On the probabilistic approach to the N-body problem

Romero, Mario; Ascasíbar, Y.

doi:10.1093/mnras/sty1728

Cited by 3 publications

(2 citation statements)

References 40 publications

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“…As noted by , gravitational systems are intrinsically inhomogeneous and one important question is whether the number of constituent particles (or stars) suffices for the continuum limit (N → ∞) to accurately describe the evolution of the system over the timescales of interest -see also Romero & Ascasibar (2018). The results of § 7 show that for a finite-N grav-itational system in an external potential the entropy increases significantly after a typical time…”

Section: Meaning Of the Entropy Estimatormentioning

confidence: 98%

The Discreteness-driven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, N-dependence, and the Role of Chaos

Silva

Pedra

Valluri

et al. 2019

ApJ

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We investigate the old problem of the fast relaxation of collisionless N-body systems which are collapsing or perturbed, emphasizing the importance of (non-collisional) discreteness effects. We integrate orbit ensembles in fixed potentials, estimating the entropy to analyze the time evolution of the distribution function. These estimates capture the correct physical behavior expected from the 2nd Law of Thermodynamics, without any spurious entropy production. For self-consistent (i.e. stationary) samples, the entropy is conserved, while for non-self-consistent samples, it increases within a few dynamical times, stabilizing at a maximum (even in integrable potentials). Our results make transparent that the main ingredient for this fast collisionless relaxation is the discreteness (finite N) of gravitational systems in any potential. Additionally, in non-integrable potentials, the presence of chaotic orbits accelerates the entropy production. Contrary to the traditional violent relaxation scenario, our results indicate that a time-dependent potential is not necessary for this relaxation. For the first time, in connection with the Nyquist-Shannon theorem we derive the typical timescale T /τ cr ≈ 0.1N 1/6 for this discreteness-driven relaxation, with slightly weaker N-dependencies for non-integrable potentials with substantial fractions of chaotic orbits. This timescale is much smaller than the collisional relaxation time even for small-N systems such as open clusters and represents an upper limit for the relaxation time of real N-body collisionless systems. Additionally, our results reinforce the conclusion of Beraldo e Silva et al. (2017) that the Vlasov equation does not provide an adequate kinetic description of the fast relaxation of collapsing collisionless N-body systems.

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Section: Meaning Of the Entropy Estimatormentioning

confidence: 98%

The Discreteness-driven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, N-dependence, and the Role of Chaos

Silva

Pedra

Valluri

et al. 2019

ApJ

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“…For instance, the close Nbody encounters and collective effects due to particle shot noise can have some dramatic, possibly cumulative effects (see, e.g. Aarseth, Lin, & Papaloizou 1988;Kandrup & Smith 1991;Boily, Athanassoula, & Kroupa 2002;Binney 2004;Joyce, Marcos, & Sylos Labini 2009;Colombi et al 2015;Beraldo e Silva et al 2017;Romero & Ascasibar 2018), particularly when initial conditions are cold or close to cold (see, e.g., Melott et al 1997;Melott 2007). While Vlasov codes do not use particles, they are still subject to non trivial numerical effects, because a phasespace grid still remains a discrete representation of the system (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

Phase-space structure analysis of self-gravitating collisionless spherical systems

Halle

Peirani

2018

A&A

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In the mean field limit, isolated gravitational systems often evolve towards a steady state through a violent relaxation phase. One question is to understand the nature of this relaxation phase, in particular the role of radial instabilities in the establishment/destruction of the steady profile. Here, through a detailed phase-space analysis based both on a spherical Vlasov solver, a shell code and a N-body code, we revisit the evolution of collisionless self-gravitating spherical systems with initial power-law density profiles ρ(r) ∝ r n , 0 ≤ n ≤ −1.5, and Gaussian velocity dispersion. Two sub-classes of models are considered, with initial virial ratios η = 0.5 ("warm") and η = 0.1 ("cool"). Thanks to the numerical techniques used and the high resolution of the simulations, our numerical analyses are able, for the first time, to show the clear separation between two or three well known dynamical phases: (i) the establishment of a spherical quasi-steady state through a violent relaxation phase during which the phase-space density displays a smooth spiral structure presenting a morphology consistent with predictions from self-similar dynamics, (ii) a quasi-steady state phase during which radial instabilities can take place at small scales and destroy the spiral structure but do not change quantitatively the properties of the phasespace distribution at the coarse grained level and (iii) relaxation to non spherical state due to radial orbit instabilities for n ≤ −1 in the cool case.

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From chaos to cosmology: insights gained from 1D gravity

Miller

Manfredi

Pirjol

et al. 2023

Class. Quantum Grav.

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The gravitational force controls the evolution of the universe on several scales. It is responsible for the formation of galaxies from the primordial matter distribution and the formation of planets from solar nebulae. Because the gravitational force is singular and has infinite range, making predictions based on fully three-dimensional models may be challenging. One-dimensional (1D) Newtonian gravity models were proposed as toy models for understanding the dynamics of gravitational systems. They can be integrated exactly and were used for computer simulations starting in the 1960s, providing the first demonstration of violent relaxation and the rapid development of long-lived quasi-stationary states. The present review provides the bases of the physics of 1D gravitational systems. It is divided into two main parts, the first concerning the approach to equilibrium and the second applications to cosmology. Each part is self-contained and can be read independently of the other. In the first part, we provide an introduction to the equilibrium thermodynamics of the one-dimensional gravitational sheet (OGS) system in the Vlasov limit. Both fixed and periodic boundary conditions are considered. The relaxation to equilibrium of the OGS is studied through numerical simulations which establish the role played by quasi-stationary states and violent relaxation. We also survey existing work on the Lyapunov exponents of the OGS and on the chaotic dynamics of 1D systems with few particles, focusing on the 1D three-body problem. The second part summarizes work on dynamical structure formation in cosmology using 1D systems. By transforming to comoving coordinates, which follow the global expansion of the universe, the 1D approach provides a useful laboratory for studying structure formation in various cosmological scenarios, from Einstein-de Sitter and $\Lambda$CDM to more recent, alternative cosmological models. A key result is the appearance of scale-free behavior with fractal dimension, which can be reliably studied in 1D for large systems over many epochs. Finally, an appendix gives some details on the numerical simulation methods used in these studies.

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On the probabilistic approach to the N-body problem

Cited by 3 publications

References 40 publications

The Discreteness-driven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, N-dependence, and the Role of Chaos

The Discreteness-driven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, N-dependence, and the Role of Chaos

Phase-space structure analysis of self-gravitating collisionless spherical systems

From chaos to cosmology: insights gained from 1D gravity

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