Global attractor for weakly damped Nonlinear Schr\"odinger equations in L2(R)L^2(\R)

We prove that the weakly damped nonlinear Schr\"odinger flow in $L^2(\mathbb{R})$ provides a dynamical system which possesses a global attractor. The proof relies on the continuity of the Schr\"odinger flow for the weak topology in $L^2(\R)$

Uniqueness of large solutions

Given a nondecreasing nonlinearity $f$, we prove uniqueness of large solutions in the following two cases: the domain is the ball or the domain has nonnegative mean curvature and the nonlinearity is asymptotically convex

Comparison principles and applications to mathematical modelling of vegetal meta-communities

This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance). Actually we plan to study the effect of the fragmentation of the habitat on biodiversity. A simple neutral model for the evolution of abundances in a vegetal metacommunity is introduced. Migration between the communities is explicitely modelized in a deterministic way, while the reproduction process is dealt with using Wright-Fisher models, independently within each community. The large population limit of the model is considered. The hydrodynamic limit of this split-step method is proved to be the solution of a partial differential equation with a deterministic part coming from the migration process and a diffusion part due to the Wright-Fisher process. Finally, the diversity of the metacommunity is adressed through one of its indicator, the mean extinction time of a species. At the limit, using classical comparison principles, the exchange process between the communities is proved to slow down extinction. This shows that the existence of corridors seems to be good for the biodiversity

Eddy current interaction between a probe coil and a conducting plate

International audienceConsider a coil above a conducting plate. The interaction between the probe-coil and the plate is modeled by a quasi-static approximation of Maxwell's equations: the eddy current model. The associated electromagnetic transmission boundary-value problem can be solved by the integral equations method. However, the discretization of integral operators gives dense, complex and ill-conditioned linear systems. We present here a method to compute the reaction field and the coil impedance variation by solving only surface partial differential equations

Low Complexity Scalable Iterative Algorithms for IEEE 802.11p Receivers

In this paper, we investigate receivers for Vehicular to Vehicular (V2V) and Vehicular to Infrastructure (V2I) communications. Vehicular channels are characterized by multiple paths and time variations, which introduces challenges in the design of receivers. We propose an algorithm for IEEE 802.11p compliant receivers, based on Orthogonal Frequency Division Multiplexing (OFDM). We employ iterative structures in the receiver as a way to estimate the channel despite variations within a frame. The channel estimator is based on factor graphs, which allow the design of soft iterative receivers while keeping an acceptable computational complexity. Throughout this work, we focus on designing a receiver offering a good complexity performance trade-off. Moreover, we propose a scalable algorithm in order to be able to tune the trade-off depending on the channel conditions. Our algorithm allows reliable communications while offering a considerable decrease in computational complexity. In particular, numerical results show the trade-off between complexity and performance measured in computational time and BER as well as FER achieved by various interpolation lengths used by the estimator which both outperform by decades the standard least square solution. Furthermore our adaptive algorithm shows a considerable improvement in terms of computational time and complexity against state of the art and classical receptors whilst showing acceptable BER and FER performance