Small noise asymptotic of the timing jitter in soliton transmission

We consider the problem of the error in soliton transmission in long-haul optical fibers caused by the spontaneous emission of noise inherent to amplification. We study two types of noises driving the stochastic focusing cubic one dimensional nonlinear Schr\"{o}dinger equation which appears in physics in that context. We focus on the fluctuations of the mass and arrival time or timing jitter. We give the small noise asymptotic of the tails of these two quantities for the two types of noises. We are then able to prove several results from physics among which the Gordon--Haus effect which states that the fluctuation of the arrival time is a much more limiting factor than the fluctuation of the mass. The physical results had been obtained with arguments difficult to fully justify mathematically.Comment: Published in at http://dx.doi.org/10.1214/07-AAP449 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the tree-width of knot diagrams

We show that a small tree-decomposition of a knot diagram induces a small sphere-decomposition of the corresponding knot. This, in turn, implies that the knot admits a small essential planar meridional surface or a small bridge sphere. We use this to give the first examples of knots where any diagram has high tree-width. This answers a question of Burton and of Makowsky and Mari\~no.Comment: 14 pages, 6 figures. V2: Minor updates to expositio

Can we predict community-wide effects of herbicides from toxicity tests on macrophyte species?

Macrophyte communities play an essential role in the way freshwater ecosystems function. It is thus of great concern to understand how environmental factors, especially anthropogenic ones, influence their composition and diversity. The aim of this study was to examine whether the effects of a herbicide mixture (50% atrazine, 35% isoproturon, 15% alachlor) on single macrophyte species can be used to predict its impact at a community level. In a first experiment we tested the sensitivity of six species (Azolla filiculoides, Ceratophyllum demersum, Elodea canadensis, Lemna minor, Myriophyllum spicatum and Vallisneria spiralis) grown separately and exposed to 0.6–600 gL−1 of the herbicide mixture. In a second experiment, conducted in microcosms, we tested the effects of herbicides on macrophyte assemblages composed of the same six species exposed to 0, 6 or 60 gL−1 of the herbicide mixture. Species grown separately exhibited growth inhibition at 60 and 600 gL−1. At 600 gL−1 the sensitivity differed significantly between species. V. spiralis was the most resistant species, C. demersum, M. spicatum and E. canadensis exhibited intermediate sensitivities, and A. filiculoides and L. minor were the most sensitive species. In microcosms, community biomass and Shannon evenness index were reduced after 8 weeks at 60 gL−1. Communities also exhibited changes in their composition: the relative and absolute abundance of C. demersum increased at 6 gL−1, while the relative abundance of V. spiralis increased at 60 gL−1. These results are in agreement with the individual responses of these species to the herbicides. It is therefore concluded that short-term effects of herbicides on simple macrophyte communities can be predicted from the sensitivity of individual species. However, further investigations are required to examine whether longer term effects can be predicted as well, especially in more complex communities

Mid-infrared resonant ablation of PMMA

Laser ablation proved to be a reliable micro-fabrication technique for patterning and structuring of both thin film and bulk polymer materials. In most of the industrial applications ultra-violet (UV) laser sources are employed, however they have limitations such as maintenance costs and practical issues. As an alternative and promising approach, mid-infrared resonant laser ablation (RIA) has been introduced, in which the laser wavelength is tuned to one of the molecular vibrational transi-tions of the polymer to be ablated. Consequently, the technique is selective in respect of processing a diversity of polymers which usually have different infrared absorption bands. In this paper, we present mid-infrared resonant ablation of PolyMethyl MethAcrylate (PMMA), employing nanosec-ond laser pulses tunable between 3 and 4 microns. This RIA nanosecond laser set-up is based on a commercial laser at 1064 nm pumping a singly resonant Optical Parametric Oscillator (OPO) built around a Periodically-Poled Lithium Niobate (PPLN) crystal with several Quasi-Phase Matching (QPM) periods. RIA has been successfully demonstrated for structuring bulk PMMA, and selective patterning of PMMA thin films on a glass substrate has been implemented