Several observational and theoretical indications suggest that the initial mass function (IMF) becomes increasingly top-heavy (i.e., overabundant in high-mass stars with mass m > 1M) with decreasing metallicity and increasing gas density of the forming object. This affects the evolution of globular clusters (GCs) owing to the different mass-loss rates and the number of black holes formed. Previous numerical modeling of GCs usually assumed an invariant canonical IMF. Using the state-of-the-art NBODY6 code, we perform a comprehensive series of direct N-body simulations to study the evolution of star clusters, starting with a top-heavy IMF and undergoing early gas expulsion. Utilizing the embedded cluster mass-radius relation of Marks & Kroupa (2012) for initializing the models, and by varying the degree of top-heaviness, we calculate the minimum cluster mass needed for the cluster to survive longer than 12 Gyr. We document how the evolution of different characteristics of star clusters such as the total mass, the final size, the density, the mass-to-light ratio, the population of stellar remnants, and the survival of GCs is influenced by the degree of top-heaviness. We find that the lifetimes of clusters with different IMFs moving on the same orbit are proportional to the relaxation time to a power of x that is in the range of 0.8 to 1. The observed correlation between concentration and the mass function slope in Galactic GCs can be accounted for excellently in models starting with a top-heavy IMF and undergoing an early phase of rapid gas expulsion.

We investigate the Hall effect in a standard magnetized accretion disk which is accompanied by dissipation due to viscosity and magnetic resistivity. By considering an initial magnetic field, using the PLUTO code, we perform a numerical magnetohydrodynamic simulation in order to study the effect of Hall diffusion on the physical structure of the disk. Current density and temperature of the disk are significantly modified by Hall diffusion, but the global structure of the disk is not substantially affected. The changes in the current densities and temperature of the disk lead to a modification in the disk luminosity and radiation.

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.

We study the dynamical evolution of star clusters on eccentric orbits using a semianalytical approach. In particular we adapt and extend the equations of emacss code, introduced by Gieles et al. (2014), to work with eccentric orbits. We follow the evolution of star clusters in terms of mass, half-mass radius, core radius, Jacobi radius and the total energy over their dissolution time. Moreover, we compare the results of our semi-analytical models against N -body computations of clusters with various initial half-mass radius, number of stars and orbital eccentricity to cover both tidally filling and under-filling systems. The evolution profiles of clusters obtained by our semi-analytical approach closely follow those of N -body simulations in different evolutionary phases of star clusters, from pre-collapse to post-collapse. Given that the average runtime of our semi-analytical models is significantly less than that of Nbody models, our approach makes it feasible to study the evolution of large samples of globular clusters on eccentric orbits.