Anna Milano

Characterizing quasicrystals with topological quantities [PDF]
finished 2026-14
supervised by Michael Schmiedeberg

Abstract

In this work the dodecagonal Shield tiling is used as a model system to study flip induced tile rearrangements. A tile-based analysis is introduced in which the orientation of the tiles is encoded through complex phases that respect their rotational symmetry. This approach allows structural changes caused by flips to be quantified and their directional contributions to be analyzed. The framework enables systematic investigations of flip processes and provides a basis for computational studies of larger regions. The approach can also be applied to other tilings in which flips occur.