Reflectometric measurements of polarization properties in optical-fiber links

Polarization sensitive reflectometric techniques can be effectively used to perform spatially resolved measurements of polarization properties of fiber optic link — such as birefringence, polarization mode dispersion and polarization dependent loss. In particular, this contribution is focused on polarization sensitive OTDR and provides a survey of its theory and main applications. Special emphasis is given to the characterization of fiber birefringence, that allows to inspect the fiber while cabled and, consequently, to test and improve the cabling process. In addition, the analysis of the birefringence also allows to define reliable mathematical models, which are essential for the design of low polarization mode dispersion fibers. Reflectometric measurements of polarization mode dispersion and polarization dependent loss are also discussed.     

Biotransformation of arsenate to arsenosugars by Chlorella vulgaris

Chlorella vulgaris was cultivated in a growth medium containing arsenate concentration of <0.01, 10, 100 and 1000 mg l^?1. Illumination was carried out in 12 h cycles for 5 days. The health status of the culture was monitored by continuous pH and dissolved oxygen (DO) readings. Destructive sampling was used for the determination of biomass, chlorophyll, total arsenic and arsenic species. The chlorophyll a content, the DO and pH cycles were not significantly different for the different arsenate concentrations in the culture. In contrast, biomass production was significantly (p < 0.05) increased for the arsenic(V) treatment at 1000 mg l^?1 compared with 100 mg l^?1. The arsenic concentration in the algae increased with the arsenate concentration in the culture. However, the bioconcentration factor decreased a hundred‐fold with increase of arsenate from the background level to 1000 mg l^?1. The arsenic species were identified by using strong anion‐exchange high‐performance liquid chromatography–inductively coupled plasma mass spectrometry analysis after methanol/water (1 : 1) extraction. The majority (87–100%) of the extractable arsenic was still arsenate; arsenite was found to be between 1 and 6% of total extractable arsenic in the algae. In addition to dimethylarsinic acid, one unknown arsenical (almost co‐eluting with methylarsonic acid) and three different arsenosugars have been identified for the first time in C. vulgaris growing in a culture containing a mixture of antibiotics and believed to be axenic. The transformation to arsenosugars in the algae is not dependent on the arsenate concentration in the culture and varies between 0.2 and 5% of total accumulated arsenic. Although no microbiological tests for bacterial contamination were made, this study supports the hypothesis that algae, and not associated bacteria, produce the arsenosugars. Copyright © 2003 John Wiley & Sons, Ltd.     

New π‐stacked benzofulvene polymer showing thermoreversible polymerization: Studies in macromolecular and aggregate structures and polymerization mechanism

The macromolecular and aggregate structures of poly[ethyl 1‐methylene‐3‐(4‐methylphenyl)‐1H‐indene‐2‐carboxylate] (poly‐ BF1 ; a new polymer based on a functionalized benzofulvene moiety showing interesting properties, i.e., thermoreversible polymerization/depolymerization behavior, high solubility in the most common organic solvents, and susceptibility to molecular manipulation) have been investigated with NMR spectroscopy, absorption and emission spectrophotometry, and transmission electron microscopy (TEM). Moreover, the polymerization mechanism has been studied to obtain further information on the polymer structure. The collected evidence is consistent in indicating for poly‐ BF1 a vinyl (1,2) polymer structure stabilized by means of aromatic stacking interactions. Furthermore, TEM studies performed on metal replicas have shown that the polymer is liable to give nanostructured aggregates. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3289–3304, 2005     

Modular invariant partition functions in the quantum Hall effect

We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it is invariant under modular transformations of the toroidal geometry made by the angular variable and the compact Euclidean time. The Jain series of plateaus have been described by two types of edge theories: the minimal models of the W_1+∞ algebra of quantum area-preserving diffeomorphisms, and their non-minimal version, the theories with affine algebra. We find modular invariant partition functions for the latter models. Moreover, we relate the Wen topological order to the modular transformations and the Verlinde fusion algebra. We find new, non-diagonal modular invariants which describe edge theories with extended symmetry algebra; their Hall conductivities match the experimental values beyond the Jain series.     

On the effects of an uncertainty on the evolution law in dynamical systems

We show that a small perturbation of the evolution law of chaotic dynamical systems is practically equivalent to the finite precision on the knowledge of the initial condition. In spite of the short predictability time t_p on a single trajectory we found that the statistical properties are not sensitive to small changes in the evolution law or initial probability distribution. This feature holds also for correlation functions at a delay larger than t_p. We discuss the roundoff effects on integrable systems.     

A Laplace integral on a Kähler manifold and Calabi's diastasis function

In this paper we give a different proof of Engliš's result [J. Reine Angew. Math. 528 (2000) 1-39] about the asymptotic expansion of a Laplace integral on a real analytic Kähler manifold (M,g) by using the link between the metric g and the associated Calabi's diastasis function D. We also make explicit the connection between the coefficients of Engliš' expansion and Gray's invariants [Michigan Math. J. (1973) 329-344].     

Numerical aspects of TV flow

The singular diffusion equation called total variation (TV) flow plays an important role in image processing and appears to be suitable for reducing oscillations in other types of data. Due to its singularity for zero gradients, numerical discretizations have to be chosen with care. We discuss different ways to implement TV flow numerically, and we show that a number of discrete versions of this equation may introduce oscillations such that the scheme is in general not TV-decreasing. On the other hand, we show that TV flow may act self-stabilising: even if the total variation increases by the filtering process, the resulting oscillations remain bounded by a constant that is proportional to the ratio of mesh widths. For our analysis we restrict ourselves to the one-dimensional setting.