Three-dimensional general solutions of orthorhombic quasicrystals with constraints

Abstract

This study employs the Lur'e operator method to derive generalized solutions for orthorhombic quasicrystals, incorporating anisotropy factors as a constraint. The obtained solutions encompass the Lekhnitskii-Hu-Nowacki and Elliott-Lodge formulations. Consequently, our analysis of the fundamental solution within infinite space offers a comprehensive characterization of quasicrystal anisotropy, employing both analytical and numerical approaches. It is noteworthy that the analytical solutions for orthorhombic quasicrystals can be simplified to accommodate hexagonal quasicrystals or conventional orthorhombic crystals, enhancing their versatility for broader engineering applications.