CW-pumped polarization-maintaining Brillouin fiber ring laser: I. Self-structuration of Brillouin solitons

Stimulated Brillouin scattering (SBS) of a cw-pump in a long optical fiber ring cavity generates for a given gain G, below a critical feedback R_crit, a backward soliton Stokes pulse at the roundtrip repetition rate, through resonant three-wave interaction between the optical pump wave and backward Stokes wave, and a high frequency (GHz) axial acoustic wave. In Part I, we perform a systematic experimental and numerical exploration of the whole soliton localisation domain for a large set of (G, R) parameters, in a polarization-maintaining Brillouin fiber ring laser in the best conditions of stability and coherence, and we confirm the excellent quantitative agreement of the coherent three-wave model and the experiments.     

Discovery of a herbicidal lead using polymer-bound activated esters in generating a combinatorial library of amides and esters

Summary A combinatorial library containing mixtures of amides and esters was prepared through solid-phase chemistry. The advantages of using solid-phase chemistry over solution-phase chemistry to prepare this library are discussed. The library was screened through a high-throughput whole organism herbicidal assay upon which a mixture containing amides was found to have herbicidal activity. Deconvolution of the mixture providedN-(3-benzoylphenyl)-3-(1,1-dimethylethyl)-1-methyl)-1H-pyrazole-5-carboxamide as a herbicidal lead with broadleaf and narrowleaf pre-emergence herbicidal activity as low as 100 g/ha on some weed species. This study represents the first report of an agrochemical discovered using a combinatorial approach. Supplementary Material, comprising experimental procedures for the preparation of resin II and the reaction of II with nucleophiles, GC/MS and LC/MS data for the reaction ofII with morpholine, and a detailed experimental for the preparation of 2 with characterization data, is available upon request.     

The Millimeter-Wave Spectrum of 2,3-Dihydrofuran

The millimeter-wave spectrum of 2,3-dihydrofuran in the ground and five ring-puckering excited states has been measured in the frequency range 100–250 GHz. The ground and first ring-puckering excited states have been fitted to a two-state Hamiltonian including Coriolis coupling interaction. The determined energy difference of 18.684(7) cm⁻¹between these states and theaandbtype coupling parameters are consistent with the ring-puckering potential function and the previously observed dependence of the centrifugal distortion constants Δ_JK, Δ_K, and δ_K. A small ring-puckering dependence of the quartic centrifugal distortion constants Δ_Jand δ_Jhas been also observed. This dependence is well accounted for in terms of the ring-puckering potential function and the vibrational dependence of the rotational constants.     

Invariant measures for the2D-defocusing nonlinear Schrödinger equation

Consider the2D defocusing cubic NLSiu _t+u–u|u|²=0 with Hamiltonian . It is shown that the Gibbs measure constructed from the Wick ordered Hamiltonian, i.e. replacing ||⁴ by ||⁴ :, is an invariant measure for the appropriately modified equationiu _t + u‒ [u|u ²–2(|u|² dx)u]=0. There is a well defined flow on thesupport of the measure. In fact, it is shown that for almost all data the solutionu, u(0)=, satisfiesu(t)–e ^it C _Hs (), for somes>0. First a result local in time is established and next measure invariance considerations are used to extend the local result to a global one (cf. [B2]).     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

Magnetic discontinuities in magnetohydrodynamic turbulence and in the solar wind

Recent measurements of solar wind turbulence report the presence of intermittent, exponentially distributed angular discontinuities in the magnetic field. In this Letter, we study whether such discontinuities can be produced by magnetohydrodynamic (MHD) turbulence. We detect the discontinuities by measuring the fluctuations of the magnetic field direction, Δθ, across fixed spatial increments Δx in direct numerical simulations of MHD turbulence with an imposed uniform guide field B(0). A large region of the probability density function (pdf) for Δθ is found to follow an exponential decay, proportional to exp(-Δθ/θ(*)), with characteristic angle θ(*)≈(14°)(b(rms)/B(0))(0.65) for a broad range of guide-field strengths. We find that discontinuities observed in the solar wind can be reproduced by MHD turbulence with reasonable ratios of b(rms)/B(0). We also observe an excess of small angular discontinuities when Δx becomes small, possibly indicating an increasing statistical significance of dissipation-scale structures. The structure of the pdf in this case closely resembles the two-population pdf seen in the solar wind. We thus propose that strong discontinuities are associated with inertial-range MHD turbulence, while weak discontinuities emerge from dissipation-range turbulence. In addition, we find that the structure functions of the magnetic field direction exhibit anomalous scaling exponents, which indicates the existence of intermittent structures.     

DESIRS: a state‐of‐the‐art VUV beamline featuring high resolution and variable polarization for spectroscopy and dichroism at SOLEIL

DESIRS is a new undulator‐based VUV beamline on the 2.75 GeV storage ring SOLEIL (France) optimized for gas‐phase studies of molecular and electronic structures, reactivity and polarization‐dependent photodynamics on model or actual systems encountered in the universe, atmosphere and biosphere. It is equipped with two dedicated endstations: a VUV Fourier‐transform spectrometer (FTS) for ultra‐high‐resolution absorption spectroscopy (resolving power up to 10⁶) and an electron/ion imaging coincidence spectrometer. The photon characteristics necessary to fulfill its scientific mission are: high flux in the 5–40 eV range, high spectral purity, high resolution, and variable and well calibrated polarizations. The photon source is a 10 m‐long pure electromagnetic variable‐polarization undulator producing light from the very near UV up to 40 eV on the fundamental emission with tailored elliptical polarization allowing fully calibrated quasi‐perfect horizontal, vertical and circular polarizations, as measured with an in situ VUV polarimeter with absolute polarization rates close to unity, to be obtained at the sample location. The optical design includes a beam waist allowing the implementation of a gas filter to suppress the undulator high harmonics. This harmonic‐free radiation can be steered toward the FTS for absorption experiments, or go through a highly efficient pre‐focusing optical system, based on a toroidal mirror and a reflective corrector plate similar to a Schmidt plate. The synchrotron radiation then enters a 6.65 m Eagle off‐plane normal‐incidence monochromator equipped with four gratings with different groove densities, from 200 to 4300 lines mm^?1, allowing the flux‐to‐resolution trade‐off to be smoothly adjusted. The measured ultimate instrumental resolving powers are 124000 (174 µeV) around 21 eV and 250000 (54 µeV) around 13 eV, while the typical measured flux is in the 10¹⁰–10¹¹ photons s^?1 range in a 1/50000 bandwidth, and 10¹²–10¹³ photons s^?1 in a 1/1000 bandwidth, which is very satisfactory although slightly below optical simulations. All of these features make DESIRS a state‐of‐the‐art VUV beamline for spectroscopy and dichroism open to a broad scientific community.     

Un théorème de représentation pour les martingales discontinues

We consider a fixed integer-valued random measure (also called a random point process). We represent any local martingale as the sum of a stochastic integral with respect to this random measure, and of a local martingale which does not jump on the support of the random measure.     

Some geometric aspects of the calculus of fractions

We give necessary and sufficient conditions on class S of maps of a category C so that a good calculus of fractions is possible in C[S ^-1], and a geometric characterization of the communitative diagrams in the category of fractions. These conditions are also described simply in terms of Grothendiek topologies.We characterize the categories which arise in this manner by the fact that the functor C C[S ^-1] is uniformly flat and give some applications of this result.