Formules pour les espaces multisécants aux courbes algébriques

We give a general new algorithm to find formulas for the number of k-secant d-planes to a smooth curve in ${\mathbf{P}}^N(\mathbf{C})$, for any k, d, N. Partial results were given by Castelnuovo [Rend. Palermo 3 (1889) 27–37] and Tanturri [Ann. Mat. 4 (1900) 67–122]. See also E. Arbarello et al. [Geometry of Algebraic Curves, vol. 1, Grundlehren Math. Wiss., vol. 267, Springer-Verlag, 1985]. To cite this article: P. Le Barz, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

High-resolution gamma-ray radiography produced by a laser-plasma driven electron source

An electron beam from a laser-plasma accelerator is converted into a gamma-ray source using bremsstrahlung radiation in a dense material. The gamma-ray beam has a pointlike source size because it is generated by a high quality electron beam with a small source size and a low divergence. Using this gamma-ray source, the radiography of complex and dense objects with submillimeter resolution is performed. It is the first evidence of a gamma-ray source size of a few hundreds micrometers produced with laser-driven accelerators. This size is consistent with results from Monte Carlo simulations.     

Reconstruction method for weak-phase optical interferometry

Current optical interferometers are affected by unknown turbulent phases on each telescope. We account for this lack of phase information by introducing system aberration parameters, and we solve the image reconstruction problem by minimizing an original joint criterion in the aberrations and in the object. We validate this method by means of simulations. Tests on experimental data are under way.     

Micromechanical simulation and analysis of one-dimensional vibratory sphere packing

We present a numerical method capable of reproducing the densification process from the so-called random loose to dense packing of uniform spheres under vertical vibration. The effects of vibration amplitude and frequency are quantified, and the random close packing is shown to be achieved only if both parameters are properly controlled. Two densification mechanisms are identified: pushing filling by which the contact between spheres is maintained and jumping filling by which the contact between particles is periodically broken. In general, pushing filling occurs when the vibration intensity is low and jumping filling becomes dominant when the vibration intensity is high.     

Charge density wave dislocation as revealed by coherent x-ray diffraction

Coherent x-ray diffraction experiments have been performed on high quality crystals of the charge density wave (CDW) system K0.3MoO3. The satellite reflections associated with the CDW have been measured as a function of the 20-microm-diameter beam position. For some positions, regular fringes have been observed. We show that this observation is consistent with the presence of a single CDW dislocation. Beyond charge density wave systems, this experiment shows that coherent x-ray diffraction is a suitable tool to probe topological defects embedded in the bulk.     

Universal nuclear spin relaxation and long-range order in nematics strongly confined in mass fractal silica gels

We show how the low-frequency dependence of the proton spin-lattice relaxation time T1(nu) of octylcyanobiphenyl liquid crystals confined in high-density silica gels evidences a long-range order nematic phase in spite of the strong confinement and random disorder of the gels. The universal value and frequency dependence observed, T1(nu) proportional, variant nu(2/3), is interpreted within a relaxation model due to director fluctuations in nematic liquid crystals confined to mass fractal porous media. The model provides a relation T1(nu) proportional, variant nu(2-d/2), giving a reliable value of the structural fractal dimension d(f)=2.67 for all the host silica gels.     

Synthesis of 4,5-benzotropones by cyclization of 1,3-bis-silyl enol ethers with 1,2-dialdehydes

The cyclization of 1,3-bis-silyl enol ethers or (2,4-dioxobutylidene)triphenylphosphoranes with phthalic dialdehyde allowed a convenient synthesis of a variety of 4,5-benzotropones. The hydrogenation of benzotropones afforded functionalized benzocycloheptanones which were transformed into tricyclic butenolides.     

Relaxation of photoexcited Na$_\mathsf{3}$F

This paper describes the spectroscopy of Na₃F both in the frequency and time domains. The photoionization efficiency curve shows two thresholds, associated to two isomers. The excited electronic states of the C_2v isomer have been probed by photodepletion spectroscopy, and the results are used to analyze a time-resolved study of photoexcited Na₃F, probed by photoionization. The pump-probe signal clearly shows damped oscillations, the period of which is fitted to fs, close to twice the previously measured bending mode of Na₂F [1], while the relaxation time is fs.Received: 31 October 2003, Published online: 6 January 2004PACS: 36.40.Qv Stability and fragmentation of clusters - 33.50.-j Fluorescence and phosphorescence; radiationless transitions, quenching (intersystem crossing, internal conversion)     

Determination of the aggregation threshold of non-UV-absorbing, neutral or charged surfactants by frontal- and vacancy-frontal analysis continuous capillary electrophoresis

Supplementing our recent work on UV-absorbing anionic surfactants, new protocols based on frontal analysis continuous capillary electrophoresis (FACCE) were developed for the investigation of the aggregation threshold of non-UV absorbing anionic, cationic and neutral surfactants, and exemplified with sodium dodecyl sulfate (SDS), tetradecyltrimethylammonium bromide (TTABr) and Brij 35. Contrary to UV-absorbing surfactants, the critical micelle concentration (CMC) determination of non-UV absorbing surfactants requires the use of a marker providing adequate detection capabilities. UV-absorbing markers were selected, according to the charge of the studied surfactant (neutral for SDS and TTABr, anionic for Brij 35). In all cases, the free marker concentration was quantified as a function of the total surfactant concentration. In addition, a modified implementation of FACCE, that we called vacancy FACCE (VFACCE), was employed for the case of the neutral surfactant. VFACCE entails first filling the capillary with the system components to be studied in the background electrolyte, next continuously introducing the plain BGE electrokinetically. The salient theoretical features of FACCE and VFACCE were compared. These new protocols were successfully applied to yield reliable CMC values within short operational time and with low sample consumption.     

Organic cross-linked electropolymers as supported oxidation catalysts: poly((tetrakis(9,9'-spirobifluorenyl)porphyrin)manganese) films

Anodic oxidation of free base and manganese complexes of tetraspirobifluorenylporphyrins leads to the coating of the working electrode by insoluble electroactive poly(9,9'-spirobifluorene-free and manganese porphyrin) films which electrochemical behavior and physicochemical properties are described. After removal from the electrode, the manganese-complexed polymers were evaluated as catalysts for the oxidation of alkenes by iodobenzene diacetate or iodosylbenzene. The results show that the reactions proceeded very efficiently at room temperature with good yields. The electrosynthesized polymer catalysts can be recycled by simple filtration and reused even up to the eighth cycle without loss of activity and selectivity. These results represent an important improvement over those previously described for manganese-porphyrin-catalyzed epoxidation reactions.