A principle of images for absorbing boundary conditions

When one uses high-order finite difference schemes for the wave equation, for instance fourth order schemes, the treatment of boundary conditions poses a real difficulty since one needs several additional equations (for the nodes close to the boundary), while one single scalar boundary condition is available. In the case of perfectly reflecting boundary conditions, namely the homogeneous Neumann or Dirichlet conditions, this difficulty can be overcomed by the use of the well-known image principle, which permits the extension of the equation outside of the domain of calculation by an appropriate symmetrization of the data. We propose in this article a generalization of this principle to the absorbing boundary conditions. Through a symmetrization process, we are led to introduce a damped wave equation with a damping term supported by the boundary. The treatment of the boundary condition is then replaced by the approximation of this new damped wave equation in the whole space. The theoretical justification of our approach is based on new energy estimates for the wave equation (when high-order absorbing boundary conditions are used), and constitutes an alternative to the use of the well-known Kreiss criterion to prove the stability of the associated initial boundary value problems. © 1994 John Wiley & Sons, Inc.     

Istope effects in aromatization of 1,4-dihydrobenzene and 1,4-dihydronaphthalene with quinones

Aromatization of 1,4-dihydronaphthalene with 2,3-dichloro-5,6-p-benzoquinone or chloranil is accompanied with kinetic isotope effects of 9.9 and 8.0 respectively.     

Measurement of compound-nucleus lifetime by X-ray spectroscopy in the 106Cd(p,p')106Cd reaction

A new method for measuring compound-nucleus lifetimes in the range of 10^?18–10^?16 s is presented. The method is based on the comparison between the known lifetime of an atomic excited state used as a reference and the nuclear delay time to be measured. On-line coincidences performed between the nuclear reaction products and the emitted X-rays enable the selection of the atomic vacancies decaying during the compound stage of the nuclear interaction. The main characteristics of this technique are illustrated by measurements of lifetimes of the ¹⁰⁷In compound nucleus excited at 13.6 and 15.6 MeV in the ¹⁰⁶Cd(p, p')¹⁰⁶Cd reaction. They are found in agreement with statistical model calculations. The spurious effect associated with decay by internal conversion of final states populated by the competitive (p, n) reaction is emphasized.     

The lowest five levels of 25Na: Lifetime,spin and transition strength measurements

Particle-gamma angular correlations and lifetime measurements (delayed coincidences and DSAM) have been performed in the ²⁶Mg(t, α)²⁵Na reaction. The results for J^π (and τ_m) are $\text{3}\text{2}{}^{\mathrm{+}}\text{or}\text{5}\text{2}{}^{\mathrm{+}}\text{(7.4±0.4}\text{ns}\text{),}\text{1}\text{2}{}^{\mathrm{+}}\text{(2.3}{}_{\mathrm{?0.8}}{}^{\mathrm{+2.0}}\text{ps}\text{),}\text{3}\text{2}{}^{\mathrm{+}}\text{(<25}\text{fs}\text{),}\text{7}\text{2}{}^{\mathrm{+}}\text{(200±140}\text{fs}\text{)}\text{and}\text{3}\text{2}\text{or}\text{7}\text{2}$ for the levels at 90, 1069, 2202, 2417 and 2788 keV respectively. Branching and mixing ratios have been measured, and strengths of the transitions calculated. Evidence for configuration mixing is given. The results are compared with shell-model calculations.     

Olefin metathesis applied to cellulose derivatives—Synthesis,analysis, and properties of new crosslinked cellulose plastic films

New crosslinked cellulose‐based plastic films were synthesized with olefin metathesis as a crosslinking reaction. Microcrystalline cellulose was first dissolved in a lithium chloride/N,N‐dimethylacetamide solvent system and acylated by ω‐undecenoyl chloride under microwave irradiation with N,N‐dimethyl‐4‐aminopyridine as the catalyst. Cellulose unsaturated fatty acyl esters with a degree of substitution (DS) ranging from 1.4 to 2.0 were then crosslinked by olefin metathesis with a first generation Grubbs catalyst. Crosslinking ratios (T) ranging from 20 to 90% were obtained for low catalyst amounts (<1.2%), but gels appeared when T was too high. To avoid this gel formation, cellulose was acylated with a mixture of lauroyl and ω‐undecenoyl chlorides. This internal dilution allowed us to obtain films of every case and various T (varying from 10 to 80% for a catalyst amount below 3.5%). Plastics were characterized by Fourier transform infrared (FTIR) spectroscopy, and the fatty acid mixture resulting from the hydrolysis of cellulose esters were analyzed by gas chromatography (GC) and NMR spectroscopy. Mechanical properties showed that the elastic modulus and tensile failure stress was higher when the plastic films were crosslinked. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 407–418, 2005     

Synthesis of novel 5,7‐disubstituted 8‐hydroxyquinolines

Seven new 5,7‐disubstituted oxine derivatives have been synthesized via a Mannich reaction between a sec. amine (e.g. piperidine, pyrrolidine, morpholine, or dibenzylamine,) and 5‐cyano or 5‐azidomethyl‐8‐hydroxyquinoline, which were respectively obtained by nucleophilic displacement of 5‐chloromethyl‐8‐hydroxyquinoline by cyanide or azide anions. In all cases, a single product was isolated in medium to fair yield and characterized on the basis of ¹H and ¹³C‐NMR, MS and IR spectrometric data. The X‐ray structure of the product obtained from 5‐cyanomethyl‐8‐hydroxyquinoline and piperidine is also reported.     

Structural determination of the novel fragmentation routes of zwitteronic morphine opiate antagonists naloxonazine and naloxone hydrochlorides using electrospray ionization tandem mass spectrometry

Electrospray ionization quadrupole time-of-flight (ESI-QqToF) mass spectra of the zwitteronic salts naloxonazine dihydrochloride 1 and naloxone hydrochloride 2, a common series of morphine opiate receptor antagonists, were recorded using different declustering potentials. The singly charged ion [M+H-2HCl](+) at m/z 651.3170 and the doubly charged ion [M+2H-2HCl](2+) at m/z 326.1700 were noted for naloxonazine dihydrochloride 1; and the singly charged ion [M+H-HCl](+) at m/z 328.1541 was observed for naloxone hydrochloride 2. Low-energy collision-induced dissociation tandem mass spectrometry (CID-MS/MS) experiments established the fragmentation routes of these compounds. In addition to the characteristic diagnostic product ions obtained, we noticed the formation of a series of radical product ions for the zwitteronic compounds 1 and 2, and also the formation of a distonic ion product formed from the singly charged ion [M+H-HCl](+) of naloxone hydrochloride 2. Confirmation of the various established fragmentation routes was effected by conducting a series of ESI-CID-QqTof-MS/MS product ion scans, which were initiated by CID in the atmospheric pressure/vacuum interface using a higher declustering potential. Deuterium labeling was also performed on the zwitteronic salts 1 and 2, in which the hydrogen atoms of the OH and NH groups were exchanged with deuterium atoms. Low-energy CID-QqTof-MS/MS product ion scans of the singly charged and doubly charged deuteriated molecules confirmed the initial fragmentation patterns proposed for the protonated molecules. Precursor ion scan analyses were also performed with a conventional quadrupole-hexapole-quadrupole tandem mass spectrometer and allowed the confirmation of the genesis of some diagnostic ions.     

Specific UV photodissociation of tyrosyl-containing peptides in multistage mass spectrometry

UV photodissociation (UVPD) at 262 nm has been carried out on protonated tyrosyl-containing peptides formed by trypsin digestion of apo-transferrin. Under UVPD, the main event is the fragmentation of the C(alpha)-C(beta) bond of the tyrosyl residues leading to a radical ion 107 Da below the precursor ion. The dissociation rate of this specific cleavage appears to be strongly dependent on the peptide sequence and is more prominent on the singly protonated species than on the doubly protonated state. The fragmentation spectra resulting from collisional activation of the protonated even-electron native peptides and of the odd-electron radical species prepared by UVPD are dominated by y-type backbone cleavages. A comparison of their respective y-ion pattern shows complementarities since the combination of both increases the sequence coverage of the peptide sequence. The specific detection of the neutral loss of 107 Da from peptides witnesses the content of at least one tyrosyl residue and, though preliminary, is proposed as a potential new filtering strategy during protein database searching.     

Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part I: Generalized Fourier transform

We explore the spectral properties of the time-dependent Maxwell’s equations for a plane interface between a metamaterial represented by the Drude model and the vacuum, which fill, respectively, complementary half-spaces. We construct explicitly a generalized Fourier transform which diagonalizes the Hamiltonian that describes the propagation of transverse electric waves. This transform appears as an operator of decomposition on a family of generalized eigenfunctions of the problem. It will be used in a forthcoming paper to prove both limiting absorption and limiting amplitude principles.     

Self-induced pressure shift and temperature dependence measurements of CO2 at 2.05μm with a tunable diode laser spectrometer

By using a high resolution tunable diode laser absorption spectrometer combined with a cryogenically cooled optical multi-pass cell, we have measured the self-induced pressure shift coefficients for 8 transitions in the R branch of the (20(0)1)(III)←(00(0)0)(I) band of carbon dioxide around 2.05μm. This spectral region is of particular interest for the monitoring of atmospheric CO(2) with Differential Absorption Lidars (DiAL). The measurement of these shift coefficients was realized at five different temperatures ranging from 218 to 292K in order to determine their temperature dependence. The results are thoroughly compared to previous values reported in the literature for the (20(0)1)(III)←(00(0)0)(I) band of CO(2). The temperature dependence of the self-induced pressure shifts are reported experimentally for the first time for this specific CO(2) band.