Gravitational Dynamics of an Infinite Shuffled Lattice: Particle Coarse-grainings, Non-linear Clustering and the Continuum Limit

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dc.creatorBaertschiger, T.
dc.creatorJoyce, M.
dc.creatorGabrielli, A.
dc.creatorLabini, F. Sylos
dc.date2006-12-22
dc.date.accessioned2026-07-07T10:37:02Z
dc.date.available2026-07-07T10:37:02Z
dc.descriptionWe study the evolution under their self-gravity of infinite ``shuffled lattice'' particle distributions, focussing specifically on the comparison of this evolution with that of ``daughter'' particle distributions, defined by a simple coarse-graining procedure. We consider both the case that such coarse-grainings are performed (i) on the initial conditions, and (ii) at a finite time with a specific additional prescription. In numerical simulations we observe that, to a first approximation, these coarse-grainings represent well the evolution of the two-point correlation properties over a significant range of scales. We note, in particular, that the form of the two-point correlation function in the original system, when it is evolving in the asymptotic ``self-similar'' regime, may be reproduced well in a daughter coarse-grained system in which the dynamics are still dominated by two-body (nearest neighbor) interactions. Using analytical results on the early time evolution of these systems, however, we show that small observed differences between the evolved system and its coarse-grainings at the initial time will in fact diverge as the ratio of the coarse-graining scale to the original inter-particle distance increases. The second coarse-graining studied, performed at a finite time in a specified manner, circumvents this problem. It also makes more physically transparent why gravitational dynamics from these initial conditions tends toward a ``self-similar'' evolution. We finally discuss the precise definition of a limit in which a continuum (specifically Vlasov-like) description of the observed linear and non-linear evolution should be applicable.
dc.description21 pages, 8 eps figures, 2 jpeg figures (available in high resolution at http://pil.phys.uniroma1.it/~sylos/PRD_dec_2006/)
dc.identifierhttps://arxiv.org/abs/cond-mat/0612594
dc.identifierhttp://arxiv.org/abs/cond-mat/0612594
dc.identifierPhys.Rev.E76:011116,2007
dc.identifierdoi:10.1103/PhysRevE.76.011116
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/180249
dc.subjectStatistical Mechanics
dc.subjectAstrophysics
dc.titleGravitational Dynamics of an Infinite Shuffled Lattice: Particle Coarse-grainings, Non-linear Clustering and the Continuum Limit
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