Spherical Rings Research Articles

AK-ARBIS: An improved AK-MCS based on the adaptive radial-based importance sampling for small failure probability

The pivotal problem in reliability analysis is how to use a smaller number of model evaluations to get more accurate failure probabilities. To achieve this aim, an iterative method based on the Monte Carlo simulation and the adaptive Kriging (AK) model (abbreviated as AK-MCS) has been proposed in 2011 by Echard et al. But for small failure probability, the number of the candidate points is extremely large for convergent solution. These points need to be evaluated by the current Kriging model to select the best next sample for updating the Kriging model in AK-MCS method, and the large candidate points will make the adaptive updating process of Kriging model much more time-consuming. Therefore, to improve the applicability of the AK-MCS method for small failure probability, the adaptive radial-based importance sampling (ARBIS) is employed to reduce the number of candidate points in the AK-MCS method, and an ARBIS combined with AK model method (abbreviated as AK-ARBIS) is proposed. The idea of the ARBIS is adaptively to find the optimal β-sphere, i.e., the largest sphere of the safe domain, and then samples inside the optimal β-sphere is directly recognized as safety and do not need to call the true limit state function to judge their states (safe or failed). During the adaptive process of finding the optimal β-sphere, the Kriging model is ceaselessly updated layer after layer based on the U learning scheme in each sampling pool which only contains the samples between the current spherical rings. The updating process of Kriging model stops until the optimal β-sphere is adaptively found and the convergent condition is satisfied. By finding the optimal β-sphere, the total number of candidate samples is reduced which only includes the samples outside the optimal β-sphere. Besides, the whole candidate sampling pool is partitioned into several sub-candidate sampling pool sequentially. The proposed method not only inherits the advantage of the AK-MCS but also reduces the reliability analysis time of the AK-MCS from two aspects. One is the size reduction of the candidate sampling pool, the other is the reduction of the actual limit state function evaluations because the sampling points locating inside the adaptively searched optimal β-sphere do not need to participate in the training process. By analyzing a highly nonlinear numerical case, a non-linear oscillator system, a simplified wing box structural model, an aero-engine turbine disk and a planar ten-bar structure, the effectiveness and the accuracy of the proposed AK-ARBIS method for estimating the small failure probability are verified.

Automated positioning of transparent targets using defocusing method in a laser proton accelerator

We report an automated target positioning method with an accuracy of 2 μm for a compact laser proton accelerator. This method is based on micrometer-scale dots on the images of transparent targets. In order to interpret the variation of these dots quantitatively, we developed a defocusing method making transparent targets visible as phase objects and applied it in target positioning. Automated positioning of transparent targets can be realized by means of minimizing the standard deviations σ of the pixel values of the images. Fast positioning based on the relationship between the radius of spherical aberration ring and defocusing distance is also discussed. Laser proton acceleration experiments have been carried out to demonstrate the performance of this positioning method.

Triptycene‐based fluorescent polymers with pendant alkyl chains: interaction with fullerenes and morphology of thin films

AbstractWe report unique triptycene‐based alternating copolymers bearing long alkyl chains as pendants. Syntheses utilized 2,6‐diethynyltriptycene and appropriate alkyloxyarene monomers polymerized via Sonogashira cross‐coupling reaction to yield triptycene‐based poly(phenylene ethynylene)s. Resulting polymers are soluble in organic solvents and were characterized using various techniques. Experimental results suggest the polymers are thermally stable and fluorescent. The fluorescence emission is quenched in the presence of fullerenes (C60 and C70) suggesting strong host–guest interactions. The magnitude of the binding constant between the polymers and these fullerenes was determined to be of the order of 105 mol L−1. The effects of chain length on the morphology and wettability of the polymers on silicon substrates were studied using atomic force microscopy. Three distinct dewetting patterns, i.e. spherical domains, fractal structures and ring structures, were observed with variation in the pendant chain length. This ability to control the thin‐film morphology of the polymers may have potential technological applications, which include but are not limited to sensors, fluorescent coatings and organic electronics. © 2018 Society of Chemical Industry

Experimental investigation on the eliminating astigmatism in off-axis parabolic mirror ring cavity

The astigmatism in a ring cavity has been eliminated based on the off-axis parabolic mirror, which was utilized as the folded mirror instead of the spherical mirror in the laser resonator. There are no astigmatism-compensated elements on the beam path of the laser resonator with very simple design. The experimentally measured results have shown that the ellipticity was more than 0.98 for this kind of design. The misalignment sensitivity for the ring cavity was equivalent to that of the spherical mirror ring cavity.

Integrated research of a multi-wavelength method in anisotropic scattering flame on soot temperature and radiative coefficient reconstruction.

At present, the studies of scattering flame problems combined with multi-wavelength reconstruction technology are rather limited. In this paper, a multi-wavelength method combined with a collocation spectral method (CSM)-discrete ordinates method (DOM) forward method is developed for the simultaneous reconstruction of temperature and inhomogeneous radiative coefficient of an axisymmetric laminar ethylene diffusion flame. The scattering source term in the radiative transfer equation is solved by the forward solution method based on DOM, which couples a spatial scheme of CSM and the spherical rings arithmetic progression quadrature. The Tikhonov regularized method is employed to overcome the ill-posed matrix to obtain the global radiative source term. The boundary radiation intensity is input into the algorithm as a known value for inversion of temperature, absorption coefficient, and scattering coefficient. The retrieval results demonstrate that the temperature and the radiation parameters of the scattering flame can be well reconstructed for the flame with axisymmetric distribution, even for the flame with noisy data. In addition, the scattering coefficient is more difficult to rebuild than temperature. The inversion accuracy does not deteriorate with a slight increase in noise. Also, the addition of scattering terms to the proposed algorithm can improve the accuracy in reconstructing the radiation parameters. The developed method in this paper would be useful for multispectral algorithms, which could be used in later experiments based on hyperspectral techniques.

Influence of pressure and deflection loads on the critical behavior of flexible joints

Flexible joints are axisymmetric composite structures composed of spherical elastomeric rings alternating with reinforcement rings, an outer fixed attach ring and an inner movable attach ring. In the present work, a miniature flexible joint with silicone rubber as the elastomer was designed and tested in order to study the variation regularity of spring ratio torque with pressure and deflection loads. It was found that the spring ratio torque presents a down and up trend with the increase of pressure and vector angle. The relationship between the strain of elastomer and mechanical properties of flexible joint are obtained based on the finite element model (ANSYS) of flexible joints and constitutive model parameters of elastomeric material. Simulation results are in good agreement with the experimental data. A correspondence relationship is proved between knee points of the shear strain-modulus curve of elastomeric material and spring ratio torque-pressure (or vector angle) curve of the flexible joint. Results highlight that the above phenomenon is caused by the shear modulus of silicone rubber and relate to the value and distribution of strain. Further research found that the theory is also applicable for flexible joints with natural rubber as the elastomeric material.

Internal and external potential-field estimation from regional vector data at varying satellite altitude

When modeling global satellite data to recover a planetary magnetic or gravitational potential field and evaluate it elsewhere, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are available, or when data quality varies strongly with geographic location, the inversion problem becomes severely ill-posed. In those cases, adopting explicitly local methods is to be preferred over adapting global ones (e.g., by regularization). Here, we develop the theory behind a procedure to invert for planetary potential fields from vector observations collected within a spatially bounded region at varying satellite altitude. Our method relies on the construction of spatiospectrally localized bases of functions that mitigate the noise amplification caused by downward continuation (from the satellite altitude to the planetary surface) while balancing the conflicting demands for spatial concentration and spectral limitation. Solving simultaneously for internal and external fields in the same setting of regional data availability reduces internal-field artifacts introduced by downward-continuing unmodeled external fields, as we show with numerical examples. The AC-GVSF are optimal linear combinations of vector spherical harmonics. Their construction is not altogether very computationally demanding when the concentration domains (the regions of spatial concentration) have circular symmetry, e.g., on spherical caps or rings - even when the spherical-harmonic bandwidth is large. Data inversion proceeds by solving for the expansion coefficients of truncated function sequences, by least-squares analysis in a reduced-dimensional space. Hence, our method brings high-resolution regional potential-field modeling from incomplete and noisy vector-valued satellite data within reach of contemporary desktop machines.

Modules of systems of measures on polarizable Carnot groups

The paper presents a study of Fuglede’s \(p\)-module of systems of measures in condensers in polarizable Carnot groups. In particular, we calculate the \(p\)-module of measures in spherical ring domains, find the extremal measures, and finally, extend a theorem by Rodin to these groups.

Non‐foster impedance matching sensitivity of electrically small electric and magnetic spherical dipole antennas

The impedance bandwidth (BW) improvement property of a self-resonant folded spherical helix electric dipole and a spherical split ring (SSR) magnetic dipole is compared when a negative reactance element is loaded on the parasitic resonator of the antennas. They have the same electrical size of ka = 0.38 and both approach each lower Q -bound. It is found that the impedance characteristic reacts more sensitively to the loaded element for the SSR antenna due to the inherent two-times higher Q of the magnetic antenna. It is also found that a conventional non-Foster circuit composed of a series negative inductor and a capacitor cannot be used for wide impedance matching of the SSR antenna due to the high sensitivity. Subsequently, a circuit topology that enables more precise matching of the reactive values for widened impedance matching in the high- Q SSR antenna and satisfies the stable operating condition is proposed. It is observed that the improvement ratio of the BW is limited in practical situation. Nevertheless, the measured reflection coefficient of the 3D-printed SSR antenna loaded with the designed active matching circuit shows two-times wider impedance BW than passive matching, verifying the simulated result from the circuit and electromagnetic (EM) simulations.

Modulus of surface families and the radial stretch in the Heisenberg group

AbstractWe develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.

Surprising detection of an equatorial dust lane on the AGB star IRC+10216

Understanding the formation of planetary nebulae remains elusive because in the preceding asymtotic giant branch (AGB) phase these stars are heavily enshrouded in an optically thick dusty envelope. To further understand the morphology of the circumstellar environments of AGB stars we observe the closest carbon-rich AGB star IRC+10216 in scattered light. When imaged in scattered light at optical wavelengths, IRC+10216 surprisingly shows a narrow equatorial density enhancement, in contrast to the large-scale spherical rings that have been imaged much further out. We use radiative transfer models to interpret this structure in terms of two models: firstly, an equatorial density enhancement, commonly observed in the more evolved post-AGB stars, and secondly, in terms of a dust rings model, where a local enhancement of mass-loss creates a spiral ring as the star rotates. We conclude that both models can be used to reproduce the dark lane in the scattered light images, which is caused by an equatorially density enhancement formed by dense dust rather than a bipolar outflow as previously thought. We are unable to place constraints on the formation of the equatorial density enhancement by a binary system.

An analysis of waveguide resonator coupling in a microsphere and confocal cavity whispering gallery system

There are two kinds of coupling method in an optical-fiber taper coupled to a silica-microsphere whispering gallery mode (WGM) system. One is indirect coupling; another is direct coupling. In the case of indirect coupling, pump light is injected from the side of the micro-cavity. Thus, a ring mode results from the total internal reflection excited by spherical ring standing wave. In the case of direct coupling, pump light is injected from the front of the micro-cavity. Thus, a concentric mode or confocal mode result from the transmission input excited by spherical axial-oscillating standing wave. The ring mode and concentric mode have both been adopted in microsphere cavities. However, the confocal mode has not been reported, either in theory or experiment. In this paper, we adopt a micro-spheroid resonator as the confocal cavity, which can be obtained by exerting a pressure on the microsphere cavity. Thus, the confocal mode is produced in a micro-spheroid resonator. Then we investigate waveguide resonator coupling in a microsphere and confocal cavity WGM system. Finally, we make a detailed analysis of the full width at half maximum (FWHM), ζ, and quality factor, Q, between the indirect coupling and the direct coupling. We find that for the concentric mode, , which is nearly the same as that of the ring mode, Q = 7.2 × 104. For large diameter of injection laser beam, the confocal mode can obtain higher quality factor (Q > 1.202 × 106) than that of the ring mode (Q = 7.2 × 104).

0510 球形リングによる円柱後流の制御に関する研究

0510 球形リングによる円柱後流の制御に関する研究

Исследование теплогидравлической эффективности каналов с кольцевой накаткой и со сферическими выступами при ламинарном, переходном и турбулентном режимах течения

Исследование теплогидравлической эффективности каналов с кольцевой накаткой и со сферическими выступами при ламинарном, переходном и турбулентном режимах течения

Axial Compression Welding Hollow Hollow Ball Node Wall Fitting Surface Stress Formula

This paper mainly studies the hollow spherical wall in axial compression, considering the effects of weld, hoop stress range change in space and its regularity. This article USES the ANSYS program of hollow wall outer wall and middle tier wall are carried out in stress analysis, the finite element software computing results, comparing with the results of mechanics of elasticity formula of hollow spherical wall ring correction to stress in a reasonable manner to establish wall hollow hoop stress at different axial compression condition under the range of stress formula.

A symmetry problem with applications to finance

In this paper we will consider an overdetermined problem in an unknown ring-shaped domain, and we prove that the domain has to be spherical ring. We will apply this problem to an \(n\)-dimensional toy model in the mean field game theory introduced by Lasry-Lions too. We show that if in Lasry-Lions model, the additional extra data ”the boundary is a level set” is assumed, then the region, where the solution is harmonic, has to have spherical symmetry.

Effective Solution of the Dirichlet BVP of the Linear Theory of Thermoelasticity with Microtemperatures for a Spherical Ring

This paper is concerned with the linear theory of thermoelasticity with microtemperatures for homogeneous and isotropic solids. We consider the problem of equilibrium of a spherical ring and establish the solution of the Dirichlet boundary value problem (BVP).

Comparison of Quadrature Schemes in DOM for Anisotropic Scattering Radiative Transfer Analysis

The commonly implemented level-symmetric S N quadrature set for the discrete-ordinates method suffers from a limitation in discrete direction number to avoid physically unrealistic weighting factors. This limitation can have an adverse impact for determining radiative transfer, as directional discretization results in angular false scattering errors due to distortion of the scattering phase function in addition to the ray effect. To combat this limitation, several higher-order quadrature schemes with no directional limitation have been developed. Here, four higher-order quadrature sets (Legendre-equal weight, Legendre-Chebyshev, triangle tessellation, and spherical ring approximation) are implemented for determination of radiative transfer in a 3-D cubic enclosure containing participating media. Heat fluxes obtained at low direction number are compared to the S N quadrature and Monte Carlo predictions to gauge and compare quadrature accuracy. Investigation into the reduction/elimination of angular false scattering with increase in direction number, including heat flux accuracy with respect to Monte Carlo and computational efficiency, is presented. It is found that while the higher-order quadrature sets are able to effectively minimize angular false scattering, the number of directions required is extremely large, and thus it is more computationally efficient to implement proper phase-function normalization to obtain accurate results.

Modulus method and radial stretch map in the Heisenberg group

We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.

Dynamics and self-propulsion of a spherical body shedding coaxial vortex rings in an ideal fluid

We describe a model for the dynamic interaction of a sphere with uniform density and a system of coaxial circular vortex rings in an ideal fluid of equal density. At regular intervals in time, a constraint is imposed that requires the velocity of the fluid relative to the sphere to have no component transverse to a particular circular contour on the sphere. In order to enforce this constraint, new vortex rings are introduced in a manner that conserves the total momentum in the system. This models the shedding of rings from a sharp physical ridge on the sphere coincident with the circular contour. If the position of the contour is fixed on the sphere, vortex shedding is a source of drag. If the position of the contour varies periodically, propulsive rings may be shed in a manner that mimics the locomotion of certain jellyfish. We present simulations representing both cases.