Corner spontaneous magnetization

Details are given of a new method allowing an exact calculation of the spontaneous magnetization in the corner as well as along the edge at an arbitrary distance of the corner for a rectangular planar Ising ferromagnet.     

Rotational temperature and density measurements in a hypersonic flow by dual-line CARS

Rotational temperature and nitrogen number density are measured in the shock wave/boundary layer interaction region in the vicinity of a two-dimensional compression corner disposed in a low pressure, 55 K, Mach 10 hypersonic air flow. Spatially-resolved data are recorded using a nonlinear optical technique named dual-line coherent anti-Stokes Raman scattering (DLCARS). Averaged temperature and density profiles are compared with those predicted by a Navier-Stokes solver. Good agreement is found.     

Cems characterization of SnO2 films obtained by sputtering and sol-gel route

Conversion electron Mössbauer spectroscopy (CEMS) has been used to study tin oxide films prepared by sol-gel dipping and sputtering. The spectra of films prepared by sol-gel route result close to that of crystalline SnO₂ after heat treatment at a temperature as low as 150°C. The Mössbauer parameters of as sputter deposited films indicate that the structure of the deposited stannic oxide has an amorphous character more pronounced for thinner samples. The structure becomes predominantly that of crystalline SnO₂ by heating at 550°C for 30 min provided the film thickness is higher than 10 nm.     

Riccati-based preconditioner for computing invariant subspaces of large matrices

Summary. This paper introduces and analyzes the convergence properties of a method that computes an approximation to the invariant subspace associated with a group of eigenvalues of a large not necessarily diagonalizable matrix. The method belongs to the family of projection type methods. At each step, it refines the approximate invariant subspace using a linearized Riccati's equation which turns out to be the block analogue of the correction used in the Jacobi-Davidson method. The analysis conducted in this paper shows that the method converges at a rate quasi-quadratic provided that the approximate invariant subspace is close to the exact one. The implementation of the method based on multigrid techniques is also discussed and numerical experiments are reported. Received June 15, 2000 / Revised version received January 22, 2001 / Published online October 17, 2001     

A calorimetric study of the different thermal behaviour of DNA in the isotropic and liquid-crystalline states

A difference between the thermal behaviour of the isotropic and liquid-crystalline state of sonicated DNA in aqueous salt solution containing poly(ethyleneglycol)(PEG) has been demonstrated. On cooling, a different degree of renaturation of thermally denaturated DNA is observed between samples which form the isotropic state and more concentrated samples which on cooling form the cholesteric state.     

The prediction of coal properties using compressed infrared data from osculating polynomials

Reduction of the representation of infrared spectra from coal samples by osculating polynomials of degree nine is discussed. The reduced representation contains polynomial coefficients of order zero to four. Mathematical models of the original spectra are obtained by linear combination of the coefficients. These compressed models are statistically correlated to coal properties, namely, volatile matter, fixed carbon, ash content, heating value, hydrogen, carbon, sulphur, nitrogen, and maximum vitrinite reflectance, and the results are compared with those previously obtained from second derivatives of the same spectra. The use of compressed data, while giving slightly better correlations for some of the properties, has the advantage of requiring less computational time.     

The Dedekind-MacNeille completion as a reflector

We introduce a special type of order-preserving maps between quasiordered sets, the so-called cut-stable maps. These form the largest morphism class such that the corresponding category of quasiordered sets contains the category of complete lattices and complete homomorphisms as a full reflective subcategory, the reflector being given by the Dedekind-MacNeille completion (alias normal completion or completion by cuts). Suitable restriction of the object class leads to the category of separated quasiordered sets and its full reflective subcategory of completely distributive lattices. Similar reflections are obtained for continuous lattices, algebraic lattices, etc.     

In‐situ synthesis of transparent and conductive carbon nanotube networks

A method for the production of transparent carbon nanotube networks (CNTNs) over transparent substrates was developed. In this method, CNTNs were grown directly in the target surface by applying the catalyst in specific zones of the substrate through lithographic techniques. The networks can be also transferred from the original substrate to other surfaces. The newly grown carbon nanotubes have a very high aspect ratio (>50000). Thus far, networks with an optical transmittance of 94% at 550 nm and a surface resistivity of 3.6 kΩ/sq have been produced. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions

We prove global existence of solutions to the continuous nonhomogeneous Smoluchowski equation for coagulation rates satisfying a more general structure condition than the Galkin–Tupchiev monotony hypothesis considered in (Ph. Laurençot, S. Mischler, Arch. Rational Mech. Anal. 162 (1) (2002) 45–99). The Smoluchowski coagulation rate fulfils this condition as well as some rates which vanish on the diagonal. Under the condition of positivity of the coagulation rate outside of the diagonal we prove that solutions tend to 0 in the large time asymptotic. These results depend on a new estimate from below for the dissipation rate of the L^p-norm, p>1. To cite this article: S. Mischler, M. Rodriguez Ricard, C. R. Acad. Sci. Paris, Ser. I 336 (2003).