Collisionless Boltzmann (Vlasov) Equation and Modeling of Self-Gravitating Systems and Plasmas, Marseille, France

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Date:  2017-10-30  -  2017-11-03

Location:  Marseille, France

The modelling of the matter interactions at long range is a fertile problem for Mathematics, a major issue in Physics and a challenge for Analysis and Numerical Simulations. The aim of this meeting is to conjugate all these aspects, with a special attention to the simulations, and trying to infuse a stimulating working atmosphere, such as in a workshop, with few key lectures (part of these will be chosen when finalizing the program). The final program will be settled six months prior to the conference.

The foundations of galactic dynamics are based on the association of Boltzmann’s collisionless kinetic equation with Poisson’s equation describing the Newtonian gravitational potential. This combination of equations is also widely used to model the dynamics of Cold Dark Matter (and even a fraction of the visible) in the framework of the standard cosmological model of the Universe.

In plasma physics, the same Boltzmann equation (it transforms into the Vlasov equation) characterizes a system of charged particles moving under Coulomb interaction. However, contrary to gravitation, the Coulomb force repels charged particles of the same sign. The Debye screening process leads, as a first approximation, to a finite range of the effective force between charges. Moreover, magnetic field effects often cannot be neglected in plasmas. These important differences have led the two communities to develop their own separate numerical methods. One of the main goals of the meeting is to bring them together to confront the latest progress.

For instance, new adaptive symplectic techniques have been elaborated in the field of numerical galactic dynamics, whereas plasma physics has witnessed the resurgence of Fourier-Hermite schemes and symplectic model reduction. These developments come along with new physical intuition that begs to be debated.

Furthermore, the analysis of the Vlasov-Poisson system was rejuvenated by Mouhot and Villani’s breakthrough, and is the arena for exciting new research, in particular on the coupling with macroscopic charges. Visualisation of results and diagnostics that can be used to assess the accuracy of simulations will also be central to the meeting.