Step energies and equilibrium shape of strained monolayer islands

Using a simple atomistic model of anharmonic nearest-neighbors interaction, we have calculated the step energies of strained hexagonal monolayer islands. These have been found to decrease with the absolute value of the misfit due to the strain relaxation at steps. The effect is significantly more pronounced in the case of positive misfit owing to the stronger repulsive interatomic forces. Furthermore, (111)-faceted steps are favored at positive misfit (compressed islands) and, to a lesser extent, (100)-faceted steps at negative misfits (tensile islands). The result is rationalized in terms of the different bonding geometries at step edges and a comparison with experiments is included. Thus, the equilibrium shape transforms from regular hexagons at zero misfit to threefold symmetric hexagons with increasing misfit.Comment: 6 pages, 5 figures, 1 table. Improved, finally accepted version including a new figure, a new table and several minor modifications resulting from discussions with referee

On Rank Driven Dynamical Systems

We investigate a class of models related to the Bak-Sneppen model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of "complex behavior" such as self-organized criticality that is often observed in physical and biological systems. In this model, random fitnesses in $[0,1]$ are associated to agents located at the vertices of a graph $G$. Their fitnesses are ranked from worst (0) to best (1). At every time-step the agent with the worst fitness and some others \emph{with a priori given rank probabilities} are replaced by new agents with random fitnesses. We consider two cases: The \emph{exogenous case} where the new fitnesses are taken from an a priori fixed distribution, and the \emph{endogenous case} where the new fitnesses are taken from the current distribution as it evolves. We approximate the dynamics by making a simplifying independence assumption. We use Order Statistics and Dynamical Systems to define a \emph{rank-driven dynamical system} that approximates the evolution of the \emph{distribution} of the fitnesses in these rank-driven models, as well as in the Bak-Sneppen model. For this simplified model we can find the limiting marginal distribution as a function of the initial conditions. Agreement with experimental results of the BS model is excellent.Comment: 12 gigures, 20 page

A subsampling method for the computation of multivariate estimators with high breakdown point

All known robust location and scale estimators with high breakdown point for multivariate sample's are very expensive to compute. In practice, this computation has to be carried out using an approximate subsampling procedure. In this work we describe an alternative subsampling scheme, applicable to both the Stahel-Donoho estimator and the estimator based on the Minimum Volume Ellipsoid, with the property that the number of subsamples required is substantially reduced with respect to the standard subsampling procedures used in both cases. We also discuss some bias and variability properties of the estimator obtained from the proposed subsampling process

Near-infrared spectroscopy of nearby Seyfert galaxies - II. Molecular content and coronal emission

We present sub-arcsec near-infrared 1.5 - 2.5 micron moderate resolution long-slit spectra of eight nearby Seyfert galaxies (z<0.01), both parallel to the ionization cone and perpendicular to it. These spectra complement similar data on six Seyferts, presented in Reunanen, Kotilainen & Prieto (2002). Large concentrations of molecular gas (H2) are present in the nucleus regardless of the Seyfert type. The spatial extent of the H2 emission is larger perpendicular to the cone than parallel to it in 6/8 (75 %) galaxies, in agreement with the unified models of Active Galactic Nuclei. Broad BrGamma was detected in nearly half of the optically classified Seyfert 2 galaxies, including two objects with no evidence for hidden polarized Broad Line Region. Nuclear [FeII] emission is generally blueshifted which together with high BrGamma/[FeII] ratios suggests shocks as the dominant excitation mechanism in Seyfert galaxies. Bright coronal emission lines [SiVI] and [SiVII] are common in Seyferts, as they are detected in ~60 % of the galaxies. In three galaxies the coronal lines are extended only in the direction parallel to the cone. This could be explained by shock excitation due to the jet or superwind interacting with the interstellar medium.Comment: 19 pages, accepted for publication in MNRA