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     

On the interaction of femtosecond laser pulses with cluster targets

The heating of clusters by femtosecond laser pulses is studied theoretically and experimentally. Both the formation of a cluster target and the results of experimental studies of the cluster plasma by the methods of X-ray emission spectroscopy are considered. A numerical model of cluster formation in a supersonic gas jet is proposed. It is shown that detailed studies of two-phase gas-dynamic processes in a nozzle forming the jet give the spatial distributions of all parameters required for the correct calculation of the cluster heating by short laser pulses. Calculations of nozzles of different configurations show that in a number of cases an almost homogeneous cluster target can be formed, whereas in other cases the distributions of parameters prove to be not only inhomogeneous but also even nonmonotonic. A simple physical model of the plasma production by a femtosecond laser pulse and a picosecond prepulse is proposed. It is shown that a comparison of X-ray spectra with detailed calculations of the ion kinetics makes it possible to determine the main parameters of the plasma being produced.     

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).     

Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).     

Local velocity measurements in the shear-thickening transition of dilute micellar solutions of surfactants

Local velocimetry and rheometric measurements are performed on three dilute micellar solutions which undergo the shear-thickening transition. The three surfactants, namely, alkyltrimethyl ammonium bromide (C(n)TAB), all belong to the same family and only differ by the length of the aliphatic chain. Simultaneous ultrasonic velocimetry and rheometry recordings provide convincing evidence for a heterogeneous flow in the shear-thickening domain. A detailed analysis allows us to demonstrate surprisingly similar evolutions of the wall slip magnitude and of the apparent viscosity as well as subtle differences between the three systems. Together with the velocimetry results, the direct observation of the flow in the vorticity-velocity plane reveals that the shear-thickening transition is associated with the emergence of a three-dimensional unstable flow.