  The magnetoresistance of thin superconducting strips subject to a
perpendicular magnetic field B and low temperatures T manifests a sequence of
alternating superconductor-insulator transitions (SIT). We study this
phenomenon within a quasi one-dimensional (1D) model for the quantum dynamics
of vortices in a line-junction between coupled parallel SC wires, at parameters
close to their SIT. Mapping the vortex system to 1D Fermions at a chemical
potential dictated by B, we find that a quantum phase transition of the Ising
type occurs at critical values of the vortex filling, from a SC phase near
integer filling to an insulator near 1/2-filling. For T->0, the resulting
magnetoresistance R(B) exhibits oscillations similar to the experimental
observation.
