A study of the entanglement in systems with periodic boundary conditions

We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking to assess the extent of entanglement in a polymer melt we study the effect of CReTA algorithm on the entanglement of polyethylene chains. Our numerical results show that the statistics of the local periodic linking number observed for polymer melts before and after the application of CReTA are the same.Comment: 11 pages, 11 figure

On the push&pull protocol for rumour spreading

The asynchronous push&pull protocol, a randomized distributed algorithm for spreading a rumour in a graph $G$, works as follows. Independent Poisson clocks of rate 1 are associated with the vertices of $G$. Initially, one vertex of $G$ knows the rumour. Whenever the clock of a vertex $x$ rings, it calls a random neighbour $y$: if $x$ knows the rumour and $y$ does not, then $x$ tells $y$ the rumour (a push operation), and if $x$ does not know the rumour and $y$ knows it, $y$ tells $x$ the rumour (a pull operation). The average spread time of $G$ is the expected time it takes for all vertices to know the rumour, and the guaranteed spread time of $G$ is the smallest time $t$ such that with probability at least $1-1/n$, after time $t$ all vertices know the rumour. The synchronous variant of this protocol, in which each clock rings precisely at times $1,2,\dots$, has been studied extensively. We prove the following results for any $n$-vertex graph: In either version, the average spread time is at most linear even if only the pull operation is used, and the guaranteed spread time is within a logarithmic factor of the average spread time, so it is $O(n\log n)$. In the asynchronous version, both the average and guaranteed spread times are $\Omega(\log n)$. We give examples of graphs illustrating that these bounds are best possible up to constant factors. We also prove theoretical relationships between the guaranteed spread times in the two versions. Firstly, in all graphs the guaranteed spread time in the asynchronous version is within an $O(\log n)$ factor of that in the synchronous version, and this is tight. Next, we find examples of graphs whose asynchronous spread times are logarithmic, but the synchronous versions are polynomially large. Finally, we show for any graph that the ratio of the synchronous spread time to the asynchronous spread time is $O(n^{2/3})$.Comment: 25 page

Model of Centauro and strangelet production in heavy ion collisions

We discuss the phenomenological model of Centauro event production in relativistic nucleus-nucleus collisions. This model makes quantitative predictions for kinematic observables, baryon number and mass of the Centauro fireball and its decay products. Centauros decay mainly to nucleons, strange hyperons and possibly strangelets. Simulations of Centauro events for the CASTOR detector in Pb-Pb collisions at LHC energies are performed. The signatures of these events are discussed in detail.Comment: 19 pages, LaTeX+revtex4, 14 eps-figures and 3 table

Genetic Algorithms in Antennas and Smart Antennas Design Overview: Two Novel Antenna Systems for Triband GNSS Applications and a Circular Switched Parasitic Array for WiMax Applications Developments with the Use of Genetic Algorithms

Genetic algorithms belong to a stochastic class of evolutionary techniques, whose robustness and global search of the solutions space have made them extremely popular among researchers. They have been successfully applied to electromagnetic optimization, including antenna design as well as smart antennas design. In this paper, extensive reference to literature related antenna design efforts employing genetic algorithms is taking place and subsequently, three novel antenna systems are designed in order to provide realistic implementations of a genetic algorithm. Two novel antenna systems are presented to cover the new GPS/Galileo band, namely, L5 (1176 MHz), together with the L1 GPS/Galileo and L2 GPS bands (1575 and 1227 MHz). The first system is a modified PIFA and the second one is a helical antenna above a ground plane. Both systems exhibit enhanced performance characteristics, such as sufficient front gain, input impedance matching, and increased front-to-back ratio. The last antenna system is a five-element switched parasitic array with a directional beam with sufficient beamwidth to a predetermined direction and an adequate impedance bandwidth which can be used as receiver for WiMax signals