Current states in superconducting films: numerical results and   approximations
  We present numerical solution of equations by Aslamazov and Lempitskiy (AL) for the distribution of the transport current density in thin superconducting films in the absence of external magnetic field, in both the Meissner and the vortex states. This solution describes smooth transition between the regimes of a wide film and a narrow channel and enables us to find the critical currents and current-voltage characteristics within a wide range of the film width and temperatures. We propose simple approximating formulas for the current density distributions and critical currents. 
E.V. Bezuglyi
cond-mat.supr-con