On the Structure of Higher Order Voronoi Cells

The classic Voronoi cells can be generalized to a higher-order version by considering the cells of points for which a given $k$-element subset of the set of sites consists of the $k$ closest sites. We study the structure of the $k$-order Voronoi cells and illustrate our theoretical findings with a case study of two-dimensional higher-order Voronoi cells for four points.Comment: Minor correction

Solid superheating observed in two-dimensional strongly-coupled dusty plasma

It is demonstrated experimentally that strongly-coupled plasma exhibits solid superheating. A 2D suspension of microspheres in dusty plasma, initially self-organized in a solid lattice, was heated and then cooled rapidly by turning laser heating on and off. Particles were tracked using video microscopy, allowing atomistic-scale observation during melting and solidification. During rapid heating, the suspension remained in a solid structure at temperatures above the melting point, demonstrating solid superheating. Hysteresis diagrams did not indicate liquid supercooling in this 2D system.Comment: 9 pages text, 3 figures, in press Physical Review Letters 200

Continuous measurements of real-life bidirectional pedestrian flows on a wide walkway

Employing partially overlapping overhead \kinectTMS sensors and automatic pedestrian tracking algorithms we recorded the crowd traffic in a rectilinear section of the main walkway of Eindhoven train station on a 24/7 basis. Beside giving access to the train platforms (it passes underneath the railways), the walkway plays an important connection role in the city. Several crowding scenarios occur during the day, including high- and low-density dynamics in uni- and bi-directional regimes. In this paper we discuss our recording technique and we illustrate preliminary data analyses. Via fundamental diagrams-like representations we report pedestrian velocities and fluxes vs. pedestrian density. Considering the density range $0$ - $1.1\,$ped/m$^2$, we find that at densities lower than $0.8\,$ped/m$^2$ pedestrians in unidirectional flows walk faster than in bidirectional regimes. On the opposite, velocities and fluxes for even bidirectional flows are higher above $0.8\,$ped/m$^2$.Comment: 9 pages, 7 figure