical valve leaflets may contribute to the long term durability of the valve. This work is very helpful to manufacture valvular leaflets with reasonable shapes and to prolong the lifetime of the bioprosthetic heart valve.

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32

Khavinson, Dmitry, Erik Lundberg, and Hermann Render. "Dirichlet’s Problem with Entire Data Posed on an Ellipsoidal Cylinder." Potential Analysis 46, no. 1 (May 24, 2016): 55–62. http://dx.doi.org/10.1007/s11118-016-9568-8.

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Bang, Jeaheang, and Seok-Bae Yun. "Stationary solutions for the ellipsoidal BGK model in a slab." Journal of Differential Equations 261, no. 10 (November 2016): 5803–28. http://dx.doi.org/10.1016/j.jde.2016.08.022.

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Park, Sa Jun, and Seok-Bae Yun. "Cauchy problem for the ellipsoidal BGK model for polyatomic particles." Journal of Differential Equations 266, no. 11 (May 2019): 7678–708. http://dx.doi.org/10.1016/j.jde.2018.12.013.

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35

Jacobsen, Petra A., Devra Becker, Daniel P. Govier, Steven G. Krantz, and Alex Kane. "Ellipsoid Analysis of Calvarial Shape." Cleft Palate-Craniofacial Journal 46, no. 5 (September 2009): 487–93. http://dx.doi.org/10.1597/06-194.1.

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Purpose: The purpose of this research was to develop a novel quantitative method of describing calvarial shape by using ellipsoid geometry. The pilot application of Ellipsoid Analysis was to compare calvarial form among individuals with untreated unilateral coronal synostosis, metopic synostosis, and sagittal synostosis and normal subjects. Methods: The frontal, parietal, and occipital bones of 10 preoperative patients for each of the four study groups were bilaterally segmented into six regions using three-dimensional skull reconstructions generated by ANALYZE™ imaging software from high-resolution computed tomography scans. Points along each segment were extracted and manipulated using a MATLAB®-based program. The points were fit to the least-squares nearest ellipsoid. Relationships between the six resultant right and left frontal, parietal, and occipital ellipsoidal centroids (FR, FL, PR, PL, OR, and OL, respectively) were tested for association with a synostotic group. Results: Results from the pilot study showed meaningful differences between length ratio, angular, and centroid distance relationships among synostotic groups. The most substantial difference was exhibited in the centroid distance PL-PR between patients with sagittal synostosis and metopic synostosis. The measures most commonly significant were centroid distances FL-PR and FL-PL and the angle OR-FR-PR. Derived centroid relationships were reproducible. Conclusion: Ellipsoid Analysis may offer a more refined approach to quantitative analysis of cranial shape. Symmetric and asymmetric forms can be compared directly. Relevant shape information between traditional landmarks is characterized. These techniques may have wider applicability in quantifying craniofacial morphology with increase in both specificity and general applicability over current methods.

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Lee, Doo-Sung. "Flow around a Triaxial Ellipsoid in a Long Circular Tube." Zeitschrift für Naturforschung A 66, no. 8-9 (September 1, 2011): 481–88. http://dx.doi.org/10.5560/zna.2011-0011.

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Abstract This paper deals with the three-dimensional analysis of viscous fluid flow in a long circular cylinder containing an ellipsoidal obstacle. The center of the ellipsoid coincides with that of the cylinder, and the flow is confined to the space between the ellipsoid and the cylinder when the fluid velocity at the large distance from the ellipsoid is uniform. The equations of the classical theory of fluid dynamics are solved in terms of an unknown function which is then shown to be the solution of a boundary integro-differential equation. A numerical solution of the integro-differential equation is obtained and the pressure on the surface of the ellipsoid is presented in graphical forms for various values of the radius of the circular tube.

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Erbil, H. Y., G. McHale, S. M. Rowan, and M. I. Newton. "Analysis of evaporating droplets using ellipsoidal cap geometry." Journal of Adhesion Science and Technology 13, no. 12 (January 1999): 1375–91. http://dx.doi.org/10.1163/156856199x00532.

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Wang, Defeng, Lin Shi, Daniel S. Yeung, Eric C. C. Tsang, and Pheng Ann Heng. "Ellipsoidal support vector clustering for functional MRI analysis." Pattern Recognition 40, no. 10 (October 2007): 2685–95. http://dx.doi.org/10.1016/j.patcog.2007.01.017.

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39

Chao, Y. J., and M. A. Sutton. "Stress analysis of ellipsoidal shell with radial nozzle." International Journal of Pressure Vessels and Piping 21, no. 2 (January 1985): 89–108. http://dx.doi.org/10.1016/0308-0161(85)90042-0.

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Seeger, Alberto, and Mounir Torki. "Inscribed and circumscribed ellipsoidal cones: volume ratio analysis." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 59, no. 4 (February 16, 2018): 717–37. http://dx.doi.org/10.1007/s13366-018-0387-5.

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Uddin, Md Wahhaj. "Large deformation analysis of ellipsoidal head pressure vessels." Computers & Structures 23, no. 4 (January 1986): 487–95. http://dx.doi.org/10.1016/0045-7949(86)90092-1.

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Zhang, Feng, Kailiang Luo, Weihao Zhai, Shiwang Tan, and Yameng Wang. "Non-probabilistic parameter sensitivity analysis for structures based on ellipsoidal model." Advances in Mechanical Engineering 10, no. 8 (August 2018): 168781401878236. http://dx.doi.org/10.1177/1687814018782362.

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Sensitivity analysis plays a crucial role in identifying the structure important parameters. In this article, a new non-probabilistic parameter sensitivity analysis method is proposed according to the ellipsoidal model. Meanwhile, an analytical solution of non-probabilistic parameter sensitivity analysis method based on the ellipsoidal model is derived for linear performance function, as well as an approximately analytical solution is obtained for nonlinear performance function using the first-order Taylor expansion to linearize the functions in design point. Finally, the proposed method is illustrated by three examples, which shows that it is reasonable and applicable.

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Skopinsky, V. N., and N. A. Berkov. "Stress Analysis of Ellipsoidal Shell With Nozzle Under Internal Pressure Loading." Journal of Pressure Vessel Technology 116, no. 4 (November 1, 1994): 431–36. http://dx.doi.org/10.1115/1.2929612.

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This paper presents the numerical procedure for the stress analysis of the intersecting shells consisting of an ellipsoidal shell and nozzle. Thin shell theory and finite element method are used. The developed special-purpose computer program SAIS is employed for elastic stress analysis of the model joints of the ellipsoidal shell with nozzle. The parametric study of the joints under internal pressure loading was performed. The results are presented in graphical form. Nondimensional geometric parameters are considered to analyze the effects of changing these parameters on the maximum effective stresses in the shells.

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David Mayunga, Selassie. "Determination and Analysis of Height Differences between Orthometric and Ellipsoidal Heights for Engineering Applications." International Journal of Science and Research (IJSR) 12, no. 8 (August 5, 2023): 1653–61. http://dx.doi.org/10.21275/sr23815133647.

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45

Yang, Yu-chuan, Hui-ge Xing, Xing-guo Yang, and Jia-wen Zhou. "Determining the Critical Slip Surface of Three-Dimensional Soil Slopes from the Stress Fields Solved Using the Finite Element Method." Mathematical Problems in Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/7895615.

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The slope stability problem is an important issue for the safety of human beings and structures. The stability analysis of the three-dimensional (3D) slope is essential to prevent landslides, but the most important and difficult problem is how to determine the 3D critical slip surface with the minimum factor of safety in earth slopes. Basing on the slope stress field with the finite element method, a stability analysis method is proposed to determine the critical slip surface and the corresponding safety factor of 3D soil slopes. Spherical and ellipsoidal slip surfaces are considered through the analysis. The moment equilibrium is used to compute the safety factor combined with the Mohr-Coulomb criteria and the limit equilibrium principle. Some assumptions are introduced to reduce the search range of center points and the radius of spheres or ellipsoids. The proposed method is validated by a classical 3D benchmark soil slope. Simulated results indicate that the safety factor of the benchmark slope is 2.14 using the spherical slip surface and 2.19 using the ellipsoidal slip surface, which is close to the results of previous methods. The simulated results indicate that the proposed method can be used for the stability analysis of a 3D soil slope.

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46

Yuan, Quan, Hai Bo Ma, Tian Qi Liu, Hai Yan Zhu, and Cheng Rui Zhang. "Stress Analysis of the Biopresthetic Heart Valve with Different Thickness." Advanced Materials Research 466-467 (February 2012): 1256–60. http://dx.doi.org/10.4028/www.scientific.net/amr.466-467.1256.

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The stress with different shapes under the same load is analysed and the thickness of the leaflets 0.2mm and 0.4mm is compared by us. We creat the spherical, paraboloidal and ellipsoidal curved surfaces in accordance with geometrical features. The experimental results of the finite element analysis show that stress distribution of the same bioprosthetic heart valve leaflets with different thickness is different. The maximal primary stress with the thickness of 0.4mm is lower than the others.With the same thickness,the stress of the ellipsoidal valve leaflets is lower. This work is very helpful to manufacture reasonable shaped valvular leaflets and to prolong the lifetime of the bioprosthetic heart valve.

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47

Friess, Fabian, Christian Wischke, and Andreas Lendlein. "Microscopic analysis of shape-shiftable oligo(ε-caprolactone) - based particles." MRS Advances 4, no. 59-60 (2019): 3199–206. http://dx.doi.org/10.1557/adv.2019.392.

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ABSTRACTSpherical particles are routinely monitored and described by hydrodynamic diameters determined, e.g., by light scattering techniques. Non-spherical particles such as prolate ellipsoids require alternative techniques to characterize particle size as well as particle shape. In this study, oligo(ε-caprolactone) (oCL) based micronetwork (MN) particles with a shape-shifting function based on their shape-memory capability were programmed from spherical to prolate ellipsoidal shape aided by incorporation and stretching in a water-soluble phantom matrix. By applying light microscopy with automated contour detection and aspect ratio analysis, differences in characteristic aspect ratio distributions of non-crosslinked microparticles (MPs) and crosslinked MNs were detected when the degrees of phantom elongation (30-290%) are increased. The thermally induced shape recovery of programmed MNs starts in the body rather than from the tips of ellipsoids, which may be explained based on local differences in micronetwork deformation. By this approach, fascinating intermediate particle shapes with round bodies and two opposite sharp tips can be obtained, which could be of interest, e.g., in valves or other technical devices, in which the tips allow to temporarily encage the switchable particle in the desired position.

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Li, Ting, Ning Mao, Haoyu Fu, Yuxin Zhang, and Li Fan. "Five New Species of the Genus Hymenogaster (Hymenogastraceae, Agaricales) from Northern China." Journal of Fungi 10, no. 4 (April 8, 2024): 272. http://dx.doi.org/10.3390/jof10040272.

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In this study, five new species from China, Hymenogaster latisporus, H. minisporus, H. papilliformis, H. perisporius, and H. variabilis, are described and illustrated based on morphological and molecular evidence. Hymenogaster latisporus was distinguished from other species of the genus by the subglobose, broad ellipsoidal, ovoid basidiospores (average = 13.7 μm × 11.6 μm) with sparse verrucose and ridge-like ornamentation (1–1.2 μm high); H. minisporus by the ellipsoidal to broadly ellipsoidal and small basidiospores (average = 11.7 μm × 9.5 μm); H. papilliformis was characterized by the whitish to cream-colored basidiomes, and broadly fusiform to citriform basidiospores with a pronounced apex (2–3 μm, occasionally up to 4 μm high), papillary, distinct warts and ridges, and pronounced appendix (2–3 μm long); H. perisporius by the dirty white to pale yellow basidiomes, broad ellipsoidal to ellipsoidal, and yellow-brown to dark-brown basidiospores with warts and gelatinous perisporium; H. variabilis by the peridium with significant changes in thickness (167–351 μm), and broad ellipsoidal to subglobose basidiospores ornamented with sparse warts and ridges. An ITS/LSU-based phylogenetic analysis supported the erection of the five new species. A key for Hymenogaster species from northern China is provided.

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Zhang, De Yuan, Li Ming Yuan, Yong Gang Xu, and Jun Cai. "A Three-Dimensional Numerical Analysis on the Effective Permittivity of Composites Including Ellipsoids." Applied Mechanics and Materials 483 (December 2013): 23–27. http://dx.doi.org/10.4028/www.scientific.net/amm.483.23.

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To investigate the effective permittivity of composites composed of ellipsoidal inclusions, three-dimension numerical models for ellipsoidal inclusions distributed randomly are built with the finite-element modeling software Comsol Multiphysics. After calculating the effective permittivity for different cases and comparing the results with analytical results from the Maxwell-Garnett mixing rule, we find that the finite-element method has an advantage in detecting details of the interaction among inclusions, which have some impacts on the effective permittivity and could not be accurately taken into account in the analytical model. The finite-element method is expected to solve more complex problems on electromagnetic computation.

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Luo, Zheng Zhi, Jing Zeng, and Jin Peng Yu. "Influences of Blank Holding Force on Stamping of Large Ellipsoidal Heads Based on Simulation." Applied Mechanics and Materials 217-219 (November 2012): 2097–100. http://dx.doi.org/10.4028/www.scientific.net/amm.217-219.2097.

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Ellipsoidal heads is a important composition of railways tank car. Sheet stamping process is a common method used for manufacturing ellipsoidal heads. An accurate and efficient finite element model was developed for analysis and prediction of ellipsoidal heads forming quality, with different degrees of reduction deformation at different binder forces considered, and self-adaptive mesh were adopted to improve computational efficiency and quality. And the results of simulation was validated by experimental results. Based on this finite element model, the distributions of stress, strain and wall thickness during this process were obtained.

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