Rectilinear Edges Research Articles

The mixed virtual element method on curved edges in two dimensions

In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical feature, such as a portion of domain boundary or an internal interface, may introduce a geometrical error that degrades the expected order of convergence of the scheme. In the present work a suitable VEM approximation space is proposed to consistently handle curvilinear geometrical objects, thus recovering optimal convergence rates. The resulting numerical scheme is presented along with its theoretical analysis and several numerical test cases to validate the proposed approach.

Meaning of Rocks Basic Enclaves in the Eburnean Granitoids of Mako Area (Kédougou-Kéniéba Inlier, Senegal): Petrogenetic Implications

The Mako area, located in eastern Sénégal, constitutes a segment of Paleoproterozoic (Birimian) formations of the Kédougou-Kéniéba Inliers (KKI) in the western part of the West African craton. The basic volcanism of the Birimian formations of the KKI has long been considered to be related to a single magmatic event associated with a Mid Oceanic Ridge Basalts (MORB) setting. The aim of this paper is to demonstrate on the basis of the architectural characteristics of the granitoids dark enclaves, the occurrence of at least two distinct phases of basic Magamtism in the Birimian of the KKI. The methodology consists of a cartography, a petrographic and architectural characterization of the dark enclaves within the Mako granitoids, in order to constrain their spatial and temporal relationships with the granitic magma. The results obtained are compared with those of the bibliography. We have pinpointed two types of enclaves depending on their shapes and the characteristics of their edge with the enclosing rocks: angular enclaves with straight edges (ante-granitoids) and the soft enclaves with uneven edges (syn-granitoids). The enclaves with straight and well-defined rectilinear edges (ante-granitoids) would be linked to a basic magma which is already consolidated before being fragmented, torn and carried away as enclaves in the granitoids. These enclaves would come from enclosing outcrops of metabasalts and metagabbros which are locally cross-cut by the granitoids. The soft enclaves with uneven edges (syn-granitoids) were co-magmatic and not solid during their incorporation into the granitoids. They come from a basic magma which is contemporaneous to the granitic one. Thus, the occurrence of two generations of dark enclaves is related to, at last, two different phases of basic magmatism in the Birimian formations of the KKI.

Rectilinear Edge Selectivity Is Insufficient to Explain the Category Selectivity of the Parahippocampal Place Area.

The parahippocampal place area (PPA) is one of several brain regions that respond more strongly to scenes than to non-scene items such as objects and faces. The mechanism underlying this scene-preferential response remains unclear. One possibility is that the PPA is tuned to low-level stimulus features that are found more often in scenes than in less-preferred stimuli. Supporting this view, Nasr et al. (2014) recently observed that some of the stimuli that are known to strongly activate the PPA contain a large number of rectilinear edges. They further demonstrated that PPA response is modulated by rectilinearity for a range of non-scene images. Motivated by these results, we tested whether rectilinearity suffices to explain PPA selectivity for scenes. In the first experiment, we replicated the previous finding of modulation by rectilinearity in the PPA for arrays of 2-d shapes. However, two further experiments failed to find a rectilinearity effect for faces or scenes: high-rectilinearity faces and scenes did not activate the PPA any more strongly than low-rectilinearity faces and scenes. Moreover, the categorical advantage for scenes vs. faces was maintained in the PPA and two other scene-selective regions—the retrosplenial complex (RSC) and occipital place area (OPA)—when rectilinearity was matched between stimulus sets. We conclude that selectivity for scenes in the PPA cannot be explained by a preference for low-level rectilinear edges.

Research on Rapid Shaped-Charge Cutting Technology of Aircraft Damaged Thin-Wall Structures

Shaped-charge cutting technology has been introduced into the field of aircraft structure repair to rapidly reshape irregular holes in thin-walled structures. In the present research, numerical calculation of the dynamic cutting process by ANSYS and experiments on shaped-charge cutting of a 2 mm-thick plate from 2A12 aluminum alloy have been carried out. It was found that rapidly produced cut/kerf is smooth and exhibits neat rectilinear edges. The incision fracture section has corrugated boundaries with clean surfaces, while the lower part has no jet penetration traces. The target plate separation method of cumulative cutting is characterized by pre-penetration and late tear patterns. The application of shaped-charge cutting technology is very lucrative for rapid repair of aircraft thin-walled structural damages.

On the efficiency of angular intraprediction.

Angular intraprediction (AIP) is a coding tool that has been incorporated into the video coding standards H.264/AVC (Advanced Audio Coding) and High Efficient Video Coding. In this paper, we study how the efficiency of AIP depends on its prediction parameters. To carry out this paper, we first theoretically analyze the variance of the error incurred when a perfectly directional signal is predicted in a certain direction. The results of this analysis are then used to study the efficiency of AIP when it is applied to a distribution of directions. To facilitate mathematical derivations, we make several assumptions about the signal and the prediction process, and we use some approximations. This allows us to obtain simple expressions for the variance of the AIP prediction error as a function of signal and prediction parameters. Finally, we compare our theoretical results with the results obtained from the prediction of images containing rectilinear edges. This comparison shows that our theoretical expressions follow the main trends of the experimental results except when AIP is performed with a very high accuracy.

On the generation of surface depressions in polishing polycrystalline diamond compacts

This paper investigates the surface depressions generated during the polishing of the (1 1 1) surfaces of polycrystalline diamond (PCD) compacts when using the dynamic friction polishing (DFP) method. It was found that surface depressions of six-sided faces along octahedral planes were the typical features created by the DFP. Although the size of the well-developed depressions can vary significantly, the rectilinear edges are always aligned with the 〈1 1 0〉 directions. Pronounced {1 1 1} planar defects (i.e., twins) were revealed underneath a depression apex. The interception of the defect plane with the polished surface accounts for the generation of the 〈1 1 0〉 aligned depressions and for the discernible asymmetry of the pyramidal faces with respect to the (1 1 1) plane. It was revealed that the attached debris layer on the PCD surfaces contained sp2-bounded amorphous carbon and nano-sized crystals.

Edge-weighted contact representations of planar graphs

We study contact representations of edge-weighted planar graphs, where vertices are rectangles or rectilinear polygons and edges are polygon contacts whose lengths represent the edge weights. We show that for any given edge-weighted planar graph whose outer face is a quadrangle, that is internally triangulated and that has no separating triangles we can construct in linear time an edge-proportional rectangular dual if one exists and report failure otherwise. For a given combinatorial structure of the contact representation and edge weights interpreted as lower bounds on the contact lengths, a corresponding contact representation that minimizes the size of the enclosing rectangle can be found in linear time. If the combinatorial structure is not fixed, we prove NP-hardness of deciding whether a contact representation with bounded contact lengths exists. Finally, we give a complete characterization of the rectilinear polygon complexity required for representing biconnected internally triangulated graphs: For outerplanar graphs complexity 8 is sufficient and necessary, and for graphs with two adjacent or multiple non-adjacent internal vertices the complexity is unbounded.

Multilayer Obstacle-Avoiding Rectilinear Steiner Tree Construction Based on Spanning Graphs

Given a set of pins and a set of obstacles on routing layers, a multilayer obstacle-avoiding rectilinear Steiner minimal tree (ML-OARSMT) connects these pins by rectilinear edges within layers and vias between layers and avoids running through any obstacle to construct a Steiner tree with a minimal total cost. The ML-OARSMT problem is very important for many very large scale integration designs with pins being located in multiple routing layers that contain numerous routing obstacles incurred from IP blocks, power networks, prerouted nets, etc. As a fundamental problem with extensive practical applications to routing and wirelength/congestion/timing estimations in early design stages, it is desired to develop an effective algorithm for the ML-OARSMT problem to facilitate the design flow. However, there is no existing work on this ML-OARSMT problem. In this paper, we first formulate the ML-OARSMT problem with rectangular obstacles and then identify key different properties of this problem from its single-layer counterpart. Based on the multilayer obstacle-avoiding spanning graph, we present the first algorithm to solve the ML-OARSMT problem. Our algorithm can guarantee an optimal solution for any two-pin net and many multiple-pin nets. Experiments show that our algorithm results in 33% smaller total costs on average than a construction-by-correction heuristic which is widely used for Steiner-tree construction in the recent literature.

Lack of relationship between forest edge proximity and nest predator activity in an eastern Canadian boreal forest

Nest predation risk often increases near forest edges in agricultural landscapes, but this pattern has rarely been found in forested landscapes. Whether this lack of relationship is general remains unclear, especially because no assessment of statistical power has been published. To (1) assess whether and how far nest predation risk is associated with forest edges and (2) avoid confounding effects of the surrounding landscape, we measured nest predator activity by placing baits at five distances (0, 30, 60, 90, and 120 m) from sharp, rectilinear forest edges that run along extensive tracts of forest. No association was found between distance to forest edges and bait discovery rates (P = 0.7). The lack of edge effect was unlikely to be caused by a lack of statistical power (1 - β > 0.8). However, bait discovery rates were significantly heterogeneous throughout the study area, and ground baits were taken at a greater rate than arboreal baits. Mice, voles, and red squirrels (Tamiasciurus hudsonicus (Erxleben)), all nest predators, were the main users of bait. Red squirrel occurrence, as estimated by playbacks, was higher in black spruce (Picea mariana (Mill.) BSP) than in balsam fir (Abies balsamea (L.) Mill.) stands but was not associated with a high bait predation rate. Our results strengthen support to the hypothesis that nests near open areas in managed boreal forests are not more at risk than forest-interior nests.

Nonlinear vibration modes of an elastic panel under periodic loading

The dynamic instability and nonlinear behavior of a nonshallow thin elastic cylindrical panel with simply supported rectilinear edges under uniformly distributed periodic load is studied. The regions of regular and chaotic dynamics are determined for symmetric and nonsymmetric bending modes of the panel. It is shown that depending on the external load frequency, the nonsymmetric buckling. which occurs when the load amplitude reaches a critical value, can lead to two different dynamic modes.

In situobservation of <110> edge and screw dislocations gliding in cube planes of Ni3Al

Abstract The glide of dislocations in the cube planes of Ni3Al is studied in situ between 573 and 1013 K. Frictional forces act on both screw and edge orientations of dislocation loops. However, rectilinear or slightly curved screw dislocations move steadily, in contrast with very rectilinear edges which move more jerkily. These edge dislocations are always dissociated in two superpartials. After some relaxation time, they become fully sessile, owing to an evolution of their core structure, probably by climb. These results are compared with those obtained post mortem in similar alloys, and with those obtained in situ in a superalloy.

A Detailed Router Based on Incremental Routing Modifications: Mighty

For the macrocell design style and for routing problems in which the routing regions are irregular, two-dimensional routers are often necessary. In this paper, a new routing technique that can be applied for general two-layer detailed routing problems, including switchboxes, channels, and partially routed areas, is presented. The routing regions that can be handled are very general: the boundaries can be described by any rectilinear edges, the pins can be on or inside the boundaries of the region, and the obstructions can be of any shape and size. The technique is based on an algorithm that routes the nets in the routing region incrementally and intelligently, and allows modifications and rip-up of nets when an existing shortest path is "far" from optimal or when no path exists. The modification steps (also called weak modification) relocate some segments of nets already routed to find a shorter path or to make room for a blocked net. The rip-up and reroute steps (called strong modifiction) remove segments of nets already routed to make room for a blocked connection; these steps are invoked only if weak modification fails. The algorithm has been rigorously proven to complete in finite time and its complexity has been analyzed. The algorithm has been implemented in the "C" programming language. Many test cases have been run, and on all the examples known in the literature the router has performed as well as or better than existing algorithms. In particular, Burstein's difficult switchbox example has been routed using one less column than the original data. In addition, the router has routed difficult channels such as Deutsch's in density and has performed better than or as well as YACR-II on all the channels available to us.

Exact vibration solutions for some irregularly shaped membranes and simply supported plates

A procedure is discussed for realizing some exact analytical eigenfunctions and corresponding eigenfrequencies for vibrating membranes with fixed rectilinear edges delineable on a grid of squares and their diagonals. By the membrane-plate analogy, the corresponding eigenmodes and frequencies of simply supported vibrating plates of the same shapes may be obtained. The fundamental modes of certain shapes with curved boundaries are also considered.

On the Stress Concentration in a Strip with a Row of Circular Holes Subjected to In-plane-bending

The stress concentration problem of a strip with a finite row of circular holes subjected to in-plane-bending is solved numerically. It is assumed that the holes have equal diameters and are placed on a center line of the strip at equal intervals. A numerical method is adopted in which a general form of stress function expressed in the polar coordinates and its transformed equation in the rectangular coordinates are recurrently used; the former is used in the method of Fourier analysis to satisfy the boundary conditions on the circular edges, and the latter is used in the method of Fourier transform to satisfy the boundary conditions on the rectilinear edges. Stress concentration factors are calculated and summarized in some diagrams. The calculated results coincide well with solutions obtained by the finite element method and experimental data obtained by electrical resistance strain gages.

On the Stress Concentration in a Strip with a Row of Circular Holes Subjected to Tension

The stress concentration problem of a strip with a finite row of circular holes subjected to tension is solved numerically. The number of holes is taken from three to six. It is assumed that the holes have equal diameters and are placed on a center line of the strip at equal intervals. A numerical method is adopted in which a general form of stress function expressed in the polar coordinates and its transformed equation in the rectangular coordinates are recurrently used; the former is used with the method of Fourier analysis to satisfy the boundary conditions on the circular edges, and the latter is used with the method of Fourier transform to satisfy the boundary conditions on the rectilinear edges. Stress concentration factors are calculated and are summarized in some diagrams. The results coincide well with the solutions obtained by the finite element method.

On the Stress Concentration in a Strip with Two Circular Holes Subjected to Tension

The stress concentration problem of a strip with two circular holes subjected to uniaxial tension is treated, assuming that the holes have equal diameters and are arranged symmetrically with regard to the center point of the strip. A numerical method is adopted in which the general form of the stress function expressed in the polar coordinates and its transformed equation in the rectangular coordinates are alternately used; the former with the method of the Fourier analysis for satisfaction of the boundary conditions on the circular edges, and the latter with the method of the Fourier transform for the conditions on the rectilinear edges. These boundary conditions are considered at points of finite numbers on both the edges. The stress concentration factors are calculated for the cases of the angles between the line connecting the centers of the holes and the center line of the strip being 0°, 45°, and 90°, and the calculated results are summarized in some diagrams.

The transverse flexure of uniformly loaded curvilinear and rectilinear polygonal plates

AbstractComplex variable methods are applied to derive exact solutions in closed forms for the small deflexions of uniformly loaded thin isotropic plates bounded by regular curvilinear polygonal contours havingnsides. The supported boundary is either clamped or has equal boundary cross-couples. For rectilinear edges the latter conditions agree with those for a simply supported boundary. The plates taken in thez-plane are conformally mapped on the unit circle in the ζ-plane by the general mapping function