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arXiv · 1909.07436

Robust matching rules for real quasicrystals

Pavel Kalugin·André Katz
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Abstract

We consider the problem of extraction and validation of matching rules, directly from the phased diffraction data of a quasicrystal, and propose an algorithmic procedure to produce the rules of the shortest possible range. We have developed a geometric framework to express such rules together with a homological mechanism enforcing the long-range quasiperiodic order. This mechanism tolerates the presence of defects in a robust way.

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Pavel Kalugin, André Katz. 2019-09-16. Robust matching rules for real quasicrystals. https://doi.org/10.1088/1742-6596/1458/1/012002

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