Higher-order modulation instability in nonlinear fiber optics

We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schr?dinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves.     

Cocroissance Des Groupes A Petite Simplification

Let be a group presented by e₁,...,e_m|r₁,...,r_k, L the freegroup generated by e₁,...,e_m, and N = Ker(L). Let c_n be thenumber of elements of length n in N. We know that c = lim sup(c_n)^1/n exists and that (2m–1) < c 2m – 1. ifN {1}. We prove that if the group satisfies a condition slightlyweaker than the small cancellation condition C^'() with <1/6, then c(2m–1) when the lengths of the relations r_itend to infinity. A consequence of this result is a theoremof Grigorchuk.     

Genealogy of Shocks in Burgers Turbulence¶with White Noise Initial Velocity

As time passes, the shocks of the solution of the inviscid Burgers equation aggregate. We characterize, in the case of white noise initial velocity, the stochastic fragmentation process obtained when time runs backwards. In other words, we specify the law of the genealogy of the shocks of the Burgers turbulence with white noise initial velocity. Received: 5 September 2000 / Accepted: 29 May 2001     

Kinetics and electron spin resonance study of the radical polymerization of n‐butyl acrylate mediated by a nitroxide precursor: C‐phenyl‐N‐tert‐butylnitrone

The C‐phenyl‐N‐tert‐butylnitrone/azobisisobutyronitrile pair is able to impart control to the radical polymerization of n‐butyl acrylate as long as a two‐step process is implemented, that is, the prereaction of the nitrone and the initiator in toluene at 85 °C for 4 h followed by the addition and polymerization of n‐butyl acrylate at 110 °C. The structure of the in situ formed nitroxide has been established from kinetic and electron spin resonance data. The key parameters (the dissociation rate constant, combination rate constant, and equilibrium constant) that govern the process have been evaluated. The equilibrium constant between the dormant and active species is close to 1.6 × 10^?12 mol L^?1 at 110 °C. The dissociation rate constant and the activation energy for the C? ON bond homolysis are 1.9 × 10^?3 s^?1 and 122 ± 15 kJ mol^?1, respectively. The rate constant of recombination between the propagating radical and the nitroxide is as high as 1.2 × 10⁹ L mol^?1 s^?1. Finally, well‐defined poly(n‐butyl acrylate)‐b‐polystyrene block copolymers have been successfully prepared. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6299–6311, 2006     

Influence of another, ruthenium containing, electroactive component on the apparent heterogeneous electron transfer rate constant of a ferrocene containing molecular wire in a Self-Assembled Monolayer of 11-hydroxyundecanethiol on gold

The co-adsorption of three thiol compounds on gold, two of them being electroactive, yields a Self-Assembled Monolayer (SAM) the behaviour of which was studied by impedance spectroscopy. The two redox active thiols have been chosen to have a good miscibility in a supporting inert component, non-degenerate first-oxidation redox couples, and distinct heterogeneous electron transfer rate constant. However, in the ternary monolayer, the slowest process was found to be concentration dependent on the other redox site. This unexpected behaviour should thus be taken into account when using multi-component SAM as a support for integrated devices.     

Alternated π‐conjugated polymers based on a 1,2‐diiminocyclohexane chiral unit for nitroaromatics sensing

The detection of 2,4‐dinitrotoluene (DNT) by fluorescence quenching of a new class of polyimines consisting in π‐conjugated segments regularly alternated with chiral C₂ symmetry units has been studied for solutions and thin films. Their photophysical properties and their sensitivity towards DNT detection has been compared to those of a small model molecule incorporating the same π‐conjugated segment. In solution, all the compounds exhibit the same photo‐physical properties and sensitivity towards DNT detection. In contrast, for thin films, better performances are observed in static conditions for this new class of polyimines compared to the small model molecule. It seems that C₂ symmetry units prevent from the stacking of the π‐conjugated segments and provide in addition to high fluorescence signal an improved diffusion of the analyte inside the films. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4141–4149, 2009     

Relevance of a prereaction for the in situ NMP of styrene using the C‐Phenyl‐N‐tert‐butylnitrone/2,2′‐azobis(isobutyronitrile) pair

In this article, we compare two routes for carrying out in situ nitroxide‐mediated polymerization of styrene using the C‐phenyl‐N‐tert‐butylnitrone (PBN)/2,2′‐azobis(isobutyronitrile) (AIBN) pair to identify the best one for an optimal control. One route consists in adding PBN to the radical polymerization of styrene, while the other approach deals with a prereaction between the nitrone and the free radical initiator prior to the addition of the monomer and the polymerization. The combination of ESR and kinetics studies allowed demonstrating that when the polymerization of styrene is initiated by AIBN in the presence of enough PBN at 110 °C, fast decomposition of AIBN is responsible for the accumulation of dead polymer chains at the early stages of the polymerization, in combination with controlled polystyrene chains. On the other hand, PBN acts as a terminating agent at 70 °C with the formation of a polystyrene end‐capped by an alkoxyamine, which is not labile at this temperature but that can be reactivated and chain‐extended by increasing the temperature. Finally, the radical polymerization of styrene is better controlled when the nitrone/initiator pair is prereacted at 85 °C for 4 h in toluene before styrene is added and polymerized at 110 °C. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1085–1097, 2009     

Biodegradability of sol–gel silica microparticles for drug delivery

The biodegradability of porous sol–gel silica microparticles in physiological buffers has been investigated using a USP4 flow-through dissolution tester. In the open configuration, which most closely models in-vivo conditions, the particles dissolved rapidly at pH 7.4, with a rate dependent on the surface area and media flow rate. In the closed configuration, the fastest dissolving 4 mg silica sample was almost completely dissolved in 100 mL of buffer after 36 h. The initial dissolution rates appeared relatively linear but dropped off as dissolved SiO₂ concentrations approached 20–25 ppm. Addition of serum proteins acted to slow dissolution by 20–30%, suggesting a slower degradation in vivo. Silica microparticles administered for controlled release drug delivery would therefore be expected to be eliminated relatively rapidly from the body, depending on the sample size and local fluid flow conditions.     

The Soave,Twu and Boston–Mathias alpha functions in cubic equations of state. Part II. Modeling of thermodynamic properties of pure compounds

Cubic equations of state (EoS) are commonly used for industrial applications, due to their simplicity in predicting pure compound and mixture thermodynamic properties in vapor and liquid phases. The accuracy of their predictions mainly depends on the choice of the attractive term a(T) and numerous models were developed in literature for this purpose. Among them, the Soave and the Twu models have acquired a wide popularity, as well as the Boston–Mathias model commonly used for supercritical applications. However, most of the works concerned with the comparison of literature attractive terms only focuses on the representation of pure component saturation properties. In particular, the analysis of the respective influence of the EoS and the first and second derivatives of the alpha function on the modeling of enthalpies and heat capacities with respect to temperature and pressure, especially in the supercritical range, was never reported in literature. This is precisely the purpose of the present study.     

Zariski's multiplicity question and aligned singularities

We answer positively Zariski's multiplicity question for special classes of nonisolated singularities. To cite this article: C. Eyral, C. R. Acad. Sci. Paris, Ser. I 342 (2006).