Nous proposons une nouvelle méthode pour calculer la mesure d'équilibre dans un problème théorie du potentiel logarithmique avec champ externe et support dans une union finie d'intervalles disjoints. Une reformulation du problème conduit à la résolution d'un système d'équations intégrales avec noyau singulier de Cauchy. On propose une méthode spectrale utilisant des fonctions rationnelles...
We consider a defocusing quasilinear nonlinear Schrödinger equation in dimension one with nonzero conditions at infinity. The talk aims to present the classification of the traveling-wave solutions of this equation in terms of two parameters: the strength of the quasilinear term and the speed of the wave.
With access to the theory of ODEs, we found multiple branches of solutions coexisting in...
In this talk, I will focus on two models for crowd motion, which minimize an energy featuring a term penalizing high values for the density of the crowd during the motion. Due to the presence of this term, numerical computations of such minimizing motions is usually carried out in a "Eulerian" way, approximating the density of the crowd with piecewise simple functions. These dicretizations...
In the storage ring of a synchrotron, the radiation produced by the electron beam is a powerful light source, which can be used in various scientific experiments. In this talk, I will present a model which describes the longitudinal dynamics of a relativistic electron bunch in this kind of particle accelerator. It consists in a Vlasov-Fokker-Planck equation with non-symmetric self-consistent...
Auto-Encoders are a kind of Neural Networks that work as a non-linear generalization of a Principal Component Analysis (PCA), and have many successful uses (uniformization of data, compression, statistical studies, even data generation), especially in the cases of images. However, applying them to meshes of surfaces in 3D is much harder, both because of a general lack of data compared to...
