The Paradyse project-team is a joint project between Inria, CNRS and the Laboratoire Paul Painlevé. It gathers mathematicians from different communities with the same motivation : to provide a better understanding of dynamical phenomena involving particles. These phenomena are described by fundamental models arising from several fields of physics. The Paradyse project-team focuses on model derivation, study of stationary states and asymptotic behaviors as well as the links between different levels of description (e.g. between micro and macro models) and numerical methods to simulate such models. The main applications include nonlinear optics, thermodynamics and ferromagnetism.
The research axes of the Paradyse project-team mainly fall into the three following categories.
- The long time analysis of the solutions of the considered models, and in particular the study of the stationary states and/or solitons and the study of their stability and instability properties, which are crucial to understand the physics. The main models are the nonlinear Schrödinger equations and that arising in ferromagnetism such as the Laudau-Lifshitz equation.
- The links between micro and macro models. The Paradyse project-team focuses on questions arising in micro-macro models of heat transfer and in particular on interactions of the systems with their boundaries. It is also interested in problems of anomalous diffusion and in Coulomb gases. The question of relaxation towards thermal equilibrium of interacting particle systems is also one of our main interests in this context, in link with the 1st research axis above.
- The numerical analysis and the simulation of the models above. In particular, the Paradyse project-team focuses on high order efficient methods for such problems, on the long time behavior of the numerical solutions, on the simulation of Landau-Lifshitz equations for ferromagnetism and of nonlinear Schrödinger equations for nonlinear optics and cold atoms physics. Another question of interest is that of the numerical simulation of large systems of interacting particles.
International and industrial relations
International collaborations of the Paradyse project-team include researchers of the following institutions :