  Quasicrystals are characterized by quasi-periodic arrangements of atoms. The
description of their mechanics involves deformation and a (so called phason)
vector field accounting at macroscopic scale of local phase changes, due to
atomic flips necessary to match quasi-periodicity under the action of the
external environment. Here we discuss the mechanics of quasicrystals,
commenting the shift from its initial formulation, as standard elasticity in a
space with dimension twice the ambient one, to a more elaborated setting
avoiding physical inconveniences of the original proposal. In the new setting
we tackle two problems. First we discuss the linear dynamics of quasicrystals
including a phason diffusion. We prove existence of weak solutions and their
uniqueness under rather general boundary and initial conditions. We then
consider phason rotational inertia, non-linearly coupled with the curl of the
macroscopic velocity, and prove once again existence of weak solutions to the
pertinent balance equations.
