Hexagonal Tilings: Tutte Uniqueness

We develop the necessary machinery in order to prove that hexagonal tilings are uniquely determined by their Tutte polynomial, showing as an example how to apply this technique to the toroidal hexagonal tiling.Comment: 12 figure

Extended reagions of radio emission not associated with the AGN phenomenon as sources of acceleration of cosmic rays: The case of cD galaxies

Diffuse, non-thermal extended emission not associated with the AGN phenomenon, found in many clusters of galaxies hosted by an AGN, are related to the acceleration of cosmic rays. In the current work we present preliminary evidence of absence of such formations in clusters of galaxies hosted by optically identified cD galaxies. Our subsample consists of three powerful low redshift radiogalaxies, centered in poor clusters of galaxies. We have searched for radio relics and (mini)halos which could be forming as a result of the confinement of cosmic rays by bubbles creayed by the AGN. We report on the work in progress.Comment: 4 pages, Conference HEPRO II

Hexagonal Tilings and Locally C6 Graphs

We give a complete classification of hexagonal tilings and locally C6 graphs, by showing that each of them has a natural embedding in the torus or in the Klein bottle. We also show that locally grid graphs are minors of hexagonal tilings (and by duality of locally C6 graphs) by contraction of a perfect matching and deletion of the resulting parallel edges, in a form suitable for the study of their Tutte uniqueness.Comment: 14 figure

Random-walk simulation of cell migration and proliferation

Cell migration and proliferation has been modelled in several works of the literature as a process similar to diffusion. However, diffusion models to simulate the proliferation and migration of cells tend to create a homogeneous distribution in the cell density, but this result is not real. Diffusion is not the mechanism of cell dispersal: cells disperse by crawling or proliferation, or are transported in a moving fluid. The use of stochastic models or other (cellular automata, models particles, etc...) can modify this limitation. Therefore, this paper presents a stochastic model (random-walk) to simulate the proliferation and migration of cells. Both processes are considered as completely stochastic as discrete. The model developed aims to predict the behavior of in vitro cell cultures performed with adult muscle satellite cells. Non homogeneous distribution of cells has been observed inside the culture well. Using previous stochastic model we have been able to predict the non homogeneous cell distribution and accurate quantitative results have been computed. In a future, the model will allow us to incorporate other aspects such as cell differentiation, incorporate several cell populations simultaneously, etc

TEMPORAL AND SPATIAL DISTRIBUTION OF POACEAE POLLEN IN AREAS OF SOUTHERN UNITED KINGDOM, SPAIN AND PORTUGAL

Overall, longer Poaceae pollen seasons coincided with earlier pollen season start dates. Winter rainfall noticeably affects the intensity of Poaceae pollen seasons in Mediterranean areas, but this was not as important in Worcester. Weekly data from Worcester followed a similar pattern to that of Badajoz and Évora but at a distance of more than 1500 km and 4-5 weeks later

Serendipitous discovery of a cluster of galaxies with a peculiar central galaxy

We report the serendipitous discovery of a cluster of galaxies at z=0.369. Thirty-eight candidate members were identified based on rough broad-band photometric redshifts, and three members were confirmed spectroscopically. The brightest cluster galaxy (BCG) is exceptionally blue, with B-V=0.12 and V-I=1.02. The surface-brightness profile of the BCG follows an r^(1/4)-law profile out to 3" in all three bands. The effective radius is significantly smaller in bluer bandpasses, resulting in a blue core and a color gradient opposite to the metallicity-induced color gradient observed in typical elliptical galaxies. Beyond 3" an extended envelope of emission in excess of the r^(1/4)-law profile is observed, the position angle of which coincides with the major axis of the galaxy cluster. The spectrum of the BCG contains strong Balmer absorption, a minimal 4000 A break, and a broad Mg II emission line, suggesting that the galaxy has undergone recent star formation and may harbor a central AGN. The presence of numerous nearby bright stars makes this cluster an interesting target for next-generation adaptive optics using natural guide stars.Comment: 21 pages, 8 figures, accepted for publication in the Astronomical Journa

Globular Clusters in Dense Clusters of Galaxies

Deep imaging data from the Keck II telescope are employed to study the globular cluster (GC) populations in the cores of six rich Abell clusters. The sample includes A754, A1644, A2124, A2147, A2151, and A2152, and spans the redshift range z = 0.035-0.066. The clusters also range in morphology from spiral-rich, irregular systems to centrally concentrated cD clusters rich in early-type galaxies. Globular cluster specific frequencies S_N and luminosity function dispersions are measured for a total of 9 galaxies in six central fields. The measured values of S_N for the six brightest cluster galaxies (BCGs) are all higher than typical values for giant ellipticals, in accord with the known S_N-density correlations. The three non-BCGs analyzed also have elevated values of S_N, confirming that central location is a primary factor. The number of GCs per unit mass for these fields are consistent with those found in an earlier sample, giving further evidence that GC number scales with mass and that the S_N variations are due to a deficit of halo light, i.e., S_N reflects mass-to-light ratio. The discussion builds on an earlier suggestion that the GCs (both metal rich and metal poor) around the central cluster galaxies were assembled at early times, and that star formation halted prematurely in the central galaxies at the epoch of cluster collapse. This is consistent with recent simulations of BCG/cluster formation. The subsequent addition of luminous material through cluster dynamical evolution can cause S_N to decrease, and we may be seeing the first evidence of this. Finally, the GC luminosity function measurements are used to constrain the relative distances of the three clusters that make up the Hercules supercluster.Comment: Uses emulateapj.sty (included); 17 pages with 9 included PostScript figures. Figures 1-6 are separate GIF images (so 15 figures total) available from http://astro.caltech.edu/~jpb/clusters -- the full PostScript version of the paper (20 pages; 2.2 Mb compressed) incorporating Figures 1-6 can also be grabbed from this URL. Accepted for publication in A

The Origin of the Brightest Cluster Galaxies

Most clusters and groups of galaxies contain a giant elliptical galaxy in their centres which far outshines and outweighs normal ellipticals. The origin of these brightest cluster galaxies is intimately related to the collapse and formation of the cluster. Using an N-body simulation of a cluster of galaxies in a hierarchical cosmological model, we show that galaxy merging naturally produces a massive, central galaxy with surface brightness and velocity dispersion profiles similar to observed BCG's. To enhance the resolution of the simulation, 100 dark halos at $z=2$ are replaced with self-consistent disk+bulge+halo galaxy models following a Tully-Fisher relation using 100000 particles for the 20 largest galaxies and 10000 particles for the remaining ones. This technique allows us to analyze the stellar and dark matter components independently. The central galaxy forms through the merger of several massive galaxies along a filament early in the cluster's history. Galactic cannibalism of smaller galaxies through dynamical friction over a Hubble time only accounts for a small fraction of the accreted mass. The galaxy is a flattened, triaxial object whose long axis aligns with the primordial filament and the long axis of the cluster galaxy distribution agreeing with observed trends for galaxy-cluster alignment.Comment: Revised and accepted in ApJ, 25 pages, 10 figures, online version available at http://www.cita.utoronto.ca/~dubinski/bcg

Classification of Complex Polynomial Vector Fields in One Complex Variable

A classification of the global structure of monic and centered one-variable complex polynomial vector fields is presented.Comment: 57 pages, 35 figures, submitted to the Journal of Difference Equations and Application