Calculation of the phase field of a vortex pair on the surface of a multiply connected substrate

The vortex pair phase field is calculated, through a solution of the Laplace equation, for a superfluid film adsorbed on the surface of a model three-dimensioanally connected porous medium. A number of different vortex-antivortex pair configurations are considered as functions of the porosity or an aspect ratio of the model porous structure. The calculated results give the energy of a pair for motion of the vortex cores around a pore or a solid rod as well as for the string configuration corresponding to a linear separation of the vortex pair through the porous medium.