Spatio-temporal dynamics and plastic flow of vortices in superconductors   with periodic arrays of pinning sites
  We present simulations of flux-gradient-driven superconducting rigid vortices interacting with square and triangular arrays of columnar pinning sites in an increasing external magnetic field. These simulations allow us to quantitatively relate spatio-temporal microscopic information of the vortex lattice with typically measured macroscopic quantities, such as the magnetization $M(H)$. The flux lattice does not become completely commensurate with the pinning sites throughout the sample at the magnetization matching peaks, but forms a commensurate lattice in a region close to the edge of the sample. Matching fields related to unstable vortex configurations do not produce peaks in $M(H)$. We observe a variety of evolving complex flux profiles, including flat terraces or plateaus separated by winding current-carrying strings and, near the peaks in $M(H)$, plateaus only in certain regions, which move through the sample as the field increases. 
C. Reichhardt, J. Groth, C. J. Olson, Stuart Field, Franco Nori