The Dense Stellar Systems Around Galactic Massive Black Holes

The central regions of galaxies show the presence of massive black holes and/or dense stellar systems. The question about their modes of formation is still under debate. A likely explanation of the formation of the central dense stellar systems in both spiral and elliptical galaxies is based on the orbital decay of massive globular clusters in the central region of galaxies due to kinetic energy dissipation by dynamical friction. Their merging leads to the formation of a nuclear star cluster, like that of the Milky Way, where a massive black hole (Sgr A*) is also present. Actually, high precision N-body simulations (Antonini, Capuzzo-Dolcetta et al. 2012, ApJ, 750, 111) show a good fit to the observational characteristics of the Milky Way nuclear cluster, giving further reliability to the cited `migratory' model for the formation of compact systems in the inner galaxy regions.Comment: Talk given at the Workshop on: Nuclei of Seyfert galaxies and QSOs - Central engine & conditions of star formation, November 6-8, 2012, Max-Planck-Insitut fuer Radioastronomie (MPIfR), Bonn, Germany. 6 pages, 4 figures, to be published in the Conference Proceedings, Proceedings of Science publishe

Merging of globular clusters within inner galactic regions. II. The Nuclear Star Cluster formation

In this paper we present the results of two detailed N-body simulations of the interaction of a sample of four massive globular clusters in the inner region of a triaxial galaxy. A full merging of the clusters takes place, leading to a slowly evolving cluster which is quite similar to observed Nuclear Clusters. Actually, both the density and the velocity dispersion profiles match qualitatively, and quantitatively after scaling, with observed features of many nucleated galaxies. In the case of dense initial clusters, the merger remnant shows a density profile more concentrated than that of the progenitors, with a central density higher than the sum of the central progenitors central densities. These findings support the idea that a massive Nuclear Cluster may have formed in early phases of the mother galaxy evolution and lead to the formation of a nucleus, which, in many galaxies, has indeed a luminosity profile similar to that of an extended King model. A correlation with galactic nuclear activity is suggested.Comment: 18 pages, 10 figures, 3 tables. Submitted to ApJ, main journa

Gravitational clustering in N-body simulations

In this talk we discuss some of the main theoretical problems in the understanding of the statistical properties of gravity. By means of N-body simulations we approach the problem of understanding the r\^ole of gravity in the clustering of a finite set of N-interacting particles which samples a portion of an infinite system. Through the use of the conditional average density, we study the evolution of the clustering for the system putting in evidence some interesting and not yet understood features of the process.Comment: 5 pages, 1 figur

Clustering in N-Body gravitating systems

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.Comment: 6 pages, 5 figures. To be published on Physica

Direct NN-body code on low-power embedded ARM GPUs

This work arises on the environment of the ExaNeSt project aiming at design and development of an exascale ready supercomputer with low energy consumption profile but able to support the most demanding scientific and technical applications. The ExaNeSt compute unit consists of densely-packed low-power 64-bit ARM processors, embedded within Xilinx FPGA SoCs. SoC boards are heterogeneous architecture where computing power is supplied both by CPUs and GPUs, and are emerging as a possible low-power and low-cost alternative to clusters based on traditional CPUs. A state-of-the-art direct $N$-body code suitable for astrophysical simulations has been re-engineered in order to exploit SoC heterogeneous platforms based on ARM CPUs and embedded GPUs. Performance tests show that embedded GPUs can be effectively used to accelerate real-life scientific calculations, and that are promising also because of their energy efficiency, which is a crucial design in future exascale platforms.Comment: 16 pages, 7 figures, 1 table, accepted for publication in the Computing Conference 2019 proceeding

The max-plus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis

We introduce a max-plus analogue of the Petrov-Galerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation. We show that the error in the sup norm can be bounded from the difference between the value function and its projections on max-plus and min-plus semimodules, when the max-plus analogue of the stiffness matrix is exactly known. In general, the stiffness matrix must be approximated: this requires approximating the operation of the Lax-Oleinik semigroup on finite elements. We consider two approximations relying on the Hamiltonian. We derive a convergence result, in arbitrary dimension, showing that for a class of problems, the error estimate is of order $\delta+\Delta x(\delta)^{-1}$ or $\sqrt{\delta}+\Delta x(\delta)^{-1}$, depending on the choice of the approximation, where $\delta$ and $\Delta x$ are respectively the time and space discretization steps. We compare our method with another max-plus based discretization method previously introduced by Fleming and McEneaney. We give numerical examples in dimension 1 and 2.Comment: 31 pages, 11 figure