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We revisit in one dimension the waterbag method to solve numerically Vlasov-Poisson equations. In this approach, the phase-space distribution function $f(x,v)$ is initially sampled by an ensemble of patches, the waterbags, where $f$ is assumed to be constant. As a consequence of Liouville theorem it is only needed to follow the evolution of the border of these waterbags, which can be done by employing an orientated, self-adaptive polygon tracing isocontours of $f$. This method, which is entropy conserving in essence, is very accurate and can trace very well non linear instabilities as illustrated by specific examples. As an application of the method, we generate an ensemble of single waterbag simulations with decreasing thickness, to perform a convergence study to the cold case. Our measurements show that the system relaxes to a steady state where the gravitational potential profile is a power-law of slowly varying index $beta$, with $beta$ close to $3/2$ as found in the literature. However, detailed analysis of the properties of the gravitational potential shows that at the center, $beta > 1.54$. Moreover, our measurements are consistent with the value $beta=8/5=1.6$ that can be analytically derived by assuming that the average of the phase-space density per energy level obtained at crossing times is conserved during the mixing phase. These results are incompatible with the logarithmic slope of the projected density profile $beta-2 simeq -0.47$ obtained recently by Schulz et al. (2013) using a $N$-body technique. This sheds again strong doubts on the capability of $N$-body techniques to converge to the correct steady state expected in the continuous limit.
We study analytically the collapse of an initially smooth, cold, self-gravitating collisionless system in one dimension. The system is described as a central S shape in phase-space surrounded by a nearly stationary halo acting locally like a harmonic
We propose a new semi-Lagrangian Vlasov-Poisson solver. It employs elements of metric to follow locally the flow and its deformation, allowing one to find quickly and accurately the initial phase-space position $Q(P)$ of any test particle $P$, by exp
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in
We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as $tto -infty$ to asymptotic dynamics as $tto +infty$. The main novelty is the construction of modified wave operators,
We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formal