Rotating waves within a hollow vortex core

The rotating waves within a hollow vortex core (polygonal patterns) are generated under shallow water conditions inside a cylindrical tank by a revolving disk at its bottom. We previously reported some basic features of these polygonal patterns during transition and at the equilibrium states. The present paper includes a more comprehensive investigation into the transition process of these polygonal patterns and expands the recent partial results that have been previously reported. We show that the parent wave (or the N-gon pattern) to disk frequencies ratio is around one-third (1/3) regardless of the flow conditions. A detailed insight into the transition process from the parent wave N-gon to daughter wave (N + 1)-gon is provided, which consists of two regimes, quasi-periodic and synchronized. Based on these observations, we explained the shrinking of the disk speed subintervals over which the N-gon patterns occur, when N increases.     

Applications purement semi-affines et tressages

In this Note, we show essentially two results which complete the article by Ait Mokhtar et al., 2008. The first one, having defined the maps purement semi-affines, consists in looking the writing clarify of the compound of these maps. The second result, having defined the tressage, consists in showing that the compound of two tressages is also a tressage.     

A qualitative mathematical analysis of a class of linear variational inequalities via semi-complementarity problems: applications in electronics

The main object of this paper is to present a general mathematical theory applicable to the study of a large class of linear variational inequalities arising in electronics. Our approach uses recession tools so as to define a new class of problems that we call “semi-complementarity problems”. Then we show that the study of semi-complementarity problems can be used to prove new qualitative results applicable to the study of linear variational inequalities of the second kind.     

Vapour pressures and excess functions of N, N, N′, N′-tetramethylalkanediamine + cyclohexane. A group contribution study of the N---N proximity effect

The vapour pressuresof liquid cyclohexane + N, N, N′, N′-tetramethylalkanediamine, (CH₃)₂ N(CH₂)_uN(CH₃)₂ (u = 1,2) + cyclohexane mixtures were measured by a static method between 303.15 and 343.15 K at 10 K intervals. The excess molar enthalpies at 303.15 K were also measured.

The molar excess Gibbs energies, calculated from the vapour-liquid equilibrium data, and the molar excess enthalpies compare satisfactorily with group contribution (DISQUAC) predictions.

The proximity effect of N atoms produces a regular decrease of the interactional parameters.     

Stabilization of linear systems with saturation: a Sylvester equation approach

A new methodology of the partial eigenstructure assignmentby state feedback via Sylvester equation is used to obtain asolution of the constrained regulator problem for linear continuous-timeand discrete-time systems by using the reduced-order technique.     

Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations

Summary. A nonlinear Galerkin method using mixed finite elements is presented for the two-dimensional incompressible Navier-Stokes equations. The scheme is based on two finite element spaces and for the approximation of the velocity, defined respectively on one coarse grid with grid size and one fine grid with grid size and one finite element space for the approximation of the pressure. Nonlinearity and time dependence are both treated on the coarse space. We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin solution is of the order of $H^2$, both in velocity ( and pressure norm). We also discuss a penalized version of our algorithm which enjoys similar properties. Received October 5, 1993 / Revised version received November 29, 1993     

Chemical composition and antibacterial activity of Lavandula coronopifolia essential oil against antibiotic-resistant bacteria

The aim of this study was to analyse the composition of the essential oil (EO) of Lavandula coronopifolia from Morocco and to evaluate its in vitro antibacterial activity against antibiotic-resistant bacteria isolated from clinical infections. The antimicrobial activity was assessed by a broth micro-well dilution method using multiresistant clinical isolates of 11 pathogenic bacteria: Klebsiella pneumoniae subsp. pneumoniae, Klebsiella ornithinolytica, Escherichia coli, Enterobacter cloacae, Enterobacter aerogenes, Providencia rettgeri, Citrobacter freundii, Hafnia alvei, Salmonella spp., Acinetobacter baumannii and methicillin-resistant Staphylococcus aureus. The main compounds of the oil were carvacrol (48.9%), E-caryophyllene (10.8%) and caryophyllene oxide (7.7%). The oil showed activity against all tested strains with minimal inhibitory concentration (MIC) values ranging between 1% and 4%. For most of the strains, the MIC value was equivalent to the minimal bactericidal concentration value, indicating a clear bactericidal effect of L. coronopifolia EO.     

Continuity in law with respect to the Hurst index of some additive functionals of sub-fractional Brownian motion

In this article, first, we prove some properties of the sub-fractional Brownian motion introduced by Bojdecki et al. [Statist. Probab. Lett. 69(2004):405–419]. Second, we prove the continuity in law, with respect to small perturbations of the Hurst index, in some anisotropic Besov spaces, of some continuous additive functionals of the sub-fractional Brownian motion. We prove that our result can be obtained easily, by using the decomposition in law of the sub-fractional Brownian motion given by Bardina and Bascompte [Collect. Math. 61(2010):191–204] and Ruiz de Chavez and Tudor [Math. Rep. 11(2009):67–74], without using the result of Wu and Xiao [Stoch. Proc. Appl. 119(2009):1823–1844] by connecting the sub-fractional Brownian motion to its stationary Gaussian process through Lamperti’s transform. This decomposition in law leads to a better understanding and simple proof of our result.     

Analysis of hydrodynamic and thermal dispersion in porous media by means of a local approach

A pore scale analysis is implemented in this numerical study to investigate the behavior of microscopic inertia and thermal dispersion in a porous medium with a periodic structure. The macroscopic characteristics of the transport phenomena are evaluated with an averaging technique of the controlling variables at a pore scale level in an elementary cell of the porous structure. The Darcy–Forchheimer model describes the fluid motion through the porous medium while the continuity and Navier–Stokes equations are applied within the unit cell. An average energy equation is employed for the thermal part of the porous medium. The macroscopic pressure loss is computed in order to evaluate the dominant microscopic inertial effects. Local fluctuations of velocity and temperature at the pore scale are instrumental in the quantification of the thermal dispersion through the total effective thermal diffusivity. The numerical results demonstrate that microscopic inertia contributes significantly to the magnitude of the macroscopic pressure loss, in some instances with as much as 70%. Depending on the nature of the porous medium, the thermal dispersion may have a marked bearing on the heat transfer, particularly in the streamwise direction for a highly conducting fluid and certain values of the Peclet number.     

Friedel-Craft acylation of ar-himachalene: synthesis of acyl-ar-himachalene and a new acyl-hydroperoxide

Friedel-Craft acylation at 100 °C of 2,5,9,9-tetramethyl-6,7,8,9-tetrahydro-5H-benzocycloheptene [ar-himachalene], a sesquiterpenic hydrocarbon obtained by catalytic dehydrogenation of α-, β- and γ-himachalenes, produces a mixture of two compounds: (3,5,5,9-tetramethyl-6,7,8,9-tetrahydro-5H-benzocyclohepten-2-yl)-ethanone (2, in 69% yield), with a conserved reactant backbone, and 3, with a different skeleton, in 21% yield. The crystal structure of 3 reveals it to be 1-(8-ethyl-8-hydroperoxy-3,5,5-trimethyl-5,6,7,8-tetrahydronaphthalen-2-yl)-ethanone. In this compound O-H…O bonds form dimers. These hydrogen-bonds, in conjunction with weaker C-H…O interactions, form a more extended supramolecular arrangement in the crystal.