Courants caractéristiques et analyse de SEREigen currents and RCS analysis

In this Note, we return to the theory of characteristic modes which was introduced 30 years ago for electromagnetic scattering problems. A simple mathematical framework is proposed and complete definitions are given. The potential interest of this theory in terms of Radar Cross Section (RCS) analysis is then discussed, especially in the low frequency case. Finally, a 3-D example is presented to illustrate the efficiency of this decomposition. To cite this article: Y. Morel et al., C. R. Mecanique 332 (2004).     

Chemo- and regioselective synthesis of 2-alkylidenetetrahydrofurans bearing a chiral sulfur atom by domino reactions of sulfoximines

The addition of the dianion of Johnson’s sulfoximine to α,ω-halogenoesters evolves by an intramolecular heterocyclization to provide a direct access to 2-alkylidenetetrahydrofurans bearing a chiral sulfur atom via domino addition-elimination/S_N reactions.     

Subpicosecond pulse generation from a 1.56 μm mode-locked VECSEL

Near-transform-limited subpicosecond pulses at 1.56 μm were generated from an optically pumped InP-based vertical-external-cavity surface-emitting laser (VECSEL) passively mode-locked at 2 GHz repetition rate with a fast InGaAsNSb/GaAs semiconductor saturable absorber mirror (SESAM). The SESAM microcavity resonance was adjusted via a selective etching of phase layers specifically designed to control the magnitude of both the modulation depth and the intracavity group delay dispersion of the SESAM. Using the same VECSEL chip, we observed that the mode-locked pulse duration could be reduced from several picoseconds to less than 1 ps with a detuned resonant SESAM.     

Mobility of electrons in SnS2−xSex

The electrical resistivities and Hall constants of the semiconducting compounds SnS_2?xSe_x have been measured at temperatures ranging from 100 to 450 K and three donor ionization energies (0.013, 0.086 and 0.25 eV) have been identified. The Hall mobilities exhibit for T> 200K a temperature dependence of the form μ～ (T/T₀)^?n separating the SnS_2?xSe_x compounds into two groups one behaving like SnS₂ and the other like SnSe₂.     

Stochastic Lyapunov method

This paper is devoted to stability properties of solutions to stochastic differential equations obtained by a stochastic Lyapunov method.     

Regulation of births for viability of populations governed by age-structured problems

We assume that the evolution of the population is governed by a controlled McKendrick age-structured partial differential equation where the mortality rate and immigrated population levels are no longer known coefficients, but contingent regulation parameters chosen for a given purpose, for instance, for requiring that the population satisfies prescribed viability constraints depending on time and age. The Lotka renewal equation relating the boundary condition (number of births) to the integral with respect to age of the population is replaced by the introduction of another regulation parameter in the boundary condition, regarded as a natality policy. We may control it by its derivative, regarded as a natality decision. We then construct a regulation map, associating with the population level, the time and the age the subset of natality policies, a mortality rates and an immigration levels needed for governing viable evolutions of the population.     

Structure and evolution of strange attractors in non-elastic triangular billiards

We study non-elastic billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls of the table are not elastic, as in standard billiards; rather, the outgoing angle of the trajectory with the normal vector to the boundary at the point of collision is a uniform factor λ < 1 smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter λ is varied. For λ∈(0,1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of λ gaps arise in the Cantor structure. For λ close to 1, the attractor splits into three transitive components, whose basins of attraction have fractal boundaries.