Refined local mode analysis of the stretching vibrational levels of C2D2

Dideuteroacetylene, C₂D₂, is a remarkable species for which the stretch-bend separability of the vibrational states is such that all the experimentally known stretching levels can be reproduced with an rms of 1.1 cm^?1 by using a simple stretching coordinate Hamiltonian model. The only two levels which deviate significantly from the calculations point out the effect of the 1/244 stretch-bend resonance previously identified. The local mode parameters retrieved from the fit of the experimental levels allow for a very satisfactory prediction of the available energy levels of the ¹²C¹³CD₂ species. A comparison between the local mode and normal mode approaches is presented.     

Tissus linéaires et théorèmes d'algébrisation de type Abdel-inverse et Reiss-inverse

A d-web in ( ,0) is given by d complex analytic foliations of codimension one in ( ,0) which are in general position. A d-web in ( ,0) is linear if all the leaves are (pieces of) hyperplanes in and is algebraic if it is associated, by duality, to a nondegenerate algebraic curve in of degree d. We characterize linear webs in ( ,0). We give explicit conditions under which a linear d-web in ( ,0) is algebraic and we obtain equations for in this case. Some related problems are discussed and some questions are posed.     

Flag Varieties and the Yang-Baxter Equation

We investigate certain bases of Hecke algebras defined by means of theYang–Baxter equation, which we call Yang–Baxter bases. These bases areessentially self-adjoint with respect to a canonical bilinear form. In thecase of the degenerate Hecke algebra, we identify the coefficients in theexpansion of the Yang–Baxter basis on the usual basis of the algebra withspecializations of double Schubert polynomials. We also describe theexpansions associated to other specializations of the generic Heckealgebra.     

Interfacial Activity of the Diprotonated 222 Cryptand at the Water/"Oil" Interface Revealed by Molecular Dynamics Simulations

Abstract

Orange II (I) is easily soluble in H₂O. It requires several months for the formation of needle-like crystals from a 0.16 M (saturated) aqueous solution. But when 0.03 M γ-cyclodextrin (γ-CD) is added to an equivalent of (I) at RT, the solution exhibits enhancement of the viscosity in an hour, and the microscopic viewing indicates the formation of a pine needle-like aggregate. Enough old millet jelly-like one shows well arranged stripe pattern upon rubbing. In the induced c.d. spectrum, the π→π* band of this complex appears at ～500 nm in the solution state, but in the aggregate state, it changes to the J-band due to the head-to-tail stacking of (I) and the H-band due to parallel stacking. When MeOH is poured onto the aggregate, the latter changes colour from orange to silver-gray, but keeps the same shape. The driving force for the aggregate formation may be 1. van der Walls contact between γ-CD and two molecules of (I),

2. π-π interaction between the two molecules of (I) in γ-CD,

3. H-bonding and stacking effects between γ-CD.

In this chiral aggregate, γ-CD works as an adhesive for the azo dye.     

Fluids confined by nanopatterned substrates of low symmetry

By means of Monte Carlo simulations in the grand canonical ensemble (GCEMC) the phase behaviour of a ‘simple’ fluid (in which molecules possess only translational degrees of freedom) confined between planar nanopatterned substrates is investigated. The fluid—substrate interaction is purely repulsive except for circular regions of radius R attracting fluid molecules. Because the circular pattern is finite in size, system properties are not translationally invariant in any spatial dimension. Thus, the grand potential Ω is not a homogeneous function of degree 1 in any of its extensive variables, which precludes a ‘mechanical’ expression for Ω in terms of stresses and conjugate strains. Therefore, in order to determine the phase behaviour, Ω versus chemical potential μ is calculated by thermodynamic integration under isothermal conditions (T = const). Besides the more conventional gas and liquid phases, fluid bridges arise as a third type of thermodynamically stable phase depending on T and μ. In a bridge phase, molecules are preferentially adsorbed by attractive circular region, and span the gap between the opposite substrate surfaces.     

An Exact Riemann Solver for Multicomponent Turbulent Flow

The main objective of this paper is to provide some adequate way to compute the non-conservative hyperbolic system which describes a multicomponent turbulent flow. The model is written for an isentropic gas. The exact solution of the Riemann Problem (RP) associated to the hyperbolic system is exhibited. It is composed of constant states separated by rarefaction waves, or shock waves and a contact discontinuity.

The selection of the admissible part of the shock curve is obtained using an entropy criterion. This entropy is the total energy of the system. Thanks to the latter, one may compute the exact solution of the Riemann problem, assuming genuinely non linear fields contain sufficiently weak shocks.     

Breathers for a Relativistic Nonlinear Wave Equation

 A new class of one-dimensional relativistic nonlinear wave equations with a singular δ-type nonlinear term is considered. The sense of the equations is defined according to the least-action principle. The energy and momentum conservation is established. The main results are the existence of time-periodic finite-energy solutions, the existence of global solutions and soliton-type asymptotics for a class of finite-energy initial data. (Accepted May 28, 2002) Published online November 12, 2002 Communicated by G. FRIESECKE     

The absorption spectrum of 12C2H2 between 12800 and 18500cm−1 II. Rotational analysis

The rotational structure of the vibrational bands of ¹²C₂H₂ is investigated in three spectral energy regions not previously systematically explored at high resolution, 12800–13500 cm^?1, 14000–15200 cm^?1 and 16500–18360 cm^?1, on the basis of new spectral data recorded by intracavity laser absorption spectroscopy. The rotational analysis of 17 new absorption bands arising from the ground state is reported (11 Σ_u ⁺ ? Σ_g ⁺ bands and 6Π_u ? Σ_g ⁺ bands). Four bands in the range studied show strong perturbations affecting both the line positions and intensities. Their detailed analysis is performed in order to determine the nature of the coupling schemes, the vibrational species and the rotational constants of the perturber states. Altogether, the vibration-rotation parameters of 21 newly observed vibrational states are derived.     

Structure of ultra-thin confined alkane films from Monte Carlo simulations

Grand canonical Monte Carlo simulations are reported of thin films of n-alkane confined fluids (1,4, 10 carbons) and i-decane under thermodynamic conditions away from the freezing line. All simulated solvation pressure profiles exhibit damped oscillations with a main period of oscillation equal roughly to the size of a methane, methyl or methylene bead (4-4.5 Å). This reflects an arrangement of the beads in layers parallel with the confining walls, which causes an oscillation of the local density across the film. However, the alkane molecules themselves are not arranged in perfect layers. The oscillations do not vanish for long chain and/or branched molecules: they are only attenuated. Also n-decane films have been simulated under thermodynamic conditions closer to surface force apparatus experiments. In contrast with an earlier molecular dynamics study, an overall continuous variation in the average number of decane molecules with the walls separation was found, consistent with the smooth transition towards slower relaxation and increasing rigidity with decreasing film thickness observed in some experiments. The possible origin of the discrepancy between the different simulation findings is discussed.     

On the role of the definition of potential models in Gibbs ensemble phase equilibria simulations of the H2S-pentane mixture

The effect of treating explicitly the coulombic and polarization interactions is investigated through the calculation of the coexistence curve of the pentane-H₂S binary mixture. In this work, potential models have been developed for hydrogen sulphide and pentane, which include electrostatic sites—estimated from ab initio calculations—and polarizable sites—estimated from experimental data—in addition to Lennard-Jones sites. Compared to existing models, these new models have the same number of fitting parameters to experimental thermodynamic data. They are shown to correctly describe the coexistence curve of the pure compounds. When applied to the case of mixtures, together with Lorentz-Berthelot combining rules, they allow one to obtain a more accurate prediction of the coexisting compositions of the mixture. Furthermore, it is shown that the interaction energy in this kind of mixture cannot be properly described by using effective potential models usually considered for pure compounds.