  Anti-plane shear deformations of a hexagonal quasi-crystal with multiple
screw dislocations are considered. Using a variational formulation, the elastic
equilibrium is characterized via limit of minimizers of a core-regularized
energy functional. A sharp estimate of the asymptotic energy when the core
radius tends to zero is obtained using higher-order $\Gamma$-convergence. Also,
the interaction between dislocations and the Peach-K\"{o}hler force at each
dislocation are analyzed.
