  The flux line lattice of superconductors has been investigated when there
exists a periodicity in the underlying system, such as can occur in
artificially layered structures. For small fields parallel to the layers the
flux lines enter the sample in sequential rows, with the possibility of jumps
in the magnetization as new rows are created. As the field is increased these
discontinuities gradually decrease, but there still exist transitions between
states that are aligned differently to the periodic direction. Increasing the
magnitude of the periodic potential reduces the competition between differently
aligned lattices and tends to lock in one particular alignment. The effect of
transitions on the shear modulus is also discussed and related to the
experiments of Theunissen et al.
