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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.
Highlights
It is commonly acknowledged that the long-range order in quasicrystals depends on a hypothetical order propagation mechanism usually referred to as matching rules
This understanding has been applied to the structure determination on a case by case basis only, for instance by trying to interpret the observed structure as a decoration of a tiling already known to have matching rules
In [1], we suggested that the exploration of matching rules should instead be the primary goal in solving quasicrystalline structures
Summary
It is commonly acknowledged that the long-range order in quasicrystals depends on a hypothetical order propagation mechanism usually referred to as matching rules. 2. Homology-based matching rules By the very nature of our program, the model should be locally derivable from the atomic structure only.
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