Beijing Institute of Mathematical Sciences and Applications

Yi Zhu

Kai Jiang

Thursday, April 21, 2022 10:00 AM - 11:30 AM

Tencent 836 6547 4971 ()

In this talk, we will introduce recent advances in computing quasiperiodic systems. Quasiperiodic systems, related to irrational numbers, are important and widely existing systems, including quasicrystals, incommensurate systems, and interfacial problems. This talk will be split into three parts. The first part will introduce some basic concepts about quasiperiodic systems. The second part will give two methods to address the quasiperiodic systems, including the periodic approximation method (PAM) and the projection method (PM). We will give the approximation theory for these methods. Results demonstrate that the Diophantine approximation error dominates the computational precision of the PAM, which is independent of numerical computation. In contrast, the PM has spectral accuracy. The third part will present some applications, including the thermodynamic stability of quasicrystals, phase transition, quasiperiodic quantum systems, and quasiperiodic interfaces.

蒋凯，湘潭大学教授，博士生导师。主要研究方向是准周期系统计算、复杂流体建模与计算等，在准晶方面的研究，是博士后合作导师张平文院士在2018年国际数学家大会的主要内容。获湖南省自然科学基金委“杰出青年科学基金”资助，主持国家自然科学基金委面上基金两项。曾获中国计算数学学会优秀青年论文一等奖。目前担任中国工业与应用数学学会“数学与航天交叉学科”专业委员会（筹）副秘书长，“科学工程计算与数值仿真”湖南省重点实验室副主任。