Elliptical Elements Research Articles

Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements

At the second post-Newtonian (2PN) order, the secular pericenter precession ω ˙ 2 PN of either a full two-body system made of well-detached non-rotating monopole masses of comparable size and a restricted two-body system composed of a point particle orbiting a fixed central mass have been analytically computed so far with a variety of approaches. We offer our contribution by analytically computing ω ˙ 2 PN in a perturbative way with the method of variation of elliptical elements by explicitly calculating both the direct contribution due to the 2PN acceleration A 2 PN , and also an indirect part arising from the self-interaction of the 1PN acceleration A 1 PN in the orbital average accounting for the instantaneous shifts induced by A 1 PN itself. Explicit formulas are straightforwardly obtained for both the point particle and full two-body cases without recurring to simplifying assumptions on the eccentricity e. Two different numerical integrations of the equations of motion confirm our analytical results for both the direct and indirect precessions. The values of the resulting effects for Mercury and some binary pulsars are confronted with the present-day level of experimental accuracies in measuring/constraining their pericenter precessions. The supermassive binary black hole in the BL Lac object OJ 287 is considered as well. A comparison with some of the results appeared in the literature is made.

Inverted Hysteresis, Magnetic Domains, and Hysterons

In this letter, we use magnetooptical Kerr effect magnetometry on extended samples to measure local hysteresis curves as a function of an externally applied field in a magnetostriction-free amorphous ribbon and an elliptical Permalloy film element. Although these materials are magnetically soft and have almost zero coercive field, we find that the local hysteresis curves have a highly nonlinear hysteretic character, displaying both counterclockwise and clockwise rotation senses when cycling the loops. This unexpected result can be explained by looking at the total hysteresis curve of the materials as a superposition of local curves and can be described mathematically using the formalism of the Preisach model. Within the framework of this model, we derive the conditions under which a superposition of clockwise and counterclockwise hysteresis loops can lead to a hysteresis-less system, and devise a technique to map the hysterons that define the first-order reversal-curve distribution to physical regions in the specimens.

Spoof surface plasmon polariton‐fed circularly polarized leaky‐wave antenna with suppressed side‐lobe levels

A wide-angle scanning circularly polarized (CP) leaky-wave antenna (LWA) with suppressed side-lobe levels (SLLs) is proposed, which can be a good candidate for future radar and wireless communication systems. The LWA consists of 12 cross slotted elliptical patch elements, which are fed by a microstrip spoof surface plasmon polariton (SSPP) line. Two fundamental modes of the patch array with two orthogonal polarizations can be excited by the electromagnetic coupling between the array and the SSPP line. By optimizing the elliptical eccentricity e and etching cross slots on the elliptical patch array, a 90° phase difference is introduced, and then, the CP radiation is realized. A tapered aperture field distribution is also realized by adjusting coupling intensities between the patch elements and the SSPP line, which is beneficial to reduce the SLLs. The electrical size of the LWA is 1.29λ0 × 6.02λ0 × 0.08λ0, where λ0 is air wavelength at 12.9 GHz (broadside direction). Both the simulated and measured results indicate that the CP operating band is 12.0 to 15.0 GHz. The proposed CP LWA scans continuously from −14° to 38°. In the whole operating band, the axial ratios are less than 3 dB, and the SLLs are less than −20 dB as well.

Detection in seismic data using curvelet transform and tensor-based elliptical adaptive structuring elements

Channels are one of the vital issues in the exploration of oil and gas. They can be considered as reservoirs if they are filled with porous and permeable material and placed in a suitable position. A detailed study of the channels can help identify the sedimentation processes of the area, the intensity, and direction of the sea currents. Manual interpretation of the channels is difficult and requires skill. Therefore, in this paper, the adaptive curvelet and morphological gradient algorithm (ACMG) is used for the automatic interpretation of the channels. First, the morphological gradient is applied to extract the edges of the channels; then, the curvelet transform is used to increase the signal-to-noise ratio. The morphological top-hat operator extracts the local maxima of curvelet sub-bands. In this workflow, we applied an elliptical adaptive structuring element (EASE) based on Gradient structure tensor (GST). For the construction of the 2D GST, the horizontal and vertical gradients of the image were calculated by the first-order Gaussian derivative. The eigenvalue decomposition of each structure tensor can provide an estimate of the direction and anisotropy rate of the image objects. Hence, parameters of the elliptical structuring element are obtained by eigenvalue decomposition of the GST. To evaluate ACMG, we compared the final output with the results of the non-adaptive curvelet and morphological gradient algorithm (CMG). Also, we compared it with the common edge-detectors such as Canny, Sobel, Laplacian of Gaussian, and similarity attribute. The comparison shows that both CMG and ACMG well extracted the edge of the channels with the higher signal-to-noise ratio.

A Configuration of Ultra-Wideband Planar Antenna Comprises Band Suppression at 5~6 and 3.3~3.7GHz

Two-slits in a UWB planar antenna in the means of suppressing the frequency bandwidths for 5~6 and 3.3~3.7GHz are studied. Frequency bandwidths for 5~6 and 3.3~3.7GHz are known as the Wireless Local Area Network (WLAN) and Worldwide Interoperable for Microwave Access (WIMAX), respectively. Both are coexisted with the UWB frequency bandwidth that is allocated between 3.1 and 10.6GHz. Coexistence between these frequency bandwidths have potentially caused interferences such as signal disruption and data lost in the respective systems. Two-slits are etched in the conductor elements in the means of generating the notched-band characteristics by producing impedance mismatched in the proposed antenna. Band notching are generated for the frequency bandwidths 5~6G and 3.3~3.7GHz, respectively. Band notch peaks are desired to achieve higher than -5dB. Slits are etched in the elliptical element and ground plane for band notching at the frequency 5~6 and 3.3~3.7GHz, and optimized proposed antenna’s peak of the reflection coefficient S11 are given -3 and -4dB, respectively. Slits parameters are studied in order to recognize the dominant parameters that affect the notched-band characteristics. It is shown that the two-slits have engendered the notched-band characteristics in the UWB planar antenna and slits parameters could be exploited in order to influence the notched-band characteristics accordingly.

Sub wavelength dielectric elliptical element as an anisotropic magnetic dipole for inversions of magnetic field

This paper proposes an experimental and model investigation of displacement current generated in a flat dielectric circuit of elliptical shape, subjected to an incident microwave. All-dielectric sub wavelength magnetic dipoles providing the inversions of magnetic inductance are designed and tested. Experimental results demonstrate the angular anisotropy of these dipoles, manifested in the dependence of depths of resonant spectral dips upon the orientation of dipoles, with respect to the direction of propagation of incident microwave.

Computation of continuum percolation threshold for pore systems composed of vugs and fractures

In this research, we study the connectivity of a network composed of pores with different shapes including combinations of vugs and fractures. For this purpose, we have developed a numerical simulation technique to determine the dependence of continuum percolation threshold on the pore-shape distribution for isotropic porous 2D and 3D networks composed by elliptical and spheroidal elements respectively. This technique is based on the following new algorithms: (1) analytical estimation of overlapping between inclusions; (2) partial discretization schemes (elements of a discrete pixel base with one continuous dimension) for numerical calculation of connected-cluster porosity; and (3) determining the percolation-threshold porosity by using Monte Carlo simulations for different relative pore sizes. By approximating the pore shapes by ellipses (2D) and spheroids (3D) and varying their aspect ratios, we can model different types of pores from vugs (spheres) to fractures (oblate spheroids) and channels (prolate spheroids). We have calculated the critical percolation porosity for the following models: (1) a network consisting of elements with constant shapes; (2) a network composed of elements with the uniform logarithmic distribution of aspect ratios; and (3) a network containing elements of two different shapes. To validate the simulation technique, we have compared the modeling results for the first model with a threshold-aspect ratio relationship published previously. Based on the modeling results we have found simple and explicit equations for 2D and 3D models to determine the percolation threshold for pore networks with the bimodal distribution of shapes. The equations use only the element concentrations and percolation-threshold values for each elements shape.

Geometric k-nearest neighbor estimation of entropy and mutual information.

Nonparametric estimation of mutual information is used in a wide range of scientific problems to quantify dependence between variables. The k-nearest neighbor (knn) methods are consistent, and therefore expected to work well for a large sample size. These methods use geometrically regular local volume elements. This practice allows maximum localization of the volume elements, but can also induce a bias due to a poor description of the local geometry of the underlying probability measure. We introduce a new class of knn estimators that we call geometric knn estimators (g-knn), which use more complex local volume elements to better model the local geometry of the probability measures. As an example of this class of estimators, we develop a g-knn estimator of entropy and mutual information based on elliptical volume elements, capturing the local stretching and compression common to a wide range of dynamical system attractors. A series of numerical examples in which the thickness of the underlying distribution and the sample sizes are varied suggest that local geometry is a source of problems for knn methods such as the Kraskov-Stögbauer-Grassberger estimator when local geometric effects cannot be removed by global preprocessing of the data. The g-knn method performs well despite the manipulation of the local geometry. In addition, the examples suggest that the g-knn estimators can be of particular relevance to applications in which the system is large, but the data size is limited.

Dual circularly polarized broadside beam antenna based on metasurfaces

Design details of a Ku band metasurface (MTS) antenna with dual circularly polarized (CP) broadside radiation is shown in this work. By means of the surface impedance tensor modulation, synchronized propagation of two transversal magnetic (TM) and transverse electric (TE) surface waves (SWs) is ensured in the structure, which contribute to the radiation in broadside direction by the generation of a CP leaky wave. The structure is implemented by elliptical subwavelength metallic elements with a cross-shaped aperture in the center, printed on top of a thin substrate with high permittivity (AD1000 with a thickness of λ0/17). For the experimental validation, the MTS prototype has been excited employing an orthomode transducer composed by a metallic stepped septum inside an air-filled waveguide. Two orthogonal TE11 modes excited with ±90° phase shift in the feed couple with the TM and TE SWs supported by the MTS and generate RHCP or LHCP broadside beam. Experimental results are compared with the simulation predictions. Finally, conclusions are drawn.

Circularly Polarized Elliptical Microstrip Patch Reflectarray

A double-layered elliptical microstrip patch element is proposed for designing a broadband circularly polarized (CP) reflectarray for the first time. The proposed reflectarray element is composed of two elliptical patches stacked on the top and middle surfaces of two substrates, and reflection phase range is generated by varying the major axes of the elliptical patches. Floquet method is employed for simulating the element, and it is found to be able to generate circular polarization (CP) with a broad reflection phase range of 550° with only two layers. With the use of the element, a CP $11\times11$ full-fledged reflectarray has been designed and fabricated. The reflectarray is fed by a linearly polarized horn. Measurement shows that the proposed CP elliptical microstrip patch reflectarray is able to achieve an antenna gain of 20.38 dBic and a 1-dB gain bandwidth of 11.6%. It also has a broad 3-dB axial ratio bandwidth of 12.47%.

Positive and negative curvatures nested in an antiresonant hollow-core fiber.

We propose a negative curvature hollow-core fiber that has a nested elliptical element in the antiresonant tubes. The additional elliptical element effectively adds two curvatures, namely, a positive and a negative curvature. Our numerical study shows that it enhances the confinement of the light in the core. Moreover, the nested elements provided an extra degree of freedom that can be exploited to suppress higher-order modes through the change of the ellipticity. The resulting low confinement loss and single-mode guidance properties of the proposed fiber make it a suitable candidate for applications in ultrashort pulse delivery and gas-based nonlinear systems.

Low Loss Hollow-Core Antiresonant Fiber With Nested Elliptical Cladding Elements

We design and investigate the optical properties of a novel hollow-core antiresonant fiber with nested elliptical cladding elements. This new structure shows low confinement loss even with a relatively small core. The lowest confinement loss of this structure is more than two orders of magnitude smaller than its circular-element counterparts. When the size of the cladding elements is properly designed, higher order core modes resonantly couple with the cladding modes effectively, resulting in an extremely high higher order-mode extinction ratio ( $>$ $10^4$ ). This good single mode performance can be achieved for a wide range of cladding element parameters, which would increase the fabrication tolerance. The new fiber also shows low bending loss for a wide range of bend radii. Moreover, dispersion properties of the new structure are also investigated under both unfilled and filled conditions. Numerical results show that antiresonant structures with the same core diameter and strut thickness have similar dispersion curves. The zero dispersion wavelength within the fundamental antiresonant transmission band can be tuned over tens of nanometers by increasing the pressure up to 50 bar when the fiber is filled with argon.

Exploring the Effect of the Core Boundary Curvature in Hollow Antiresonant Fibers

Through numerical simulations, we systematically study the leakage loss properties of a simplified novel hollow antiresonant fiber in which the core is surrounded by semi-elliptical elements. These studies lead to new insight into the effect of the curvature of the core boundary in antiresonant fibers. We observe in particular that in our design, there exists an optimum curvature of the elements—which we quantify simply through the aspect ratio of the ellipses—for which the fiber’s leakage loss is minimized. Furthermore, it is shown that elliptical elements can lead to orders of magnitude loss reduction as compared with similar fibers with circular ones.

Morphology operators construction by adaptive elliptical structuring elements based on nonlinear structure tensor

As the linear structure tensor is tending to inaccurately or even wrong estimate the gradient direction of a gray-level image, we present a novel algorithm to construct adaptive elliptical structuring elements via estimating the local anisotropy of an image based on the nonlinear structure tensor. Erosion, dilation, opening, closing and Hit-or-Miss transform are redefined according to the presented structuring elements, which have been applied to some representative images. The processed results and the quantitative analysis show that the novel morphological operators have more advantages in structure adaptation, corner protection, filtering and targets extraction than the others.

Dynamic and Magnetotransport Properties of Perpendicularly Magnetized CoFeB Magnetic Tunnel Junctions

We present the study of the dynamic properties of CoFeB (CFB) based magnetic tunnel junctions (MTJ) by Brillouin light scattering spectroscopy and micro-strip ferromagnetic resonance technique as well as magnetoresistance measurements. Two different MTJs: single and double barrier systems have been investigated. The dynamic studies revealed mostly similar perpendicular anisotropy field for both CoFeB layers for the single barrier MTJ with the thickest CFB layers, while two sensibly different perpendicular anisotropy fields were revealed in the case of the double barrier MTJ with the thickest CFB soft and hard layers. Modeling the spin wave frequencies behavior allows us the analysis of the experimental data and the derivation of the pertinent magnetic parameters. Our results suggest an interfacial origin of the anisotropy. Therefore, by changing the thickness of the perpendicularly magnetized CFB layers, it is possible to obtain a free and pinned layer usually ensured by the use of synthetic antiferromagnetic material. The tunnel magnetoresistance has been measured in elliptical elements of double barrier MTJ of different sizes. Strong size-dependent switching fields and antiparallel state being more unstable in the smallest device are observed. Patterning effect, lowering the anisotropies around the edge areas and increasing the dipolar coupling that favors the parallel state in the case of stacked layers, are probably the origin.

Reduced model for precessional switching of thin-film nanomagnets under the influence of spin torque

We study the magnetization dynamics of thin-film magnetic elements with in-plane magnetization subject to a spin-current flowing perpendicular to the film plane. We derive a reduced partial differential equation for the in-plane magnetization angle in a weakly damped regime. We then apply this model to study the experimentally relevant problem of switching of an elliptical element when the spin-polarization has a component perpendicular to the film plane, restricting the reduced model to a macrospin approximation. The macrospin ordinary differential equation is treated analytically as a weakly damped Hamiltonian system, and an orbit-averaging method is used to understand transitions in solution behaviors in terms of a discrete dynamical system. The predictions of our reduced model are compared to those of the full Landau--Lifshitz--Gilbert--Slonczewski equation for a macrospin.

Beamforming and Angle-of-Arrival Estimation of Square Planar Antenna Array

This paper presents a dual-band planar antenna array for ISM band applications (2.4 GHz and 2.45 GHz). This antenna is proposed for indoor applications and enables adaptive beamforming and angle of arrival (AOA) estimation. An adaptive beamforming algorithm is applied for a planar antenna array, which is able to steer its main beam and nulls in azimuth and elevation planes over a wide frequency band. Planar antenna array operates as a spatial filter in 3D space, processing the received signals with weighting schemes. A planar antenna array is designed for AOA estimation in azimuth and elevation planes by using MUltiple SIgnal Classification (MUSIC) based on subspace algorithm. The Base Station (BS) equipped with this planar antenna is preferred to be at the center position on the room ceiling to cover all sectors of the room. It is designed to use four directional triangular elements arranged to form a square planar antenna array. Planar antenna with four elliptical slotted triangular elements (PAFESTE) is used to obtain optimal directivity in four directions in azimuth plane with specific orientation of 30? in elevation plane. It is characterized by half power beamwidth in elevation plane of about 60? and half power beamwidth in azimuth plane of about 90?.

Generation of virtual asphalt mixture porosity for computational modelling

A new algorithm is proposed for the computational generation of realistic asphalt mixture porosity for computational simulations. The algorithm starts by generating in a 2D domain a number of randomly positioned circular or elliptical elements that are meant to represent virtual asphalt aggregate particles. These elements are then grown by mimicking the biological mechanism called contact inhibition until a target air void content (AVC), chosen by the user, is met. In addition, multiple 2D domains can be converted to 3D and combined to generate a multi-layered realistic representation of the porosity present in asphalt mixtures. In this paper, the working mechanism of the algorithm is described and its efficiency is assessed. Moreover, the validity of the results is discussed, and virtual domains, in both 2 and 3 dimensions, are compared with real CT scans in order to show the efficacy of this approach. It was found that the virtual representations of the asphalt mixture porosity show realistic characteristics in terms of air void content and that the air void size distribution is consistent with that of real specimens.

A Study on a Single Band Notch Characteristic of a UWB Planar Antenna with an Elliptical Element

UWB planar antenna comprising an elliptical element with a single band notch characteristic are studied and presented. A novel UWB planar antenna characteristic is compared with proposed design. Slanting slit is etched in the elliptical element. The slit is considered to generate the band notch characteristic. The elliptical element and ground plane are composed on top of the substrate. The band notch is characterized to eliminate the Wireless Local Area Network (WLAN). The proposed antenna maximum gain is better when compared with the novel UWB planar antenna. The radiation patterns are unchanged.

Extended Penalty Coefficients For Elimination The Locking Effects In Moderately Thick Beam And Plate Finite Elements

AbstractThe present paper is dedicated to presentation and energy verification of the methods of stabilization the strain energy by penalty coefficients. Verification of the methods is based on the consistency and ellipticity conditions to be satisfied by the finite elements. Three methods of stabilization are discussed. The first does not satisfy the above requirements. The second is consistent but cannot eliminate parasitic energy terms. The third method, proposed by the author, is based on the decomposition of the element stiffness matrix. The method can help to eliminate locking of the finite elements. For two-noded beam element with linear shape functions and exact integration a stabilized free of locking (and elliptical) element is received (equivalent to reduced integration element). Two plate finite elements are analyzed: four-noded rectangular element and DSG triangle. A new method of stabilization with the use of four independent parameters is proposed. The finite elements with this kind of stabilization satisfy the consistency condition. In the rectangular element it was not possible to eliminate one parasitic term of energy which appears during the procedure. For DSG triangle all parasitic terms of energy are eliminated. The penalty coefficients depends on the geometry of the triangle.