On the Josephson Coupling between a disk of one superconductor and a   surrounding superconducting film of a different symmetry
  A cylindrical Josephson junction with a spatially dependent Josephson coupling which averages to zero is studied in order to model the physics of a disk of d-wave superconductor embedded in a superconducting film of a different symmetry. It is found that the system always introduces Josepshon vortices in order to gain energy at the junction. The critical current is calculated. It is argued that a recent experiment claimed to provide evidence for s-wave superconductivity in $YBa_2Cu_3O_7$ may also be consistent with d-wave superconductivity. Figures available from the author on request. 
A. J. Millis (A.T.& T. Bell Laboratories, 600 Mountain Avenue, Murray   Hill, N. J.USA)