PhD Student in Mathematics (M/F)

Job Description

Thesis Subject

This PhD project focuses on the numerical analysis and simulation of kinetic models, which arise in various fields such as plasma physics, kinetic theory of gases, and fluid mechanics.
In these models, each particle species is described by a function depending on time, position, and velocity, representing the statistical distribution of particles in phase space. While these models provide an accurate description of the system's behavior, their implementation can be complex and computationally expensive. For dense particle systems, it is often more efficient to use fluid models, which describe macroscopic quantities. Depending on the scaling considered and the number of moments taken into account, different fluid models can be derived.
The main objective of this project is to develop and analyze finite volume numerical methods capable of preserving, among others, two fundamental properties:

exponential return to equilibrium in the long-time limit (hypocoercivity property);
the diffusion limit towards a fluid model.
Initially, the study will focus on a linear Vlasov-Fokker-Planck model with an external confining potential. Subsequently, the results will be extended to the Vlasov-Fokker-Planck-Poisson system, which introduces a self-consistent electric potential defined by coupling with the Poisson equation, thus making the problem nonlinear.

Your Work Environment

The Jean Leray Mathematics Laboratory is primarily affiliated with Nantes Université and the CNRS, with Centrale Nantes as a secondary affiliation. It comprises 109 members, including 55 permanent faculty researchers and researchers. The laboratory is organized into five research teams: Partial Differential Equations Analysis; Probability and Randomness; Global Geometry and Analysis; Modeling, Numerical Analysis, and Scientific Computing; and Topology, Geometry, and Algebra.
The recruited individual will be attached to the Modeling, Numerical Analysis, and Scientific Computing (MACS) team, which centers its activities around several major axes:
- mathematical modeling using differential equations (ODEs, PDEs),
- design and analysis of numerical schemes,
- optimization and inverse problems,
- coupling models with data.

Compensation and benefits

Compensation

2300 € gross monthly

Annual leave and RTT

44 jours

Remote Working practice and compensation

Pratique et indemnisation du TT

Transport

Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€

About the offer

About the CNRS

The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.

CNRS

The research professions