  We have developed a set of numerical tools for the quantitative analysis of
defect dynamics in quasiperiodic structures. We have applied these tools to
study dislocation motion in the dynamical equation of Lifshitz and Petrich
[Phys. Rev. Lett. 79 (1997) 1261] whose steady state solutions include a
quasiperiodic structure with dodecagonal symmetry. Arbitrary dislocations,
parameterized by the homotopy group of the D-torus, are injected as initial
conditions and quantitatively followed as the equation evolves in real time. We
show that for strong diffusion the results for dislocation climb velocity are
similar for the dodecagonal and the hexagonal patterns, but that for weak
diffusion the dodecagonal pattern exhibits a unique pinning of the dislocation,
reflecting its quasiperiodic nature.
