Symmetric Plane Research Articles

Differential surface plasmon polaritons transmission line with controllable common mode rejection

In this paper, a spoof surface plasmon polarions (SPPs) transmission line is designed by patterning thin metal film in open-cross shape arranged in array. Numerical simulations show the proposed open-cross array can support spoof SPPs with enlarged propagation constant and hence enhanced confinement at metal/dielectric interface as compared to the reported ultra-thin plasmonic waveguide with the rectangular groove or solid-cross. Furthermore, a differential transmission line pair is built with such two close plasmonic arrays. A narrow metal strip locates at the symmetrical plane of the two SPPs waveguides and acts as a resonator to realize common-mode rejection at specific frequency. The notch frequency for common mode can be adjusted by tuning the metal strip length of the resonator while differential mode propagation remains unaffected. Both simulated and experimental results with good agreement are given to verify the proposed idea.

Capacitance of an elliptical disk on a semi-infinite dielectric material

Using an integral transform, the mixed boundary value problem of a conducting, elliptical disk on a dielectric half-space in an electric field is reduced to the solution of an integral equation. An analytical expression of the electric system capacitance is derived, which is a function of the eccentricity of the elliptical disk. The electric charge and electric stress distribute non-uniformly over the surface of the elliptical disk and display local singularities at the edge of the elliptical disk. The square root singularity of the electric field at the edge of the elliptical disk leads to the divergent of the resultant force on the elliptical disk, which is physically unrealistic. There likely exist geometrical constraint and/or field constraint to limit the presence of the square root singularity of the electric field. For any symmetric conductor in an infinite space that consists of air (vacuum) and a semi-infinite dielectric material with symmetric plane being in the interface between the air and the dielectric material, the electric potential in the space is independent of the dielectric constant of the dielectric material.

Cyclic lateral response and failure mechanisms of semi-rigid pile in soft clay: centrifuge tests and numerical modelling

Previous studies on laterally loaded piles in clay have mainly focused on flexible and rigid piles. Little attention has been paid to semi-rigid piles (whose pile–soil stiffness lies somewhere between those of rigid and flexible piles), which may behave as either flexible piles or rigid piles, depending on the change in soil stiffness during cycling. This study aims to understand the cyclic lateral response of a repeatedly loaded semi-rigid pile in soft clay and the failure mechanisms of the soil around the pile, through a series of centrifuge model tests and three-dimensional finite element analyses using an advanced hypoplastic clay model. Numerical parametric studies were also performed to investigate the evolution of soil flow mechanisms with increasing pile rigidity. It is revealed that the semi-rigid pile behaved as if it were a flexible pile (i.e., flexural deformation dominated) during the first few cycles, but tended to behave like a rigid pile (i.e., rotational movement prevailed) during subsequent cycles, which progressively softened the surrounding soil. As a result, the mechanisms of soil flow around the semi-rigid pile exhibited an intermediate behaviour combining the mechanisms of both flexible and rigid piles. Three distinctive mechanisms were identified: a wedge-type mechanism near the surface, a full-flow mechanism (within the transverse sections) near the middle of the pile, and a rotational soil flow mechanism (in the vertical symmetrical plane of the pile) near the lower half of the pile. By ignoring the rotational soil flow mechanism, which has a much lower resistance than the full-flow mechanism, the American Petroleum Institute code (published in 2007) underestimated the cyclic bending moment and the lateral pile displacement by 10% and 69%, respectively. Application of jet grouting around the semi-rigid pile at shallow depth significantly altered the soil flow mechanism (i.e., it was a solely wedge-type mechanism around the grouted zone).

Structural properties of GeSn thin films grown by molecular beam epitaxy

GeSn thin films on Ge (001) with various Sn concentrations from 3.36 to 7.62% were grown by molecular beam epitaxy and characterized. The structural properties were analyzed by reciprocal space mapping in the symmetric (004) and asymmetric (224) planes by high resolution X-ray diffraction (XRD). The lateral correlation length (LCL) and the mosaic spread (MS) were extracted for the epi-layer peaks in the asymmetric (224) diffraction. With the increase of Sn concentration, the LCL reduces while the MS increases, indicating degrading crystalline quality. Dislocations were observed in the sample with 7.62% Sn concentration by transmission electron microscope, consistent with the strain relaxation found in XRD mapping. Besides, the surface morphologies were investigated.

Three-dimensional numerical study on the interaction of contralateral insect wings in asymmetric stroke

Asymmetric flight of insects and birds is often seen in nature which is a conventional way for them to obtain the flexibility of maneuver in turning, hovering, and gliding. A numerical study on the interaction between contralateral wings of a dragonfly in asymmetric forward flight is carried out using the finite volume method. Various asymmetric flights with different advance ratios are considered where the aerodynamic forces, torques of each wing, pressure distributions, vorticity, and velocity fields are analyzed. A number of symmetric flights corresponding to the asymmetric flights are also studied. The results indicate that the interaction between the contralateral wings of a dragonfly is very small even when the dragonfly is in an asymmetric flight no matter how the advance ratios vary in the range concerned. With a typical example of asymmetric forward flights the difference in the mean value of vertical force coefficient is generally less than 5% compared with that for its corresponding symmetric flight. It is found that a small lateral flow region (LFR) is formed near the body, and there is a small lateral flow across the symmetric plane of the body. But this flow is very weak and resulted interaction between contralateral wings is very small. The result has confirmed in a way that dragonflies take a quite different way from fruit flies to obtain the lift with the contralateral wings. That is, fruit flies employ clap-and-fling mechanism which needs contralateral wings to be close enough to extrude the flow and generate lift, which means the contralateral two wings are so close that strong interaction happens, while dragonflies flap their contralateral wings on two sides of the vertical central plane with a relatively far distance between the wings where the interaction of contralateral wings is negligibly weak.

Differential substrate integrated waveguide bandpass filter with improved common‐mode suppression utilising complementary split‐ring resonators

A novel differential substrate integrated waveguide bandpass filter is proposed. The TE102-mode cavities arranged on the symmetrical plane could efficiently reduce the common-mode (CM) signal, meanwhile, transmitting the differential-mode signal. Additional transmission zeros have been obtained by using cross coupling in the dual-mode cavities. Moreover, by symmetrically etching complementary split-ring resonators on the bottom layer of the substrate, the CM could be suppressed whereas differential signals are not affected. To verify the above design concept, a prototype operating at 8.07 GHz has been realised and shows the desired filtering performance.

Numerical study of unsteady flows with cavitation in a high-speed micro centrifugal pump

The unsteady flows caused by the interaction between the impeller and the volute in a high-speed micro centrifugal pump are numerically studied. The internal flows of both with and without cavitations are analyzed using the CFX. The characteristics of unsteady pressure on the blade surfaces and the symmetric plane of the volute are presented and compared. The results show that the amplitudes of pressure fluctuations of critical cavitation on the blade pressure surface (PS) are bigger as compared with those at the non-cavitation condition, but on the suction surface (SS), the situation is on the contrary. When cavitation occurs, reduction of load in the impeller is a result. In the present study, such reduction of load is observed mainly on the first half of the blades. Pressure fluctuations at five monitoring points, denoted by WK1 to WK5 in the volute, are also analyzed. No matter at the critical cavitation or at the non-cavitation conditions, the monitored pressure fluctuations are at the same frequencies, which equal to the blade passing frequency (BPF) and its multiples. However, the amplitudes of the fluctuations at critical cavitation condition are considerably stronger, as compared with those for without cavitation.

A factorization theorem for lozenge tilings of a hexagon with triangular holes

In this paper we present a combinatorial generalization of the fact that the number of plane partitions that fit in a $2a\times b\times b$ box is equal to the number of such plane partitions that are symmetric, times the number of such plane partitions for which the transpose is the same as the complement. We use the equivalent phrasing of this identity in terms of symmetry classes of lozenge tilings of a hexagon on the triangular lattice. Our generalization consists of allowing the hexagon have certain symmetrically placed holes along its horizontal symmetry axis. The special case when there are no holes can be viewed as a new, simpler proof of the enumeration of symmetric plane partitions.

Regrowth of GaN on Strain-relief porous GaN template fabricated by Anodized Alumina Oxide mask

The growth of Gallium nitride on sapphire substrate generated a high density of threading dislocations in the order of ~108-109 /cm2. In this work, porous GaN template with different pore sizes was generated using Anodized Alumina oxide mask prepared by anodization with set voltage ranging from 40 V to 100V. Inductive coupled plasma etching generated porous GaN using the oxide mask. The etched pores have an estimated depth of 150 nm and the pores diameter range from 35 nm to 150 nm. Regrowth of GaN with embedded air voids provide a strain relaxed overgrown GaN layer with dislocation annihilation at the voids region. High resolution X-ray rocking curves at the symmetrical plane (002), (004) and (006) was obtained for the overgrown GaN demonstrate a significant reduction in FWHM for overgrown GaN on porous GaN template as compared to conventional GaN template. Dislocation density reduction estimated using Ayer model revealed an order of magnitude reduction of screw and mixed dislocation to higher order of 107cm-2 for overgrown on porous GaN with size of 70 nm to 100nm. Pits density counts which can be correlated to threading dislocations in the materials shows that the regrowth GaN samples on strain relief GaN has an order of magnitude lower pits density as compared to that conventional GaN sample.

Research on numerical simulation and noise reduction of aerodynamic noise in connection section of the high-speed train

The flow field distribution characteristics of side windshields and full windshields installed in the connection section of a high-speed train were numerically computed to reduce the aerodynamic noise and improve operating environment of the high-speed train. As shown from the result, the maximum pressure was at the nose tip of the high-speed train; and the greatest flow velocity of fluid was centered in the middle section of the body, while the flow velocity at both ends of the body was relatively small. After installing a side windshield, the fluid pressure of the side was significantly lower than the upper and lower surfaces, and the pressure and turbulence intensity were greater at the corner of the connection section steps. The fluid flowed to the steps from the roof of the train, and then spread gradually down along the side, with the decreasing flow rate. Therefore, the airflow was effectively prohibited from flowing into the train through installing side windshields. However, after further installing full windshields, the pressure, flow velocity and turbulence intensity in the connection section of the high-speed train were further improved. Then, the boundary element method was applied to compute the radiation noises of two kinds of windshields installed in the connection section of the high-speed train. As shown from the result, broadband radiation noise was in the upper connection section, the maximum sound pressure level (SPL) value was between 50-100 Hz and some directivity of sound pressure was shown in the high-frequency range. A certain periodicity of sound pressure distribution was presented in the longitudinal symmetrical plane of the high-speed train. At the same observation point, the sound pressure level of full windshield was slightly reduced at most frequency points, and the maximum reduction value was 23.6 dB. Finally, the wind tunnel test was conducted on the high-speed train, and the connection section of the high-speed train was the obvious noise source, thus indicating that the research in the paper was very meaningful. Besides, from SPL comparisons of the observation point, experiments and simulations were consistent with each other whether side windshields or full windshields were installed in the connection section. As a result, the reliability of the numerical computational model and the effectiveness of the results and analysis were verified.

Numerical computation of aerodynamic noises of the high speed train with considering pantographs

With the improvement of the speed, aerodynamic noises of trains also become more obvious. Reducing the aerodynamic noise has become a key factor to control noises of the high speed train. This paper uses large eddy simulation and boundary element method to compute the flow field and aerodynamic noises of pantographs and trains. The result presents that there are obvious eddies at the head, push rod, and base. Two obvious separation eddies can be found around the guide rod of the head and the push rod of pantographs. The front part of the base has a layer of shear flow, which leads to a separation eddy in the back of the base while the flow moves backward. Noises of pantographs mainly concentrate around the head, base and pushrod. With the increase of the analyzed frequency, the strength of pantograph noise source is weaker and weaker. When the analyzed frequency is 500 Hz, the noise source of pantographs is mainly around joints of several structures. By comparing the computational and the experimental result of aerodynamic noises of pantographs, this result presents that they are consistent with each other in the change tendency and value within the whole analyzed frequency. This indicates that the computational model of aerodynamic noises of pantographs is effective. Pantographs have an obvious influence on the distribution of the flow field around high speed trains, especially at the end of high speed trains. High speed trains with pantographs only have an eddy at the end, but high speed trains without pantographs have two eddies at the end. When this paper conducts on numerical computation for high speed trains, pantographs should not be ignored. In the low frequency, radiation noises of high speed trains can be found mainly around pantographs and at the end of trains. At the longitudinal symmetric plane of high speed trains, the sound pressure level at the end of trains is the highest. The radiation noise around pantographs mainly concentrates around the pushrod, then base, and the last is the head.

High-quality AlN template grown on a patterned Si(111) substrate

To obtain a high-quality AlN template on a Si substrate for high-quantum efficiency AlGaN-based deep-UV LED applications, we fabricated a high-density micro-patterned Si(111) substrate. An about 8-µm-thick AlN template was grown on the Si(111) substrate in a metal-organic chemical vapor deposition reactor by using NH3 pulsed-flow multilayer AlN growth and epitaxial lateral overgrowth methods. The template had a small X-ray full width at half-maximum with rocking curves of 620 and 1141″ for the symmetric and asymmetric (002 and 102) planes. A threading dislocation density at the best region as low as 107cm−2 was also obtained.

Numerical Heat Transfer Investigation in a Heat Exchanger Tube with Hexagonal Conical-ring Inserts

The hexagonal conical rings (HCR) modified from the typical conical ring (CR) are used as a turbulence promoter for producing the vortex flows to enhance the heat transfer rate in a heat exchanger tube. To reduce the pressure loss, the V-shaped HCR (V-HCR) obtained by cutting both symmetric plane of the cone-tip of HCR at 30°, 45° and 60° is offered in the present work. The tube fitted with V-HCR elements having a fixed inlet and outlet diameter is numerically investigated. The computation is carried out for Reynolds number in a range of 3000 to 20,000 in a uniform heat-fluxed test tube. The numerical results show that the V-HCR insert leads to much higher heat transfer than the typical CR/HCR insert or the smooth tube alone and also provides lower friction factor. The 30° V-shaped HCR gives the highest heat transfer and thermal performance due to the lowest friction loss, indicating the promising device of the V-HCR.

Theoretical solutions for displacement and stress of a circular opening reinforced by grouted rock bolt

This paper presented solutions of displacement and stress for a circular opening which is reinforced with grouted rock bolt. It satisfies the Mohr-Coulomb (M-C) or generalized Hoek-Brown (H-B) failure criterion, and exhibits elastic-brittle-plastic or strain-softening behavior. The numerical stepwise produce for strain-softening rock mass reinforced with grouted rock bolt was developed with non-associative flow rules and two segments piecewise linear functions related to a principle strain-dependent plastic parameter, to model the transition from peak to residual strength. Three models of the interaction mechanism between grouted rock bolt and surrounding rock proposed by Fahimifar and Soroush (2005) were adopted. Based on the axial symmetrical plane strain assumption, the theoretical solution of the displacement and stress were proposed for a circular tunnel excavated in elastic-brittle-plastic and strain-softening rock mass compatible with M-C or generalized H-B failure criterion, which is reinforced with grouted rock bolt. It showed that Fahimifar and Soroush's (2005) solution is a special case of the proposed solution for n = 0.5. Further, the proposed method is validated through example comparison calculated by MATLAB programming. Meanwhile, some particular examples for M-C or generalized H-B failure criterion have been conducted, and parametric studies were carried out to highlight the influence of different parameters (e.g., the very good, average and very poor rock mass). The results showed that, stress field in plastic region of surrounding rock with considering the supporting effectiveness of the grouted rock bolt is more than that without considering the effectiveness of the grouted rock bolt, and the convergence and plastic radius are reduced.

Compact dual-band filtering-response power divider with high in-band frequency selectivity

A novel compact dual-passband filtering-response power divider using modified stepped impedance resonators (SIRs) is presented. The quarter-wavelength transmission lines of conventional Wilkinson power divider are replaced by the dual-band bandpass filters to realize dual-passband bandpass response, and the phase shift of the proposed filters is tuned to be 90°. An isolation resistance R is placed at the center of the symmetric plane to realize good isolation between the two output ports. Two modified SIRs are adopted in the dual-passband filters to improve the return loss in both two passbands and control the resonant frequencies. The characteristic of the modified SIR is also analyzed. Meanwhile, the resonant frequencies can be tuned by changing impedance ratio of SIR. The source–load coupling is utilized to improve the frequency selectivity and achieve a high out-of-band rejection. A prototype of the proposed power divider is designed, fabricated, and measured. Reasonable agreement between the simulated results and measured ones is demonstrated.

Vortex reconnection in the late transition in channel flow

Vortex reconnection, as the topological change of vortex lines or surfaces, is a critical process in transitional flows, but is challenging to accurately characterize, particularly in shear flows. We apply the vortex-surface field (VSF), whose isosurface is the vortex surface consisting of vortex lines, to study vortex reconnection in the Klebanoff-type temporal transition in channel flow. The VSF evolution can capture the reconnection of the hairpin-like vortical structures evolving from the initial vortex sheets in opposite halves of the channel. The incipient vortex reconnection is characterized by the vanishing minimum distance between a pair of vortex surfaces and the reduction of vorticity flux through the region enclosed by the wall and the VSF isoline of the channel half-height on the spanwise symmetric plane. We find that the surge of the wall-friction coefficient begins at the identified reconnection time. From the Biot–Savart law, the rapid reconnection of vortex lines can induce a velocity opposed to the mean flow, which partially blocks the flow near the central region and generally accelerates the near-wall fluid motion in the flow with constant mass flux. Therefore, the vortex reconnection appears to play an important role in the sudden increase of wall friction in transitional channel flows.

Dissipative propagation of pressure waves along the slip-lines of yielding material

Traditional slip-line field theory considers steady-state pressure distributions. This work examines the evolution of pressure at yield. We show that, for a two phase material in plane strain at the point of plastic yield of the main constituent, pressure develops according to dissipative wave mechanics. The pressure wave equations are examined in more detail for the special case of radially symmetric plane strain, and for Von Mises and Drucker-Prager yield envelopes. The positions of pressure troughs are compared to the separation of slip-lines formed during the expansion by internal pressurisation of a cylinder of mild steel.

Statistical shape analysis-based determination of optimal midsagittal reference plane for evaluation of facial asymmetry.

The purpose of this study was to determine, by statistical shape analysis of original and mirroredskeletal landmarks, the optimal landmark-based midsagittal reference plane for evaluation of facial asymmetry. The study sample comprised 69 patients with facial asymmetry (36 men, 33 women; mean age, 23.0±4.1years). All landmarks were obtained with cone-beam computed tomography using a 3-dimensional coordinate system. For identifying the landmark-based midsagittal reference plane, the 3 landmarks nearest to the symmetric midsagittal reference plane were selected by ordinary and generalized Procrustes analyses. To verify the 3-landmark-based midsagittal reference plane's compatibility with the symmetric midsagittal reference plane, asymmetry measurements were calculated and tested for each. The 3 nearest landmarks (nasion, anterior nasal spine, and posterior nasal spine) were selected for the 3-landmark-based midsagittal reference plane. The averages of the sums of the squared Euclidean distance and the squared Procrustes distance differences between the 2 configurations and shapes fabricated by the symmetric and landmark-based midsagittal reference planes, respectively, were calculated as 0.121±0.241 mm and 1.69×10(-6) ± 3.25×10(-6). The testing results for the symmetric and landmark-based midsagittal reference planes were almost the same. The results indicated that a 3-dimensional midsagittal reference plane constructed of nasion, anterior nasal spine, and posterior nasal spine could be a valuable tool for the evaluation of patients with facial asymmetry.

Cell division plane orientation based on tensile stress in Arabidopsis thaliana

Cell geometry has long been proposed to play a key role in the orientation of symmetric cell division planes. In particular, the recently proposed Besson-Dumais rule generalizes Errera's rule and predicts that cells divide along one of the local minima of plane area. However, this rule has been tested only on tissues with rather local spherical shape and homogeneous growth. Here, we tested the application of the Besson-Dumais rule to the divisions occurring in the Arabidopsis shoot apex, which contains domains with anisotropic curvature and differential growth. We found that the Besson-Dumais rule works well in the central part of the apex, but fails to account for cell division planes in the saddle-shaped boundary region. Because curvature anisotropy and differential growth prescribe directional tensile stress in that region, we tested the putative contribution of anisotropic stress fields to cell division plane orientation at the shoot apex. To do so, we compared two division rules: geometrical (new plane along the shortest path) and mechanical (new plane along maximal tension). The mechanical division rule reproduced the enrichment of long planes observed in the boundary region. Experimental perturbation of mechanical stress pattern further supported a contribution of anisotropic tensile stress in division plane orientation. Importantly, simulations of tissues growing in an isotropic stress field, and dividing along maximal tension, provided division plane distributions comparable to those obtained with the geometrical rule. We thus propose that division plane orientation by tensile stress offers a general rule for symmetric cell division in plants.

A simplified approach to determine the unique direction of sliding in 3D slopes

Based on the Spencer's method, this paper presents a simplified approach to assess the stability of three-dimensional (3D) asymmetrical slopes. The approach allows for satisfaction of the force equilibrium in all three directions and the moment equilibrium about two co-ordinate axes. A unique direction of sliding is involved here to calculate the factor of safety. The direction of sliding (DOS) is always parallel to the plane of symmetry for symmetrical slopes. However, the DOS in asymmetrical slopes could deviate from the symmetrical plane and affect the stability assessments. Through two simple asymmetrical examples, the calculated results demonstrate that the deviation of the sliding from the symmetry could destabilize the slopes and cause failures. Neglecting the DOS in 3D asymmetrical slopes will overestimate their stability. Application of the presented approach into complex asymmetrical problems is straightforward.