Structural transformations in quasicrystals induced by higher dimensional lattice transitions

Abstract

We study the structural transformations induced, via the cut-and-project method, in quasicrystals and tilings by lattice transitions in higher dimensions, with a focus on transition paths preserving at least some symmetry in intermediate lattices. We discuss the effect of such transformations on planar aperiodic Penrose tilings, and on threedimensional aperiodic Ammann tilings with icosahedral symmetry. We find that locally the transformations in the aperiodic structures occur through the mechanisms of tile splitting, tile flipping and tile merger, and we investigate the origin of these local transformation mechanisms within the projection framework.

Structural constraints on the three-dimensional geometry of simple viruses: case studies of a new predictive tool

“…Finally, we interrogated the capsid structure of CCMV (cowpea chlorotic mottle virus) before (Speir et al, 1995) and after (Tama & Brooks, 2002;Liu et al, 2003) expansion. Bestfit point arrays provided coarse-grained models that were used to determine features of the structural transition via a lattice approach (Indelicato, Keef et al, 2012).…”

On the subgroup structure of the hyperoctahedral group in six dimensions

“…sentation H in the class and a maximal subgroup P of H, then there exists exactly one other representation K in the class such that P ¼ H \ K. As explained in the Introduction, this can be used to describe transitions which keep intermediate symmetry encoded by P. In particular, this result implies in this context that a transition from a structure arising from H via projection will result in a structure obtainable for K via projection if the transition has intermediate symmetry described by P. Therefore, this setting is the starting point to analyse structural transitions between icosahedral quasicrystals, following the methods proposed in Kramer (1987), Katz (1989) and Indelicato et al (2012), which we are planning to address in a forthcoming publication. These mathematical tools also have many applications in other areas.…”

“…The set ðH; k Þ is the starting point for the construction of quasicrystals via the cut-and-project method (Senechal, 1995;Indelicato et al, 2012).…”

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An algorithm for the arithmetic classification of multilattices

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