Geometric quantization of the BRST charge

In the first half of this paper (Sects. 1–4) we generalise the standard geometric quantization procedure to symplectic supermanifolds. In the second half (Sects. 5, 6) we apply this to two examples that exhibit classical BRST symmetry, i.e., we quantize the BRST charge and the ghost number. More precisely, in the first example we consider the reduced symplectic manifold obtained by symplectic reduction from a free group action with Ad^*-equivariant moment map; in the second example we consider a foliated configuration space, whose cotangent bundle admits the construction of a BRST charge associated to this foliation. We show that the classical BRST symmetry can be described in terms of a hamiltonian supergroup action on the extended phase space, and that geometric quantization gives us a super-unitary representation of this supergroup. Finally we point out how these results are related to reduction at the quantum level, as compared with the reduction at the classical level.Research supported by the Dutch Organization for Scientific Research (NWO)     

Crystalline Mean Curvature Flow of Convex Sets

We prove a local existence and uniqueness result of crystalline mean curvature flow starting from a compact convex admissible set in . This theorem can handle the facet breaking/bending phenomena, and can be generalized to any anisotropic mean curvature flow. The method provides also a generalized geometric evolution starting from any compact convex set, existing up to the extinction time, satisfying a comparison principle, and defining a continuous semigroup in time. We prove that, when the initial set is convex, our evolution coincides with the flat φ-curvature flow in the sense of Almgren-Taylor-Wang. As a by-product, it turns out that the flat φ-curvature flow starting from a compact convex set is unique.     

Freezing and thawing porous media: experimental study with a dielectric capacitive method

A capacitive sensor-based apparatus has been used to study the ice/water phase change in consolidated porous media subjected to freezing and thawing. This technique relies on the dielectric properties of water, ice, air, and the mineral substrate in the radio-frequency range. It gives directly the freezing and thawing temperature depressions and indirectly provides an estimation of pore size distribution through the Gibbs–Thomson relation. It also holds good promise for evaluating the amount of liquid water in frozen porous media by combining drying and freezing tests. To cite this article: T. Fen-Chong, A. Fabbri, C. R. Mecanique 333 (2005).     

Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate

The purpose of this work is to study the existence of solutions for an unsteady fluid-structure interaction problem. We consider a three-dimensional viscous incompressible fluid governed by the Navier–Stokes equations, interacting with a flexible elastic plate located on one part of the fluid boundary. The fluid domain evolves according to the structure’s displacement, itself resulting from the fluid force. We prove the existence of at least one weak solution as long as the structure does not touch the fixed part of the fluid boundary. The same result holds also for a two-dimensional fluid interacting with a one-dimensional membrane.     

VOCs Are Relevant Biomarkers of Elicitor-Induced Defences in Grapevine

Grapevine is susceptible to fungal diseases generally controlled by numerous chemical fungicides. Elicitors of plant defence are a way of reducing the use of these chemicals, but still provide inconsistent efficiency. Easy-to-analyse markers of grapevine responses to elicitors are needed to determine the best conditions for their efficiency and position them in protection strategies. We previously reported that the elicitor sulphated laminarin induced the emission of volatile organic compounds (VOCs) by grapevine leaves. The present study was conducted to characterise and compare VOC emissions in response to other elicitors. Bastid^® was first used to test the conditions of VOC collection and analysis. Using SBSE-GC-MS, we detected several VOCs, including the sesquiterpene α-farnesene, in a time-dependent manner. This was correlated with the induction of farnesene synthase gene expression, in parallel with stilbene synthesis (another defence response), and associated to resistance against downy mildew. The other elicitors (Redeli^®, Romeo^®, Bion^®, chitosan, and an oligogalacturonide) induced VOC emission, but with qualitative and quantitative differences. VOC emission thus constitutes a response of grapevine to elicitors of various chemical structures. Therefore, VOC analysis is relevant for studying the impact of environmental factors on grapevine defence responses and optimising the performance of elicitors in vineyards.     

Isotachophoretic purification of nanoparticles: tuning optical properties of quantum dots

Synthesized nanoparticles often require fine fractionation according to shape, dimension, mass, chemical composition, charge, and other properties in order to become suitable for practical use. Quantum dots (QDs) are luminescent nanocrystals with narrow emission peaks. This property has been widely utilized for the multiplexed sensing and barcoding of microparticles. QDs with narrower emission peaks are preferred for such applications. The width of the emission peaks can be significantly reduced after purification. A newly developed preparative isotachophoretic method employs the dependence of spectral properties and electrophoretic mobility on the diameter of QDs. Separated fractions of QDs revealed narrower emission peaks (72% of the original width) and improved quantum yield (two-fold). The usefulness of the developed isotachophoresis for purification and analysis of other nanostructures, for example, plasmonic nanoparticles and nanobioconjugates, is expected, too.     

Biotinylation of quantum dots for application in fluoroimmunoassays with biotin-avidin amplification

A competitive microplate fluoroimmunoassay was developed for the determination of human serum albumin in urine. It is based on the use of biotinylated CdTe quantum dots (QDs) whose synthesis is optimised in terms of storage stability, purification, and signal-to-noise ratio. The bioconjugated QDs were characterised by gel chromatography and gel electrophoresis. Storage stability and quantum yield were investigated. The excitation/emission wavelengths are 360/620?nm. The immunoassay of human serum albumin in urine has a working range from 1.7 to 10?μg.mL^?1, and the limit of detection is 1.0?μg.mL^?1.

Synthesis and characterization of bis[dicarboxylatotetraorganodistannoxane] units involving 5-[(E)-2-(aryl)-1-diazenyl]-2-hydroxybenzoic acids: An investigation of structures by X-ray diffraction, NMR, electrospray ionisation MS and assessment of in vitro cytotoxicity

Reactions of 5-[(E)-2-(aryl)-1-diazenyl]-2-hydroxybenzoic acids (LHH′, where the aryl group is an R-substituted phenyl ring such that for L¹HH′: R = H; L²HH′: R = 2′-CH₃; L³HH′: R = 3′-CH₃; L⁴HH′: R = 4′-CH₃; L⁵HH′: R = 4′-Cl; L⁶HH′: R = 4′-Br) with ⁿBu₂SnO in a 1:1 molar ratio yielded complexes of composition {[ⁿBu₂Sn(LH)]₂O}₂. The complexes have been characterized by ¹H, ¹³C, ¹¹⁹Sn NMR, ESI-MS, IR and ^119mSn Mössbauer spectroscopic techniques in combination with elemental analyses. The crystal structures of {[ⁿBu₂Sn(L¹H)]₂O}₂ (1), {[ⁿBu₂Sn(L⁴H)]₂O}₂ (4), {[ⁿBu₂Sn(L⁵H)]₂O}₂ (5) and {[ⁿBu₂Sn(L⁶H)]₂O}₂ (6) were determined. The compounds are centrosymmetric tetranuclear bis(dicarboxylatotetrabutyldistannoxane) complexes containing a planar Sn₄O₂ core in which two μ₃-oxo O-atoms connect an Sn₂O₂ ring to two exocyclic Sn-atoms. The four carboxylate ligands display two different modes of coordination where both modes involve bridging of two structurally distinct Sn-atoms. The solution structures were confirmed by ¹¹⁹Sn NMR spectroscopy by observing two tin resonances in compounds 1, and 4-6. The observed difference between the two tin resonances was about 3 ppm while the differences in ¹³C resonances were even smaller. Compounds {[ⁿBu₂Sn(L²H)]₂O}₂ (2) and {[ⁿBu₂Sn(L³H)]₂O}₂ (3) undergo a very complex exchange processes in deuteriochloroform solution. The in vitro cytotoxic activity of compounds 1 and 4 against WIDR, M19 MEL, A498, IGROV, H226, MCF7 and EVSA-T human tumour cell lines is reported.     

Use of E corr vs time plots for the qualitative analysis of metallic elements from scientific and technical objects: the SPAMT Test Project

A new analytical tool for copper alloys based on the monitoring of E _corr vs time is presented. This tool is particularly adapted to condition surveys carried out on-site by conservators on historic objects and was optimised so to respond to the needs of the conservation field such as the minimal impact on the artefacts, the portability of the instruments and its ease to use. A database constituted of 66 reference alloys representative of the materials found on technical artefacts with their electrochemical behaviour in three different solutions (Henniez mineral water, KNO₃ and sodium sesquicarbonate) was realised. The validation of the tool and the relevance of the database were assessed on two Swiss collections of technical, scientific and horology artefacts.