Ridge Network in Crumpled Paper

The network formed by ridges in a straightened sheet of crumpled paper is studied using a laser profilometer. Square sheets of paper were crumpled into balls, unfolded and their height profile measured. From these profiles the imposed ridges were extracted as networks. Nodes were defined as intersections between ridges, and links as the various ridges connecting the nodes. Many network and spatial properties have been investigated. The tail of the ridge length distribution was found to follow a power-law whereas the shorter ridges followed a log-normal distribution. The degree distribution was found to have an exponentially decaying tail, and the degree correlation was found to be disassortative. The facets created by the ridges and the Voronoi diagram formed by the nodes have also been investigated.Comment: 8 pages, 10 figure, 2 tables Replaced due to wrong formating of author name

Divergence and convergence of inertial particles in high Reynolds number turbulence

Inertial particle data from three-dimensional direct numerical simulations of particle-laden homogeneous isotropic turbulence at high Reynolds number are analyzed using Voronoi tessellation of the particle positions, considering different Stokes numbers. A finite-time measure to quantify the divergence of the particle velocity by determining the volume change rate of the Voronoi cells is proposed. For inertial particles the probability distribution function (PDF) of the divergence deviates from that for fluid particles. Joint PDFs of the divergence and the Voronoi volume illustrate that the divergence is most prominent in cluster regions and less pronounced in void regions. For larger volumes the results show negative divergence values which represent cluster formation (i.e. particle convergence) and for small volumes the results show positive divergence values which represents cluster destruction/void formation (i.e. particle divergence). Moreover, when the Stokes number increases the divergence takes larger values, which gives some evidence why fine clusters are less observed for large Stokes numbers. Theoretical analyses further show that the divergence for random particles in random flow satisfies a PDF corresponding to the ratio of two independent variables following normal and gamma distributions in one dimension. Extending this model to three dimensions, the predicted PDF agrees reasonably well with Monte-Carlo simulations and DNS data of fluid particles.Comment: 23 pages, 9 figure

V-Proportion: a method based on the Voronoi diagram to study spatial relations in neuronal mosaics of the retina

The visual system plays a predominant role in the human perception. Although all components of the eye are important to perceive visual information, the retina is a fundamental part of the visual system. In this work we study the spatial relations between neuronal mosaics in the retina. These relations have shown its importance to investigate possible constraints or connectivities between different spatially colocalized populations of neurons, and to explain how visual information spreads along the layers before being sent to the brain. We introduce the V-Proportion, a method based on the Voronoi diagram to study possible spatial interactions between two neuronal mosaics. Results in simulations as well as in real data demonstrate the effectiveness of this method to detect spatial relations between neurons in different layers