Adaptive Binning of X-ray data with Weighted Voronoi Tesselations

We present a technique to adaptively bin sparse X-ray data using weighted Voronoi tesselations (WVTs). WVT binning is a generalisation of Cappellari & Copin's (2001) Voronoi binning algorithm, developed for integral field spectroscopy. WVT binning is applicable to many types of data and creates unbiased binning structures with compact bins that do not lead the eye. We apply the algorithm to simulated data, as well as several X-ray data sets, to create adaptively binned intensity images, hardness ratio maps and temperature maps with constant signal-to-noise ratio per bin. We also illustrate the separation of diffuse gas emission from contributions of unresolved point sources in elliptical galaxies. We compare the performance of WVT binning with other adaptive binning and adaptive smoothing techniques. We find that the CIAO tool csmooth creates serious artefacts and advise against its use to interpret diffuse X-ray emission.Comment: 14 pages; submitted to MNRAS; code freely available at http://www.phy.ohiou.edu/~diehl/WVT/index.html with user manual, examples and high-resolution version of this pape

Multi-dimensional Boltzmann Sampling of Languages

This paper addresses the uniform random generation of words from a context-free language (over an alphabet of size $k$), while constraining every letter to a targeted frequency of occurrence. Our approach consists in a multidimensional extension of Boltzmann samplers \cite{Duchon2004}. We show that, under mostly \emph{strong-connectivity} hypotheses, our samplers return a word of size in $[(1-\varepsilon)n, (1+\varepsilon)n]$ and exact frequency in $\mathcal{O}(n^{1+k/2})$ expected time. Moreover, if we accept tolerance intervals of width in $\Omega(\sqrt{n})$ for the number of occurrences of each letters, our samplers perform an approximate-size generation of words in expected $\mathcal{O}(n)$ time. We illustrate these techniques on the generation of Tetris tessellations with uniform statistics in the different types of tetraminoes.Comment: 12p

The clustering morphology of freely rising deformable bubbles

We investigate the clustering morphology of a swarm of freely rising deformable bubbles. A three-dimensional Vorono\"i analysis enables us to quantitatively distinguish between two typical clustering configurations: preferential clustering and a grid-like structure. The bubble data is obtained from direct numerical simulations (DNS) using the front-tracking method. It is found that the bubble deformation, represented by the aspect ratio \chi, plays a significant role in determining which type of clustering is realized: Nearly spherical bubbles with \chi <~ 1.015 form a grid-like structure, while more deformed bubbles show preferential clustering. Remarkably, this criteria for the clustering morphology holds for different diameters of the bubbles, surface tension, and viscosity of the liquid in the studied parameter regime. The mechanism of this clustering behavior is connected to the amount of vorticity generated at the bubble surfaces.Comment: 10 pages, 5 figure

Crossover from quasi-static to dense flow regime in compressed frictional granular media

We investigate the evolution of multi-scale mechanical properties towards the macroscopic mechanical instability in frictional granular media under multiaxial compressive loading. Spatial correlations of shear stress redistribution following nucleating contact sliding events and shear strain localization are investigated. We report growing correlation lengths associated to both shear stress and shear strain fields that diverge simultaneously as approaching the transition to a dense flow regime. This shows that the transition from quasi static to dense flow regime can be interpreted as a critical phase transition. Our results suggest that no shear band with a characteristic thickness has formed at the onset of instability