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VLASIX: Vlasov-Poisson in 6 dimensions

Welcome to the VLASIX project web page. The VLASIX project is funded by Agence Nationale de la Recherche (ANR) , Programme National de Cosmologie et Galaxies (PNCG) and by Institut Lagrange de Paris (ILP). Its purpose is to develop direct Vlasov solvers in various number of dimensions to bring improvements over traditional N-body methods (Figure 1). The main goal is ultimately to solve Vlasov-Poisson equations in 6-dimensional phase-space in the cold case, i.e. in the case where the initial velocity dispersion of the phase-space fluid is null or very small, as expected in the concordance model of large scale structure formation in the Universe. However, we are also interested in the warm case, which can apply to galactic dynamics and to plasma physics. Although mainly focusing on gravitational dynamics, our approach is indeed multidisciplinary.

Figure 1: Justification for using direct Vlasov solvers: N-body versus exact solution in 1D gravity. On the left, the “exact” evolved state of the distribution function in phase space of an initially Gaussian shaped distribution, with the entropy conserving waterbag code VlaPoly, on the right, the result obtained with a N-body code. One can see holes in phase-space, as well as an unstable unphysical region in the N-body simulation. Images realized by S. Colombi, C. Alard and J. Touma.

Codes and methods

The numerical methods we develop can be mainly classified in four categories:

While our main efforts go into Vlasov solvers, we also develop and use N-body codes. For instance, we have implemented a simple 1D cosmological Particle-Mesh code and we employ largely the public treecode Gadget-2 when comparing our Vlasov codes to the N-body approach.

Figure 2: Projected density obtained from a simulation of an initially cold system in 4D phase-space with the adaptive tessellation technique using ColDICE, evidencing sharp caustic structures. From Sousbie & Colombi (2016).

Theory and analysis

In addition to developing codes, we study mathematical properties and convergence of various schemes, we compare Vlasov codes to the traditional N-body approach and we apply our codes to specific problems where analytical theories can be tested. One of the goals of this project is for instance to confirm and to understand universal properties of dark matter halos.