Several observational and theoretical studies suggest that the initial mass function (IMF) slope for massive stars in globular clusters (GCs) depends on the initial cloud density and metallicity, such that the IMF becomes increasingly top-heavy with decreasing metallicity and increasing the gas density of the forming object. Using N-body simulations of GCs starting with a top-heavy IMF and undergo early gas expulsion within a Milky Way-like potential, we show how such a cluster would evolve. By varying the degree of top-heaviness, we calculate the dissolution time and the minimum cluster mass needed for the cluster to survive after 12 Gyr of evolution.

Spiral structures in the disk galaxies have been extensively studied by many theoretical papers, but conventional steady-state models are not consistent with what we observe in time-dependent, multi-dimensional numerical simulations and also in real galaxies. Here we review recent progress in numerical modeling of stellar and gas spirals in disk galaxies. The spiral arms excited in a stellar disk can last for 10 Gyrs without the ISM, but each spiral arm is short-lived and is recurrently formed. The stellar spirals are not waves propagating with a single pattern speed. The ISM is concentrated in local potential minima, which roughly follow the galactic rotation together with the stellar arms, therefore galactic dust lanes are not the classic ‘galactic shocks’.

Some circumstantial evidence for residual planetesimals is constructed based on the recent discovery of a dusty ring around a young white dwarf at the center of the Helix nebula (Su et al. 2007). This ring extends between about 35 and 150 AU from the nebula center, and have a total mass of about 0.13 M⊕. In this paper we propose that this ring is the by-product of planets and planetesimals' orbital evolution during the epoch when the central star rapidly lost most of its mass. We examine the dynamical evolution of planetary systems similar to the solar system (i.e. with gas giant planets and residual planetesimals) as their host stars evolve off the main sequence. During the process, some planetesimals will be captured by the gas giants into mean motion resonances and their mutual collisions will form a dust ring similar to that observed at the center of the Helix nebula.

Two mechanisms involving purely dynamical processes can lead to the formation of a bulge after its disc: 1) small bulges (1 – 2 kpc), including box-shaped bulges and mildly triaxial bulges, can result from the formation and destruction of a bar; 2) big bulges (> 2kpc) à la Sombrero can grow following the accretion of small satellites. Fully consistent N-body simulations show that the fraction of galaxy mass accreted in this way needs to be larger than about 5%. Less accretion does not create smaller bulges, but heats the whole disc. These dynamical effects transforming Hubble types from SB to SA and vice-versa over ≈ 1 – 2 Gyr also indicate, by the secular growth of bulges, a general sense of galactic evolution from Sd to Sa.

The dynamical evolution of the planetary rings is simulated by means of a numerical model in which particles interact through mutual attraction and inelastic collisions. We use a mixed simulation: a deterministic integration of the N - body problem for large distances (“particle-mesh” method with an expansion of density and potential in spherical harmonics) and a Monte Carlo treatment for the close encounters. The implementation is done in the Connection Machine in order to be able to make a detailed simulation using a greater number of particles (of the order of 105). The deterministic calculation of the action of a shepherding satellite on the particles will allow us to study the effect of resonances on the formation and the evolution of the sharp edges of the rings.