Higher-order topological sensitivity for 2-D potential problems. Application to fast identification of inclusions

This article concerns an extension of the topological derivative concept for 2-D potential problems involving penetrable inclusions, whereby a cost function J is expanded in powers of the characteristic size ε of a small inclusion. The O(ε⁴) approximation of J is established for a small inclusion of given location, shape and conductivity embedded in a 2-D region of arbitrary shape and conductivity, and then generalized to several such inclusions. Simpler and more explicit versions of this result are obtained for a centrally-symmetric inclusion and a circular inclusion. Numerical tests are performed on a sample configuration, for (i) the O(ε⁴) expansion of potential energy, and (ii) the identification of a hidden inclusion. For the latter problem, a simple approximate global search procedure based on minimizing the O(ε⁴) approximation of J over a dense search grid is proposed and demonstrated.     

Microstructural effects in non linear stratified composites

In this paper, we analyze the microstructural effects on non linear elastic and periodic composites within the framework of asymptotic homogenization. We assume that the constitutive laws of the individual constituents derive from strain potentials. The microstructural effects are incorporated by considering the higher order terms, which come from the asymptotic series expansion. The complete solution at any order requires the resolution of a chain of cell problems in which the source terms depend on the solution at the lower order. The influence of these terms on the macroscopic response of the non linear composite is evaluated in the particular case of a stratified microstructure. The analytic solutions of the cell problems at the first and second order are provided for arbitrary local strain–stress laws which derive from potentials. As classically, the non-linear dependence on the applied macroscopic strain is retrieved for the solution at the first order. It is proved that the second order term in the expansion series also exhibits a non linear dependence with the macroscopic strain but linearly depends on the gradient of macroscopic strain. As a consequence, the macroscopic potential obtained by homogenization is a quadratic function of the macroscopic strain gradient when the expansion series is truncated at the second order. This model generalizes the well known first strain gradient elasticity theory to the case of non linear elastic material. The influence of the non local correctors on the macroscopic potential is investigated in the case of power law elasticity under macroscopic plane strain or antiplane conditions.     

Towards highly efficient,intelligent and bimodal imaging probes: Novel approaches provided by lanthanide coordination chemistry

Gd³⁺ complexes are widely used as contrast enhancing agents in medical magnetic resonance imaging (MRI). In recent years, new fields have emerged in their development. The general tendency of using higher magnetic fields in biomedical and clinical MRI for a better signal to noise ratio calls for new contrast agents specifically optimized for such high field applications. Molecular imaging, aiming at the non-invasive visualisation of expression and function of bioactive molecules, requires imaging probes that provide a specific magnetic response to a particular molecular event. Finally, bimodal imaging may allow for combining the excellent resolution of MRI with a good sensitivity of other imaging modalities, such as optical methods. It requires bimodal imaging probes that satisfy requirements for both modalities within a single molecule. Here we review our latest efforts to develop novel lanthanide-based contrast agents in these specific fields and demonstrate the possibilities offered by lanthanide coordination chemistry.     

Paramagnetic Relaxation Enhancements in Acetate and Its Fluorine Derivatives Interacting with Gd3+: Complex Formation,Structure, and Transmetallation

The relative spatial distribution and motion with respect to Gd³⁺ of the ¹H and ¹⁹F nuclei in the acetate ion and its fluorine derivatives are studied in D₂O solutions through the paramagnetic relaxation rate enhancements (PREs) of these nuclei. We derive general theoretical expressions of the longitudinal PRE in terms of the analytical concentrations of metal and ligands, formation constants of the complexes, metal–nucleus distances, and coordination lifetimes of the ligands. The observed formation constants of the 1 metal: 1 ligand complexes markedly decrease with increasing number of fluorine atoms, the electronegativity of which reduces the negative partial charge of the coordinating COO^? group. The coordination lifetimes are very short at the scale of the relaxation times of the protons of metal bound acetate, that is, shorter than about 10 μs. The average distance of the acetate protons from Gd³⁺ is in fair agreement with independent crystallographic determination. The release of free Gd³⁺ from the very stable Gddtpa (dtpa=diethylene‐triaminepentaacetate) complex caused by the competition of Zn²⁺ for dtpa, is evidenced by an increase of the PREs with Zn²⁺ concentration. The observed PRE increase is consistent with the known equilibrium constants governing the speciation involving Gd³⁺, Zn²⁺, and dtpa. The present case study illustrates a method which easily yields experimental tunable properties suitable to test the ongoing theories of lanthanide Ln³⁺ complexation in solution.     

Robustness study of a reversed-phase liquid chromatographic method for the analysis of carboxylic acids in industrial reaction mixtures

The robustness study of the reversed-phase liquid chromatographic method developed for the quantitative analysis of carboxylic acids is a real asset to prepare method transfer because it provides an indication of its reliability during routine use. Indeed, it was possible to predict the consequences of small variations in operating conditions on the responses. The design of experiments approach was applied to model the effects and interactions of a high number of factors varying simultaneously with a limited number of runs. First we identified the factors which potentially affect the chromatographic responses used for carboxylic acids quantitation: detection wavelength (λ), column temperature (T), acetonitrile ratio in mobile phase (Me), duration of the plateau before the gradient (L) and gradient slope (S). Then we estimated the order of magnitude of realistic variations to assign factor levels. Finally a central composite design was carried out around the nominal conditions defined during method optimization. The statistical treatment of responses (retention factors, and concentrations) showed that the column temperature, the acetonitrile ratio in the mobile phase, the duration of the plateau before the gradient and the gradient slope were the most influent factors. The building of the robust domain from response-surfaces allowed us to give tolerance limits for the factors (216 nm < λ < 222 nm, 49.3 °C < T < 51.4 °C, 4.90% < Me < 5.18%, v/v, 4.5 min < L < 5.4 min, 9% < S < 11%) for which the performances of the method were maintained.     

Parity conservation and polarization of differential cross sections in complex-forming chemical reactions

For complex-forming chemical reactions, such as atom-diatom insertion reactions, quantum scattering and quantum statistical calculations usually predict sharp forward/backward peaks in the Differential Cross Sections (DCS). Conversely, the corresponding classical calculations are unable to reproduce these peaks. We show here that the basic reason for such an intriguing failure is that parity conservation is ignored in classical mechanics. A by-product of the analysis is a simple parity-restoring approximation that might significantly increase the ability of classical mechanics to describe DCSs over the whole angular range for the title processes.     

Challenging Near InfraRed Spectroscopy discriminating ability for counterfeit pharmaceuticals detection

This study was initiated by the laboratories and control department of the French Health Products Safety Agency (AFSSAPS) as part of the fight against the public health problem of rising counterfeit and imitation medicines. To test the discriminating ability of Near InfraRed Spectroscopy (NIRS), worse cases scenarios were first considered for the discrimination of various pharmaceutical final products containing the same Active Pharmaceutical Ingredient (API) with different excipients, such as generics of proprietary medicinal products (PMP). Two generic databases were explored: low active strength hard capsules of Fluoxetine and high strength tablets of Ciprofloxacin. Then 4 other cases involving suspicious samples, counterfeits and imitations products were treated. In all these cases, spectral differences between samples were studied, giving access to API or excipient contents information, and eventually allowing manufacturing site identification.A chemometric background is developed to explain the optimisation methodology, consisting in the choices of appropriate pretreatments, algorithms for data exploratory analyses (unsupervised Principal Component Analysis), and data classification (supervised cluster analysis, and Soft Independent Modelling of Class Analogy). Results demonstrate the high performance of NIRS, highlighting slight differences in formulations, such as 2.5% (w/w) in API strength, 1.0% (w/w) in excipient and even coating variations (<1%, w/w) with identical contents, approaching the theoretical limits of NIRS sensitivity. All the different generic formulations were correctly discriminated and foreign PMP, constituted of formulations slightly different from the calibration ones, were also all discriminated. This publication addresses the ability of NIRS to detect counterfeits and imitations and presents the NIRS as an ideal tool to master the global threat of counterfeit drugs.     

Synthesis, structure and reactivity of palladium(II) complexes of chiral N-heterocyclic carbene-imine and -amine hybrid ligands

The synthesis and structures of chiral N-heterocyclic carbene (NHC)-N-donor complexes of silver(I) and palladium(II) are reported. The X-ray structure of an NHC-imine silver(I) complex [((nPr)CN(CHPh))AgBr](2) exhibits an Ag(2)Br(2) dimer motif where the imine group is not coordinated to the silver atom. Reaction between 2 and [PdCl(2)(MeCN)(2)] gives the palladium(II) complex [(kappa(2)-(nPr)CN(CHPh))PdCl(2)](3) that contains a chelating NHC-imine ligand as shown by single-crystal X-ray diffraction. Slow hydrolysis of related complexes [(kappa(2)-(nPr)CN(CHPh))PdCl(2)](3) and [(kappa(2)-((Ph)(2)CH)CN(CHPh))PdCl(2)](4) using triethylammonium chloride and water lead to the precipitation of single crystals of insoluble NHC-amino palladium(II) complexes [(kappa(2)-(nPr)CN(H(2)))PdCl(2)](6) and [(kappa(2)-((Ph)(2)CH)CN(H(2)))PdCl(2)](7), respectively. In the solid state, complexes 6 and 7 both exhibit intermolecular hydrogen bonding between chlorine and an amino-hydrogen atom resulting in an infinite chain structure. Substitution of an amino hydrogen for an ethyl group gives the soluble complex [(kappa(2)-(iPr)CN((H)Et))PdCl(2)](12). Reaction between two equivalents of 2 and [PdCl(2)(MeCN)(2)] gives the di-NHC complex [(kappa(1)-(nPr)CN(CHPh))(2)PdCl(2)](5) that does not contain a coordinated imine as shown by single crystal X-ray diffraction. Conproportionation between 5 and an equivalent of [PdCl(2)(MeCN)(2)] to does not occur at temperatures up to 100 degrees C in CD(3)CN.