Attractors for 2D-Navier-Stokes models with delays

The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous. However, on some occasions, the attractors may attract not only in the pullback sense but in the forward one as well. Also, this formulation allows to treat, in a unified way, terms containing various classes of delay features (constant, variable, distributed delays, etc.). As a consequence, some results for the autonomous model are deduced as particular cases of our general formulation.     

Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Synthesis of polycyclic structures by the Diels-Alder reaction of inner-outer-ring 1,3-bis(trimethylsilyloxy)dienes

A Diels-Alder reaction of novel inner-outer-ring 1,3-silyloxydienes 5-8 with a variety of dienophiles to afford highly functionalized polycyclic structures is reported. The inner-outer-ring 1,3-silyloxydienes 5-8 containing five- to seven-membered carbocyclic and heterocyclic rings were prepared in a single reaction vessel from 2-acetylcyclocarbonyls in quantitative yields. The Diels-Alder reaction with 1,4-benzoquinone (BQ), dimethyl acetylenedicarboxylate (DMAD), and methyl vinyl ketone (MVK) proceeded smoothly at room temperature, affording functionalized polycyclic naphthols, phenols, and enones with high regioselectivity and good yields (39-75%). Moreover, dienes 5-8 also reacted in a hetero-Diels-Alder reaction with benzaldehyde (BA) and N-benzylideneaniline (NBA) in the presence of catalytic amounts of ZnCl2, affording substituted polycyclic pyranones and pyridinones in good yields (40-93%). Overall, our synthetic strategy provides straightforward access to an interesting set of polycyclic structures useful for natural and nonnatural product synthesis.     

Thermal decomposition of sodium nitrite and sodium nitrate pre-adsorbed on TiO2 surfaces

The thermal decomposition of sodium nitrite or nitrate pre-adsorbed upon TiO₂ surfaces has been investigated by employing several techniques as infrared spectroscopy (IR) and temperature programmed desorption in conjunction with mass spectrometry analysis (TPD-MS) to study the features observed during these thermal decompositions. Differential thermal analysis (DTA) in combination with X-ray diffraction analysis (XRD) were used to investigate the possibility of a solid state chemical reaction between the solid products originated from the thermal decomposition of the pre-adsorbed species and the TiO₂. On the basis of our results, various characteristic features of these thermal decomposition reactions will be discussed.This work was supported by JUNTA DE ANDALUCIA (financial support for research groups/1990).     

An Investigation of Photo‐ and Pressure‐Induced Effects in a Pair of Isostructural Two‐Dimensional Spin‐Crossover Framework Materials

Two new isostructural iron(II) spin‐crossover (SCO) framework (SCOF) materials of the type [Fe(dpms)₂(NCX)₂] (dpms=4,4′‐dipyridylmethyl sulfide; X=S ( SCOF‐6(S) ), X=Se ( SCOF‐6(Se) )) have been synthesized. The 2D framework materials consist of undulating and interpenetrated rhomboid (4,4) nets. SCOF‐6(S) displays an incomplete SCO transition with only approximately 30 % conversion of high‐spin (HS) to low‐spin iron(II) sites over the temperature range 300–4 K (T_1/2=75 K). In contrast, the NCSe^? analogue, SCOF‐6(Se) , displays a complete SCO transition (T_1/2=135 K). Photomagnetic characterizations reveal quantitative light‐ induced excited spin‐state trapping (LIESST) of metastable HS iron(II) sites at 10 K. The temperature at which the photoinduced stored information is erased is 58 and 50 K for SCOF‐6(S) and SCOF‐6(Se) , respectively. Variable‐pressure magnetic measurements were performed on SCOF‐6(S) , revealing that with increasing pressure both the T_1/2 value and the extent of spin conversion are increased; with pressures exceeding 5.2 kbar a complete thermal transition is achieved. This study confirms that kinetic trapping effects are responsible for hindering a complete thermally induced spin transition in SCOF‐6(S) at ambient pressure due to an interplay between close T_1/2 and T(LIESST) values.     

Magnetic microsphere-based methods to study the interaction of teicoplanin with peptides and bacteria

Teicoplanin (teic) from Actinoplanes teichomyceticus is a glycopeptide antibiotic used to treat many Gram-positive bacterial infections. Glycopeptide antibiotics inhibit bacterial growth by binding to carboxy-terminal d-Ala-d-Ala intermediates in the peptidoglycan of the cell wall of Gram-positive bacteria. In this paper we report the derivatization of magnetic microspheres with teic (teic-microspheres). Fluorescence-based techniques have been developed to analyze the binding properties of the microspheres to two d-Ala-d-Ala terminus peptides. The dissociation constant for the binding of carboxyfluorescein-labeled d-Ala-d-Ala-d-Ala to teic on microspheres was established via fluorimetry and flow cytometry and was determined to be 0.5 × 10⁻⁶ and 3.0 × 10⁻⁶ mol L⁻¹, respectively. The feasibility of utilizing microparticles with fluorescence methods to detect low levels (the limit of bacterial detection was determined to be 30 colon-forming units; cfu) of Gram-positive bacteria has been demonstrated. A simple microfluidic experiment is reported to demonstrate the possibility of developing microsphere-based affinity assays to study peptide–antibiotic interaction.     

Thermal, pressure and light switchable spin-crossover materials

This article reviews the most relevant chemical and structural aspects that influence the spin-crossover phenomenon (SCO). Special attention is focussed on the recent development of SCO coordination polymers. The different approaches currently being explored in order to achieve multifunctionality in SCO materials are discussed.     

A procedure for the evaluation of vibrations induced by the passing of a train and its application to real railway traffic

In recent years, ground vibrations have become an important issue due to the growing awareness of the society about environmental living conditions. In this way, vibrations caused by trains running near houses or workplaces are considered disturbing for residents. Within this framework, this paper presents a procedure to estimate the vibration path caused by the passing of a train. In order to achieve this, the equations which describe the physical phenomenon are set in the frequency and wavenumber domain and solved by using the Fourier Transform. The obtained analytical solution is transformed back into the time and space domain by means of the Fourier series. The obtained theoretical results are compared with experimental measurements carried out in the Madrid–Barcelona High Speed Line in order to analyse the performance of this procedure.     

Asymptotic behaviour of the three-dimensional α-Navier-Stokes model with delays

We prove the existence and exponential stability of the stationary solutions for a three-dimensional α-Navier-Stokes model with delays. Instead of working directly with the model, we establish the results for a general abstract delay model, and then we apply them to our particular situation. We use two techniques in the stability analysis: the Lyapunov and Razumikhin approaches.