Grid generation using classical techniques

A brief historical review of conformal mapping and its applications to problems in fluid mechanics and electromagnetism is presented. The use of conformal mapping as a grid generator is described. The philosophy of the 'closed form' approach and its application to a Neumann problem is discussed. Karman-Trefftz mappings and grids for ablated, three dimensional bodies are also discussed

Imagery and long-slit spectroscopy of the Polar-Ring Galaxy AM2020-504

Interactions between galaxies are very common. There are special kinds of interactions that produce systems called Polar Ring Galaxies (PRGs), composed by a lenticular, elliptical, or spiral host galaxy, surrounded by a ring of stars and gas, orbiting in an approximately polar plane. The present work aims to study AM2020-504, a PRG with an elliptical host galaxy, and a narrow and well defined ring, probably formed by accretion of material from a donor galaxy, collected by the host galaxy. Our observational study was based on BVRI broad band imagery as well as longslit spectroscopy in the wavelenght range 4100--8600\AA, performed at the 1.6m telescope at the Observat\'orio do Pico dos Dias (OPD), Brazil. We estimated a redshift of z= 0.01683, corresponding a heliocentric radial velocity of 5045 +/-23 km/s. The (B-R) color map shows that the ring is bluer than the host galaxy, indicating that the ring is a younger structure. Standard diagnostic diagrams were used to classify the main ionizing source of selected emission-line regions (nucleus, host galaxy and ring). It turns out that the ring regions are mainly ionized by massive stars while the nucleus presents AGN characteristics. Using two empirical methods, we found oxygen abundances for the HII regions located in the ring in the range 12+log(O/H)=8.3-8.8 dex, the presence of an oxygen gradient across the ring, and that AM2020-504 follows the metallicity-luminosity relation of spiral galaxies. These results support the accretion scenario for this object and rules out cold accretion as source for the HI gas in the polar ring

The polar ring galaxy AM1934-563 revisited

We report long-slit spectroscopic observations of the dust-lane polar-ring galaxy AM1934-563 obtained with the Southern African Large Telescope (SALT) during its performance-verification phase. The observations target the spectral region of the Ha, [NII] and [SII] emission-lines, but show also deep NaI stellar absorption lines that we interpret as produced by stars in the galaxy. We derive rotation curves along the major axis of the galaxy that extend out to about 8 kpc from the center for both the gaseous and the stellar components, using the emission and absorption lines. We derive similar rotation curves along the major axis of the polar ring and point out differences between these and the ones of the main galaxy. We identify a small diffuse object visible only in Ha emission and with a low velocity dispersion as a dwarf HII galaxy and argue that it is probably metal-poor. Its velocity indicates that it is a fourth member of the galaxy group in which AM1934-563 belongs. We discuss the observations in the context of the proposal that the object is the result of a major merger and point out some observational discrepancies from this explanation. We argue that an alternative scenario that could better fit the observations may be the slow accretion of cold intergalactic gas, focused by a dense filament of galaxies in which this object is embedded (abridged).Comment: 19 pages, 13 figures, submitted to MNRAS. Some figures were bitmapped to reduce the size. Full resolution version is available from http://www.saao.ac.za/~akniazev/pub/AM1934_563.pd

Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria

We study the collective dynamics of elongated swimmers in a very thin fluid layer by devising long, filamentous, non-tumbling bacteria. The strong confinement induces weak nematic alignment upon collision, which, for large enough density of cells, gives rise to global nematic order. This homogeneous but fluctuating phase, observed on the largest experimentally-accessible scale of millimeters, exhibits the properties predicted by standard models for flocking such as the Vicsek-style model of polar particles with nematic alignment: true long-range nematic order and non-trivial giant number fluctuations.Comment: 6 pages, 4 figures. Supplemental Material: 6 pages, 3 figure

A Fisher-Rao metric for paracatadioptric images of lines

In a central paracatadioptric imaging system a perspective camera takes an image of a scene reflected in a paraboloidal mirror. A 360° field of view is obtained, but the image is severely distorted. In particular, straight lines in the scene project to circles in the image. These distortions make it diffcult to detect projected lines using standard image processing algorithms. The distortions are removed using a Fisher-Rao metric which is defined on the space of projected lines in the paracatadioptric image. The space of projected lines is divided into subsets such that on each subset the Fisher-Rao metric is closely approximated by the Euclidean metric. Each subset is sampled at the vertices of a square grid and values are assigned to the sampled points using an adaptation of the trace transform. The result is a set of digital images to which standard image processing algorithms can be applied. The effectiveness of this approach to line detection is illustrated using two algorithms, both of which are based on the Sobel edge operator. The task of line detection is reduced to the task of finding isolated peaks in a Sobel image. An experimental comparison is made between these two algorithms and third algorithm taken from the literature and based on the Hough transform