Vortex Pinning and Dynamics in Layerd Superconductors with Periodic   Pinning Arrays
  We examine vortex dynamics and pinning in layered superconductors using three-dimensional molecular dyanmics simulations of magnetically interacting pancake vortices. Our model treats the magnetic interactions of the pancakes exactly, with longe-range logarithmic interactions both within and between planes. At the matching field the vortices are aligned with the pinning array. As a function of tilt angle for the pinning arrays a series of commensuration effects occur, seen as peaks in the critical current, due to pancakes finding a favorable alignment. 
Charles Reichhardt, Cynthia J. Olson and Niels Gronbech-Jensen