标题： 无限方形格点中线缺陷的局域化 显示英文标题

标题： Localisation for a line defect in an infinite square lattice

摘要： 由嵌入无限方形晶格中的几个质量组成的有限线缺陷产生的局域化缺陷模式，利用单个质量缺陷的格林函数的线性叠加进行了分析。提出了晶格格林函数的几种表示形式并加以讨论。问题被简化为一个特征值系统，并详细检查了相应矩阵的性质，以获得关于对称和反对称模式数量的信息。提出了与长波长均匀化相关的远场渐近展开式。还讨论了接近带边界的格林函数的渐近表达式。给出了几个例子，其中计算了与该系统相关的特征频率和相应的特征模式，并与渐近展开式进行了比较。无穷缺陷的情况也被考虑，并得到了显式的色散关系。当线缺陷中的质量数较多时，证明可以通过无限链的色散图来预测特征频率的范围。 显示英文摘要

摘要： Localised defect modes generated by a finite line defect composed of several masses, embedded an infinite square cell lattice, are analysed using the linear superposition of Green's function for a single mass defect. Several representations of the lattice Green's function are presented and discussed. The problem is reduced to an eigenvalue system and the properties of the corresponding matrix are examined in detail to yield information regarding the number of symmetric and skew-symmetric modes. Asymptotic expansions in the far field, associated with long wavelength homogenisation are presented. Asymptotic expressions for Green's function in the vicinity of the band edge are also discussed. Several examples are presented where eigenfrequencies linked to this system and the corresponding eigenmodes are computed for various defects and compared with the asymptotic expansions. The case of an infinite defect is also considered and an explicit dispersion relation is obtained. For the case when the number of masses within the line defect is large, it is shown that the range of the eigenfrequencies can be predicted using the dispersion diagram for the infinite chain.