Raytracing/Fokker–Planck (FP) simulations used to model lower-hybrid current drive (LHCD) often fail reproduce experimental results, particularly when LHCD is weakly damped. A proposed reason for this discrepancy the lack of ‘full-wave’ effects, such as diffraction and interference, in raytracing breakdown approximation. Previous studies using non-Maxwellian full-wave/FP have been performed, bu...

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N -body diffusion processes, in the context of Kac’s propagation-of-chaos limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N → ∞ of a simple linear diffusion equation on 3N − C-dimens...

We shall prove new contraction properties of general transportation costs along nonnegative measure-valued solutions to Fokker– Planck equations in Rd , when the drift is a monotone (or λ-monotone) operator. A new duality approach to contraction estimates has been developed: it relies on the Kantorovich dual formulation of optimal transportation problems and on a variable-doubling technique. Th...

Complex systems are frequently governed by a hierarchy of dynamics on different time scales. Superstatistics, which is a “statistics of statistics” with several largely separated time scales, aims to describe their nonequilibrium stationary states. Here, a prototype system, i.e., a Brownian particle moving through a fluctuating medium with slowly varying temperature, is considered, and a Fokker...