Formation of topological defects in thin superconducting rings

We report on analytical and numerical results for the problem of superconductivity in rings and shells. We first derive a lower dimensional approximation of the Ginzburg-Landau equations. The model is then analysed by several methods. A perturbation theory is carried out for nearly uniform geometries. For some special geometries we provide explicit or numerical solutions. A theory of networks of rings is presented. Our results indicate that for a range of temperatures below T-c, the topology of the order parameter changes whenever the flux divided by the fundamental flux unit is half an integer.