7 papers
Framework for Quasiperiodic Interfaces: Proximal Coincidence Point Set and Computation
Suining Xiong, Wenwen Zou, Pingwen Zhang +1
We present a unified theoretical and computational framework that bridges mathematical quasiperiodicity with classical crystallographic models. Based on a rigorous cut-and-projecti…
Representation of quasi-periodic functions and Hausdorff-Young inequalities for Besicovitch almost periodic functions
Aihua Fan, Kai Jiang, Pingwen Zhang
For a class of -ations and -actions on the -dimensional torus , we characterize their unique ergodicity and establish a theorem of Weyl…
Stability of diverse dodecagonal quasicrystals in T-shaped liquid crystalline molecules
Xin Wang, An-Chang Shi, Pingwen Zhang +1
Quasicrystals are intriguing ordered structures characterized by the lack of translational symmetry and the existence of rotational symmetry. The tiling of different geometric unit…
Designing a minimal Landau theory to stabilize desired quasicrystals
Wei Si, Shifeng Li, Pingwen Zhang +2
Interparticle interactions with multiple length scales play a pivotal role in the formation and stability of quasicrystals. Choosing a minimal set of length scales to stabilize a g…
Nucleation and phase transition of decagonal quasicrystals
Tiejun Zhou, Lei Zhang, Pingwen Zhang +2
In this work, we study the nucleation of quasicrystals from liquid or periodic crystals by developing an efficient order-order phase transition algorithm, namely the nullspace-pres…
Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems
Kai Jiang, Xueyang Li, Yao Ma +3
In this paper, we propose a new algorithm, the irrational-window-filter projection method (IWFPM), for quasiperiodic systems with concentrated spectral point distribution. Based on…
Theory of polygonal phases self-assembled from T-shaped liquid crystalline molecules
Zhijuan He, Xin Wang, Pingwen Zhang +2
Extensive experimental studies have shown that numerous ordered phases can be formed via the self-assembly of T-shaped liquid crystalline molecules (TLCMs) composed of a rigid back…