Rectangular Edge Research Articles

Ｍｇ‐Ａｌ‐Ｚｎ系合金切削チップの熱間押出し性と形材表面性状

Hot extrusion tests for the purpose of recycling of cutting chips were carried out for AZ31B and AZ91D magnesium alloys. The tensile properties at room temperature and the surface quality of the extrusions were evaluated. Excellent mechanical properties at room temperature were obtained for an extrusion temperature of 423 K for AZ31B and for 573 K for AZ91D alloy, respectively. The tensile strength and yield strength of AZ31B cutting chip extrusion were higher than those of the extrusion from AZ31B cast billet, probably due to a grain refinement effect. However, the peculiar and wavy surface roughness almost perpendicular to the extrusion direction was formed in the extrusions from cast billet as well as in the extrusions from cutting chips of both alloys. On the extrusion surface of AZ31B alloy cutting chips, a mixed texture of basal and non-basal planes was formed. Moreover, a strong basal plane texture was observed in the layer approximately 0.4 mm from the surface. Discontinuous metal flow due to the difficulty of basal plane slip along the die exit corner with a sharp rectangular edge appeared to form the peculiar and wavy surface roughness.

Structure and energetics of a turbulent trailing edge flow

Results from a direct numerical simulation (DNS) of turbulent flow over a rectangular trailing edge geometry are used to study energy transfers in detail. The numerical procedure employs a separate boundary layer simulation which is used to generate inflow turbulence and provide the inflow boundary condition data for the trailing edge flow simulation. The calculations are performed at a Reynolds number of 1000 based on the trailing edge thickness and free stream velocity. Characteristics of the vortex shedding are identified from instantaneous flow visualizations, two-point time correlations, and spectra. Turbulence kinetic energy production is found to be negative in the region behind the trailing edge, in agreement with simple analysis. The topology of the turbulence kinetic energy flux field is studied in conjunction with the production and dissipation, revealing pathways by which turbulence energy is transported from zones of creation to zones of destruction.

Prediction of Rotational Instabilities of Rectangular and Semi-Circular Leading Edge Sections

In this paper we investigate the rotational galloping instability due to fluid/structure interaction of two bodies of the same aspect ratio but different leading edges using a previously developed algorithm [1]. This numerical technique utilises a two-dimensional spectral/hp element method and a frame of reference transformation to ensure efficient computations. Rotational motion of idealised bridge deck sections are simulated at reduced velocities of sufficient magnitude to promote a galloping and divergence responses. Comparison with quasi-steady theory is found to be favourable. The differences, in terms of the flow field and resulting critical reduced velocity, between sections with rectangular and semi-circular leading edge sections are reported.

Real time adaptive slicing for fused deposition modelling

Improvement of part surface quality and geometric accuracy in Rapid Prototyping has been a major concern. Reduction in build time and increase of part surface quality are two factors which contradict with each other as decreasing build time detracts part quality because of staircase effect. There has been a number of attempts to tackle this problem and adaptive slicing procedures are proposed. In these procedures the layer edge profiles are implicitly assumed as rectangular. But in real practice the edge profiles of a layer manufactured part are not rectangular and is found to be parabolic in case of Fused Deposition Modelling. A geometrical parameter known as cusp height is limited to a pre-specified value in existing adaptive slicing procedures, which is defined for rectangular edge profiles only. In this paper, a slicing procedure is proposed for Fused Deposition Modelling based on real time edge profile of deposited layers. The procedure is implemented and examples are included to explain the adaptive slicing method.

Analytical modelling of steady-state temperature distribution in thermal microsensors using Fourier method

An analytical method is presented that allows one to determine the steady-state temperature distribution in thermal microsensors based on thermally isolated structures with arbitrary rectangular edges. The structure of thermal microsensors is treated as a 2D structure with a number of rectangular regions which are classified into some types depending on the boundary conditions at their edges. For each type of the regions, the equivalent parameters and heat exchange conditions are determined and the expression for temperature distribution in the region is obtained by means of Fourier method. Heat flux densities between the regions are represented as sums of orthogonal functions with weighting coefficients. The expressions for temperature distribution in the regions contain unknown weighting coefficients whose values are determined from adjoint boundary conditions between all the adjacent regions. The system of equations for the weighting coefficients obtained with the help of the adjoint boundary conditions is that of linear equations. As an example, a system of linear equations for the weighting coefficients of thermal microsensors based on the membrane thermally isolated structure is presented.

Direct Numerical Simulation of Turbulent Trailing-Edge Flow with Base Flow Control

Direct numericalsimulationhas been carried out for turbulent flow over a rectangular trailing edge at a Reynolds number of 1x10(3) (based on the freestream quantities and the trailing-edge thickness) and ratio of boundarylayerdisplacement thickness to trailing-edge thickness close to unity. Two types of flow control were studied: base transpiration and secondary splitter plate. Simulation of base transpiration was performed using different slit heights and volume flow rates. It was found that even small flow rates could produce significant changes in overallaerodynamic performance, measured, for example, by the base pressure coefficient. It was also found that for the same volume flow rate, a greater increase in base pressure (drag reduction) was obtained by blowing slowly through a wide slit rather than quickly through a narrowslit. The effectiveness of a secondary splitter plate located on the trailing-edge centerline was investigated by varying the plate length from one to five times the trailing-edge thickness. A significant increase in the base pressure coefficient (about 25%) was achieved, even with the shortest splitter plate equal to the trailing-edge thickness. The base pressure coeffi cient increased monotonically with the splitter plate length, and no intermediate maximum value was found.

Direct Numerical Simulation of Turbulent Flow over a Rectangular Trailing Edge

This paper describes a direct numerical simulation (DNS) study of turbulent flow over a rectangular trailing edge at a Reynolds number of 1000, based on the freestream quantities and the trailing edge thickness h; the incoming boundary layer displacement thickness '* is approximately equal to h. The time-dependent inflow boundary condition is provided by a separate turbulent boundary layer simulation which is in good agreement with existing computational and experimental data. The turbulent trailing edge flow simulation is carried out using a parallel multi-block code based on finite difference methods and using a multi-grid Poisson solver. The turbulent flow in the near-wake region of the trailing edge has been studied first for the effects of domain size and grid resolution. Then two simulations with a total of 256 2 512 2 64 (~ 8.42106) and 512 2 1024 2 128 (~ 6.72107) grid points in the computational domain are carried out to investigate the key flow features. Visualization of the instantaneous flow field is used to investigate the complex fluid dynamics taking place in the near-wake region; of particular importance is the interaction between the large-scale spanwise, or Karman, vortices and the small-scale quasi-streamwise vortices contained within the inflow boundary layer. Comparisons of turbulence statistics including the mean flow quantities are presented, as well as the pressure distributions over the trailing edge. A spectral analysis applied to the force coefficient in the wall normal direction shows that the main shedding frequency is characterized by a Strouhal number based on h of approximately 0.118. Finally, the turbulence kinetic energy budget is analysed.

Experimental studies of capsular equator rings of soft latex

Purpose To determine the efficacy of wide equatorial rings of various materials in reducing posterior capsule opacification (PCO) and maintaining the circular contour of the capsular equator in a rabbit model. Setting Laboratory for Intraocular Microsurgery and Implants, Goldschleger Eye Research Institute, Tel-Aviv University, Sheba Medical Center, Tel-Hashomer, Israel. Methods Closed rings made of poly(methyl methacrylate), Teflon®, polyurethane, and latex were introduced into the capsular bags of rabbit eyes after removal of the lens material. The soft latex rings were deemed the only practical rings for atraumatic implantation through a small incision. Latex rings of 2 dimensions with rectangular edges were implanted in 8 rabbits. One eye served as a control after lens removal and no ring implantation. The eyes were followed for up to 5 months and then evaluated by light microscopy. Results Posterior capsule opacification was minimal or absent in all animals implanted with the latex rings. Mild to moderate inflammatory reaction was noted in most eyes. It was caused by the ring material or secondary to long-standing pressure on the ciliary tissue. The rings also maintained well the circular contour of the capsular bags. Conclusions Equatorial rings of soft latex with sharp rectangular edges were effective in minimizing PCO and maintaining the shape of the capsule after lens removal in rabbits. Soft rings made of a biocompatible material may be effective in humans.

Preventing lens epithelial cell migration using intraocular lenses with sharp rectangular edges

Purpose To compare the preventive effect on posterior capsule opacification (PCO) of an acrylic intraocular lens (IOL) and a silicone IOL, both with sharp rectangular optic edges. Setting Jinshikai Medical Foundation, Nishi Eye Hospital, Osaka, Japan. Methods After phacoemulsification, an acrylic IOL (AcrySof®) was implanted in 1 eye and a silicone IOL (CeeOn 911) in the contralateral eye of 7 rabbits, one of which was omitted from evaluation. Results The Miyake–Apple view and histopathological findings 3 weeks after surgery revealed that the lens capsule wrapped tightly around the optic edges, conforming to a distinctly sharp bend, with both IOL types in 5 rabbits. Migrating lens epithelial cells (LECs) were inhibited at the site. The AcrySof IOL had a better capsular bend effect in the histological sections, but there was no apparent difference in PCO development between the 2 IOLs. Conclusions The CeeOn 911 silicone IOL, with sharp rectangular optic edges, showed an effect on preventing PCO that was similar to that of the AcrySof IOL. When a discontinuous capsular bend is created by an IOL with sharp optic edges, the bend may induce contact inhibition of migrating LECs regardless of the lens’ material composition.

Posterior capsule opacification after phacoemulsification: foldable acrylic versus poly(methyl methacrylate) intraocular lenses

Purpose To study the effects of foldable acrylic and poly(methyl methacrylate) (PMMA) intraocular lens (IOL) implantation on posterior capsule opacification (PCO). Setting Department of Ophthalmology, Dokuz Eylül University School of Medicine, Izmir, Turkey. Methods This consecutive series comprised 157 eyes having phacoemulsification with implantation of a foldable acrylic IOL with rectangular optic edges and a 5.5 mm optic (AcrySof®) (n = 80 eyes) or a PMMA IOL with rounded optic edges and 5.5 mm optic (n = 77). Evaluated were incidence, location, and degree of PCO. Mean postoperative follow-up was 17.8 months ± 1.7 (SD) (range 16 to 22 months). Results Posterior capsule opacification occurred in 8.7% of eyes in the foldable acrylic IOL group and in 24.7% of eyes in the PMMA IOL group. The difference between the 2 groups was statistically significant ( P < .01). Centrally located PCO was significantly lower in the acrylic group ( P < .01). There were 3 eyes with severe PCO in the PMMA group and none in the acrylic group. Anterior capsule contraction and fibrosis were present in 4 eyes in the PMMA group but none in the acrylic group. Soemmering’s ring cataract formation was detected in 3 eyes, all with the AcrySof IOL. Conclusion In addition to its optic material and rectangular optic edges, the AcrySof IOL provides additional advantages in lowering the incidence of PCO compared with rounded-edge PMMA IOLs.

Design of a broadband directional coupler using microstrip-like multilayer technology

An improved 3 dB broadband double-sided slot-coupled directional coupler has been designed and implemented. The slot is modified by trimming the sharp rectangular edges and the coupled microstrip lines in the coupling region. The performance of the coupler shows good agreement with the simulated frequency response. The main improvement is in the significant reduction of ripple amplitude in the design bandwidth. Insertion loss of the novel coupler has also been reduced compared to the conventional rectangular slot coupler. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 273–275, 1999.

Rectangular edge synchronization for intensity modulated radiation therapy with dynamic multileaf collimation

The implementation of intensity modulated radiotherapy by dynamic multileaf collimator control involves the use of interpreter software which creates leaf trajectory plans for each leaf pair. Interpreter software for use with an Elekta SL15 linear accelerator and dedicated multileaf collimator has been written and tested. In practice the ideal trajectory plans often predict contact between leaves from opposing leaf banks, but this is prohibited by control software on the Elekta system as it could lead to mechanical damage. If the modulation within the geometric limits of a shaped field is not to be compromised then strategies to avoid leaf contact result in additional unwanted doses outside the geometric edge. The magnitude of any such additional dose can be reduced to acceptable levels by a technique which we have called rectangular edge synchronization. The performance of interpreter software which incorporates rectangular edge synchronization has been compared with that of potentially more efficient software which does not. The option containing the rectangular edge synchronization algorithm was shown to work consistently well at high monitor unit rates, and without incurring leaf contacts, under a wide range of test conditions. It therefore provides a sound basis for using intensity modulation to replace mechanical wedges, to simulate customized patient shape compensators, or to implement the results of inverse treatment planning processes that require superimposed intensity modulated beams.

Inhibition of Migrating Lens Epithelial Cells at the Capsular Bend Created by the Rectangular Optic Edge of a Posterior Chamber Intraocular Lens

To study the mechanism of the reportedly low incidence of posterior capsule opacification (PCO) in eyes treated with a posterior chamber intraocular lens (PC IOL). Various IOL designs, including the PC IOL, were studied using scanning electron microscopy. Rabbit lens capsules were studied histopathologically 2, 3, and 4 weeks after implantation of a PC IOL in one eye and a biconvex polymethylmethacrylate (PMMA) IOL in the contralateral eye as a control. The optic edge of the PC IOL was sharp and rectangular, whereas that of the biconvex PMMA or silicone IOLs from various manufacturers had been smoothed and rounded by polishing. PCO was significantly reduced in the eye with a PC IOL in all rabbits. The lens capsule wrapped tightly around the optic edge of the PC IOL so that it conformed to the same shape and thereby created a distinct rectangular bend in the capsule or a rectangle between the optic edge and the posterior capsule. Migrating lens epithelial cells (LECs) were obviously inhibited at that site. A discontinuous capsular bend or rectangle created by the sharp, square optic edge of the PC IOL may have induced contact inhibition to migrating LECs and reduced PCO. How, whether, and to what extent this design-dependent effect is influenced by features of the IOL material needs to be clarified by comparison with results achieved with an IOL made from the same material in a different design and vice versa.

Effects of Woodland Shape on the Spatial Distribution and Density of 17-year Periodical Cicadas (Homoptera: Cicadidae)

-We tested the hypothesis that the shape of woodland fragments influences the spatial distribution and density of three species of 17-year periodical cicadas (Homoptera: Cicadidae: Magicicada spp.). These characteristics were quantified for periodical cicadas emerging in four rectangular woodlots (mean size = 3.4 ? 0.7 ha), four linear wooded fencerows (>400 m long by mean width = 15.9 + 3.9 m), and the last remaining stand (81 ha) of primary beech-maple forest in southwestern Ohio, during the emergence of Brood X, May-June 1987. The shape of woodland fragments influenced spatial distribution and density of cicadas, although other factors, particularly the disturbance history of the sites, were equally important. Emergence began earlier in linear wooded fencerows and rectangular woodlot edges than in the interior of woodlots. Density of emerging individuals was greatest in the least disturbed edge areas and was low within the interior of rectangular woodlots. The relative abundances of the cicada species differed significantly between the woodland fragments and the primary forest. The smaller species, M. cassini (Fisher) and M. septendecula (Alexander and Moore), constituted over 93% of all individuals in all the linear and rectangular forest fragments, but the larger species, M. septendecim (L.), constituted 68% of individuals in the interior of the primary forest. We concluded that woodland shape influenced the spatial distribution of cicadas within the fragments, mainly due to the concentration of cicadas in edge areas. Our data also indicated that forest fragmentation shifted the relative abundances of these cicada species to the detriment of M. septendecim.

Scattering of light by polydisperse, randomly oriented, finite circular cylinders

We use the T-matrix method, as described by Mishchenko [Appl. Opt. 32, 4652 (1993)], to compute rigorously light scattering by finite circular cylinders in random orientation. First we discuss numerical aspects of T -matrix computations specific for finite cylinders and present results of benchmark computations for a simple cylinder model. Then we report results of extensive computations for polydisperse, randomly oriented cylinders with a refractive index of 1.53 + 0.008i, diameter-to-length ratios of 1/2, 1/1.4, 1, 1.4, and 2, and effective size parameters ranging from 0 to 25. These computations parallel our recent study of light scattering by polydisperse, randomly oriented spheroids and are used to compare scattering properties of the two classes of simple convex particles. Despite the significant difference in shape between the two particle types (entirely smooth surface for spheroids and sharp rectangular edges for cylinders), the comparison shows rather small differences in the integral photometric characteristics (total optical cross sections, single-scattering albedo, and asymmetry parameter of the phase function) and the phase function. The general patterns of the other elements of the scattering matrix for cylinders and aspect-ratio-equivalent spheroids are also qualitatively similar, although noticeable quantitative differences can be found in some particular cases. In general, cylinders demonstrate much less shape dependence of the elements of the scattering matrix than do spheroids. Our computations show that, like spheroids and bispheres, cylinders with surface-equivalent radii smaller than a wavelength can strongly depolarize backscattered light, thus suggesting that backscattering depolarization for nonspherical particles cannot be universally explained by using only geometric-optics considerations.

A shell-model analysis of the structure and dynamics of crystal edges of alkali halides

The static relaxation and the lattice dynamics of rectangular edges of quadratic bars of four rock-salt-structured alkali halides is calculated using a shell model. The relaxation includes a large-scale contraction of the bar as well as tip-localized microscopic static displacements. The phonon spectra of relaxed quadratic bars are presented and modes localized at the edges are identified.

Full‐wave, edge‐accounting calculation of losses in rectangular‐groove waveguides

AbstractA loss‐calculation approach that takes into account the exact field behavior near the rectangular edge has been developed for rectangular‐groove waveguides. A new type of groove waveguide with a rectangle‐shaped groove and central symmetry is discussed. A new algorithm for optimizing the losses and overall dimensions of rectangle‐groove guides is described. Sample numerical results for the losses and overall dimensions are presented for a centrally symmetric rectangular‐groove guide and also for a traditional symmetric rectangular‐groove guide. © 1995 John Wiley &amp; Sons, Inc.

Pressure factors for edge regions on low rise building roofs

Point and area-averaged pressures are presented for enclosed low rise (height ( h)/breadth (b) = 1 3 building roof, based on 1:100 scale wind tunnel measurements obtained in a simulated suburban atmospheric surface layer. Large magnitude mean and peak suction pressures were measured close to the leading edges under the separating shear layer. Significantly larger magnitude mean and peak pressures were measured on 0.2 h (wide) by 1.0 h (long) rectangular edge strips compared to the pressures on 1.5 h by 1.0 h roof sections. Pressure factors of the order of 3.0 for suction pressures were obtained for these regions which are larger than code values. However, measured peak area-averaged suction pressures were significantly smaller than code values.

Scalar Quantum Fields Confined by Rectangular Boundaries

A collection of local Casimir problems is studied in detail. These problems are generated by confining a scalar quantum field within boundaries consisting of planes, edges and corners. The boundaries include isolated infinite planes, rectangular edges and corners, parallel planes, the rectangular waveguide and the rectangular cavity. Calculations are done for massless and massive confined fields and for fields at zero and nonzero temperature. Each example has its finite global Casimir effect, which must be computable from the exact local description. The latter however contains known boundary divergences which seem to imply an infinite global Casimir effect. A physical picture and mathematically explicit method is presented for computing finite global Casimir effects from the divergent local description. Divergent boundary functions extending outward in space away from a given boundary ϱ𝔐 represent the distortion of the virtual particle sea of the confined field caused by ϱ𝔐. This distortion of the virtual sea is inseparable from the existence of ϱ𝔐, and may be regarded as the cost of construction of ϱ𝔐 out of nothing. Thus a given divergent boundary function is intrinsic to its ϱ𝔐 — where here is meant specifically the complete boundary function extending (if it does) all the way to infinity. Different boundaries cut off parts of each other's boundary functions, and this plays a vital role in the global Casimir effect as will be explained. It is shown in the examples considered how to compute the global Casimir effect by integration of the exact local description over the region within which the quantum field is confined. Rectangular boundary geometry makes calculations relatively simple; however the method can be applied to boundaries of arbitrary shape. At finite temperature the confined quantum field represents a thermal gas as well as a virtual particle sea. Boundaries also distort this gas of real particles in a way which can be computed. Exact local calculations are done for the rectangular boundaries considered. Beyond these considerations for free fields, systems with interacting fields present additional very interesting local Casimir phenomena. A model two-field interacting theory is discussed briefly for illustration.

On the in-plane acceleration sensitivity of contoured quartz resonators supported along rectangular edges

It is shown that the resultant in-plane acceleration sensitivity of contoured quartz resonators symmetrically supported along rectangular edges always vanishes. This result is a consequence of symmetry and applies to any shape for which the support system is symmetric with respect to the center of the mode shape. When the active plate is supported on one side only, a state of flexure is induced in the resonator which degrades the in-plane sensitivity. This emphasizes the importance of a symmetric support system to achieve low acceleration sensitivities. The extensional and induced in-plane flexural biasing deformations are determined by means of our variational approximation procedure using the variational principles in which all conditions appear as natural conditions. The resulting biasing states are employed in an existing perturbation equation along with the mode shapes of the contoured resonators to calculate the nonvanishing acceleration sensitivities when the resonator is supported on one side only.