11. The Possible 7-, 9-, and 14-fold Symmetry Quasicrystals in Soft Matter

The chapter delves into the fascinating world of quasicrystals with 7-, 9-, and 14-fold symmetries in soft matter, focusing on their mathematical dynamics and constitutive laws. It introduces generalized dynamics models suggested by Fan, highlighting the unique couplings between phonons and phasons. The discussion includes the point group descriptions and phonon-phason constitutive laws, leading to a comprehensive set of governing equations. Notably, the chapter provides numerical solutions for the dynamics of 14-fold symmetry quasicrystals under dynamic loading, offering unprecedented insights into their behavior. Additionally, it suggests an incompressible complex fluid model for these quasicrystals, paving the way for further research and understanding of these intriguing materials.