标题： 通过振幅方程模拟准晶体中的位错 显示英文标题

标题： Modeling dislocations in quasicrystals through amplitude equations

摘要： 准晶体（QCs）是一类在各种系统中出现的非周期性有序结构，从金属合金到软物质和驱动的非平衡系统。 在基于准晶体（QCs）缓慢变化的复振幅的介观理论中，我们将位错作为由振幅承载的拓扑缺陷，并表征其伯格斯矢量和引起的变形。 我们研究了半共格界面上位错的形成，特别是那些来自旋转内含物的位错，并发现此类界面上形成了位错的层次结构。 我们进一步分析了应变系统中的界面，揭示了周期性位错阵列出现的条件，并讨论了与不同声子和相位变形相关的位错的能量学。 位错偶极子和四极子的稳定性、相互作用和运动也进行了讨论。 这些发现为准晶体（QCs）中位错的介观建模提供了新的见解，并展示了其与传统晶体的不同行为，同时展示了一个用于研究具有准晶体有序系统的位错的通用框架。 显示英文摘要

摘要： Quasicrystals (QCs) are a class of aperiodic ordered structures that emerge in various systems, from metallic alloys to soft matter and driven non-equilibrium systems. Within a mesoscale theory based on slowly-varying complex amplitudes for QCs, we track dislocations as topological defects harbored by the amplitudes and characterize their Burgers vectors and induced deformations. We study the formation of dislocations at semicoherent interfaces, particularly those emerging from rotated inclusions, and find a hierarchy of dislocations forming at such interfaces. We further analyze interfaces in strained systems, revealing conditions for the emergence of periodic dislocation arrays and discussing the energetics of dislocations associated with different phonon and phason deformations. The stability, interaction, and motion of dislocation dipoles and quadrupoles are also discussed. These findings provide new insights into the mesoscale modeling of dislocations in QCs and their distinct behavior compared to conventional crystals, while demonstrating a versatile framework for studying dislocations in systems exhibiting quasicrystalline order.