A New Differential Method Applied to the Study of Arbitrary Cross Section Microstructured Optical Fibers

The present work adapts a recent grating theory called “Fast Fourier factorization” to cylindrical coordinates in order to study microstructured optical fibers (MOFs). Compared with the classical differential method, this new differential method takes into account the truncation of Fourier series and the discontinuities of the fields across the diffracting surface with the help of new factorization rules. The main advantage of this method is that the directrix of the diffracting cylindrical surface is arbitrary and permits anisotropic and inhomogeneous media although its numerical application needs longer computation time, compared with other well-known numerical methods. The S-propagation algorithm is used to avoid numerical contaminations. The numerical results are validated and compared with the well-established Multipole method in the case of a MOF with six circular cylinders. Further, a new cross-sectional profile (with sectorial inclusions) that the Multipole method cannot consider is studied.     

Free energy of the spherical mean field model

We compute at any temperature the free energy of the multi p-spin spherical model when only terms for p even are considered. Work partially supported by an NSF grant     

Continuity properties of the normal cone to the level sets of a quasiconvex function

Two main properties of the subgradient mapping of convex functions are transposed for quasiconvex ones. The continuity of the functionxf(x)^–1f(x) on the domain where it is defined is deduced from some continuity properties of the normal coneN to the level sets of the quasiconvex functionf. We also prove that, under a pseudoconvexity-type condition, the normal coneN(x) to the set {x:f(x)f(x)} can be expressed as the convex hull of the limits of type {N(x _n)}, where {x _n} is a sequence converging tox and contained in a dense subsetD. In particular, whenf is pseudoconvex,D can be taken equal to the set of points wheref is differentiable.This research was completed while the second author was on a sabbatical leave at the University of Montreal and was supported by a NSERC grant. It has its origin in the doctoral thesis of the first author (Ref. 1), prepared under the direction of the second author.The authors are grateful to an anonymous referee and C. Zalinescu for their helpful remarks on a previous version of this paper.     

Study of the reactione + e −→K + K − in the energy range1350 \leqq \sqrt s \leqq 2400 MeV

Thee ⁺ e ^?→K ⁺ K ^? cross section has been measured from about 750 events in the energy interval \(1350 \leqq \sqrt s \leqq 2400 MeV\) with the DM2 detector at DCI. TheK ^± form factor |F _F ^±| cannot be explained by the ρ, ω, ? and ρ′(1600). An additional resonant amplitude at 1650 MeV has to be added as suggested by a previous experiment.     

Group additive values for the gas phase standard enthalpy of formation of hydrocarbons and hydrocarbon radicals

A complete and consistent set of 95 Benson group additive values (GAV) for the standard enthalpy of formation of hydrocarbons and hydrocarbon radicals at 298 K and 1 bar is derived from an extensive and accurate database of 233 ab initio standard enthalpies of formation, calculated at the CBS-QB3 level of theory. The accuracy of the database was further improved by adding newly determined bond additive corrections (BAC) to the CBS-QB3 enthalpies. The mean absolute deviation (MAD) for a training set of 51 hydrocarbons is better than 2 kJ mol(-1). GAVs for 16 hydrocarbon groups, i.e., C(C(d))(3)(C), C-(C(d))(4), C-(C(t))(C(d))(C)(2), C-(C(t))(C(d))(2)(C), C-(C(t))(C(d))(3), C-(C(t))(2)(C)(2), C-(C(t))(2)(C(d))(C), C-(C(t))(2)(C(d))(2), C-(C(t))(3)(C), C-(C(t))(3)(C(d)), C-(C(t))(4), C-(C(b))(C(d))(C)(H), C-(C(b))(C(t))(H)(2), C-(C(b))(C(t))(C)(H), C-(C(b))(C(t))(C)(2), C(d)-(C(b))(C(t)), for 25 hydrocarbon radical groups, and several ring strain corrections (RSC) are determined for the first time. The new parameters significantly extend the applicability of Benson's group additivity method. The extensive database allowed an evaluation of previously proposed methods to account for non-next-nearest neighbor interactions (NNI). Here, a novel consistent scheme is proposed to account for NNIs in radicals. In addition, hydrogen bond increments (HBI) are determined for the calculation of radical standard enthalpies of formation. In particular for resonance stabilized radicals, the HBI method provides an improvement over Benson's group additivity method.     

The crystal structure of bis(triphenylphosphine)-(η-cyclohexa-1,3-diene)rhenium trihydride

Bis(triphenylphosphine)(η-cyclohexa-1,3-diene)rhenium trihydride, (Ph₃P)₂(η-C₆H₈)ReH₃ (I) crystallises in the space group C2/c with cell dimensions a 22.76(2), b 10.14(1) c 29.813(6) Å, β 97.69(8)°. The final refinement of 126 variables using 1580 non-zero reflections resulted in a final R value of 0.064. In spite of uncertainties in some of the atomic positions, the structure of I is compatible with a trihydrido diene compound with a distorted pentagonal bipyramidal configuration, rather than with a dihydrido cyclohexenyl compound having an “agostic” CH ? Re interaction. The factors which govern the structure of the complexes (Ph₃P)₂(η-1,3-diene)ReH₃ are discussed.     

Poly(vinyl chloride) stabilization with organo-tin compounds: Part VI—The behavior of dibutyltin dilaurate

The reaction between dibutyltin dilaurate (DBTL) and chloro-4-hexene-2 (containing its isomer chloro-2-hexene-3) as a model compound for the allylic chlorine atom in poly(vinyl chloride) has been studied in dichlorobutane solution at 80°C. The reactions observed—elimination of HCl to give hexadiene and substitution of the laurate group to give hexenyl laurate—are believed to obey E2 and SN2 mechanisms through a common intermediate carbocation, with a rather low selectivity towards the substitution owing to the associated structure of the DBTL. The kinetics are complex because of the complex nature of the exchange reaction between DBTL and Bu₂SnCl₂. A reverse reaction between the hexenyl laurate and the organo-tin chloride is proposed to explain the limitation of the substitution reaction.     

Lamellar Organo-Bridged Silicones

The acid-hydrolysis of an organo-bridged bisdiethoxysilylated molecular precursor bearing urea groups, (EtO)₂MeSi(CH₂)₃NHCONH(CH₂)₁₂NHCONH(CH₂)₃SiMe(OEt)₂, has been performed in pure aqueous medium. Scanning electron microscopy (SEM) analysis of the resulting insoluble solid revealed plate-like forms with a lamellar structure as determined by powder X-ray diffraction (PXRD) studies with a sharp peak at 28.5 Å. The solid state ²⁹Si MAS-NMR spectrum of this bridged siloxane hybrid is consistent with a moderately condensed material with complete preservation of the Si–C bonds throughout the hybrid network. In comparison, the classical sol–gel hydrolysis-condensation of the molecular precursor in ethanol with stoichiometric amount of water and fluoride anion as catalyst produced an amorphous featureless solid.