  Quasiperiodic arrangements of the constitutive materials in composites result
in effective properties with very unusual electromagnetic and elastic
properties. The paper discusses the cut-and-projection method that is used to
characterize effective properties of quasiperiodic materials. Characterization
of cut-and-projection convergence limits of partial differential operators is
presented, and correctors are established. We provide the proofs of the results
announced in (Wellander et al., 2018) and give further examples. Applications
to problems of interest in physics include electrostatic, elastostatic and
quasistatic magnetic cases.
