论文标题
扭曲kagomes格子二元边界的声子景观的对称性
Symmetry of the phonon landscape across the duality boundary of twisted kagomes lattices
论文作者
论文摘要
在这项工作中，我们研究了扭曲的kagome晶格的声子景观的对称性。这项研究的灵感来自Fruchart等人最近的工作。 [Nature，577，2020]，他将双重性的概念专门用于Kagome Lattices的机械问题，并将其与在配置空间中关键过渡点对称的配置之间的偶性转换链接在一起。我们的第一个目标是阐明双重配置之间的匹配声子光谱的存在如何在可观察到的波场特征方面表现出来。为此，我们探索了将双重kagome构型汇总成几何异质性但保留机械均匀响应的双层域晶格的可能性。我们的第二个目标是将分析扩展到梁的结构晶格，这些晶石代表了逼真的细胞超材料。我们表明，在这种情况下，跨双重边界的声子景观的对称性被损坏了，这意味着双重行为的条件不仅取决于几何形状，还取决于细胞的主要机制，表明几何学和功能双重性之间的二分法。
In this work, we investigate the symmetry of the phonon landscape of twisted kagome lattices across their duality boundary. The study is inspired by recent work by Fruchart et al. [Nature, 577, 2020], who specialized the notion of duality to the mechanistic problem of kagome lattices and linked it to the existence of duality transformations between configurations that are symmetrically located across a critical transition point in configuration space. Our first goal is to elucidate how the existence of matching phonon spectra between dual configurations manifest in terms of observable wavefield characteristics. To this end, we explore the possibility to aggregate dual kagome configurations into bi-domain lattices that are geometrically heterogeneous but retain a mechanically homogeneous response. Our second objective is to extend the analysis to structural lattices of beams, which are representative of realistic cellular metamaterials. We show that, in this case, the symmetry of the phonon landscape across the duality boundary is broken, implying that the conditions for dual behavior do not merely depend on the geometry, but also on the dominant mechanisms of the cell, suggesting a dichotomy between geometric and functional duality.
