Digital in-line holography with a sub-picosecond laser beam

The diffraction of an ultrashort pulsed laser beam by an opaque particle is studied. The case of a pulse with a Gaussian spectrum is investigated analytically by using the steepest descent method. This analytical solution allows us to calculate the intensity distribution of the diffraction field. This result enables to determine the optimal fractional orders Fourier transform to reconstruct digital in-line particle hologram.     

A theoretical study of saturated sp nitrogen rings

Ab initio calculations on molecular structures composed of hexagonal rings of sp³-hybridated nitrogen atoms (the external nitrogen atoms being saturated with hydrogens) are presented. All the studied systems are local minima on the potential energy surface, and dissociate producing nitrogen dimer and ammonia in different proportions. A periodic Hartree–Fock study of the infinite layer is also presented, and it is shown that the molecular structural parameters quickly converge towards the infinite-system values. Accordingly to the computed dissociation energies, these systems have a very high energy content.     

On the evaluation of some differential formulations for the pom-pom constitutive model

In recent years, progress has been made in modelling long chain branched polymers by the introduction of the so-called pom-pom model. Initially developed by McLeish and Larson (1998), the model has undergone several improvements or alterations, leading to the development of new formulations. Some of these formulations however suffer from certain mathematical defects. The purpose of the present paper is to review some of the formulations of the pom-pom constitutive model, and to investigate their possible mathematical defects. Next, an alternative formulation is proposed, which does not appear to exhibit mathematical defects, and we explore its modelling performance by comparing the predictions with experiments in non-trivial rheometric flows of an LDPE melt. The selected rheometric flows are the double step strain, as well as the large amplitude oscillatory shear experiments. For LAOS experiments, the comparison involves the use of Fourier-transform analysis.     

Application of a 1H δ‐resolved 2D NMR experiment to the visualization of enantiomers in chiral environment,using sample spatial encoding and selective echoes

We present the application of a 2D broadband homodecoupled proton NMR experiment to the visualization of enantiomers. In a chiral environment, the existence of diastereoisomeric intermolecular interactions can yield—generally slight—variations of proton chemical shifts from one enantiomer to another. We show that this approach, which relies on a spatial encoding of the NMR sample, is particularly well suited to the analysis of enantiomeric mixtures, since it allows, within one single 2D experiment, to detect subtle chemical shift differences between enantiomers, even in the presence of several couplings. This sequence, which uses semiselective radio‐frequency (rf) pulses combined to a z‐field gradient pulse, produces different selective echoes in various parts of the sample. The resulting homonuclear decoupling provides an original δ‐resolved spectrum along the diagonal of the 2D map where it becomes possible to probe the chiral differentiation process through every proton site where the resulting variation in the chemical shift is detectable. We discuss the advantages and drawbacks of this approach, regarding other experiments which provide homodecoupled proton spectra. This methodology is applied to the observation of enantiomers of (1) ( ± )2‐methyl‐isoborneol coordinated to europium (III) tris[3‐(trifluoromethyl‐hydroxymethylene)‐(+)‐camphorate] in isotropic solution, and (2) ( ± )3‐butyn‐2‐ol dissolved in a chiral liquid‐crystal solvent, in order to show the robustness of this pulse sequence for a wide range of chiral samples. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

A new lower bound on the strong connectivity of an oriented graph. Application to diameters with a particular case related to Caccetta Häggkvist conjecture

In this paper, by using minimum out-degree and minimum in-degree, we give a new lower bound on the vertex-strong connectivity of an oriented graph. In the case of a tournament, our lower bound improves that of Thomassen obtained in 1980 and which use the notion of irregularity (see [C. Thomassen, Hamiltonian-connected tournaments, J. Combin. Theory Ser. B 28 (1980) 142–163]). As application, we determine a pertinent upper bound on the diameter of some oriented graphs, and in a particular case, related to Caccetta Häggkvist conjecture, we improve a result of Broersma and Li obtained in 2002 (see [H.J. Broersma, X. Li, Some approaches to a conjecture on short cycles in digraphs, Discrete Appl. Math. 120 (2002) 45–53]).     

Random data Cauchy theory for supercritical wave equations I: local theory

We study the local existence of strong solutions for the cubic nonlinear wave equation with data in H ^s (M), s<1/2, where M is a three dimensional compact Riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense). However, after a suitable randomization, we are able to construct local strong solution for a large set of initial data in H ^s (M), where s≥1/4 in the case of a boundary less manifold and s≥8/21 in the case of a manifold with boundary. Mathematics Subject Classification (2000)  35Q55, 35BXX, 37K05, 37L50, 81Q20