Linear-Time Poisson-Disk Patterns

We present an algorithm for generating Poisson-disc patterns taking O(N) time to generate $N$ points. The method is based on a grid of regions which can contain no more than one point in the final pattern, and uses an explicit model of point arrival times under a uniform Poisson process.Comment: 4 pages, 2 figure

The Potential-Density Phase Shift Method for Determining the Corotation Radii in Spiral and Barred Galaxies

We have developed a new method for determining the corotation radii of density waves in disk galaxies, which makes use of the radial distribution of an azimuthal phase shift between the potential and density wave patterns. The approach originated from improved theoretical understandings of the relation between the morphology and kinematics of galaxies, and on the dynamical interaction between density waves and the basic-state disk stars which results in the secular evolution of disk galaxies. In this paper, we present the rationales behind the method, and the first application of it to several representative barred and grand-design spiral galaxies, using near-infrared images to trace the mass distributions, as well as to calculate the potential distributions used in the phase shift calculations. We compare our results with those from other existing methods for locating the corotations, and show that the new method both confirms the previously-established trends of bar-length dependence on galaxy morphological types, as well as provides new insights into the possible extent of bars in disk galaxies. Application of the method to a larger sample and the preliminary analysis of which show that the phase shift method is likely to be a generally-applicable, accurate, and essentially model-independent method for determining the pattern speeds and corotation radii of single or nested density wave patterns in galaxies. Other implications of this work are: most of the nearby bright disk galaxies appear to possess quasi-stationary spiral modes; that these density wave modes and the associated basic state of the galactic disk slowly transform over time; and that self-consistent N-particle systems contain physics not revealed by the passive orbit analysis approaches.Comment: 48 pages, 16 figures. Accepted for publication in the Astronomical Journa

Numerical simulations of the Accretion-Ejection Instability in magnetised accretion disks

The Accretion-Ejection Instability (AEI) described by Tagger & Pellat (1999) is explored numerically using a global 2d model of the inner region of a magnetised accretion disk. The disk is initially currentless but threaded by a vertical magnetic field created by external currents, and frozen in the flow. In agreement with the theory a spiral instability, similar in many ways to those observed in self-gravitating disks, develops when the magnetic field is, within a factor of a few, at equipartition with the disk thermal pressure. Perturbations in the flow build up currents and create a perturbed magnetic field within the disk. The present non-linear simulations give good evidence that such an instability can occur in the inner region of accretion disks, and generate accretion of gas and vertical magnetic flux toward the central object, if the equilibrium radial profiles of density and magnetic flux exceed a critical threshold.Comment: single tar file with GIF figure

Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm