Faceting and branching in 2D crystal growth

The official published version of the Article can be accessed from the link below - Copyright @ 2011 APSUsing atomic scale time-dependent density functional calculations we confirm that both diffusion-controlled and diffusionless crystallization modes exist in simple 2D systems. We provide theoretical evidence that a faceted to nonfaceted transition is coupled to these crystallization modes, and faceting is governed by the local supersaturation at the fluid-crystalline interface. We also show that competing modes of crystallization have a major influence on mesopattern formation. Irregularly branched and porous structures are emerging at the crossover of the crystallization modes. The proposed branching mechanism differs essentially from dendritic fingering driven by diffusive instability.This work has been supported by the EU FP7 Collaborative Project ENSEMBLE under Grant Agreement NMP4-SL-2008-213669 and by the Hungarian Academy of Sciences under Contract No. OTKA-K-62588

HI scaling relations of galaxies in the environment of HI-rich and control galaxies observed by the Bluedisk project

Our work is based on the "Bluedisk" project, a program to map the neutral gas in a sample of 25 HI-rich spirals and a similar number of control galaxies with the Westerbork Synthesis Radio Telescope (WSRT). In this paper we focus on the HI properties of the galaxies in the environment of our targeted galaxies. In total, we extract 65 galaxies from the WSRT cubes with stellar masses between $10^8M_{\odot}$ and $10^{11}M_{\odot}$. Most of these galaxies are located on the same HI mass-size relation and "HI-plane" as normal spiral galaxies. We find that companions around HI-rich galaxies tend to be HI-rich as well and to have larger R90,HI/R50,HI. This suggests a scenario of "HI conformity", similar to the colour conformity found by Weinmann et al. (2006): galaxies tend to adopt the HI properties of their neighbours. We visually inspect the outliers from the HI mass-size relation and galaxies which are offset from the HI plane and find that they show morphological and kinematical signatures of recent interactions with their environment. We speculate that these outliers have been disturbed by tidal or ram-pressure stripping processes, or in a few cases, by accretion events.Comment: 16 pages, 12 figures; accepted for publication in MNRA

Perfect fluid spheres with cosmological constant

We examine static perfect fluid spheres in the presence of a cosmological constant. New exact matter solutions are discussed which require the Nariai metric in the vacuum region. We generalize the Einstein static universe such that neither its energy density nor its pressure is constant throughout the spacetime. Using analytical techniques we derive conditions depending on the equation of state to locate the vanishing pressure surface. This surface can in general be located in regions with decreasing area group orbits. We use numerical methods to integrate the field equations for realistic equations of state and find consistent results.Comment: 15 pages, 6 figures; added new references, removed one figure, improved text, accepted for publication in PR

On geometric graph Ramsey numbers

For any two-colouring of the segments determined by 3n-3 points in general position in the plane, either the first colour class contains a triangle, or there is a noncrossing cycle of length n in the secondcolour class, and this result is tight. We also give a series of more general estimates on off-diagonal geometric graph Ramsey numbers in the same spirit. Finally we investigate the existence of large noncrossing monochromatic matchings in multicoloured geometric graphs

The cyclomatic number of connected graphs without solvable orbits

A graph is without solvable orbits if its group of automorphisms acts on each of its orbits through a non-solvable quotient. We prove that there is a connected graph without solvable orbits of cyclomatic number c if and only if c is equal to 6, 8, 10, 11, 15, 16, 19, 20, 21, 22, or is at least 24, and briefly discuss the geometric consequences