Clustering in N-body gravitating systems

Abstract

Self-gravitating systems have acquired growing interest in statistical mechanics, due to the peculiarities of the 1/r potential. Indeed, the usual approach of statistical mechanics cannot be applied to a system of many point particles interacting with the Newtonian potential, because of (i) the long range nature of the 1/r potential and of (ii) the divergence at the origin. We study numerically the evolutionary behavior of self-gravitating systems with periodical boundary conditions, starting from simple initial conditions. We do not consider in the simulations additional effects as the (cosmological) metric expansion and/or sophisticated initial conditions, since we are interested whether and how gravity by itself can produce clustered structures. We are able to identify well defined correlation properties during the evolution of the system, which seem to show a well defined thermodynamic limit, as opposed to the properties of the "equilibrium state". Gravity-induced clustering also shows interesting self-similar characteristics.

Gravitational dynamics of an infinite shuffled lattice of particles

“…The simplest interpretation of this behavior -and the usual one in cosmology -is that this corresponds to a fluid-like behavior of the system i.e. to an evolution which can be described, at both linear and non-linear scales, by a set of non-linear fluid equations approximating the particle dynamics 28 . If this interpretation is correct, any δ-dependent effects in the evolution of SL with different δ, but with the same large scale fluctuations (i.e.…”

Scaling in Cosmic Structures

“…On the contrary, this is not true for the final state of equilibrium, when the system has formed a single cluster 15 .…”

Correlations, spectra, and instability of phase-space density fluctuations in open-cluster models

“…Table 1 also lists the phase velocities v f , v v , and v r (in pc/Myr; 1 pc/Myr 1 km/s) determined using the PSCS computed with the 11th-order integration method and with the allowance for the correlation parameters in models 1-6 adopted from [7]. It is evident from Table 1 that the phase velocities v f and v v in cluster models 1-4 are substantially (by a factor of [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] smaller than the corresponding phase velocities for models 5 and 6. In the case of v r , the difference between the models is not so pronounced.…”

“…The formulas for the correlation functions derived by Chavanis [1][2][3] have a rather complex form making them difficult to use for analyzing dynamic processes in such systems. In our opinion, it is more productive to compute the correlation functions directly by numerically integrating the equations of motion of gravitating particles in the problems of clustering of galaxies and the evolution of the Universe (see, e.g., [4][5][6]), and also when modeling the dynamics of open star clusters (OCl) [7].…”

“…The formulas for the correlation functions derived by Chavanis [1-3] have a rather complex form making them difficult to use for analyzing dynamic processes in such systems. In our opinion, it is more productive to compute the correlation functions directly by numerically integrating the equations of motion of gravitating particles in the problems of clustering of galaxies and the evolution of the Universe (see, e.g., [4][5][6]), and also when modeling the dynamics of open star clusters (OCl) [7].In one of our previous papers [7] we computed the two-time correlation functions for r = |r|, v = |v|, and the energy ε per unit star mass, as well as twoparticle correlations of r, v, ε, stellar number density n = n(r, t) and PSD f = f (r, v, t) for open star …”