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

Existence results in the linear dynamics of quasicrystals with phason diffusion and non-linear gyroscopic effects