Groupoid description of modular structures
M. Nespolo, B. Souvignier, Berthold Stöger
Abstract
Modular structures are crystal structures built by subperiodic (zero-, mono- or diperiodic) substructures, called modules. The whole set of partial operations relating substructures in a modular structure build up a groupoid; modular structures composed of identical substructures are described by connected groupoids, or groupoids in the sense of Brandt. A general approach is presented to describe modular structures by Brandt's groupoids and how to obtain the corresponding space groups, in which only the partial operations that have an extension to the whole crystal space appear.
Topics & Concepts
Modular designExtension (predicate logic)Set (abstract data type)Space (punctuation)Algebra over a fieldComputer sciencePure mathematicsMathematicsProgramming languageOperating systemQuasicrystal Structures and PropertiesDiatoms and Algae Researchsemigroups and automata theory