Elliptical Disk Research Articles

A universal elliptical disc (UED) model to represent natural rock fractures

Since natural fractures are often non-equidimensional, the circular disc model still has great limitations. By contrast, the elliptical disc model is more applicable to representing natural fractures, especially for slender ones. This paper developed a universal elliptical disc (UED) model by incorporating the center point, size, and azimuth of fractures as variables. Specifically, with respect to the azimuth of elliptical fractures in three-dimensional (3D) space, we proposed a paradigm to construct its probability density function (PDF) by coupling the orientation and rotation angle of long axis based on three coordinate transformations. To illustrate the construction process of the PDF of the fracture azimuth, we took the orientation following the Fisher distribution and the rotation angle following Von Mises distribution as an example. A rock slope is used to show the use of the developed UED model, and the 3D DFNs for the slope rock mass are generated by Monte Carlo simulation. In addition, the DFNs for the rock mass are also generated based on the existing circular disc model and non-universal elliptical disc model. The comparison results from the three models clearly illustrate the superiority of the UED model over the existing circular and non-universal elliptical disc models.

Highly sensitive refractive index sensor by floating nano-particles in the solution for the detection of glucose/fructose concentration

In this research, an optimum design is proposed for better utilization of field resonance. More interaction of the field formed around nano-particles with a solution, which has refractive index variations, can substantially increase the sensitivity of the plasmonic biosensors. More interaction could be provided by floating nano-particles in the solution. The proposed structure, which has peak plasmonic resonance, has better light sensing features in comparison to similar non-floating structures. While without floating nano-particle, sensitivity is 265.8 nm/RIU with the realization of the full floating nano-particles, the sensitivity of the structure with elliptic disc and circular disc nano-particles are 574.2 nm/RIU and 425 nm/RIU, respectively. Full width at half maximum (FWHM) of the structure with elliptic disc and circular disc nano-particles are 57.4 nm and 49.4 nm, respectively. In presence of meshed SiO2 network and pseudo-floating form, sensitivity and FWHM of the structure are 504 nm/RIU and 58.4 nm for elliptic discs and 372 nm/RIU and 49.9 nm for circular discs, respectively.

A Proof of the Elliptical Range Theorem via Kippenhahn's Theorem

The elliptical range theorem asserts that the field of values (or numerical range) of a two-by-two matrix with complex entries is an elliptical disk, the foci of which are the eigenvalues of the given matrix. Many proofs of this result are available in the literature, but most, with one exception, are computational and quite involved. In this note, it is shown that the elliptical range theorem follows from the properties of plane algebraic curves and a straightforward application of a well-known result due to Kippenhahn.

Review of the Lepadichthys lineatus complex (Gobiesocidae: Diademichthyinae) with descriptions of three new species.

The Lepadichthys lineatus complex (Gobiesocidae: Diademichthyinae) is defined by three unique characters within Lepadichthys: (a) upper-jaw lip fused with snout skin, usually lacking a distinct groove between the dorsal lip margin and snout (if present, very weak, restricted to posterior portion of jaw); (b) snout tip well extended, distinctly beyond lower-jaw tip; and (c) inner surface of both lips with oral papillae. A taxonomic review of the complex recognized four valid species: Lepadichthys geminus sp. nov. (southern Japan and Indonesia), Lepadichthys heemstraorum sp. nov. (southwestern Indian Ocean), Lepadichthys polyastrous sp. nov. (southwestern Indian Ocean) and L. lineatus Briggs, 1966 (Red Sea, Arabian Sea, Seychelles and Sri Lanka). L. geminus and L. lineatus are distinct from L. heemstraorum and L. polyastrous in having a circular (vs. elliptical) disc and more posteriorly located anus [L. geminus and L. lineatus with disc length and width 15.0-18.7 (mean 16.9) and 12.9-16.5 (14.6) % LS , respectively, and length to width ratio 1.03-1.25 cf. L. heemstraorum and L. polyastrous, 17.0-21.5 (18.9) and 11.6-15.2 (13.0) % LS , respectively, and 1.26-1.61; pre-anus length and disc to anus length 65.1-73.6 (68.7) and 25.7-31.6 (28.6) % LS , respectively vs. 60.2-68.3 (65.3) and 21.6-28.9 (25.5) % LS , respectively]. Body depth (as % of LS ) is also useful to distinguish L. geminus and L. polyastrous from L. heemstraorum and L. lineatus [viz., 12.7-16.1 (14.4) in L. geminus and 10.8-14.9 (13.1) in L. polyastrous vs. 15.0-17.1 (15.9) in L. heemstraorum and 14.6-18.9 (16.8) in L. lineatus]. L. geminus differs distinctly from other species in the complex as follows: snout tip directed upward, usually on same horizontal level with lower margin of eye lens (lateral view) (vs. directed somewhat downward, horizontal level usually between lower margins of eye and eye lens in L. heemstraorum and L. lineatus, lower margin of eye in L. polyastrous); and lower abdomen with two yellow stripes (vs. a single stripe along ventral midline in L. polyastrous and L. lineatus, unknown in L. heemstraorum). L. polyastrous has unique patterns of yellow dots on the dorsal and ventral body surfaces, forming c. six to eight and three to five longitudinal rows, respectively [vs. usually forming c. three to five longitudinal rows and a single broken line, respectively, in L. geminus and L. lineatus; yellow dots usually absent in L. heemstraorum]. A poorly known species, Lepadichthys caritus Briggs, 1969, is regarded as a junior synonym of L. lineatus.

Angle-of-arrival and time-of-arrival statistics of multipaths arising from scatterers on an elliptical disc with conic spatial density around the mobile

This paper presents the angle-of-arrival (AOA) and time-of-arrival (TOA) statistics of multipaths arriving from scatterers with conic spatial density and located on an elliptical disc around the mobile. For simplification of analysis, a common practice in geometric channel modeling of macrocell networks in the open literature is to assume the scatterers to be located on a circular disc around the mobile for non-uniform scatterers’ spatial densities. This paper extends the analysis for scatterers with conic spatial density on a circular disc around the mobile to that on an elliptical disc around the mobile. The AOA-TOA joint probability densities and AOA marginal probability densities from the base station and mobile station sides were derived analytically in closed form. The TOA marginal probability densities for both the base-station and mobile-station sides were also studied. The effect of the eccentricity of the elliptical disc on the derived probability densities was discussed. In most cases, increase in the eccentricity results to reduction in the AOA support region.

Semi-analytical investigations on bistable cross-ply laminates with MFC actuators

Most existing semi-analytical models to analyse multistable structures are based on the principle of minimum potential energy, which inherently does not satisfy the in-plane equilibrium equations in a strong sense. Although such models predict the multistable shapes with reasonable accuracy, there is a significant discrepancy in predicting the snap-through behaviour when compared to the finite element (FE) or experimental results. In this work, a refined analytical model is derived to analyse a bistable cross-ply elliptical disc using Föppl von Kármán kinematics. The Rayleigh–Ritz approach with a decoupled energy formulation is used, where the stretching and bending energies are separated using the semi-inverse constitutive equation. The in-plane stress resultants are expressed in terms of curvatures using the compatibility and the in-plane equilibrium equations. A closed-form solution for the curvatures is derived to predict the cured bistable shapes of elliptical laminates. A layer of macro fibre composite actuator is added to trigger the snap-through between the stable shapes. Consequently, the critical voltage at which the snap-through occurs is predicted using the analytical model. The model is further extended to square plates, where the solutions of the differential equations emanating from the compatibility and in-plane equilibrium equations are obtained by converting the resulting differential equations into the form of standard FE elasticity problem. The in-plane stress resultants for the square plates are calculated by numerically solving the resulting elasticity problem using a standard FE discretization approach. The solutions are further compared with previous experimental studies and the results from a fully geometrically non-linear FE model.

ОБОСОВАНИЕ ПАРАМЕТРОВ ЭЛЛИПСОВИДНОГО ИГОЛЬЧАТОГО ДИСКА ПОЧВООБРАБАТЫВАЮЩЕГО ОРУДИЯ

Due to the well-known advantages, rotary tillage implements are widely used in the cultivation of many agricultural crops. Structurally, the working units of rotary implements are located (installed) on the frame, as a rule, sequentially one after the other. This reduces the maneuverability of the tillage unit, increases the material consumption of the implement and the energy consumption of the technological operation. In the rotary tillage tool developed at Kazan State Agrarian University for pre-sowing soil cultivation, these disadvantages are eliminated by installing a spiral-screw working unit and a section of active ellipsoidal needle disks on the frame coaxially. The research was carried out in order to determine and substantiate the design parameters of the elliptical needle disk. A theoretical dependence is obtained to substantiate the angle α of inclination of the major axis of the ellipsoid disk to the axis of rotation. It was revealed that its rational value must correspond to the condition: α> 44°…62°. An expression for determining the number of needles on a disk is given. The calculation carried out with a disk diameter D= 0.4 m, an angle α= 65 °, an indicator of a kinematic mode λ= 2, a mulching depth a= 0.04 m, a ridging h= 0.004 m showed that a rational number of needles per disc k= 16. Analytically, a theoretical expression for determining the angle of inclination of the needles to the axis of rotation has been derived. The calculation performed at α= 65 ° revealed that the first needle is inclined to the axis of rotation at a minimum angle jmin= 65 °, the fifth and thirteenth needles are inclined to the axis of rotation at an angle of 90 °, the ninth needle is inclined to the axis of rotation at a maximum angle jmax= 115 °. Also obtained are theoretical dependences for determining the angle of attachment of the needles on the hub and the length of the needles along the entire perimeter of the disk. The calculation showed that each needle is fixed on the disc hub at its calculated angle of inclination, equal to 29.0°...32.6°, and the length of the needles along the perimeter of the hub varies within 0.1372 ... 0.1503 m

An AMUSING look at the host of the periodic nuclear transient ASASSN-14ko reveals a second AGN

ABSTRACT We present Multi-Unit Spectroscopic Explorer (MUSE) integral-field spectroscopy of ESO 253−G003, which hosts a known active galactic nucleus (AGN) and the periodic nuclear transient ASASSN-14ko, observed as part of the All-weather MUse Supernova Integral-field of Nearby Galaxies survey. The MUSE observations reveal that the inner region hosts two AGN separated by $1.4\pm 0.1~\rm {kpc}$ (≈1${_{.}^{\prime\prime}}$7). The brighter nucleus has asymmetric broad permitted emission-line profiles and is associated with the archival AGN designation. The fainter nucleus does not have a broad emission-line component but exhibits other AGN characteristics, including $\hbox{$v_{\rm {FWHM}}$} \approx 700~\hbox{km~s$^{-1}$}$ forbidden line emission, $\rm{\log _{10}(\rm{[O\,\small {III}]}/\rm{H\beta})} \approx 1.1$, and high-excitation potential emission lines, such as [Fe vii] λ6086 and He ii λ4686. The host galaxy exhibits a disturbed morphology with large kpc-scale tidal features, potential outflows from both nuclei, and a likely superbubble. A circular relativistic disc model cannot reproduce the asymmetric broad emission-line profiles in the brighter nucleus, but two non-axisymmetric disc models provide good fits to the broad emission-line profiles: an elliptical disc model and a circular disc + spiral arm model. Implications for the periodic nuclear transient ASASSN-14ko are discussed.

Optimized monolithic edge-cladding glass for N31-type Nd-doped high power laser glass

In this paper, six edge-cladding glasses are prepared and analyzed, which are designed to clad the elliptical disk of N31-type Nd-doped phosphate laser glass by monolithic edge-cladding technique. The transition temperatures, soften temperatures, thermal expansion coefficients, high temperature viscosities and refractive indices of the prepared edge-cladding glasses are determined, which must be consistent with these parameters of N31 glass as possible. The residual stresses and residual reflectivities are determined for the cladded N31 elliptical disks and slab samples, which are the most important parameters for the monolithic edge-cladding technique and must be as low as possible to meet the index requirements for high power laser applications. The interface bubbles, edge-cladding interface and the controllability of divalent Cu2+ ions are also discussed. By the optimized edge-cladding glass, it is verified that the elliptical disk of N31-type Nd-doped phosphate laser glass can be successfully cladded by the optimized monolithic edge-cladding glass, which can be utilized securely in a strong liquid cooling to pursue a better high-power laser performance with a higher laser shot rate.

On Unique and Nonunique Fixed Points in Metric Spaces and Application to Chemical Sciences

We introduce the notions of a generalized Θ -contraction, a generalized Θ E -weak contraction, a Ψ E -weak JS-contraction, an integral-type Θ E -weak contraction, and an integral-type Ψ E -weak JS-contraction to establish the fixed point, fixed ellipse, and fixed elliptic disc theorems. Further, we verify these by illustrative examples with geometric interpretations to demonstrate the authenticity of the postulates. The motivation of this work is the fact that the set of nonunique fixed points may include a geometric figure like a circle, an ellipse, a disc, or an elliptic disc. Towards the end, we provide an application of Θ -contraction to chemical sciences.

Empirical methods to quickly select an appropriate discrete fracture network (DFN) model representing the natural fracture facets

The accuracy of the established discrete fracture networks (DFNs) has a significant impact on the effectiveness of solving engineering problems, while the accuracy is affected by the selection of the model. Concerning the natural fracture facets, the existing method based on the Accuracy Representation Index (ARI) to select the circular or elliptical disc models is relatively complex, costly and time-consuming, and is not convenient for engineers at the field site. This study proposed two new empirical methods for engineers to quickly choose an appropriate model. The triangular, rectangular and diamond-shaped fractures are chosen as the basic shapes. For the fractures with other convex shapes, their ARI can be estimated on the basis of the three basic shapes. Moreover, a validation of a real case from an open-pit mine in the USA was made, three volunteers estimated the values of ARIc and ARIe of 56 fractures based on the proposed empirical methods, where ARIc and ARIe represent the values of ARI of circular and elliptical disc models, respectively, and the absolute error (er) from the empirical estimating method is calculated. The results show that the values of er are less than 0.1 and there is no obvious difference between results from the three volunteers. It illustrates that the proposed empirical methods are effective and applicable.

English

We identify new classes of structured matrices whose numerical range is of the elliptical type, that is, an elliptical disk or the convex hull of elliptical disks.

Measuring Black Hole Masses from Tidal Disruption Events and Testing the MBH–σ* Relation

Abstract Liu and collaborators recently proposed an elliptical accretion disk model for tidal disruption events (TDEs). They showed that the accretion disks of optical/UV TDEs are large and highly eccentric and suggested that the broad optical emission lines with complex and diverse profiles originate in a cool eccentric accretion disk of random inclination and orientation. In this paper, we calculate the radiation efficiency of the elliptical accretion disk and investigate the implications for observations of TDEs. We compile observational data for the peak bolometric luminosity and total radiation energy after peak brightness of 18 TDE sources and compare these data to the predictions from the elliptical accretion disk model. Our results show that the observations are consistent with the theoretical predictions and that the majority of the orbital energy of the stellar debris is advected into the black hole (BH) without being converted into radiation. Furthermore, we derive the masses of the disrupted stars and the masses of the BHs of the TDEs. The BH masses obtained in this paper are also consistent with those calculated with the M BH–σ * relation. Our results provide an effective method for measuring the masses of BHs in large numbers of TDEs to be discovered in ongoing and next-generation sky surveys, regardless of whether the BHs are located at the centers of galactic nuclei or wander in disks and halos.

Elliptical Accretion Disk as a Model for Tidal Disruption Events

Abstract Elliptical accretion disk models for tidal disruption events (TDEs) have been recently proposed and independently developed by two groups. Although these two models are characterized by a similar geometry, their physical properties differ considerably. In this paper, we further investigate the properties of the elliptical accretion disk of the nearly uniform distribution of eccentricity within the disk plane. Our results show that the elliptical accretion disks have distinctive hydrodynamic structures and spectral energy distributions, associated with TDEs. The soft X-ray photons generated at pericenter and nearby are trapped in the disk and advected around the ellipse because of large electron scattering opacity. They are absorbed and reprocessed into emission lines and low-frequency continuum via recombination and bremsstrahlung emission. Because of the rapid increase of bound–free and free–free opacities with radius, the low-frequency continuum photons become trapped in the disk at large radius and are advected through apocenter and back to the photon-trapping radius. Elliptical accretion disks predict sub-Eddington luminosities and emit mainly at the photon-trapping radius of thousands of Schwarzschild radii with a blackbody spectrum of nearly single temperature of typically about 3 × 104 K. Because of the self-regulation, the photon-trapping radius expands and contracts following the rise and fall of accretion rate. The radiation temperature is nearly independent of BH mass and accretion rate and varies weakly with the stellar mass and the viscosity parameter. Our results are well consistent with the observations of optical/UV TDEs.

Evidence of a non-conservative mass transfer in the ultra-compact X-ray source XB 1916-053

Context. The dipping source XB 1916-053 is a compact binary system with an orbital period of 50 min harboring a neutron star. It shows a positive and a negative superhump, which suggests the presence of a precessing elliptic accretion disk tilted with respect to the equatorial plane of the system. The orbital ephemeris indicates a large orbital period derivative, Ṗ/P = 1.53 × 10−7 yr−1, that can be explained assuming a high non-conservative mass transfer rate. Finally, the spectrum shows prominent absorption lines indicating the presence of an ionized absorber along the line of sight. Aims. Using ten new Chandra observations and one Swift/XRT observation, we are able to extend the baseline of the orbital ephemeris; this allows us to exclude some models that explain the dip arrival times. The Chandra observations provide a good plasma diagnostic of the ionized absorber and allow us to determine whether it is placed at the outer rim of the accretion disk or closer to the compact object. Methods. From the available observations we are able to obtain three new dip arrival times extending the baseline of the orbital ephemeris from 37 to 40 years. The Chandra spectra are fitted adopting a Comptonized continuum. To fit the absorption lines we adopt the ZXIPCF component obtaining information on the ionization parameter and the equivalent hydrogen column density of the ionized absorber. Results. From the analysis of the dip arrival times we confirm an orbital period derivative of Ṗ = 1.46(3) × 10−11 s s−1. Furthermore, the unabsorbed 0.1–100 keV luminosity observed from the Chandra spectra show a variation between 3 × 1036 and 1.4 × 1037 erg s−1. We show that the Ṗ value and the luminosity values are compatible with neutron star masses higher than 1.4 M⊙ with a mass accretion rate lower than 10% of the mass transfer rate. We show that the mass ratio q = m2/m1 of 0.048 explains the apsidal precession period of 3.9 d and the nodal precession period of 4.86 d deduced from the superhump and infrahump detected period. The observed absorption lines are associated with the presence of Ne X, Mg XII, Si XIV, SXVI, and Fe XXVI ions. We observe a redshift in the absorption lines between 1.1 × 10−3 and 1.3 × 10−3. By interpreting it as gravitational redshift, as recently discussed in the literature, we find that the ionized absorber is placed at a distance of 108 cm from the neutron star with a mass of 1.4 M⊙ and has a hydrogen atom density greater than 1015 cm−3. Instead, the absorber is more distant and could be placed at the outer rim of the accretion disk (1.7 × 1010 cm) during the dip activity. Conclusions. We show that the mass ratio of the source is 0.048; this value is obtained from the nodal precession period of the disk and from the apsidal precession period taking into account the pressure term due to the spiral wave present in the disk. From our analysis we estimate a pitch angle of the spiral wave smaller than 30°, in agreement with the values observed in several cataclysmic variables. We show that the outer radius of the disk is truncated at the radius in which a 3:1 resonance occurs, which is 1.7 × 1010 cm for a neutron star mass of 1.4 M⊙. The large orbital period derivative is likely due to a high non-conservative mass transfer with a mass transfer rate of 10−8 M⊙ yr−1. The variation in observed luminosity could be explained assuming that the ejection point from which the matter leaves the system moves close to the inner Lagrangian point.

Integrated Spectrum Sensing and Frequency Reconfigurable Antennas for Inter-Weave Cognitive-Radio Applications

A dual-port antenna configuration composed of an ultra-wideband (UWB) sensing antenna and a dual-band reconfigurable communicating antenna is proposed and studied in this paper. The sensing antenna is an elliptical disk radiator covers a frequency range of (1.8-11) GHz. The communicating antenna is a modified dual-band rectangular radiator. By controlling the length of a stub attached to the communicating antenna with the aid of two PIN-diodes, the dual-band antenna can reconfigure its resonant frequencies to (2, 2.2) GHz, (3.25, 3.8) GHz, and (4.3, 5.6) GHz. Both simulated and experimental results for the return loss, mutual coupling, radiation patterns and gain are presented, and they reveal the antenna compatibility with the inter-weave cognitive radio applications.

Symmetric and Antisymmetric Multipole Mode-based Fano Resonances in Split Theta-shaped Nanocavities

Split theta-shaped nanocavities composed of an elliptical disk embedded in a nonconcentric split ring are theoretically investigated by the finite-difference time-domain method. Symmetric and antisymmetric mode-based Fano resonances are both formed, due to the interference between the bright mode of the cavity and two types of multipole modes of the split ring, and experience different changes through adjusting the degree of symmetry breaking via an asymmetry of the ring width and displacement of the disk. As the cavity remains symmetrical with respect to the axis of the split ring, only the symmetric Fano resonances are observed. Further breaking the cavity symmetry, the antisymmetric Fano resonances appear and increase, while symmetric ones decrease. When the overall degree of symmetry breaking becomes larger due to an increasing offset of the disk relative to the asymmetric ring, this change trend becomes more complicated, and some Fano resonances are suppressed or enhanced again. Our work demonstrates that the proposed cavities with tunable Fano line shape could be used as platforms for multiwavelength biochemical sensors and enhanced spectroscopies.

Study on torque density enhancement mechanism of elliptic arc multi-disk MRF coupling

The transfer energy of a magnetorheological fluid (MRF) coupling can be dynamically regulated by changing the MRF mechanical properties of its input and output shafts. In addition, the dynamic characteristics of its drive system can automatically be in the tune with its load characteristics to effectively suppress vibration and shock responses, to achieve overload protection of the system, and to improve its mechanical performance and safety reliability. However, the weak mechanical properties of MRF materials result in so small a coupling torque density that the MRF coupling applications for high-torque transfer is restricted. Thus, to increase the coupling torque density is becoming an urgent key technological challenge in this field. A technique based on shear-pressure mixed mode was proposed here to increase the torque density by utilizing the formation mechanism of MRF arc flux linkage. Futhermore, a new high torque arc multi-disk MRF coupling structure was designed and its corresponding mechanical torque transfer model was established. A FEA electromagnetic simulation was performed to study the distribution of the magnetic field in the MRF chamber under different current excitations. Effects of the key parameters of the elliptical arc on its transfer torque were also investigated. Finally, experimental analysis of the mechanical properties of the elliptical disk MRF coupling was conducted to verify the feasibility of the proposed technique and the validity of the torque transfer model.

Quantum limited superresolution of extended sources in one and two dimensions

We calculate the quantum Fisher information (QFI) for estimating, using a circular imaging aperture, the length of a uniformly bright incoherent line source with a fixed mid-point and the radius of a uniformly bright incoherent disk shaped source with a fixed center. Prolate spheroidal wavefunctions (PSWFs) on a centered line segment and its generalized version on a centered disk furnish the respective bases for computing the eigenstates and eigenvalues of the one-photon density operator, from which we subsequently calculate QFI with respect to the spatial parameters of the two sources. Zernike polynomials provide a good set into which to project the full source wavefront, and such classical wavefront projection data can realize quantum limited estimation error bound in each case. We subsequently generalize our approach to analyze sources of arbitrary brightness distributions and shapes using a certain class of Bessel Fourier functions that are closely related to the PSWFs. We illustrate the general approach by computing QFI for estimating the lengths of the principal axes of a uniformly bright, centered elliptical disk.

Long term sedimentation of an elliptic disc subject to an electrostatic field using smoothed particle hydrodynamics method

A two dimensional incompressible smoothed particle hydrodynamics scheme for long term sedimentation of rising or falling particulates (bubbles, drops or rigid particles) in Newtonian fluids is presented and validated by simulating the sedimentation of a single elliptic disc. The proposed method is then used to simulate the sedimentation of an elliptic disc subject to an external electric field parallel to the gravitational field. A range of electric field intensities, permittivity ratios, blockage ratios and density ratios are covered in this study. The results show that for given blockage and density ratios, the final sedimentation orientation of the ellipse is dependent on a combination of permittivity ratio and electric field intensity, ranging from horizontal to vertical. Compared to non-electrified sedimentation, an increase in electric field intensity and permittivity ratio lead to vertical sedimentation. As the channels grow wider, the presence of electric field leads to faster ellipse descent, regardless of its initial orientation.