A group theoretical approach to structural transitions of icosahedral quasicrystals and point arrays

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Zappa , E , Dykeman , E C , Geraets , J A & Twarock , R 2016 , ' A group theoretical approach to structural transitions of icosahedral quasicrystals and point arrays ' Journal of Physics A: Mathematical and Theoretical , vol. 49 , no. 17 , 175203 . DOI: 10.1088/1751-8113/49/17/175203

Title: A group theoretical approach to structural transitions of icosahedral quasicrystals and point arrays
Author: Zappa, Emilio; Dykeman, Eric C.; Geraets, James A.; Twarock, Reidun
Contributor: University of Helsinki, Institute of Biotechnology
Date: 2016-04-29
Language: eng
Number of pages: 20
Belongs to series: Journal of Physics A: Mathematical and Theoretical
ISSN: 1751-8113
URI: http://hdl.handle.net/10138/231735
Abstract: In this paper we describe a group theoretical approach to the study of structural transitions of icosahedral quasicrystals and point arrays. We apply the concept of Schur rotations, originally proposed by Kramer, to the case of aperiodic structures with icosahedral symmetry; these rotations induce a rotation of the physical and orthogonal spaces invariant under the icosahedral group, and hence, via the cut-and-project method, a continuous transformation of the corresponding model sets. We prove that this approach allows for a characterisation of such transitions in a purely group theoretical framework, and provide explicit computations and specific examples. Moreover, we prove that this approach can be used in the case of finite point sets with icosahedral symmetry, which have a wide range of applications in carbon chemistry (fullerenes) and biology (viral capsids).
Subject: structural transitions
icosahedral quasicrystals
Schur rotations
icosahedral point arrays
SYMMETRY
PHASE
VIROLOGY
ROTATION
VIRUSES
ORDER
1183 Plant biology, microbiology, virology
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