Langevin dynamics simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced point defects as a smoothened distribution of a random potential. Both the electromag
netic and Josephson interactions among pancake vortices were included. A special shaking and annealing process was introduced to let the system approach the equilibrium configuration. We are able to see the inverse melting transition from the Bragg-glass to the amorphous vortex glass state, in agreement with recent experiments.
In this paper we use London Langevin molecular dynamics simulations to investigate the vortex matter melting transition in the highly anisotropic high-temperature superconductor material Bi_2Sr_2CaCu_2O$_{8+delta}$ in the presence of low concentratio
n of columnar defects (CDs). We reproduce with further details our previous results obtained by using Multilevel Monte Carlo simulations that showed that the melting of the nanocrystalline vortex matter occurs in two stages: a first stage melting into nanoliquid vortex matter and a second stage delocalization transition into a homogeneous liquid. Furthermore, we report on new dynamical measurements in the presence of a current that identifies clearly the irreversibility line and the second stage delocalization transition. In addition to CDs aligned along the c-axis we also simulate the case of tilted CDs which are aligned at an angle with respect to the applied magnetic field. Results for CDs tilted by $45^{circ}$ with respect to c-axis show that the locations of the melting and delocalization transitions are not affected by the tilt when the ratio of flux lines to CDs remains constant. On the other hand we argue that some dynamical properties and in particular the position of the irreversibility line should be affected.
