The Mathematics Department, Imperial College London, was the perfect place for a long-duration academic visit. It has given me the opportunity to discuss with researchers from various teams and to attend many seminars.
I am involved in the mathematical analysis of populations of individuals driven by self-propelling forces and pairwise attractive and repulsive interaction. Some of my previous works in collaboration with J.-A. Carrillo were dedicated to asymptotic regimes such that the propulsion and friction forces dominate the potential interaction between particles. A simplifed formalism was introduced, which allows us to handle more complicated models, including diffusion. We have discussed as well the asymptotic regime corresponding to a large alignment frequency.
During my visit to ICL, in collaboration with P. Aceves-Sanchez, J.-A. Carrillo, P. Degond, I considered asymptotic regimes for self-propelled particles with relaxation toward the normalized mean velocity, together with a radially symmetric potential, including noise.
I met D. Crisan (ICL) and J. Barré (University of Orléans), and I had the opportunity to work on a simple mathematical model describing anisotropic magneto-optical traps. The behavior of particles is mainly driven by self-consistent attractive forces, but the force field does not result from a potential. We expect to handle this problem by adapting the averaging method I have used when analysing parabolic problems perturbed by stiff transport terms.
Beyond the excellent scientific framework, the opportunity to live in London, to experience its culture, and to meet many people was amazing!
Host: Professor Jose Carrillo