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Abstract We provide a general and rigorous proof for the strong consistency of maximum likelihood estimators of the cumulative distribution function of the mixing distribution and structural parameter under finite mixtures of location-scale distributions with a structural parameter. The consistency results do not require the parameter space of location and scale to be compact. We illustrate the results by applying them to finite mixtures of location-scale distributions with the component density function being one of the commonly used density functions: normal, logistic, extreme-value, or t. An extension of the strong consistency results to finite mixtures of multivariate elliptical distributions is also discussed. Highlights • We study finite mixtures of location-scale distributions with a structural parameter. • We establish the strong consistency of maximum likelihood estimators. • The consistency results do not require the parameter space to be compact. • We extend the results to finite mixtures of multivariate elliptical distributions. [ABSTRACT FROM AUTHOR]

This paper reports on mechanical design, optimization, and experimental testing of a novel piezo-actuated elliptical vibration-assisted cutting (EVC) system constructed by flexure hinges. The stroke and natural frequency were analyzed based on the theoretical modeling. An enhanced central composite design was chosen as the design of experiments methodology to reduce the modeling error, and a nondominated sorted genetic algorithm-II (NSGA-II) was adopted for structure optimization. The optimized EVC generator was manufactured and experimentally tested to investigate practical properties of the proposed EVC system. It shows that the stroke of input end can reach to 30 μ m with a motion resolution of 10 nm, and the first natural frequency can reach to 2600 Hz without considering the manufacturing error. Besides, a relatively small cross-axis coupling ratio (within 0.21%) can be effectively obtained. The developed EVC system is advantageous not only to being equipped with machine tools with various configurations, but also to easily achieving arbitrary vibrations in three-dimensional space through two actuators, which is especially important for the generation of complex structured surfaces. With this paper, it is of great significance to promote industrial application of EVC techniques. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to present the results of mixing promotion and screech frequency of controlled elliptical supersonic jet.Design/methodology/approach Flow field characteristics of low-aspect-ratio elliptical jets are examined at over-expanded, under-expanded and correctly expanded conditions. The tabs are placed at elliptical jet exit along the major and minor axes.Findings The results show that the mixing done by the minor axis is superior to the tabs along major axis. At all pressure ratios, the content of jet noise and the frequency are high for the tabs along the major axis because of increase in the amplitude of screech frequency. Further the tabs along minor axis show a dominance of large-scale vertical structures. In under-expanded conditions, the shock cell shows the rapid change because of the presence of tabs. The tabs along minor axis are making the shock weaker, hence no evidence of axis switching.Practical implications To achieve the greater performance of jet, the authors need to reduce the potential core length of the issuing jet. This can be achieved by implementing different types of tabs at the exit of the nozzle.Originality/value The present paper represents the flow of controlled jet using inverted triangular tabs. By achieving the controlled jet flow, the performance of propulsion systems can be improved. This can be used in systems such as combustion chamber, missile’s noise reduction and thrust vector control. [ABSTRACT FROM AUTHOR]

We propose a principal scheme to generate the cylindrical and the elliptical symmetrical vector beam based on a modified Mach-Zehnder interferometer. The modified Mach-Zehnder interferometer, the wave plates, the Polarizing Beam Splitter (PBS) and the Dove prism are used in this optical system. Two different order polarized beams can be generated and combined by this system and the arbitrary-order cylindrical and elliptical vector beams can be obtained. With the help of this simple optical system, the various profile vector beams can be generated flexibly. [ABSTRACT FROM AUTHOR]

In this paper, an extended fast factorized back projection (FFBP) algorithm is proposed to focus the missile-borne bistatic forward-looking synthetic aperture radar (BFSAR) data. It is also based on the subaperture processing technique to reduce the computational burden, but represents the subimages on the elliptical polar coordinates referenced to the tracks of both transmitter and receiver. First, the imaging geometry and signal model of the missile-borne BFSAR are established. Then, considering the special configuration of the missile-borne BFSAR, a novel elliptical polar coordinate system whose origin is determined by the positions of both transmitter and receiver is established. The subaperture processing approach based on this coordinate system is presented. Successively, based on the range error analysis, the sampling requirements of the elliptical polar subimages are derived to provide a tradeoff between the imaging quality and efficiency. Finally, the computational burden of the proposed algorithm is discussed, and the speed-up factor of the proposed algorithm with respect to the direct back projection algorithm is derived. The experimental results with simulated data prove the validity and feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents and analyzes a low profile planar antenna array of elliptical elements with inner counter-elliptical slots. The antenna has single feed and provides two main directive radiation components (front and back), with gain higher than 7 dBi and circular polarization (CP) over the entire 5 GHz ISM& UNII bands. This approach also cancels the null over the elevation plane, which makes it suitable for bidirectional communications, also for proximity coverage. The inner slot of elliptical shape provides three additional degrees of freedom to match the planar monopole and/or array in impedance and polarization over the desired frequency band. An electromagnetic (EM) model of the proposed antenna is developed for numerical analysis and optimization. The principle of operation and parametric study of the antenna are provided. The antenna is fabricated and experimental results are presented. The number of elements in the array are chosen according to the desired gain and the inner elliptical slot parameters (major radius, elliptical ratio and rotation) scaled for impedance and polarization matching. [ABSTRACT FROM AUTHOR]

Because elliptical beams have many special properties and applications, an elliptical Airy beam with and without a vortex phase has been proposed. Based on the definition of the elliptical Airy beam, an experimental setup for the generation is given, and the formula for the evolution of the intensity is derived. Meanwhile, from the propagation of the Airy beam in vacuum, the abruptly autofocusing length is derived. Based on the formula of the abruptly autofocusing length, the intensity distributions at some special locations are analyzed and discussed, especially in the autofocusing point. Study shows that some interesting intensity profiles are reformed due to the asymmetry intensity distribution of the elliptical Airy beam and abrupt autofocusing of the circular Airy beam during propagation. The different eccentricity of the elliptical Airy beam has similar properties, such as the beam split with the propagation distance and the reformed beam shaped like a ”light knife” (very narrow beam) at some positions due to the convergence process out of synchronization along the x- and y-axis. When we impart a vortex on the elliptical Airy beam, the intensity distribution will rotate and split with the propagation distance. [ABSTRACT FROM AUTHOR]

This research report deals with an experimental and analytical study of the ultrasonic elliptical vibration cutting (UEVC) process on medium steel alloy (AISI 1045) for sustainable machining of round-shaped (R-shaped) microgrooves via relatively low-speed machining (0.5-2.5 m/min). The need for microgroove patterns on planar surfaces in the tribology field has increased significantly owing to superior lubrication performance in decreasing the coefficient of friction. Analyzing the surface roughness, microgroove morphology, cutting force, and chip formation during microgrooving are the main objectives of this experimental study. The experimental results showed that the UEVC process evidently produces lower surface roughness, lower cutting forces, better groove shape morphology, thinner chip thickness, and higher flow shear angle when compared to the conventional cutting process. A new approach in methods to analyze surface roughness and cutting force in UEVC microgrooving has also been developed and validated with the experimental results. Finally, these experimental studies indicate the achievement of sustainable machining of the R-shaped microgroove pattern using the UEVC process. [ABSTRACT FROM AUTHOR]

This paper presents analysis of stress intensity factors at blade mounting locations of steam turbine rotor system. General expressions for the stresses induced in a rotating disc are derived and these equations are applied to steam turbine rotor disc. It is observed that the radial stress increases instantly at blade mounting location which indicates the probability of crack initiation and growth. A semi elliptical crack is considered at that location and weight function approach is used to determine the stress intensity factors. The results are validated with the influence coefficient approach. The differences of present approach with influence coefficient approach are less than 3 %. Hence the present approach is suitable for determination of stress intensity factors in a semi elliptical crack at blade mounting locations of a steam turbine rotor disc. [ABSTRACT FROM AUTHOR]

In this paper, the historical context of the development of what is now known as ‘Fracture Mechanics’ is selectively developed. We start from the safety and economic motivations, and review the essential efforts, over the centuries, to develop the ability to predict fracture and those factors leading up to final catastrophic events. The experimental and analytical quantitative aspects, and their interdependence, are emphasized. It is shown how these efforts were integrated to define the field we now know as Fracture Mechanics. The paper concludes with some thoughts on unmet needs and new directions. [ABSTRACT FROM AUTHOR]

A comparative analysis of the laminar flows of air and M-20 oil around a circular cylinder and an elliptical cylinder with a ratio between its semiaxes of 0.3:0.5, located at right angles to an incident flow, at Re = 60 has been performed. The thermal and hydrothermal efficiencies of the vortex intensification of the heat exchange in these flows in the case of moderate heating of the cylinders were estimated. [ABSTRACT FROM AUTHOR]

In the present paper, the nonlinear interaction of elliptical laser beam with quantum plasma is investigated. In the present analysis, relativistic nonlinearity is taken in to account. The differential equations for the beam width parameters of semi major axis and semi minor axis of elliptical laser beam have been obtained by using parabolic equation approach under the usual Wentzel-Kramers-Brillouin (WKB) and paraxial approximations. Further, these equations have been solved numerically by using fourth order Runge-Kutta method. The variation of beam width parameter against normalized distance of propagation is presented graphically by varying parameters such as laser beam intensity, plasma density and Fermi temperature. Results of present analysis are compared with the case of cold quantum plasma and classical relativistic plasma. [ABSTRACT FROM AUTHOR]

The extraordinary optical transmission and Faraday effects of the bilayer heterostructure consisting of a metallic film perforated with subwavelength hole arrays and a uniform dielectric film magnetized perpendicular to its plane were systematically studied by three-dimensional finite-difference time-domain method. Results of the calculation found that for the magneto-plasmonic crystals under polarized incident light with transverse magnetic mode, the resonant transmittance reached 36.9%, the Faraday rotation acquired 1.216°, and the ellipticity got a positive value of 0.840. The value of Faraday rotation and ellipticity is respectively 15.2 and 93.3 times enhancement of the 0.08° and −0.009 of the bare BIG film at the wavelength. In the transverse electric mode, the Faraday effects of the systems also had a large enhancement in contrast to the bare magnetic film. The magneto-optical effects of the systems could be manipulated by polarization mode of incident light, geometry of perforated subwavelength hole arrays, and thickness of metallic and magnetic films. Evolution of the magneto-optical properties on the structural parameters was also analyzed. Possible mechanisms underlying the extraordinary phenomena were profoundly discussed. All these results indicated that the systems could find potential applications in magneto-optical devices such as data storages, sensors, and telecommunications. [ABSTRACT FROM AUTHOR]

This paper presents an analytical investigation on the thermo-elastic response of a clamped elliptical plate made of either transversely isotropic functionally graded materials (FGMs) or a novel functionally graded nanocomposite reinforced with graphene nanoplatelets (GPLs) whose weight fraction varies continuously and smoothly along the thickness direction according to three uniform and non-uniform distribution patterns. Based on three-dimensional elasticity theory and the generalized Mian and Spencer’s method, 3D elasticity solutions are obtained for the elliptical plate under thermo-mechanical loading whose mid-plane displacements are constructed to satisfy the clamped boundary conditions in which the unknown constants are determined from the governing equations of the plate. The present analytical solutions are validated through comparisons with those available in open literature. A parametric study is then conducted, with a particular focus on the effects of GPL weight fraction, distribution pattern, geometry and size as well as the major to minor axis ratio of the plate on the thermo-mechanically induced stress and deformation fields. [ABSTRACT FROM AUTHOR]

An ultrasonic elliptical vibration tool utilizing the coupled resonant vibration modes is the key component in the elliptical vibration cutting/texturing process, which has been successfully applied to ultra-precision machining and surface texturing. In this paper, an analytical approach is proposed to analyze the resonant frequency and mode shapes of the ultrasonic elliptical vibration tool. A new design of ultrasonic elliptical vibration tool based on a portal frame structure is presented and analyzed using the proposed model. The model assumes Euler-Bernoulli beams and utilizes the transfer matrix technique to reduce the order of the system to only six variables. The model can be utilized to provide a systematic approach for an optimal design and be extended to dynamic analysis of the tool for study of machine-tool dynamics. Finite element simulation results as well as experimental data based on the prototype design are presented to verify the model. An application of the proposed tool is also demonstrated in machining micro/nano-structured surfaces for structural coloration. [ABSTRACT FROM AUTHOR]

Elliptical cylindrical shell is one of shells with special shape. Up to date, there is no publication on vibration and dynamic of functionally graded elliptical cylindrical shells. Therefore, the purpose of the present study is to investigate the nonlinear dynamic response and vibration of imperfect eccentrically stiffness functionally graded elliptical cylindrical shells on elastic foundations using both the classical shell theory (CST) and Airy stress functions method with motion equations using Volmir's assumption. The material properties are assumed to be temperature - dependent and graded in the thickness direction according to a Sigmoid power law distribution (S-FGM). The S-FGM elliptical cylindrical shell with metal-ceramic-metal layers are reinforced by outside metal stiffeners. Both the S-FGM elliptical shell and metal stiffeners are assumed to be in thermal environment and both of them are deformed under temperature simultaneously. Two cases of thermal loading (uniform temperature rise and temperature variation through thickness) are considered. The nonlinear motion equations are solved by Galerkin method and Runge-Kutta method (nonlinear dynamic response, natural frequencies). The effects of geometrical parameters, material properties, elastic foundations Winkler and Pasternak, the nonlinear dynamic analysis and nonlinear vibration of the elliptical cylindrical shells are studied. The some obtained results are validated by comparing with those in the literature. [ABSTRACT FROM AUTHOR]

A deeply modulated, regular, continuous, oscillating current waveform is reliably and repeatably achieved during electropolishing of niobium single-cell elliptical radiofrequency cavities. Details of the technique and cavity test results are reported here. The method is applicable for cavity frequencies in the range 500 MHz to 3.9 GHz and can be extended to multicell structures. [ABSTRACT FROM AUTHOR]

We report the magnetization reversal behavior of microstructured Ni80Fe20 rings using magnetooptic indicator film imaging and magnetometry. While the reversal behavior of rings with a symmetric (circular) interior hole agrees with micromagnetic simulations of an onion → vortex → onion transition, we experimentally demonstrate that rings possessing an elliptical hole with an aspect ratio of 2 exhibit complex reversal behavior comprising incoherent domain propagation in the rings. Magneto optic images reveal metastable magnetic configurations that illustrate this incoherent behavior. These results have important implications for understanding the reversal behavior of asymmetric ferromagnetic rings. [ABSTRACT FROM AUTHOR]

A novel circular switched parasitic array (CSPA) antenna operating in the Q-band and capable of electronically switching its main beam over a large field of view of 360° in the horizontal plane is presented. The core component facilitating the beam switching consists of a circular parallel plate waveguide (PPW) section containing a printed circuit board with a central parallel plate mode (PPM) launcher surrounded by 12 electronically switchable PPM reflectors with increased bandwidth. The circular PPW section is flared into a radial waveguide whose diameter is reduced by shaping a foam filling material, originally incorporated for mechanical stability reasons, into a circumferential elliptical lens. By doing so, a small elevation half-power beamwidth is achieved with a size-limited geometry. A tube-like radome protects the circumferential aperture and further increases mechanical stability. Details on antenna design, manufacturing, and measurement results are given, successfully demonstrating the functionality of the concept. The antenna represents a step toward a cost-effective solution for future small-cell mobile networks millimeter-wave wireless backhauls. [ABSTRACT FROM PUBLISHER]

The stability of a long scale equilibrium vortex structure to short scale perturbations is studied in a strongly coupled dusty plasma in the framework of a generalized hydrodynamic model. It is shown that the free energy associated with the velocity shear of the vortex can drive secondary instabilities consisting of transverse shear waves when the resonance condition between the vortex rotation frequency and the secondary wave frequency is met. Such a process can transfer energy from the long scale vortex to the short scale secondary wave and thereby provide a saturation mechanism for long scale vortices in plasmas in a manner analogous to that in neutral fluids. [ABSTRACT FROM AUTHOR]

The near-field and phase distribution patterns of surface plasmon polaritons excited on different types of irregular elliptical rings are investigated with respect to linear and circular polarized lightwave. It is interestingly found that under linear polarization, the rings exhibit the dipole-like field and phase patterns, while under circular polarization they provide the omnidirectional vortex field and phase patterns. The field patterns produced by different rings demonstrated different shapes and amplitudes. The reason is due to different phase-matching conditions, which arise from internal geometrical variations of elliptical rings. These specified phase and near-field manipulations are of high potential for many applications such as optical trapping and beam shaping. [ABSTRACT FROM AUTHOR]

The propagation of electromagnetic waves in an elliptical plasma waveguide including strongly magnetized plasma column and a dielectric rod is investigated. The dispersion relation of guided hybrid electromagnetic waves is obtained. Excitation of the waves by a thin annular relativistic elliptical electron beam will be studied. The time growth rate of electromagnetic waves is obtained. The effects of relative permittivity constant of dielectric rod, radius of dielectric rod, accelerating voltage, and current density of the annular elliptical beam on the growth rate and the frequency spectra are numerically presented. [ABSTRACT FROM AUTHOR]

In this paper complex geometrical optics (CGO) is applied for the evolution of elliptical Gaussian beam (GB) propagating in nonlinear media of Kerr type. Instead of solving commonly accepted Nonlinear Schrodinger Equation, we propose equations of geometrical optics: complex eikonal equation and complex transport equation. Eikonal equation let us derive immediately the ordinary differential equations for principle widths omitting this way complicated variational process used in nonlinear optics. From the transport equation we obtain first order ordinary differential equation for complex amplitude evolution and conservation principle for energy flux in the GB cross-section. We prove in this paper that principle curvatures of the wave front can introduce into the description the additional ellipticity of the beam, which can effectively limit collapse effect. Moreover, we discus the evolution of elliptical Gaussian beam in nonlinear inhomogeneous fibre and we present conditions for stable propagation in the region without collapse effect. Under these conditions GB approaches asymptotically to stationary solutions when parameters of the fibre changes along propagation distance. We discus in this paper also the influence of initial wave front curvatures on Gaussian beam evolution in nonlinear medium of Kerr type and in nonlinear inhomogeneous fibre. We demonstrate high ability and effectively of CGO method as compared with commonly accepted methods of nonlinear optics such as variational method approach and method of moments. Moreover, we compare obtained results with solutions of Nonlinear Schrodinger Equation for ordinary and rotating elliptical beam propagating in nonlinear medium of Kerr type. [ABSTRACT FROM AUTHOR]

Within the Ginzburg-Landau theory we consider Abrikosov vortex pinning on a columnar defect with the characteristic size of the cross-section much smaller than the coherence length. We present a simple analytical approach to the problem of pinning potential calculation suitable for cases of the defect situated inside as well as outside the vortex core. We determine the depinning current for a cavity in the form of a circular cylinder and the pinning potential for a defect with a general elliptical cross-section. For a range of applied currents below the depinning threshold we predict the possibility to observe a stable bound state where the vortex center is located outside the cavity. [ABSTRACT FROM AUTHOR]

The spreading of bloodstains on matt, vinyl silk and gloss painted surfaces, following both perpendicular and non-perpendicular impact, has been studied with a view to understanding whether surface-specific properties affect the size and shape of the final stain. In all cases the dimensions of the stains on the rougher, matt paint are up to 5% less than on the other painted surfaces though this difference decreases with impact velocity. Both the diameter of circular stains and the width of elliptical stains have been successfully modelled as a function of the perpendicular component of impact velocity vn using a modification of the energy conservation approach through the inclusion of a single, empirical constant characteristic of the surface itself. By further development of this theory, the characteristic dynamical length parameter which governs the spreading has been modified to be dependent on angle thus enabling the length of elliptical stains to be predicted independently for the first time. For all these surfaces, experiment shows that the impact angles, calculated using the conventional trigonometric formula, are in deficit by around 1° at high vn increasing to around 5° at lower vn. By modelling this deficit independently using the theoretical expressions for stain width and length, this variation with vn has been successfully explained. This work has demonstrated some of the fundamental systematic sources of error in using the conventional formula for interpreting elliptical stains and established some of the basic theory on which to develop the interpretation of casework stains on surfaces, in the future. [ABSTRACT FROM AUTHOR]

We present a technique for determining the X-ray spectral quality from each region of an elliptically curved PET(002) crystal. The investigative technique utilizes the shape of the crystal rocking curve which changes significantly as the radius of curvature changes. This unique quality information enables the spectroscopist to verify where in the spectral range that the spectrometer performance is satisfactory and where there are regions that would show spectral distortion. A collection of rocking curve measurements for elliptically curved PET(002) has been built up in our X-ray laboratory. The multi-lamellar model from the XOP software has been used as a guide and corrections were applied to the model based upon measurements. But, the measurement of RI at small radius of curvature shows an anomalous behavior; the multi-lamellar model fails to show this behavior. The effect of this anomalous RI behavior on an X-ray spectrometer calibration is calculated. It is compared to the multi-lamellar model calculation which is completely inadequate for predicting RI for this range of curvature and spectral energies. [ABSTRACT FROM AUTHOR]

In the context of modulated‐symmetry distributions, there exist various forms of skew‐elliptical families. We present yet another one, but with an unusual feature: the modulation factor of the baseline elliptical density is represented by a distribution function with an argument that is not an odd function, as it occurs instead with the overwhelming majority of similar formulations, not only with other skew‐elliptical families. The proposal is obtained by going back to the use of a lemma known since 1999, which can be seen as the general frame for a vast number of existing formulations, and use it on a different route. The broader target is to show that this "mother lemma" can still generate novel progeny. The final part of the paper examines a further level of generalization of the "mother‐lemma" where symmetry conditions are removed. Copyright © 2018 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Physical systems such as optical traps and microwave cavities are realistically modeled by billiards with soft walls. In order to investigate the influence of the wall softness on the billiard dynamics, we study numerically a smooth two-dimensional potential well that has the elliptical (hard-wall) billiard as a limiting case. Considering two parameters, the eccentricity of the elliptical equipotential curves and the wall hardness, which defines the steepness of the well, we show that (1) whereas the hard-wall limit is integrable and thus completely regular, the soft wall elliptical billiard exhibits chaos, (2) the chaotic fraction of the phase space depends nonmonotonically on the hardness of the wall, and (3) the effect of the hardness on the dynamics depends strongly on the eccentricity of the billiard. We further show that the limaçon billiard can exhibit enhanced chaos induced by wall softness, which suggests that our findings generalize to quasi-integrable systems. [ABSTRACT FROM AUTHOR]

In this paper, a novel type of colloidal template with broken symmetry was generated using commercial, inductively coupled plasma reactive ion etching (ICP-RIE). With proper but simple treatment, the traditional symmetric non-close-packed colloidal template evolves into an elliptical profile with high uniformity. This unique feature can add flexibility to colloidal lithography and/or other lithography techniques using colloidal particles as building blocks to fabricate nano-/micro-structures with broken symmetry. Beyond that the novel colloidal template we developed possesses on-site tunability, i.e. the transformability from a symmetric into an asymmetric template. Sandwich-type particles with eccentric features were fabricated utilizing this tunable template. This distinguishing feature will provide the possibility to fabricate structures with unique asymmetric features using one set of colloidal template, providing flexibility and broad tunability to enable nano-/micro-structure fabrication with colloidal templates. [ABSTRACT FROM AUTHOR]

We investigate the semiclassical Kepler/Coulomb problem using the classical constants of the motion in the framework of Nelson’s stochastic mechanics. This is done by considering the eigenvalue relations for a family of coherent states (known as the atomic elliptic states) whose wave functions are concentrated on the elliptical orbit corresponding to the associated classical problem. We show that these eigenvalue relations lead to identities for the semiclassical energy, angular momentum and Hamilton–Lenz–Runge vectors in the elliptical case. These identities are then extended to include the cases of circular, parabolic and hyperbolic motions. We show that in all cases the semiclassical wave function is determined by our identities and so our identities can be seen as defining a semiclassical Kepler/Coulomb problem. The results are interpreted in terms of two dynamical systems: one a complex valued solution to the classical mechanics for a Coulomb potential and the other the drift field for a semiclassical Nelson diffusion. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) elliptically cylindrical invisible cloaks with multiple regions are designed based on the transformation optics and the complementary media theory. Multiple invisible cloak regions can be obtained by properly using the compressed or folded transformation in each space layer. The constitutive parameter tensor expressions for each region have been obtained. The results of full wave simulations by using finite element software confirm the validity of the constitutive parameter tensor expressions. In addition, the parameters are relatively easier to realize. [ABSTRACT FROM AUTHOR]