Du discret au continu pour des modèles de réseaux aléatoires d'atomes

We study in this Note the continuum (macroscopic) limit for some atomistic models for crystals. The purpose is to derive densities of mechanical energies from microscopic models. In contrast to the setting of a previous study, where the microscopic structure was assumed to be periodic, it is modelled here by a stochastic lattice, which enjoys some stationarity and ergodicity properties, following notions previously introduced elsewhere. To cite this article: X. Blanc et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Atomic step motion during the dewetting of ultra-thin films

We report on three key processes involving atomic step motion during the dewetting of thin solid films: (i) the growth of an isolated island nucleated far from a hole; (ii) the spreading of a monolayer rim; and (iii) the zipping of a monolayer island along a straight dewetting front. Kinetic Monte Carlo results are in good agreement with simple analytical models assuming diffusion-limited dynamics.     

Image recovery via total variation minimization and related problems

Summary. We study here a classical image denoising technique introduced by L. Rudin and S. Osher a few years ago, namely the constrained minimization of the total variation (TV) of the image. First, we give results of existence and uniqueness and prove the link between the constrained minimization problem and the minimization of an associated Lagrangian functional. Then we describe a relaxation method for computing the solution, and give a proof of convergence. After this, we explain why the TV-based model is well suited to the recovery of some images and not of others. We eventually propose an alternative approach whose purpose is to handle the minimization of the minimum of several convex functionals. We propose for instance a variant of the original TV minimization problem that handles correctly some situations where TV fails. Received December 21, 1995 / Revised version February 26, 1996     

Scalar conservation laws: Initial and boundary value problems revisited and saturated solutions

We revisit the classical theory of multidimensional scalar conservation laws. We reformulate the notion of the classical Kruzkov entropy solutions and study some new properties as well as the well-posedness of the initial value problem with inhomogeneous fluxes and general initial data. We also consider Dirichlet boundary value problems. We put forward a new and transparent definition for solutions and give a simple proof for their well-posedness in domains with smooth boundaries. Finally, we introduce the notion of saturated solutions and show that it is well-posed.     

Structure-based approach for identification of novel phenylboronic acids as serine-β-lactamase inhibitors

β-Lactamases are bacterial enzymes conferring resistance to β-lactam antibiotics in clinically-relevant pathogens, and represent relevant drug targets. Recently, the identification of new boronic acids (i.e. RPX7009) paved the way to the clinical application of these molecules as potential drugs. Here, we screened in silico a library of ~1400 boronic acids as potential AmpC β-lactamase inhibitors. Six of the most promising candidates were evaluated in biochemical assays leading to the identification of potent inhibitors of clinically-relevant β-lactamases like AmpC, KPC-2 and CTX-M-15. One of the selected compounds showed nanomolar K _i value with the clinically-relevant KPC-2 carbapenemase, while another one exhibited broad spectrum inhibition, being also active on Enterobacter AmpC and the OXA-48 class D carbapenemase.