4 research outputs found
Solving the Vlasov equation for one-dimensional models with long range interactions on a GPU
We present a GPU parallel implementation of the numeric integration of the
Vlasov equation in one spatial dimension based on a second order time-split
algorithm with a local modified cubic-spline interpolation. We apply our
approach to three different systems with long-range interactions: the
Hamiltonian Mean Field, Ring and the self-gravitating sheet models. Speedups
and accuracy for each model and different grid resolutions are presented
Towards a classification of bifurcations in Vlasov equations
We propose a classification of bifurcations of Vlasov equations, based on the
strength of the resonance between the unstable mode and the continuous spectrum
on the imaginary axis. We then identify and characterize a new type of generic
bifurcation where this resonance is weak, but the unstable mode couples with
the Casimirs, which are constants of motion, to form a size 3 Jordan block. We
derive a three-dimensional reduced noncanonical Hamiltonian system describing
this bifurcation: coupling with the Casimirs controls the phase space portrait.
Comparison of the reduced dynamics with direct numerical simulations on a test
case gives excellent agreement. We finally discuss the relevance of this
bifurcation to specific physical situations.Comment: 6 pages, 2 figures. Supplemental material available at the URL
https://www.idpoisson.fr/barre/publications-et-preprints