Bending loss measurement using a fiber cavity ringdown scheme

A novel sensitive technique for the determination of losses in fiber cavities is presented. The method is based on the cavity ringdown scheme implemented in silica-based single-mode fibers. Bending losses of fiber cavities of different lengths have been measured showing all an oscillating behavior with respect to the curvature radius of the fiber as predicted by a theoretical model. The best minimum detectable absorbance per cavity pass achieved by this new method is 1.72×10⁻³ dB within a 10 m-long cavity. This limit suffices well for an accurate determination of optical bending losses even in bend-insensitive fibers. Furthermore, the comparison of the measured bending losses with a theoretical model allows the extraction of different fiber parameters. Good agreement has been found between the experimentally derived parameters and literature data.     

Une note sur les lemmes div–curl

Let $\text{Ω}$ be a strongly Lipschitz domain of $\text{R}{}^{\mathrm{n}}$ (n?2). We give endpoint versions of div–curl lemmata on $\text{Ω}$, for a given function f on $\text{Ω}$ whose gradient belongs to a Hardy space on $\text{Ω}$. To cite this article: P. Auscher et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

tert‐Butyl (6S)‐4‐hydroxy‐6‐isobutyl‐2‐oxo‐1,2,5,6‐tetra­hydropyridine‐1‐carboxyl­ate and tert‐butyl (4R,6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxopiperidine‐1‐carboxyl­ate

X‐ray studies reveal that tert‐butyl (6S)‐6‐iso­butyl‐2,4‐dioxo­piperidine‐1‐carboxyl­ate occurs in the 4‐enol form, viz. tert‐butyl (6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxo‐1,2,5,6‐tetra­hydropyri­dine‐1‐carboxyl­ate, C₁₄H₂₃NO₄, when crystals are grown from a mixture of di­chloro­methane and pentane, and has an axial orientation of the iso­butyl side chain at the 6‐position of the piperidine ring. Reduction of the keto functionality leads predominantly to the corresponding β‐hydroxy­lated δ‐lactam, tert‐butyl (4R,6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxo­piperidine‐1‐car­boxyl­ate, C₁₄H₂₅NO₄, with a cis configuration of the 4‐hydroxy and 6‐iso­butyl groups. The two compounds show similar molecular packing driven by strong O—H⋯O=C hydrogen bonds, leading to infinite chains in the crystal structure.     

The Spirit Is Willing: Nonlinearity, Bifurcations, and Mental Control

In recent years there has been considerable interest in the construction of nonlinear models of the dynamics of human behavior. In this exploratory article we argue that attempts at controlling problematic thoughts, emotions, or behaviors can lead to nonlinearity in mental/behavioral dynamics. We illustrate our model by fitting threshold autoregression models to self-recorded time series of the daily highs in intensity of anxiety and obsessive ruminations, kept by an individual in therapy for this problem. In our discussion, we raise the possibility that bifurcations that occur in this nonlinear model may offer insight into mental control paradoxes.     

Influence de la longue mémoire sur le comportement asymptotique d'estimateurs fonctionnelsInfluence of long memory on the asymptotic behaviour of functional estimators

This Note gives asymptotic results for kernel estimators of several functionals (density, failure rate and distribution functions) of a long-memory process. The results are presented in such a way as to highlight the influence of the long dependence on the rates of convergence. To cite this article: G. Estevez-Perez, P. Vieu, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 271–274.     

Comprehensive study on the formation of polyelectrolyte complexes from (quaternized) poly[2‐(dimethylamino)ethyl methacrylate] and poly(2‐acrylamido‐2‐methylpropane sodium sulfonate)

Polyelectrolyte complexes (PECs) have been prepared from well‐defined (quaternized) poly[2‐(dimethylamino)ethyl methacrylate] (PDMAEMA) and high molecular weight poly(2‐acrylamido‐2‐methylpropane sodium sulfonate) (PAMPSNa) after a thorough study of their viscometric properties. The effect of pH and quaternization degree of PDMAEMA on PECs stoichiometry has been examined. PEC‐based materials have been characterized in terms of thermal stability, equilibrium swelling degree, and free/bound water composition. The stoichiometry and swellability of the physically crosslinked hydrogels obtained from fully quaternized PDMAEMA/PAMPSNa complexes do not depend on pH. In contrast, PECs made of non quaternized PDMAEMA and PAMPSNa are highly affected by pH, and could reversibly disintegrate at pH ≥ 9. Partially quaternized PDMAEMA/PAMPSNa PECs exhibit intermediate properties and form stable loose structures in the whole investigated pH range. Finally, stable dispersions of PECs nanoparticles have been successfully produced from dilute solutions of the complementary polyelectrolytes. The nanoparticle average diameter as determined by dynamic light scattering proved to depend on the molar fraction of DMAEMA‐based subunits and on the initial polyelectrolyte concentration. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5468–5479, 2006     

Soluble models for dynamics driven by a super-diffusive noise

We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given.     

Bell's theorem based on a generalized EPR criterion of reality

First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedankenexperiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almostwith certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future.