Thermodynamics of a bouncer model: a simplified one-dimensional gas

Some dynamical properties of non interacting particles in a bouncer model are described. They move under gravity experiencing collisions with a moving platform. The evolution to steady state is described in two cases for dissipative dynamics with inelastic collisions: (i) for large initial energy; (ii) for low initial energy. For (i) we prove an exponential decay while for (ii) a power law marked by a changeover to the steady state is observed. A relation for collisions and time is obtained and allows us to write relevant observables as temperature and entropy as function of either number of collisions and time.Comment: 36 pages, 10 figures. To appear in: Communications in Nonlinear Science and Numerical Simulation, 201

Counting Carambolas

We give upper and lower bounds on the maximum and minimum number of geometric configurations of various kinds present (as subgraphs) in a triangulation of $n$ points in the plane. Configurations of interest include \emph{convex polygons}, \emph{star-shaped polygons} and \emph{monotone paths}. We also consider related problems for \emph{directed} planar straight-line graphs.Comment: update reflects journal version, to appear in Graphs and Combinatorics; 18 pages, 13 figure

Statistical investigation and thermal properties for a 1-D impact system with dissipation

The behavior of the average velocity, its deviation and average squared velocity are characterized using three techniques for a 1-D dissipative impact system. The system -- a particle, or an ensemble of non interacting particles, moving in a constant gravitation field and colliding with a varying platform -- is described by a nonlinear mapping. The average squared velocity allows to describe the temperature for an ensemble of particles as a function of the parameters using: (i) straightforward numerical simulations; (ii) analytically from the dynamical equations; (iii) using the probability distribution function. Comparing analytical and numerical results for the three techniques, one can check the robustness of the developed formalism, where we are able to estimate numerical values for the statistical variables, without doing extensive numerical simulations. Also, extension to other dynamical systems is immediate, including time dependent billiards.Comment: To appear in Physics Letters A (2016

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

The lichen flora of the Chagos Archipelago : including a comparison with other island and coastal tropical floras

The 1996 Chagos Expedition provided the first opportunity to study the archipelago’s lichen flora. Seventeen of the 55 islands were ecologically investigated, some in more detail than others, and lists and representative collections of lichens have been assembled for many of them. In all, 67 taxa have been recorded, 52 to specific level. Although the islands have a low biodiversity for cryptogamic plants, as would be expected in terms of their relatively young age, remoteness and small terrestrial surface areas, those taxa that are present are often found in abundance and play significant ecological roles. There is a good correlation between total lichen biodiversity and island size, despite the fact that Cocos nucifera is such an important substratum for cryptogamic plants and its presence on all islands studied provides a consistently high associated species count. Comparisons of lichen floras for ten island and coastal tropical areas show good correlations (based on the Sörensen Coefficient) within the Indian Ocean as would be expected, but poorer correlations exist within and between Pacific Ocean and neotropical floras. Ranked correlations between Chagos and other floras are in the sequence Maldives > Laing Island > Aldabra > Tuamotu > Pitcairn > N.Mariana & Belize > Guadeloupe > Cook. When coefficients are calculated using only the Physciaceae, different correlations and sequences are derived, but the affinities of the Indian Ocean islands remain strong. However, although the lichen flora of Chagos is characteristic for an Indian Ocean, it is dominated by pantropical species

Faint laser quantum key distribution: Eavesdropping exploiting multiphoton pulses

The technological possibilities of a realistic eavesdropper are discussed. Two eavesdropping strategies taking profit of multiphoton pulses in faint laser QKD are presented. We conclude that, as long as storage of Qubits is technically impossible, faint laser QKD is not limited by this security issue, but mostly by the detector noise.Comment: 7 pages, 6 figure

Escape through a time-dependent hole in the doubling map

We investigate the escape dynamics of the doubling map with a time-periodic hole. We use Ulam's method to calculate the escape rate as a function of the control parameters. We consider two cases, oscillating or breathing holes, where the sides of the hole are moving in or out of phase respectively. We find out that the escape rate is well described by the overlap of the hole with its images, for holes centred at periodic orbits.Comment: 9 pages, 7 figures. To appear in Physical Review E in 201