  The dynamics of vortices in a type-II superconductor with defects are studied
by solving the time-dependent Ginzburg-Landau equations in two and three
dimensions. We show that vortex flux tubes are trapped by volume defects up to
a critical current density where they begin to jump between pinning sites along
static flow channels. We study the dependence of the critical current on the
pinning distribution and find for random distributions a maximum critical
current equal to a few percent of the depairing current at a pinning density
three times larger than the vortex line density. Whereas for a regular
triangular pinning array, the critical current is significantly larger when the
pinning density matches the vortex line density.
