Quasiperiodic systems: algorithms, analysis and applications

发布时间：2021-09-28 作者：浏览次数：

Speaker:	蒋凯教授	DateTime:	2021年9月29日下午4:30-5:30
Brief Introduction to Speaker: 蒋凯，湘潭大学教授。		Place:	六号楼二楼报告厅
Abstract:Quasiperiodic systems, related to irrational numbers, are important and widely existing systems, including periodic crystals, quasicrystals, incommensurate systems, interfacial problems, and so on. Due to the irrational numbers, the quasiperiodic system is a space-filling structure without decay, which results in difficulty in numerical computation. A widely used method is a periodic approximation method which uses a periodic system to approximate the quasiperiodic system. It produces a Diophantine approximation error and related errors. In this talk, we will establish the approximation thoery of the periodic approximation method. Furthermore, we propose an efficient and precise method, i.e., the projection method, to avoid the Diophantine approximation and obtain high accurate quasiperiodic structures. We also apply the novel method to some applications, including quasicrystals, quasiperiodic interfaces, order-order nucleation, and quasiperiodic quantum systems.