Elliptical Geometry Research Articles

Three-dimensional Geometry of the Electron-scale Magnetic Hole in the Solar Wind

Abstract Electron-scale magnetic holes filled with high-energy electrons can provide a seed population of electrons in the magnetosphere and might play an important role in the interaction between the magnetosphere and solar wind. Theoretical studies have investigated their generation mechanisms based on the 1D or 2D geometry of the structure. However, the generation mechanism is still unclear. Here we report on the 3D geometry of the electron-scale magnetic hole in the solar wind based on the Magnetospheric Multiscale mission. We find that the cross section of the magnetic hole with a size of ∼0.2–0.6 ρ i (ion gyroradius) is either circular or 2D sheet-like. Electron vortices exist in both kinds of cross sections. The ellipse is a possible candidate for the geometry of the magnetic hole in the plane including its axis. Surprisingly, such an elliptical geometry suggests that the axial lengths of all our selected magnetic holes are ∼1–2 ρ i. This 3D geometry might shed some light on the generation mechanism and role of the electron-scale magnetic hole in the astrophysical plasma.

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

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

Stress analysis of strain wave gear drives with four different geometries of wave generator

The comparison of strain wave gear drives with four different geometries of the wave generator is presented. The commonly used elliptical geometry of the wave generator is compared with a simplified geometry based on two rolling elements, a geometry based on four rollers, and a newly proposed parabolic geometry for the wave generator. The comparison will be performed in terms of the average maximum stresses caused in the flexible spline due to the rotation of the wave generator. The finite element method and fully-parameterized automatically-generated two-dimensional finite element models are being used in this work. The flexible spline and the ring gear are considered deformable elements whereas the wave generator is considered as a rigid element in the finite element model. The results show that the best mechanical performance in terms of lower average values of maximum von Mises and tensile stresses is achieved with the simplified and parabolic wave generator geometries. Although yielding slightly higher maximum von Mises and tensile stresses, the elliptical wave generator provides the lowest average maximum absolute compressive stress. The worst mechanical performance was obtained with the four roller wave generator.

Effect of tube shape on thermo-fluid performance of a winglet supported fin-and-tube heat exchanger having staggered tubes

Abstract The heat transfer and pressure drop performance of a fin-and-tube heat transfer surface has been presented in this paper. The circular and elliptical tube geometries have been considered for the present analysis. The two tube geometries are compared for both baseline (without winglet) and winglet supported fin-and-tube heat transfer surface. Three staggered tube rows have been considered and rectangular winglets have been selected as heat transfer enhancement tool. The heat transfer and pressure drop performance of the heat transfer surface has been described in terms of Nu and f respectively. To account for the combined effect of Nu and f, an enhancement factor η has also been presented. The winglets are placed at three different stream-wise locations with respect to the tubes and optimum winglet locations for both the tube geometries are presented based on the highest enhancement factor.

Neutron Ray-Tracing Simulations of a New Supermirror Guide for the Osiris Spectrometer

A new supermirror guide has been proposed to replace the current neutron guide of the indirect time-of-flight near-backscattering spectrometer OSIRIS at the ISIS facility. Here we present an extensive Monte Carlo simulation study for the design and optimisation of a new guide system. Among the several guide geometry assessed, a curved guide with elliptical defocusing and focusing sections is shown to perform best. The estimated gain in intensity is a factor of 5–6 at the sample position with a homogeneous distribution of the divergence. The elliptic geometry results in a smaller beam spot and smaller samples will particularly benefit from this upgrade. The proposed guide replacement will ensure that the OSIRIS spectrometer will remain competitive in the years to come.

Optimized geometry of the carotid artery cross-section: Comparison between circular and elliptical approximations in B-mode ultrasound images

Cross-sectional area (CSA) measurement obtained from transverse ultrasound images is the general method used for carotid artery stenosis calculation which assumes a circular CS, however, atherosclerotic stenosis may change the CSA geometry and lead to miscalculation. This study aims to determine the accuracy of circular or elliptical approximation of the normal and stenosed carotid artery CSA. Sixty transverse B-mode ultrasound images (30 from healthy and 30 from stenosed carotid arteries) were recorded. Contours of the internal lumen of the arteries were segmented and the encompassed lumen area was calculated. Based on the fitting accuracy and computational cost effectiveness, pattern search (PS) optimization algorithm was selected by which the parameterized equations of the circular and elliptical geometries were fitted to the segmented point clouds. Goodness of fit analysis of two geometries was carried out using root mean square error (RMSE) and the relative deviation of the approximated CSA. Results of this study showed that elliptical approximation better fits to the artery CS of carotid arteries, with the average RMSE of [Formula: see text] and [Formula: see text] pixels in healthy and [Formula: see text] and [Formula: see text] pixels in stenosed carotid arteries, respectively, for circle and ellipse approximation. Mean values of the relative deviation of the approximated CSA by circle and ellipse geometries were 5.14%[Formula: see text]±[Formula: see text]4.53% and 3.89%[Formula: see text]±[Formula: see text]4.19% in normal arteries; and 12.18%[Formula: see text]±[Formula: see text]10.94% and 4.59%[Formula: see text]±[Formula: see text]3.75% in stenosed arteries, respectively. This study represented that elliptical approximation provides increased accuracy for carotid artery CSA for both normal and stenosed carotid arteries.

Effect of variable pitch on flow around a helically twisted elliptic cylinder

We propose a new geometric disturbance called a variable pitch helically twisted elliptical (VPHTE) cylinder that was obtained by combining helically twisted elliptic (HTE) and asymmetric geometries for passive flow control. We confirmed that the new geometric disturbance reduces the drag and lift fluctuations compared with the smooth and HTE cylinders at the Reynolds number (Re) of 3000. Large eddy simulation was used for the evaluation of the flow control performance of the VPHTE cylinder at Re = 3000, which corresponds to the subcritical regime. A parametric study was conducted on the variable pitch ratio (VP). The smallest value of the time-averaged drag coefficient of the VPHTE cylinder is lower by about 16.7% and 4.1% than those of the smooth and HTE cylinders, respectively. Furthermore, a VPHTE cylinder reduces the root-mean-square value of the lift coefficient by 96.2% compared with a smooth cylinder. The vortex formation length related to the stabilization of the shear layer of the VPHTE cylinders is longer than those of the smooth and HTE cylinders, and it is consistently elongated as the VP increases. In addition, time-averaged pressure coefficients for different cylinders were compared to analyze the reason for the drag reduction. We systematically investigated the additional flow control performance of the VPHTE cylinders and VP effects by analyzing physical values such as the swirl strength, turbulent kinetic energy, and vorticity components around the VPHTE cylinders.

Features of electromagnetic wave propagation in a longitudinally magnetized gyrotropic elliptic waveguide

In scientific literature the electromagnetic waves propagation in gyrotropic elliptic waveguides has not been studied enough due to: 1) difficulties of deriving Helmholtz equations for gyrotropic elliptic waveguides in arbitrary magnetization directions, 2) difficulties of solving Helmholtz equations and deriving the dispersion equations, 3) difficulties of solving the dispersion equations themselves. In this work, for the first time, dispersion equations for longitudinally magnetized gyrotropic elliptic waveguides were solved. Basing on the solutions results, the dependencies of the constant propagation: 1) on the strength and direction of the magnetizing field, 2) on the waveguide ellipticity at a constant ferrite magnetization were investigated. Studies have revealed previously unknown features inherent only to the electromagnetic waves in such waveguides propagation and showed that: 1) with the ferrite magnetization increase -3,1 times the polarization plane rotation angle increases by «5,4 times; 2) the gyrotropic elliptic waveguide polarization plane rotation angle is greater than that of a similar round waveguide. The results show the main advantage of gyrotropic elliptic guide systems over circular ones consists in the possibilities of varying both external and geometric parameters of gyrotropic elliptic guide systems and obtaining significant phase raids, which in turn allows developing more efficient phase shifters.

Semianalytical Solution for Determination of Wave Amplification Characteristics in a Complex Elliptical Dielectric Waveguide Including Strongly Magnetized Plasma Circular Column

In this research, the excitation of hybrid electromagnetic waves in a complex dielectric-plasma waveguide is investigated semianalytically using the perturbation method and applying the suitable boundary conditions. Under this study waveguide combines circular and elliptical geometries, eccentrically. This elliptical waveguide has been filled with a dielectric material, whereas two axial hollows with circular section have been created in its focuses. In one of the hollows, there is an axial strongly magnetized plasma and a relativistic solid circular electron beam (RSCEB) is injected inside the other hollow. In addition, the growth rate of slow waves amplified by the electron beam is numerically calculated. The effects of accelerating voltage, current density of RSCEB, and geometrical parameters, such as radii of plasma column and electron beam, on the growth rate, electric field profile, and the frequency spectra are studied. Finally with considering the results, we will propose the optimum configuration to obtain maximum amplification of slow waves.

Comments on the Kramer Kramer Man’ko 2 × 2 matrix multiplication

This article is a complement to a paper by Kramer et al. that proposes a new matrix product, which is like a mixture of the usual and the Hadamard (or Schur) product. This new product is then related to the transformation group in the hyperbolic plane. Actually variations in the definition of internal operations lead to an infinity of products that can be associated with any of the Euclidean, hyperbolic or elliptic geometries in quite different manners. By the way: This article is not a review. The review can be found at the end of the paper.

Elliptic supersonic jet morphology manipulation using sharp-tipped lobes

Elliptic nozzle geometry is attractive for mixing enhancement of supersonic jets. However, jet dynamics, such as flapping, gives rise to high-intensity tonal sound. We experimentally manipulate the supersonic elliptic jet morphology by using two sharp-tipped lobes. The lobes are placed on either end of the minor axis in an elliptic nozzle. The design Mach number and the aspect ratio of the elliptic nozzle and the lobed nozzle are 2.0 and 1.65. The supersonic jet is exhausted into ambient under almost perfectly expanded conditions. Time-resolved schlieren imaging, longitudinal and cross-sectional planar laser Mie scattering imaging, planar Particle Image Velocimetry (PIV), and near-field microphone measurements are performed to assess the fluidic behavior of the two nozzles. Dynamic Mode Decomposition (DMD) and proper orthogonal decomposition analyses are carried out on the schlieren and the Mie scattering images. Mixing characteristics are extracted from the Mie scattering images through the image processing routines. The flapping elliptic jet consists of two dominant DMD modes, while the lobed nozzle has only one dominant mode, and the flapping is suppressed. Microphone measurements show the associated noise reduction. The jet column bifurcates in the lobed nozzle enabling a larger surface contact area with the ambient fluid and higher mixing rates in the near-field of the nozzle exit. The jet width growth rate of the two-lobed nozzle is about twice that of the elliptic jet in the near-field, and there is a 40% reduction in the potential core length. PIV contours substantiate the results.

A property of five lines in ℙ3 and four generated 4-instantons

We show that there exist mathematical 4-instanton bundles F on the projective 3-space such that F(2) is globally generated (by four global sections). This is equivalent to the existence of elliptic space curves of degree 8 defined by quartic equations. There is a (possibly incomplete) intersection theoretic argument for the existence of such curves in D’Almeida [Bull. Soc. Math. France 128 (2000), 577–584] and another argument, using results of Mori [Nagoya Math. J. 96 (1984), 127–132], in Chiodera and Ellia [Rend. Istit. Univ. Trieste 44 (2012), 413–422]. Our argument is quite different. We prove directly the existence of 4-instantons with the above property using the method of Hartshorne and Hirschowitz [Ann. Scient. Éc. Norm. Sup. (4) 15 (1982), 365–390] and a geometric result, of classical flavor, stating that the union of five general lines in the projective 3-space is the zero scheme of a global section of T(2), where T is the tangent bundle of the space. This approach sheds, also, some light on the set of jumping lines of a 4-instanton.

Numerical Study of the Heat Transfer Behavior in Helical Microcoil Tube

This work introduces a numerical study of the convective heat transfer of helical micro coils tube heat exchanger coil. It tested for both circle and elliptical geometry with 18 mm pitch and diameter of copper pipes. It is very difficult and time-consuming if these analyses could be carried out experimentally. Water is used as a working fluid by using 80°C for hot water and 25°C for cold water. The Reynolds number selected in the range of 200 to 1800 for hot water, while specified 5000 for cold water. ANSYS-FLUENT 18.0 has been used to investigate the heat transfer behavior. In computational fluid dynamics (CFD), the partial differential equations was represented by using the finite volume method (FVM) in the form of algebraic equations and the Navier-Stokes equations were solved by using a numerical procedure which is the Semi Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The elementary results observed a proportionality relationship between the heat transfer and the Reynolds number raised values. Also, the circular configuration present maximum heat transfer performance and the maximum values are 5.6, 3.42 for Thermal performance factor and Nuselte number respectively at Reynolds number 1800.

Simulation of Elliptical Liquid Jet Primary Breakup In Supersonic Crossflow

The study of elliptical liquid jets in supersonic flow in a Mach 2.0 is performed numerically. The primary breakup process of the elliptical liquid jet is simulated for a Weber number 223, liquid/gas flux momentum 4.0. The aspect ratios of elliptical geometries are set to be 0.25, 0.5, 1, 2, and 5. The results show a remarkable difference in liquid jet disintegration morphology at different aspect ratios. Under supersonic crossflow conditions, the elliptical liquid jet shows more breakup characteristics than the round liquid jet. As the aspect ratio grows, the penetration depth decreases. The elliptical liquid jet with AR=0.25 has the largest penetration depth in all cases. Moreover, the round jet has a maximum spreading angle of 50.2°. The changing trends of the column breakup length both x direction and y direction are similar. The elliptical jet at a lower aspect ratio has a shorter breakup length due to the narrower windward area. The liquid jet has a pair of larger horseshoe vortex structure and a wider wake region at a higher aspect ratio. Two pairs of reversal vortex pairs with obvious characteristics can be observed in all the simulations.

Tribological Investigations on Tool Surfaces for Temperature-Supported Forming of Magnesium AZ31 Sheets.

Aiming to decrease friction coefficient () during the forming of magnesium alloy sheets, nine (9) tools with different hole geometries in their surface (flat, elliptical, and circular) were manufactured from steel Boehler W400 VMR (as known as DIN 1.2343). Tribological investigations were accomplished on a strip drawing machine at 288 °C without lubricants. When compared with a standard tool (surface flat), on average, tools with circular geometries in their surface showed the smallest friction coefficient, while tools with elliptical geometries shown higher. The friction coefficient also was confronted with the ratio between area occupied by holes in the surface of the tool and the total tool surface (i.e., factor f (%)), hole diameter (Ø), and the distance between circle centers (d(c,c)). Principal Component Analysis (PCA) complemented the experimental approach. In summary, both approaches (experimental and theoretical) indicated that the manufactured tool with circular geometries on its surface presented lower friction coefficient values on the forming processes of the magnesium AZ31 sheets.

Classification of rational homotopy type for 10-cohomological dimension elliptic spaces

Classification of rational homotopy type for 10-cohomological dimension elliptic spaces

Isoptic Curves of Generalized Conic Sections in the Hyperbolic Plane

We recall the notion of generalized hyperbolic angle between proper and improper straight lines, which is only available in Hungarian and Esperanto. Then we summarize the generalized hyperbolic conic sections. After investigation of the real conic sections and their isoptic curves in the hyperbolic plane $\mathbf{H}^2,$ we consider the problem of isoptic curves of generalized conic sections in the extended hyperbolic plane. This problem is widely investigated in the Euclidean plane $\mathbf{E}^2$ but, in the hyperbolic and elliptic planes, there are few results. Furthermore, we determine and visualize the generalized isoptic curves to all hyperbolic conic sections. For our computations, we use the classical models based on the projective interpretation of hyperbolic geometry. In this way, the isoptic curves can be visualized in the Euclidean screen of a computer.

Effect of the curvature during the course of adsorption in elliptical pores: a study under the framework of the Broekhoff de Boer approximation

This paper analyses the effect of an adsorbed layer of variable curvature during the course of adsorption. To this end the capillary condensation and evaporation verified in pores endowed with elliptical geometry is studied. An adsorption potential within the pore walls is defined and it is numerically derived in accordance with the curvature of the pores and the attraction between the adsorbate and solid molecules. By using the Broekhoff de Boer approach, the condensation and evaporation conditions were calculated in two types of elliptical pores, prolates and oblates. The nitrogen adsorption isotherms, for ink-bottle pores, are presented and discussed. Also, an analysis of the values of the thickness of the condensed layer on the surface of the elliptical pores is carried out. Both the variation of the curvature of the liquid–gas interface and the surface tension result as the most important features that direct the course of the adsorption process.

An exact analytical solution for fractional-order thermoelasticity in a multi-stacked elliptic plate

Thermoelastic analysis of an isotropic homogeneous multi-stacked elliptical plate has been considered in this research. For which multi-layered plate is taken into consideration on a plane-parallel elliptic geometry perpendicular to the z-direction. The governing equations are considered in the context of time-fractional derivative of the order α with temperature distribution in each s layer of the stacked plate with time-dependent sectional heat supply on the lower and upper face. The multi-stacked profile consists of s discrete plates each of a different material with perfect thermal contact at each of its s-1 interface. The general solution, which perfectly satisfies the fundamental equation of heat conduction, is obtained using an integral transformation technique. It is solved using a type of quasi-orthogonality relationship by modifying Vodicka’s method and the Laplace transformation. The analysis is based on the small-deflection theory corresponding to the fundamental solutions for the fractional-order heat conduction equation. In addition to this, the intensities of bending moments, forces, maximum normal stresses and its associated stresses are formulated involving the Mathieu functions. As a special case, a multi-stacked circular plate is also discussed in detail as a limiting case. Numerical calculations are also performed, and the results are graphically illustrated.

On a Conjecture of Yamaguchi and Yokura

Let F⟶E⟶pB be a fibration of simply connected elliptic spaces. Our paper investigates the conjecture proposed by T. Yamaguchi and S. Yokura, states that dim Ker π∗pℚ≤ dim Ker H∗p;ℚ+1. Our goal is to prove this conjecture when F and B satisfy the condition πevenFℚ=πevenBℚ=0. We go also on to establish a well-known conjecture of Hilali for a class of spaces which puts it into the context of fibration.