Rigorous Generalization of Young's Law for Heterogeneous and Rough Substrates

We consider a SOS type model of interfaces on a substrate which is both heterogeneous and rough. We first show that, for appropriate values of the parameters, the differential wall tension that governs wetting on such a substrate satisfies a generalized law which combines both Cassie and Wenzel laws. Then in the case of an homogeneous substrate, we show that this differential wall tension satisfies either the Wenzel's law or the Cassie's law, according to the values of the parameters.     

Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Electron diffraction investigation of PPTA/nylon 3T blends from shear-oriented anisotropic solutions

Nematic solutions of PPTA and nylon 3T were prepared in H₂SO₄ Optical microscopy was used to ascertain the phase behaviour of the blends. In the studied concentration range, no phase separation was observed. The solutions were shear-oriented and coagulated, and the resulting samples were studied by x-ray and electron diffraction. Nylon 3T crystallised even at a low concentration, which is indicative of a phase separation. Electron diffraction investigations of the oriented samples showed that well-oriented areas, which were predominantly composed of PPTA, adjoined areas where the major component, nylon 3T, showed no orientation. The relative proportion of the unoriented areas increased with increasing nylon concentration. It was concluded that, upon coagulation, the nylon was segregated into separate phases and crystallised unoriented, whereas for PPTA, crystallisation proceeded with very little chain rearrangement therefore preserving the orientation.     

Time‐integrated energy domain measurements with synchrotron radiation

A new time integrated method for the study of resonant nuclear scattering of synchrotron radiation in the forward direction or in Bragg directions is introduced. This method gives in principle similar information as the well known time differential method. A brief comparison of both methods is presented. The idea is to excite coherently the nuclei incorporated in two absorbers, one moving with respect to the other. The fields radiated by the nuclei from both absorbers interfere and each time the nuclear energy in one absorber matches, by Doppler modulation, the nuclear energy of the other, an extremum in the time integrated intensity is observed. The results of the first experiments at the Advanced Photon Source at the Argonne National Laboratory will be presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Anisotropy of optical phonons in semiconductor superlattices: Raman scattering experiments

Experiments on Raman scattering in the “forward” geometry, permitting observation of anisotropy of the optical phonons, are performed on specially prepared short-period GaAs/AlAs superlattice structures with the substrates removed and the surfaces covered with an antireflective layer. The experimental data agree well with the computational results obtained for the angular dispersion of optical phonons in superlattices on the basis of a modified continuum model. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 50–55 (10 July 1998)     

Extension of multivariate regression trees to interval data. Application to electricity load profiling

Summary  Several data can be presented as interval curves where intervals reflect a within variability. In particular, this representation is well adapted for load profiles, which depict the electricity consumption of a class of customers. Electricity load profiling consists in assigning a daily load curve to a customer based on their characteristics such as energy requirement. Within the load profiling scope, this paper investigates the extension of multivariate regression trees to the case of interval dependent (or response) variables. The tree method aims at setting up simultaneously load profiles and their assignment rules based on independent variables. The extension of multivariate regression trees to interval responses is detailed and a global approach is defined. It consists in a first stage of a dimension reduction of the interval response variables. Thereafter, the extension of the tree method is applied to the first principal interval components. Outputs are the classes of the interval curves where each class is characterized both by an interval load profile (e.g. the class prototype) and an assignment rule based on the independent variables.     

Near-infrared laser photoacoustic detection of methane: the impact of molecular relaxation

A photoacoustic sensor has been developed for trace-gas monitoring using a near-infrared semiconductor laser emitting in the 2ν₃ band of methane at 1.65 μm. The apparatus was designed for on-line process control in the manufacturing of the novel low-water-peak fibres developed for optical telecommunications. The importance of collisional relaxation processes in the generation of the photoacoustic signal is reported in the particular case of CH₄ detection in dry O₂ and O₂–N₂ mixtures. The negative influence of these effects results in a strongly reduced and phase-shifted photoacoustic signal, induced by a fast resonant coupling between the vibrational states of methane and oxygen, associated with the slow relaxation of the excited oxygen molecules. An unusual parabolic response of the sensor with respect to the methane concentration has been observed and is discussed. Finally, the beneficial effect of several species, including water vapour and helium, acting as a catalyst to hasten the relaxation of the CH₄–O₂ system, is demonstrated. PACS 42.62.Fi; 33.20.Ea; 34.50.Ez     

Higher-Order Simple Lie Algebras

It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order “structure constants”) which characterise the Lie algebra cocycles. This analysis allows us to present a classification of the higher-order simple Lie algebras as well as a constructive procedure for them. Our results are synthesised by the introduction of a single, complete BRST operator associated with each simple algebra. Received: 3 June 1996 / Accepted: 8 November 1996