Article

A cloudy Vlasov solution

06/2004; DOI:doi:10.1111/j.1365-2966.2005.08889.x
Source: arXiv

ABSTRACT We propose to integrate the Vlasov-Poisson equations giving the evolution of a dynamical system in phase-space using a continuous set of local basis functions. In practice, the method decomposes the density in phase-space into small smooth units having compact support. We call these small units ``clouds'' and choose them to be Gaussians of elliptical support. Fortunately, the evolution of these clouds in the local potential has an analytical solution, that can be used to evolve the whole system during a significant fraction of dynamical time. In the process, the clouds, initially round, change shape and get elongated. At some point, the system needs to be remapped on round clouds once again. This remapping can be performed optimally using a small number of Lucy iterations. The remapped solution can be evolved again with the cloud method, and the process can be iterated a large number of times without showing significant diffusion. Our numerical experiments show that it is possible to follow the 2 dimensional phase space distribution during a large number of dynamical times with excellent accuracy. The main limitation to this accuracy is the finite size of the clouds, which results in coarse graining the structures smaller than the clouds and induces small aliasing effects at these scales. However, it is shown in this paper that this method is consistent with an adaptive refinement algorithm which allows one to track the evolution of the finer structure in phase space. It is also shown that the generalization of the cloud method to the 4 dimensional and the 6 dimensional phase space is quite natural. Comment: 46 pages, 25 figures, submitted to MNRAS

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    Article: Generation of Vorticity and Velocity Dispersion by Orbit Crossing
    Sebastian Pueblas, Roman Scoccimarro
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    ABSTRACT: We study the generation of vorticity and velocity dispersion by orbit crossing using cosmological numerical simulations, and calculate the backreaction of these effects on the evolution of large-scale density and velocity divergence power spectra. We use Delaunay tessellations to define the velocity field, showing that the power spectra of velocity divergence and vorticity measured in this way are unbiased and have better noise properties than for standard interpolation methods that deal with mass weighted velocities. We show that high resolution simulations are required to recover the correct large-scale vorticity power spectrum, while poor resolution can spuriously amplify its amplitude by more than one order of magnitude. We measure the scalar and vector modes of the stress tensor induced by orbit crossing using an adaptive technique, showing that its vector modes lead, when input into the vorticity evolution equation, to the same vorticity power spectrum obtained from the Delaunay method. We incorporate orbit crossing corrections to the evolution of large scale density and velocity fields in perturbation theory by using the measured stress tensor modes. We find that at large scales (k~0.1 h/Mpc) vector modes have very little effect in the density power spectrum, while scalar modes (velocity dispersion) can induce percent level corrections at z=0, particularly in the velocity divergence power spectrum. In addition, we show that the velocity power spectrum is smaller than predicted by linear theory until well into the nonlinear regime, with little contribution from virial velocities. Comment: 27 pages, 14 figures. v2: reorganization of the material, new appendix. Accepted by PRD
    09/2008;
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Keywords

6 dimensional phase space
 
adaptive refinement algorithm
 
analytical solution
 
change shape
 
cloud method
 
clouds
 
coarse graining
 
dynamical system
 
dynamical time
 
dynamical times
 
finite size
 
induces small aliasing effects
 
local basis functions
 
local potential
 
main limitation
 
significant fraction
 
small smooth units
 
small units ``clouds''
 
times
 
whole system