Perfect single-crystalline materials do not exist. Interfaces are prevalent in crystalline materials and exert a significant influence on material properties. The study of interface structures has long been recognized as one of the core issues in materials science. Most investigations focus on periodic interfaces; by contrast, the understanding of quasiperiodic interfaces—despite their ubiquity—remains limited. In this talk, we elucidate the origin of quasiperiodic order in interfaces by employing a unified theoretical and computational framework. Within the proximal coincidence point set theory we developed, quasiperiodicity arises intrinsically from cut-and-project constructions with visually indistinguishable perturbations, and is encoded in the corresponding Fourier-Bohr spectral structures. These spectral characteristics underpin our efficient numerical framework, which integrates the conserved Landau-Brazovskii model with the projection method to enable accurate entire-domain simulations. In this framework, quasiperiodicity is governed by the intensity distribution in reciprocal space and manifested in the resulting interfacial ordering. We report compelling quasiperiodic signatures across tilt grain boundaries, twist grain boundaries, and general interfaces, including finite local complexity, repetitivity, emergent generalized Fibonacci sequences, as well as 12-fold and 8-fold interfacial quasicrystal structures.

蒋凯, 教授, 主要从事无理数引发的应用数学方面的研究, 在 SINUM、SISC、SIMA、JCP、PNAS、Adv. Sci.、Macromolecules、Phys. Rev. B/E/R 等期刊发表学术论文60余篇; 入选教育部高层次青年人才奖励计划; 研究得到国家重点研发计划课题、国家自然科学基金面上基金、湖南省科技创新领军人才计划等资助; 获得宝钢教育优秀教师奖、湖南省优秀博士论文指导教师等; 现担任《计算数学》编委。