Bottom Left Corner Research Articles

Comments on "Filling algorithms and analyses for layout density control"

Theorem 2 of the title paper (A.B. Kahng et al., ibid. vol. 18, pp.445-462, 1999) presents layout density bounds for any fixed r-dissection w-by-w window given the layout density of at least L and at most U for all w-by-w windows whose bottom left corners are at points (i(w/r), j(w/r)), i, j=0, 1, ..., r((n/w)-1) on an n-by-n layout plane. However, the bounds are not tight for certain combinations of U (L) and r. Here, the authors present an approach to obtaining the tight lower and upper bounds for all possible combinations of U (L) and r.

Highly efficient parallel algorithm for finite difference solution to Navier–Stoke's equation on a hypercube

It has been shown in [Nuclear Science and Engineering 93 (1986) 6799] that the finite difference discretization of Navier–Stoke's equation leads to the solution of N× N system written in the matrix form as My= B, where M is a quasi-tridiagonal having non-zero elements at the top right and bottom left corners. We present an efficient parallel algorithm on a p-processor hypercube implemented in two phases. In phase I a generalization of an algorithm due to Kowalik [High Speed Computation, Springer, New York] is developed which decomposes the above matrix system into smaller quasi-tridiagonal ( p+1)×( p+1) subsystem, which is then solved in Phase II using an odd–even reduction method.

Monotone bipartitioning problem in a planar point set with applications to VLSI

A new problem called monotone bipartitioning of a planar point set is identified which is found to be useful in VLSI layout design. Let F denote a rectangular floor containing a set A of n points. The portion of a straight line formed by two points from the set A is called a line segment. A monotone increasing path ( MP ) in F is a connected and ordered sequence of line segments from the bottom-left corner of F to its top-right corner, such that the slope of each line segment is nonnegative, and each pair of consecutive line segments share a common point of A . An MP is said to be maximal ( MMP ) if no other point in A can be included in it preserving monotonicity. Let A L denote the subset of A corresponding to the end points of the line segments in an MMP , L . The path L partitions the set of points A \ A L into two subsets lying on its two sides. The objective of monotone bipartitioning is to find an MMP L , such that the difference in the number of points in these two subsets is minimum. This problem can be formulated as finding a path between two designated vertices of an edge-weighted digraph (the weight of an edge being an integer lying in the range [- n, n ]), for which the absolute value of the algebraic sum of weights is minimized. An O ( n × e ) time algorithm is proposed for this problem, where e denotes the number of edges of the graph determined from the geometry of the point set. The monotone bipartitioning problem has various applications to image processing, facility location, and plant layout problems. A related problem arises while partitioning a VLSI floorplan. Given a floorplan with n rectangular blocks, the goal is to find a monotone staircase channel from one corner of the floor to its diagonally opposite corner such that the difference in the numbers of blocks lying on its two sides is minimum. The problem is referred to as the staircase bipartitioning problem. The proposed algorithm for a point set can be directly used to solve this problem in O ( n 2 ) time. However, an improved O ( n ) time algorithm is reported for this special case. This leads to an O ( n log n ) time algorithm for hierarchical decomposition of a floorplan with a sequence of staircase channels. Staircase bipartitioning has many applications to channel and global routing.

The Position of Static and on-off Banners in WWW Displays on Subsequent Recognition

With the growing popularity of the World Wide Web (WWW), more companies are advertising on the Internet with the intention of influencing purchasing decisions. While companies would like to capture people's attention every time a banner ad appears on a viewer's computer screen, there is some research that suggests that they do not. In Experiment 1, static display of banners at each of the four corners of the screen was investigated using a subsequent recognition test. Experiment 2 examined more locations on the screen with on-off banners. The results of both experiments showed that participants better recognized the content of banners positioned on the top left and bottom right corners than the top right and bottom left corners. Experiment 2 showed that participants were more likely to recognize the content of on-off banners that positioned closer to the center of the screen than those at the edges of the screen. Implications for attention capture and distraction are discussed with respect to producing more effective advertisements and communicating priority information are discussed.

Nonequilibrium Natural Convection in a Differentially Heated Cavity Filled With a Saturated Porous Matrix

Steady state, natural convection in an enclosure filled with a saturated porous medium is investigated numerically. Brinkman-Forchheimer’s extension of Darcy flow with a nonequilibrium model is used in the analysis. The paper intends to address the validity of the equilibrium model for natural convection. The predicted results indicated that the equilibrium model is difficult to justify for non-Darcy regime and when the solid thermal conductivity is higher than the fluid thermal conductivity. The maximum differences in the temperatures between the two phases take place at the bottom-left corner and due to skew-symmetry of the problem at the upper-right corner. [S0022-1481(00)00402-3]

An Endorsement

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Photorealistic image generation of molecular structure on PC screen using the ray-tracing technique

A PC version of three-dimensional molecular graphics package has been developed to run under MS-DOS environment on IBM PC-compatible computers equipped with a VGA graphics board. The program consists of two parts: a menu-driven interactive system module in EGA mode, and a ray-tracing module in VGA mode. In the 256-color VGA mode, ray-tracing images are represented with a 4-color map, with 64 levels for each color: 32 levels of illuminance and 32 levels of saturation. Molecular structure can be analyzed along various directions with various light sources. Ray-tracing images are also represented in a 16-color EGA mode with the half-toning method, which can display 76 gray levels for each color. To obtain good photo-realistic images in an efficient way, we have used two light sources, with an intensity ratio of 7:3, which are located in front of the top right and bottom left corners of the screen.

An Economical Touch Panel Using SAW Absorption

Surface waves are readily absorbed when a soft object such as a fingertip touches the substrate. This familiar observation is put to use in a touch-sensing display panel to provide readouts of finger location and finger pressure. Reflective array strips placed a long the panel edges s urround the entire panel area. A short pulse launched, say, along the top edge from left to right arrives at the bottom left corner having a long rectangular envelope, w ith each point in time corresponding to a specific vertical path across t he panel. A finger touch causes an amplitude dip whose timing and depth indicate location and finger pressure. Low frequencies (4-10 MHz) make low-cost arrays p ractical. Signal/noise ratio is very high, so the c enter of the dip can be located precisely; r esolution is determined by the associated digital circuits.

Drilling and Fracturing Improvements for Low-Permeability Gas Wells in Western Canada

Summary Laboratory and field research have developed better drilling and fracturig fluids for extremely water-sensitive gas-producing formations in western Canada. Other improved techniques include perforating in dry hole, stage fracturing using baffles and balls, higher rates, higher sand concentrations, larger volumes, and immediate flowback with carbon dioxide assist. Introduction A Map of the area involved in this study of gas fields in the Alberta basin of southern Calberta is shown in Fig. 1. The first commercial gas production in Alberta began in the Medicine Hat area in 1890.1 Since then, many advances in completion and stimulation techniques have been made in Canada. The intent of this study is to present some of these recent improvements. A study2 of the geology of the Alberta basin shows a stratigraphic column with sediments ranging from Pleistocene through Cambrian covering more than 7,000 ft (2133 m), including the most productive Upper Cretaceous. The Upper Cretaceous, from the base of the Fish Scale formation to the Milk River formation, is about 1,200 ft (366 m). The lithology consists of a thick marine shale containing several sandstone and siltstone zones. These zones provide the majority of the gas production. Three of the main producers - the Milk River and Medicine Hat formations, the Second White Specks sands, and productive zones such as the Glauconite and Cardium - are shown in Fig. 2. The Medicine Hat formation and the Second White Specks sands are offshore bar types deposited in a high-energy environment. Reservoir qualities are fair to good, with permeabilities ranging from 0.1 to 5 md. The Milk River formation, which is usually thicker and more widespread than the other zones, consists of fine-grained sediments. These sediments were transported beyond the high-energy environment and deposited in quieter waters offshore, resulting in thin-bedded sands with high silt content interbedded with shale. The Milk River sand porosities vary from 10 to 15% in the better sand stringers. The net thicknesses of productive Milk River formation vary from about 1 to 30 ft (0.3 to 9 m) thick, with as much as 300 ft (90 m) gross thickness. Gas formations in Alberta usually contain high clay content, as shown in the petrographic and X-ray diffraction analyses (Tables 1 and 2) of typical cores from the Milk River, Medicine Hat, and Fish Scale formations. The gas formations in Alberta may contain 20 to 30% mixed-layer clays containing smectite and other clays (Table 2), causing these formations to be extremely water sensitive. Clays can be observed in the scanning electron microscope micrographs shown in Figs. 3 and 4. Fig. 3 is a micrograph of a typical Milk River formation core showing a pore space infilled with and surrounded by mixed-layer clays and chlorite with a pocket of siderite at the bottom left corner. The trace of siderite, an iron carbonate, was not detected by the X-ray diffraction analysis. A micrograph of Medicine Hat formation core, Fig. 4 shows a high concentration of mixed-layer clay with some kaolinite, illite, chlorite, calcite, and dolomite scattered throughout. The sand grains appear to be heavily coated with clays. The pore space is partially filled with mixed-layer and kaolinite clays.

A Symmetry Property of Transfer Matrices

The transfer matrix method of vibration analysis is widely used for the calculation of the natural frequencies of turbo-generator rotors, and of propeller blades, axial compressor blades, turbine blades, and helicopter rotors. A comprehensive account of the method has been given by Pestel and Leckie. The basis of the method is to deine a state vector, which gives all the generalised displacements and forces at a given cross-section of the system. The state vector at one cross-section is then related to the state vector at a neighbouring cross-section by means of a transfer matrix. It is found that, by a suitable choice of the order and signs of the elements of the state vector, the transfer matrix can in many cases be made symmetrical about the secondary diagonal; that is the diagonal running from the top right corner to the bottom left corner of the matrix and is also often called the “cross diagonal”.