Erratum: Gravitational dynamics of an infinite shuffled lattice of particles [Phys. Rev. E<b>75</b>, 021113 (2007)]

Baertschiger, Thierry; Joyce, Michael; Gabrielli, Andrea; Labini, Francesco Sylos

doi:10.1103/physreve.75.059905

Cited by 14 publications

(87 citation statements)

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“…As remarked in [3,4] the form of this early time correlation function coincides, to a very good approximation, with that which is also observed in the asymptotic scaling regime attained by the system at longer times. This suggests strongly (but does not prove) that the physical mechanism leading to the former correlations, which we identify here, is also that which gives rise to the latter correlations.…”

Section: Introductionsupporting

confidence: 54%

“…not predicted analytically or semi-analytically). We have noted in [3,4], however, that this form emerges, to a good approximation, in our simulations prior to the asymptotic bscaling regime, in the preceding transient phase in which strong non-linear correlations first develop. In this paper we extend and detail our analysis of this phase.…”

Section: Introductionmentioning

confidence: 97%

“…II we discuss some of the relevant properties of the initial conditions of our simulations. In the next section we give the details of the simulations considered here and summarize briefly the main relevant results of [3,4]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

“…Progress in understanding would be very useful in providing analytical guidance for numerical simulations, and in particular better control on their precision in representing the relevant continuum limit. In a series of recent papers [3,4] we have studied a reduced version of the full cosmological problem, considering a very simple class of randomly perturbed lattices as initial conditions, and evolution in a static universe 1 . One of our primary results is that, despite the simplifications, the system we study has qualitative behavior very similar to that observed in the more complex cosmological simulations (correlated perturbations in initial conditions, expanding universe).…”

Section: Introductionmentioning

confidence: 99%

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Gravitational dynamics of an infinite shuffled lattice: Early time evolution and universality of nonlinear correlations

et al. 2008

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In two recent articles a detailed study has been presented of the out of equilibrium dynamics of an infinite system of self-gravitating points initially located on a randomly perturbed lattice. In this article we extend the treatment of the early time phase during which strong non-linear correlations first develop, prior to the onset of "self-similar" scaling in the two point correlation function. We establish more directly, using appropriate modifications of the numerical integration, that the development of these correlations can be well described by an approximation of the evolution in two phases: a first perturbative phase in which particles' displacements are small compared to the lattice spacing, and a subsequent phase in which particles interact only with their nearest neighbor. For the range of initial amplitudes considered we show that the first phase can be well approximated as a transformation of the perturbed lattice configuration into a Poisson distribution at the relevant scales. This appears to explain the "universality" of the spatial dependence of the asymptotic non-linear clustering observed from both shuffled lattice and Poisson initial conditions.

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Section: Introductionsupporting

confidence: 54%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gravitational dynamics of an infinite shuffled lattice: Early time evolution and universality of nonlinear correlations

et al. 2008

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“…Further if the clustering in the strongly non-linear regime does not depend on this scale one would expect to obtain a scale-free behaviour of spatial correlations in this regime. Such power law behaviour has been observed in both expanding (see, e.g., Efstathiou et al (1988); Smith et al (2003) and references therein) and static 3D simulations (Baertschiger et al 2007a) for a range of power law initial conditions. 3D simulations, however, can show such behaviour over a very limited spatial range, making it difficult to establish if it is associated with a true scale invariance of the non-linear clustering.…”

Section: Stable Clustering Predictionsmentioning

confidence: 99%

Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations

Benhaiem

Joyce

Sicard

2013

Monthly Notices of the Royal Astronomical Society

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One dimensional versions of dissipationless cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. Their interest lies in the fact that they can resolve a much greater range of time and length scales, and admit exact numerical integration. We use such models here to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the three dimensional EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly nonlinear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent γ depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter κ controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which γ depends strongly on both n and κ and where it agrees very well with a simple generalisation of the so-called stable clustering hypothesis in three dimensions, and (2) a region in which γ is more or less independent of both the spectrum and the expansion of the universe. The boundary in (n, κ) space dividing the "stable clustering" region from the "universal" region is very well approximated by a "critical" value of the predicted stable clustering exponent itself. We explain how this division of the (n, κ) space can be understood as a simple physical criterion which might indeed be expected to control the validity of the stable clustering hypothesis. We compare and contrast our findings to results in three dimensions, and discuss in particular the light they may throw on the question of "universality" of non-linear clustering in this context.

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Infinite self-gravitating systems and cosmological structure formation

Joyce¹

2008

AIP Conference Proceedings

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The usual thermodynamic limit for systems of classical self-gravitating point particles becomes well defined, as a {\it dynamical} problem, using a simple physical prescription for the calculation of the force, equivalent to the so-called ``Jeans' swindle''. The relation of the resulting intrinsically out of equilibrium problem, of particles evolving from prescribed uniform initial conditions in an infinite space, to the one studied in current cosmological models (in an expanding universe) is explained. We then describe results of a numerical study of the dynamical evolution of such a system, starting from a simple class of infinite ``shuffled lattice'' initial conditions. The clustering, which develops in time starting from scales around the grid scale, is qualitatively very similar to that seen in cosmological simulations, which begin from lattices with applied correlated displacements and incorporate an expanding spatial background. From very soon after the formation of the first non-linear structures, a spatio-temporal scaling relation describes well the evolution of the two-point correlations. At larger times the dynamics of these correlations converges to what is termed ``self-similar'' evolution in cosmology, in which the time dependence in the scaling relation is specified entirely by that of the linearized fluid theory. We show how this statistical mechanical ``toy model'' can be useful in addressing various questions about these systems which are relevant in cosmology. Some of these questions are closely analagous to those currently studied in the literature on long range interactions, notably the relation of the evolution of the particle system to that in the Vlasov limit and the nature of approximately quasi-stationary states.Comment: 32 pages, 9 figures, chapter of the volume ``Dynamics and Thermodynamics of systems with long range interactions: theory and experiments'', A. Campa, A. Giansanti, G. Morigi, F. Sylos Labini Eds., American Institute of Physics Conference proceedings, 970 (2008). See this URL: http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=970&Issue=

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Erratum: Gravitational dynamics of an infinite shuffled lattice of particles [Phys. Rev. E75, 021113 (2007)]

Cited by 14 publications

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Gravitational dynamics of an infinite shuffled lattice: Early time evolution and universality of nonlinear correlations

Gravitational dynamics of an infinite shuffled lattice: Early time evolution and universality of nonlinear correlations

Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations

Infinite self-gravitating systems and cosmological structure formation

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