Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface increases in complexity with crossing number. In this paper, we generalize chec...

Scanning tunneling microscopy (STM) studies of the high-T superconductors have led to a number of important discoveries. In particular, STM has revealed spatial patterns in electronic density due to phenomena such as checkerboard order and quasiparticle interference. This thesis presents two studies of these patterns and their implications. In the first, I present a doping and temperature depen...

Camera calibration plays a critical role in 3D computer vision tasks. The most commonly used calibration method utilizes a planar checkerboard and can be done nearly fully automatically. However, it requires the user to move either the camera or the checkerboard during the capture step. This manual operation is time consuming and makes the calibration results unstable. In order to solve the abo...

A spin dynamics algorithm, combining checkerboard updating and a rotation algorithm based on the local second-rank ordering field, is developed for the Lebwohl-Lasher model of liquid crystals. The method is shown to conserve energy well and to generate simulation averages that are consistent with those obtained by Monte Carlo simulation. However, care must be taken to avoid the undesirable effe...

In an inhomogeneous checkerboard surround, the lighter check darkens an incremental test patch more than the darker check lightens it. However, decremental test patches are influenced equally [Schirillo & Shevell, 1996. Vision Research, 36, 1783-1796]. In the current study, we manipulate the spatial arrangement of a checkerboard surround to produce T-junctions that perceptually group the checks...