  By solving the Bogoliubov - de Gennes equation self-consistently in the
presence of a non-equilibrium quasi-particle distribution, we compute the
current-voltage characteristic of a phase coherent superconducting island with
a tunnel barrier at one end. The results show significant structure, arising
from the competition between scattering processes at the boundaries of the
island and modification of the order parameter by quasi-particles and
superflow. This structure is not present in non self-consistent descriptions of
normal-superconducting nano-structures.
