Research
Emergence and self-organization in complex systems
Complex systems are characterized by the spontaneous formation of spatio-temporal structures as a result of simple local interactions between agents without leaders. Complex systems mostly appear in the biological and social contexts but can also be encountered in physics, chemistry, etc. My project aims to undertand the emergence of self-organization through a multiscale approach combining the use of microscopic (agent-based) models with mesoscopic (kinetic) and macroscopic (fluid) models.
Theoretical aspects of emergence >>> read more
Emergence in applications >>> read more
Numerical methods for emergence and other asymptotic problems
Quite broadly, I am interested in two classes of methods:
Asymptotic-Preserving (AP) methods >>> Read more
Multiscale methods >>> Read more
Other topics
Other works concerning the following topics can be found on the 'publications' page
Micro-macro passage in physical systems
Plasmas (general)
Energy-transport models for plasmas and semiconductors
Fokker-Planck-SHE (Spherical Harmonics Expansion) models for plasmas and semiconductors
Diffusion and Hydrodynamic limits
Diffusion by solid boundaries: applications to plasmas
Diffusion by interfaces: applications to semiconductor super-lattices
High-field diffusion models
Quantum systems
Relativistic systems
Wave-particle collisions and applications to cometary flows and turbulence
Polymers
Homogenization
Homogenization in rarefied gases and Knudsen pumps
Homogenization in quantum systems and Einstein rate equations
Schrödinger-Poisson systems with scattering states or Wigner-Poisson systems
Entropic numerical methods for Boltzmann and Fokker-Planck Landau operators
Child-Langmuir law
Hyperbolic systems (hydrodynamics, Maxwell, etc.): theory and numerics
Particle methods
Mathematical theory of Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck