Elasticity and hydrodynamics of quasicrystals with 7-, 14-, 9- and 18-fold symmetries

TL;DR

This paper develops a theoretical framework for the elasticity and hydrodynamics of quasicrystals with unusual symmetries using a 6D embedding space, providing equations and solution methods relevant for solid and soft matter phases.

Contribution

It introduces a novel theoretical approach to describe the elasticity and hydrodynamics of quasicrystals with multiple-fold symmetries using a 6D embedding space and symmetry breaking principles.

Findings

Governing equations for quasicrystals with 7-, 14-, 9-, and 18-fold symmetries established.

Solution procedures for initial-boundary value problems discussed.

Framework applicable to both solid and soft matter phases.

Abstract

This letter reports theory of elasticity and hydrodynamics of quasicrystals with 7-, 14-, 9- and 18-fold symmetries in solid phase, in which the 6-dimensional embedding space concept is used. Based on the concept and the Landau-Anderson symmetry breaking principle and the Lubensky hydrodynamics, the governing equations for the above quasicrystal systems have been set up, the solving procedure for the initial-boundary value problems of the equations is discussed as well. Though the discussion is concerned only for the quasicrystals, in particular for one of 18-fold symmetry, in solid phase, it may be a basis for those in soft matter phase observed recently.