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.     

Fragment-based drug design: computational & experimental state of the art

Fragment-based screening is an emerging technology which is used as an alternative to high-throughput screening (HTS), and often in parallel. Fragment screening focuses on very small compounds. Because of their small size and simplicity, fragments exhibit a low to medium binding affinity (mM to μM) and must therefore be screened at high concentration in order to detect binding events. Since some issues are associated with high-concentration screening in biochemical assays, biophysical methods are generally employed in fragment screening campaigns. Moreover, these techniques are very sensitive and some of them can give precise information about the binding mode of fragments, which facilitates the mandatory hit-to-lead optimization. One of the main advantages of fragment-based screening is that fragment hits generally exhibit a strong binding with respect to their size, and their subsequent optimization should lead to compounds with better pharmacokinetic properties compared to molecules evolved from HTS hits. In other words, fragments are interesting starting points for drug discovery projects. Besides, the chemical space of low-complexity compounds is very limited in comparison to that of drug-like molecules, and thus easier to explore with a screening library of limited size. Furthermore, the "combinatorial explosion" effect ensures that the resulting combinations of interlinked binding fragments may cover a significant part of "drug-like" chemical space. In parallel to experimental screening, virtual screening techniques, dedicated to fragments or wider compounds, are gaining momentum in order to further reduce the number of compounds to test. This article is a review of the latest news in both experimental and in silico virtual screening in the fragment-based discovery field. Given the specificity of this journal, special attention will be given to fragment library design.     

Regioselective Radical Additions to 7-Oxabicyclo[2.2.1]hept-5-en-2-one

Radical addition to 7-oxabicylco[2.2.1]hept-5-en-2-one ( 1 ) was examined from a regiochemical point of view, and despite the small electronic anisotropy of the double bond, electrophilic radicals were found to add preferentially at C(5) with selectivities of up to 5:1. We also report the first case of an inversion of the regioselectivity of a radical reaction using Lewis acids.     

Superparamagnetic iron oxide particles and positive enhancement for myocardial perfusion studies assessed by subsecond T1-weighted MRI

Superparamagnetic iron oxide particles (SPIOs) are usually referred to as T₂ MR contrast agents, reducing signal intensity (SI) on T₂-weighted MR images (negative enhancement). This study reports the original use of SPIOs as T₁-enhancing contrast agents, primarily assessed in vitro, and then applied to an in vivo investigation of a myocardial perfusion defect. Using a strongly T₁-weighted subsecond MR sequence with SPIOs intravenous (IV) bolus injection, MR imaging of myocardial vascularization after reperfusion was performed, on a dog model of coronary occlusion followed by reperfusion. Immediately after the intravenous bolus injection of 20 μmol/kg of SPIOs, a positive signal intensity enhancement was observed respectively, in the right and left ventricular cavity and in the nonischemic left myocardium. Moreover, compared to normal myocardium, the remaining ischemic myocardial region (anterior wall of the left ventricle) appeared as a lower and delayed SI enhancing area (cold spot). Mean peak SIE in the nonischemic myocardium (posterior wall) was significantly higher than in the ischemic myocardium (anterior wall) (110 ± 23% vs. 74 ± 22%, Mann-Whitney test < 1%, n₁ = 6, n₂ − n₁ = 0, U > 2). In conclusion, the T₁ effect of SPIOs at low dose, during their first intravascular distribution, suggests their potential use as positive markers to investigate the regional myocardial blood flow and some perfusion defects such as the “no-reflow phenomenon”.     

Symplectic hypersurfaces in the complement of an isotropic submanifold

Using Donaldson's approximately holomorphic techniques, we construct symplectic hypersurfaces lying in the complement of any given compact isotropic submanifold of a compact symplectic manifold. We discuss the connection with rational convexity results in the K?hler case and various applications. Received: 9 January 2001 / Published online: 19 October 2001