Numerical simulations are important tools for the study of space plasma physics. This grant is for continued research support to study the properties of shock waves and discontinuities in dissipative MHD and kinetic theory, the dynamics of the magnetosphere, and collisionless tearing instability in the magnetotail. Hybrid and implicit particle simulations will be used to study the kinetic properties of intermediate shocks and the possible role of such structures in dayside reconnection in the Earth's magnetotail will be investigated using increasingly realistic models of the near Earth plasma sheet. The principal aim will be to understand how and when a new neutral line forms within the pre-existing closed field lines of the plasma sheet.