  From a very simple description of vortices and pinning centers and without
using any electrodynamical assumptions, we obtain nonlinear density profiles of
vortices in type-II dirty superconductors that result from raising or lowering
an external magnetic field. The results confirm a modified Bean model
description of these systems, and in particular, follow the Kim empirical form
that relates the current inside the material to the local magnetic field. We
also obtain realistic magnetization hysteresis loops and examine the discrete
evolution of the density profiles in our systems. This evolution is not
continuous, but takes place by the occurrence of avalanches of vortices
promoted by the addition or extraction of vortices from the edges of the
system.
