Tomasz Tyranowski (University of Twente)
Stochastic variational principles for the collisional Vlasov–Maxwell and Vlasov–Poisson equations
Wednesday, 1 October 2025, 15:30–16:30 in HG03.085
Abstract
The first part of the talk will provide a general introduction to geometric numerical methods for deterministic and stochastic dynamical systems, in particular symplectic methods for Hamiltonian systems and variational methods for Lagrangian systems. In the second part of the talk, I will discuss the geometric structure of the Vlasov–Maxwell equations—the fundamental equations of kinetic plasma theory. I will recast the collisional Vlasov-Maxwell and Vlasov-Poisson equations as systems of coupled stochastic and partial differential equations, and I will derive stochastic variational principles which underlie such reformulations. I will also propose a stochastic particle method for the collisional Vlasov-Maxwell equations and provide a variational characterization of it, which can be used as a basis for a further development of stochastic structure-preserving particle-in-cell integrators.