Lagrangian/Eulerian solvers and simulations for Vlasov-Poisson

Static shells for the Vlasov-Poisson and Vlasov-Einstein systems

We prove the existence of static, spherically symmetric solutions of the stellar dynamic Vlasov-Poisson and Vlasov-Einstein systems, which have the property that their spatial support is a finite, spherically symmetric shell with a vacuum region at the center.

Splitting methods for Vlasov–Poisson and Vlasov–Maxwell equations

A rigorous convergence analysis of the Strang splitting algorithm for Vlasov-type equations in the setting of abstract evolution equations is provided. It is shown that, under suitable assumptions, the convergence is of second order in the time step τ . As an example, it is verified that the Vlasov–Poisson equations in 1+1 dimensions fit into the framework of this analysis. Further, numerical e...

Poisson Solvers

Symmetrization of Vlasov-Poisson Equations

We detail the spectrum of the linearized Vlasov-Poisson equation, and construct an original integro-differential operator which is related to the eigenstructure. It gives a new representation formula for the electric field, and yields new estimates for the linear Landau damping. Then we apply the technique to a problem with a dependence to the Debye length, and show weaker damping for small Deb...

Tsallis Entropy and the Vlasov - Poisson Equations

We revisit Tsallis Maximum Entropy Solutions to the Vlasov-Poisson Equation describing gravitational N -body systems. We review their main characteristics and discuss their relationship with other applications of Tsallis statistics to systems with long range interactions. In the following considerations we shall be dealing with a D-dimensional space so as to be in a position to investigate poss...