We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n). No known input causes our algorithm to use area Ω(n ) for any > 0; finding such an input would represent significant progress on the famous k-set problem from discrete geometry. Drawing line arrangement graphs is the main task in the Planarity puz...

Cell junction of the myelinated nerve mesaxon in the sciatic nerve and spinal posterior funiculus of rabbits and rats was examined by the freeze-fracture method. In replicas of fractured specimens, the cell junctions were the tight junction which was composed of parallel arrays of membrane particles. The rows of particles were straight or gently undulating along the long axis of the fibers. Occ...

In this study, a pellet scale model was developed for trickle bed reactor utilizing CFD techniques. Drag coefficients were calculated numerically at different velocities and bulk porosities in the case of single phase flow through the dry bed. The simulation results were then compared with the prediction of Kozeny-Carman (K-C) equation. The results indicated that drag coefficients calculated fr...

Given a line arrangement A with n lines, we show that there exists a path of length n/3−O(n) in the dual graph of A formed by its faces. This bound is tight up to lower order terms. For the bicolored version, we describe an example of a line arrangement with 3k blue and 2k red lines with no alternating path longer than 14k. Further, we show that any line arrangement with n lines has a coloring ...

The realizability problem for rank 3 oriented matroids (see [1]) is equivalent to the pseudoline stretchability problem (see [4]). This paper uses an example to illustrate a new approach to this problem. The main theorem of this paper, like the trigonometric form of Ceva’s theorem, shows a non-trivial relationship amongst the angles in a specific line arrangement figure (c). We work in polar co...

A strain of Chromobacterium violaceum has been isolated which produces bacteriophage tail-like particles in high numbers. The extracellular morphology and the intracellular arrangement of these particles are described.

Macroscopic properties of electrorheological (ER) fluids are often determined by the spatial arrangement of the suspended particles. We investigate the microstructure of polydisperse ER fluids at low concentrations in a DC electric field. Optical microscopy reveals that the particles with polydispersity in size or in both size and dielectric property are mixed in stable single particle width ch...