On the Convergence of Descent Algorithms

It is proved that any cluster point of a sequence defined by a steepest descent algorithm in a general normed vector space is a critical point. The function is just assumed to be continuously differentiable. The class of algorithms we consider encompasses several choices such as the Cauchy steplength and the Curry steplength.     

Classes caractéristiques pour les cônes projectifs et homologie d'intersection

Sans résumé En hommage à Jean Louis Verdier     

Control of structural and excitonic properties of self-organized InAs/GaAs quantum dots

A systematic dependence of excitonic properties on the size of self-organized InAs/GaAs quantum dots is presented. The bright exciton fine-structure splitting changes from negative values to more than 0.5 meV, and the biexciton binding energy varies from antibinding to binding, as the height of truncated pyramidal dots increases from 2 to above 9 InAs monolayers. A novel mode of metalorganic vapor phase epitaxy was developed for growing such quantum dots with precise shape control. The dots consist of pure InAs and feature heights varying in steps of complete InAs monolayers. Such dot ensembles evolve from a strained, rough two-dimensional layer with a thickness close to the critical value for the onset of the 2D–3D transition. Dots with a common height represent subensembles with small inhomogeneous broadening. Tuning of subensemble emission energy is achieved by varying the mean lateral extension of the respective QDs. Detailed knowledge of the structural properties of individual dots enable realistic k·p calculations to analyze the origin of the observed excitonic properties. The binding energies of charged and neutral excitons increase due to correlation by the gradually increasing number of bound states for increasing dot size. The monotonously increasing magnitude of the fine-structure splitting with dot size is shown to be caused by piezoelectricity. The identification of key parameters allows to tailor exciton properties, providing a major step towards the development of novel applications.     

Genericity of Well-Posedness, Perturbations and Smooth Variational Principles

We show that three important topics in nonlinear analysis and optimization are intimately related: the theory of perturbations, the notion of well-posedness and variational principles in the sense of Ekeland, Borwein–Preiss and Deville–Godefroy–Zizler. The concept of genericity and the new notion of flexible perturbation play a key role in these connections. This notion enables one to consider topologies on spaces of functions which have been introduced recently. A link between the Asplund and Ekeland–Lebourg methods and the Palais–Smale condition, another important topic in nonlinear analysis, is pointed out.     

Design and demonstration of a high-energy booster amplifier for a high-repetition rate petawatt class laser system

We have successfully developed a high-energy, high-repetition rate Ti:sapphire laser system that delivers 33 J before compression at 0.1 Hz. The final booster amplifier is based on a 100 mm diameter Ti:sapphire crystal pumped with 72 J of energy in six beams delivered by three frequency-doubled high-repetition rate Nd:glass lasers. This system is, to the best of our knowledge, the first demonstrated petawatt class laser system running at a high repetition rate.     

Fully three-dimensional direct numerical simulation of a plunging breakerSimulation numérique directe tridimensionnelle du déferlement plongeant

The scope of this paper is to show the results obtained for simulating three-dimensional breaking waves by solving the Navier–Stokes equations in air and water. The interface tracking is achieved by a Lax–Wendroff TVD scheme (Total Variation Diminishing), which is able to handle interface reconnections. We first present the equations and the numerical methods used in this work. We then proceed to the study of a three-dimensional plunging breaking wave, using initial conditions corresponding to unstable periodic sinusoidal waves of large amplitudes. We compare the results obtained for two simulations, a longshore depth perturbation has been introduced in the solution of the flow equations in order to see the transition from a two-dimensional velocity field to a fully three-dimensional one after plunging. Breaking processes including overturning, splash-up and breaking induced vortex-like motion beneath the surface are presented and discussed. To cite this article: P. Lubin et al., C. R. Mecanique 331 (2003).