Nonlinear Diffusion and Image Contour Enhancement

The theory of degenerate parabolic equations of the forms $$u_t=(\Phi(u_x))_{x} \quad {\rm and} \quad v_{t}=(\Phi(v))_{xx}$$ is used to analyze the process of contour enhancement in image processing, based on the evolution model of Sethian and Malladi. The problem is studied in the framework of nonlinear diffusion equations. It turns out that the standard initial-value problem solved in this theory does not fit the present application since it it does not produce image concentration. Due to the degenerate character of the diffusivity at high gradient values, a new free boundary problem with singular boundary data can be introduced, and it can be solved by means of a non-trivial problem transformation. The asymptotic convergence to a sharp contour is established and rates calculated.Comment: 29 pages, includes 6 figure

The Arecibo Galaxy Environment Survey VII : A Dense Filament With Extremely Long HI Streams

We present completed observations of the NGC 7448 galaxy group and background volume as part of the blind neutral hydrogen Arecibo Galaxy Environment Survey (AGES). Our observations cover a region spanning 5x4 degrees, over a redshift range of approximately -2,000 < cz < 20,000 km/s. A total of 334 objects are detected, mostly in three overdensities at cz $\sim$7,500, cz $\sim$9,600 and cz $\sim$ 11,400 km/s. The galaxy density is extremely high (15 per square degree) and many ($\sim$24%) show signs of extended HI emission, including some features as much as 800 kpc in projected length. We describe the overall characteristics of this environment : kinematics, typical galaxy colours and mass to light ratios, and substructure. To aid in the cataloguing of this data set, we present a new FITS viewer (FRELLED : Fits Realtime Explorer of Low Latency in Every Dimension). This incorporates interactive source cataloguing tools which increase our source extraction speed by approximately a factor of 50.Comment: 15 pages, 13 figures, accepted for publication in MNRA

Activities of \gamma-ray emitting isotopes in rainwater from Greater Sudbury, Canada following the Fukushima incident

We report the activity measured in rainwater samples collected in the Greater Sudbury area of eastern Canada on 3, 16, 20, and 26 April 2011. The samples were gamma-ray counted in a germanium detector and the isotopes 131I and 137Cs, produced by the fission of 235U, and 134Cs, produced by neutron capture on 133Cs, were observed at elevated levels compared to a reference sample of ice-water. These elevated activities are ascribed to the accident at the Fukushima Dai-ichi nuclear reactor complex in Japan that followed the 11 March earthquake and tsunami. The activity levels observed at no time presented health concerns.Comment: 4 pages, 8 figure

Analytical Solution of the Voter Model on Disordered Networks

We present a mathematical description of the voter model dynamics on heterogeneous networks. When the average degree of the graph is $\mu \leq 2$ the system reaches complete order exponentially fast. For $\mu >2$, a finite system falls, before it fully orders, in a quasistationary state in which the average density of active links (links between opposite-state nodes) in surviving runs is constant and equal to $\frac{(\mu-2)}{3(\mu-1)}$, while an infinite large system stays ad infinitum in a partially ordered stationary active state. The mean life time of the quasistationary state is proportional to the mean time to reach the fully ordered state $T$, which scales as $T \sim \frac{(\mu-1) \mu^2 N}{(\mu-2) \mu_2}$, where $N$ is the number of nodes of the network, and $\mu_2$ is the second moment of the degree distribution. We find good agreement between these analytical results and numerical simulations on random networks with various degree distributions.Comment: 20 pages, 8 figure