  The vortex patterns stabilized by the square array of artificial pinning
sites with a tunable pinning strength are studied by using a phenomenological
approach in the London limit. The transitions between pinned and deformed
triangular lattices are analyzed as a function of the amplitude of the
vortex-pinning site interaction and the characteristic length-scale of this
interaction. The critical current and different phases of vortex lattice are
studied in presence of external transport current.
