Quantitative interpretation of the very fast electronic relaxation of most Ln3+ ions in dissolved complexes

In a reference frame rigidly bound to the complex, we consider two Hamiltonians possibly at the origin of the very fast electronic relaxation of the paramagnetic lanthanide Ln(3+) ions (Ln = Ce to Nd, Tb to Yb), namely the mean (static) ligand-field Hamiltonian and the transient ligand-field Hamiltonian. In the laboratory frame, the bombardment of the complex by solvent molecules causes its Brownian rotation and its vibration-distorsion dynamics governing the fluctuations of the static and transient terms, respectively. These fluctuations are at the origin of electronic relaxation. The electronic relaxation of a Ln(3+) ion is defined by the decays of the time correlation functions (TCFs) of the longitudinal and transverse components of the total angular momentum J of its ground multiplet. The Brownian rotation of the complex and its vibration-distorsion dynamics are simulated by random walks, which enable us to compute the TCFs from first principles. It is shown that the electronic relaxation is governed mainly by the magnitude of the transient ligand-field, and not by its particular expression. The range of expected values of this ligand-field together with the lower limit of relaxation time enforced by the values of the vibration-distortion correlation time in liquids give rise to effective electronic relaxation times which are in satisfactory overall agreement with the experimental data. In particular, these considerations explain why the electronic relaxation times vary little with the coordinating ligand and are practically independent of the external field magnitude.     

Determination of triazines and amides in water using solid phase microextraction coupled with GC-MS

Summary Solid phase microextraction was coupled with gas chromatography-mass spectrometry (SPME-GC-MS) to screen for sixteen nitrogen-containing compounds, including herbicides, in water samples. The effects of stirring, extraction time, pH, salt concentration and the choice of fiber coating material were evaluated. The repeatability was in the range of 0.72–18.2 (CV % at 200 ng·L⁻¹) and the reproducibility, in the range of 5.4–34 (at 500 ng·L⁻¹).     

A quasi-optimal convergence result for fracture mechanics with XFEM

The aim of this Note is to give a convergence result for a variant of the eXtended Finite Element Method (XFEM) on cracked domains using a cut-off function to localize the singular enrichment area. The difficulty is caused by the discontinuity of the displacement field across the crack, but we prove that a quasi-optimal convergence rate holds in spite of the presence of elements cut by the crack. The global linear convergence rate is obtained by using an enriched linear finite element method. To cite this article: E. Chahine et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

An Integer Goal Programming Model to Allocate Offices to Staff in an Academic Institution

This paper investigates the problem of allocating office space to members of staff in an academic institution. We identify several conflicting objectives and formulate an integer pre-emptive goal programming model to address them. Using data from a pilot site of the University of Westminster, UK, we then experiment with alternative rankings of the objectives. Finally, given the plans to consolidate the activities of this university into fewer sites and the resulting need to relocate some staff members, we discuss how this model can be used to ensure that this process is carried out with the least possible inconvenience.