Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation

In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1.     

Thermal noise for SBS suppression in fiber optical parametric amplifiers

We demonstrate a new and simple solution to suppress stimulated Brillouin scattering in fiber optical parametric amplifiers. Cumbersome PRBS or sinusoidal generators used to broaden the pump spectrum are replaced by a filtered microwave noise source. Stimulated Brillouin scattering threshold can be increased up to large values still keeping an excellent quality of amplification of nonreturn to zero signals. The simplicity and the performances of this setup open the way for a wide variety of applications for FOPAs.     

Curvilinear finite-volume schemes using high-order compact interpolation

During the last years, the need of high fidelity simulations on complex geometries for aeroacoustics predictions has grown. Most of high fidelity numerical schemes, in terms of low dissipative and low dispersive effects, lie on finite-difference (FD) approach. But for industrial applications, FD schemes are less robust compared to finite-volume (FV) ones. Thus the present study focuses on the development of a new compact FV scheme for two- and three-dimensional applications.The proposed schemes are formulated in the physical space and not in the computational space as it is the case in most of the known works. Therefore, they are more appropriate for general grids. They are based on compact interpolation to approximate interface-averaged field values using known cell-averaged values. For each interface, the interpolation coefficients are determined by matching Taylor series expansions around the interface center. Two types of schemes can be distinguished. The first one uses only the curvilinear abscissa along a mesh line to derive a sixth-order compact interpolation formulae while the second, more general, uses coordinates in a spatial three-dimensional frame well chosen. This latter is formally sixth-order accurate in a preferred direction almost orthogonal to the interface and at most fourth-order accurate in transversal directions.For non-linear problems, different approaches can be used to keep the high-order scheme. However, in the present paper, a MUSCL-like formulation was sufficient to address the presented test cases.All schemes have been modified to treat multiblock and periodic interfaces in such a way that high-order accuracy, stability, good spectral resolution, conservativeness and low computational costs are guaranteed. This is a first step to insure good scalability of the schemes although parallel performances issues are not addressed. As high frequency waves, badly resolved, could be amplified and then destabilize the scheme, compact filtering operators have been used.Numerous test cases as the linear convection of a Gaussian wave, the convection of a Lamb–Oseen vortex and the diffraction of an acoustic wave on a plane have been realized to validate the schemes. The most efficient schemes are shown to be at least fifth-order accurate on linear and non-linear convection problems. They are also less dissipative and less dispersive on non-uniform curvilinear grids than schemes using implicit interpolation with constant coefficients of the same order on uniform cartesian grids.     

High-gain fiber, optical-parametric, chirped-pulse amplification of femtosecond pulses at 1 μm

Fiber-based optical-parametric chirped-pulse amplification is reported at 1μm in a microstructured fiber in the femtosecond regime. The signal has been highly stretched by an ?ffner triplet and then amplified with an all-fiber, pulsed-pump, fiber optical-parametric amplifier. More than 30dB gain has been achieved over 8.3nm, and the amplified signal has been recompressed.     

Tetrathiafulvalene-triazine-dipyridylamines as multifunctional ligands for electroactive complexes: synthesis, structures, and theoretical study

The electroactive ligands (2,4-bis-tetrathiafulvalene[6-(dipyridin-2'-ylamino)]-1,3,5-triazine) TTF(2)-tz-dpa (1) and (2-tetrathiafulvalene[4,6-bis-(dipyridin-2'-ylamino)]-1,3,5-triazine) TTF-tz-dpa(2) (2) have been synthesized by palladium cross-coupling catalysis, and the single crystal X-ray structure for 1 was determined. In the solid state the TTF and triazine units are practically coplanar and short intermolecular S···S contacts are established. Two neutral and one tetracationic Zn(II) complexes, formulated as (TTF(2)-tz-dpa)ZnCl(2) (3), [ZnCl(2)(TTF-tz-dpa(2))Zn(H(2)O)Cl(2)] (4), and {[(H(2)O)(2)Zn(TTF-tz-dpa(2))](ClO(4))(2)}(2) (5) have been crystallized and analyzed by single crystal X-ray analysis. A peculiar feature is the evidence for anion-π interactions, as shown by the short Cl···triazine and O(perchlorate)···triazine distances of 3.52 and 3.00 ?, respectively. A complex set of intermolecular π···π, S···S, and hydrogen bonding interactions sustain the supramolecular organizations of the complexes in the solid state. Electronic absorption spectra provide evidence for the intramolecular charge transfer from TTF to triazine, also supported by time-dependent density functional theory (TD DFT) calculations.     

ortho-Lithium/magnesium carboxylate-driven aromatic nucleophilic substitution reactions on unprotected naphthoic acids

Substitution of an ortho-fluoro or methoxy group in 1- and 2-naphthoic acids furnishing substituted naphthoic acids occurs in good to excellent yields upon reaction with alkyl/vinyl/aryl organolithium and Grignard reagents, in the absence of a metal catalyst without the need to protect the carboxyl (CO(2)H) group. This novel nucleophilic aromatic substitution is presumed to proceed via a precoordination of the organometallic with the substrate, followed by an addition/elimination.     

Synthesis of a new family of protected 1,4,7,10-tetraazacyclododecane-1,4,7-triacetic acid derivatives with thioctic acid pending arms

The synthesis and characterization of a new family of ester protected N-substituted [1,4,7,10-tetraazacyclododecane-1,4,7-triacetic acid (H3DO3A) derivatives containing a pendant thioctic acid (α lipoic acid, LA) are reported. These compounds (DO3A^tBu-NLA, DO3A^tBu-NMeNLA, and DO3A^tBu-NEtNLA) are suitable for the functionalization of gold surfaces with rare-earth complexes.     

Fluctuations of interacting Markov chain Monte Carlo methods

We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the class of nonlinear Markov chains interacting with their empirical occupation measures. We develop an original theoretical analysis based on resolvent operators and semigroup techniques to analyze the fluctuations of their occupation measures around their limiting values.     

A constraint programming approach for a batch processing problem with non-identical job sizes

This paper presents a constraint programming approach for a batch processing machine on which a finite number of jobs of non-identical sizes must be scheduled. A parallel batch processing machine can process several jobs simultaneously and the objective is to minimize the maximal lateness. The constraint programming formulation proposed relies on the decomposition of the problem into finding an assignment of the jobs to the batches, and then minimizing the lateness of the batches on a single machine. This formulation is enhanced by a new optimization constraint which is based on a relaxed problem and applies cost-based domain filtering techniques. Experimental results demonstrate the efficiency of cost-based domain filtering techniques. Comparisons to other exact approaches clearly show the benefits of the proposed approach: it can optimally solve problems that are one order of magnitude greater than those solved by a mathematical formulation or by a branch-and-price.     

Existence of Solutions for a Fractional Derivative System of Equations

We study a fractional derivative system of equations. A Newton polygonal associated with this system is partially described. Under some additional assumptions, this Newton polygonal is fully described and L ² estimates are given, as well as an existence result. We finally discuss our assumptions.