Dynamics in multi-component systems: mathematical and physical aspects

List of Communications

0. Clément Mouhot (University of Cambridge) - TBA

10/19/17, 2:00 PM

TBA

1. Maxime Hauray (Université d'Aix-Marseille) - Propagation of chaos for the 3D homogenous Landau equation with moderalty soft potential

10/19/17, 2:45 PM

I will present results obtained in collaboration with Nicolas Fournier, on the propagation of chaos for the Landau equation. The difficulty here is the presence of a singularity in the interaction kernel that appears in equation. For mild singularities, we obtain quantitative results of convergence using a weak-strong stability result for the Landau equation, and a perturbation of it, that...

2. Enrico Allaria (Sincrotrone Trieste) - Electron beam qualities required for FELs and seeded FEL

10/19/17, 4:00 PM

Modern high gain x-ray free electron lasers rely on the FEL instability that requires high brightness electron beam to develop. This has lead to the need of an accurate control of the electron beam dynamic in the linear accelerator in order to suppress other kind of instabilities that may deteriorate the electron beam quality. In the case of seeded FELs, that allow the generation of fully...

3. Julien Barré (Université d'Orléans) - Bifurcations de l'équation de Vlasov

10/19/17, 4:45 PM

Les équations de Vlasov ont une dynamique très riche. En particulier, elles possèdent une infinité d'états stationnaires, dont la stabilité est l'objet de plusieurs résultats mathématiques récents. Je m'intéresserai ici à des états stationnaires légèrement instables, typiques d'une situation de bifurcation. Je présenterai le cas connu des états stationnaires homogènes, pour lesquels une...

4. Jani Lukkarinen (University of Helsinki) - Thermalization and prethermalization in anharmonic oscillator chains

10/20/17, 9:30 AM

In a joint work with Christian Mendl and Jianfeng Lu [Phys. Rev. E 94 (2016) 062104], we consider a particle chain with an onsite anharmonicity, known to exhibit normal heat conduction. We make a direct comparison between the relevant spatially homogeneous, but time-dependent, Boltzmann-Peierls equation and the average Wigner function computed from numerical simulations of the chain, and we...

5. Dmitry Agafontsev, (University of Moscow) - Integrable turbulence and formation of rogue waves: new results

10/20/17, 10:15 AM

We study numerically the nonlinear stage of modulational instability (MI) of cnoidal waves, in the framework of the focusing one-dimensional Nonlinear Schrodinger (NLS) equation. Cnoidal waves are the exact periodic solutions of the NLS equation and can be represented as a lattice of overlapping solitons. MI of these lattices lead to development of "integrable turbulence". We study the major...

7. Nathalie Ayi (Université Pierre et Marie Curie) - High-field limit of a stochastic BGK model

10/20/17, 11:30 AM

After discussing the problematic of hydrodynamical limits in the context of gas dynamics for the Boltzmann equation, we took an interest in the more general context of BGK models which are some kinetic equations. More precisely, we study a stochastic BGK model with a high field scaling as an approximation of a hyperbolic conservation law with stochastic forcing. After establishing the...

9. Maxime Herda (UPMC) - Massless electron limit of the magnetized Vlasov-Poisson-Fokker-Planck equation

10/20/17, 2:00 PM

In this talk, I will present results obtained in collaboration with L. Miguel Rodrigues. We consider a plasma of electrons in an inhomogeneous background of ions. We are interested in the dynamics of the light particles which is modeled by the Vlasov-Poisson-Fokker-Planck equation. In the appropriate scaling where characteristic time scales are those of the ions, an important dimensionless...

10. Clément Évain (Université de Lille) - Microbunching Instability in Storage Rings

10/20/17, 2:45 PM

"In storage rings - where relativistic electron bunches circulate in a pseudo-circular orbit - a spatio-temporal instability appears when the number of electrons exceeds a threshold value. This so-called microbunching instability is characterized by the spontaneous apparition of micro-structures at the millimeter scale in the longitudinal profile of the electron bunch and form a complex...

6. Thierry Goudon (Inria Sophia Antipolis) - TBA

10/20/17, 3:25 PM

Magneto-Optical Traps (MOT) are experimental devices used to trap cold atoms. The mathematical modeling of such devices involves the Vlasov-Poisson(-Fokker-Planck) system with an external potential. We can identify physically relevant regimes which allow us to replace this equation by a model of macroscopic nature. The analysis relies on the derivation of the Incompressible Euler system from...