  Using the time-dependent Ginzburg Landau equations we study vortex motion
driven by an applied current in two dimensional superconductors in the presence
of a physical boundary. At smaller sourced currents the vortex lattice moves as
a whole, with each vortex moving at the same velocity. At larger sourced
current, vortex motion is organized into channels, with vortices in channels
nearer to the sample edges moving faster than those farther away from sample
edges, opposite to the Poiseuille flow of basic hydrodynamics where the
velocity is lowest at the boundaries. At intermediate currents, a stick-slip
motion of the vortex lattice occurs in which vortices in the channel at the
boundary break free from the Abrikosov lattice, accelerate, move past their
neighbors and then slow down and reattach to the vortex lattice at which point
the stick-slip process starts over. These effects could be observed
experimentally, e.g. using fast scanning microscopy techniques.
