Penetrations and dynamics of vortices in mesoscopic superconducting plates

As to a regular square superconducting plate with an anti-dot located at the center, for suddenly applying the field perpendicular to the plate, vortices tend to penetrate into the plate from four central points of the each square side keeping the fourfold rotational symmetry. After the penetration, we found the vortex exclusion process that residual vortices for stability of the system are expelled. For introducing external current that breaks symmetry of the system.