论文标题
弯曲表面上的被动和活性流体中的拓扑波：统一图片
Topological waves in passive and active fluids on curved surfaces: a unified picture
论文作者
论文摘要
我们研究了局限于弯曲表面上的经典流体中拓扑保护波的发生。利用拓扑结合理论和实际空间分析的结合，我们证明了在二维被动和活性流体中拓扑保护背后的系统独立机制的存在。这使我们能够制定一个索引定理，该索引定理链接由傅立叶空间拓扑确定的模式的数量，与它们托管的表面的真实空间拓扑确定。借助此框架，我们回顾了二维流体中拓扑波的两个例子，即在活性极性流体中传播在地球旋转的表面和动量波上的海洋浅水波，自发地“植入”底座上的底座“羊群”，并带有$ {\ rm u}（\ rm u}（\ rm u}（1）$ iSometry（1）$ ismetry（E。G.我们的工作提出了一些简单的规则，以在被动和主动软物质系统中的表面上设计拓扑模式。
We investigate the occurrence of topologically protected waves in classical fluids confined on curved surfaces. Using a combination of topological band theory and real space analysis, we demonstrate the existence of a system-independent mechanism behind topological protection in two-dimensional passive and active fluids. This allows us to formulate an index theorem linking the number of modes, determined by the topology of Fourier space, to the real space topology of the surface on which they are hosted. With this framework in hand, we review two examples of topological waves in two-dimensional fluids, namely oceanic shallow-water waves propagating on the Earth's rotating surface and momentum waves in active polar fluids spontaneously "flocking" on substrates endowed with a ${\rm U}(1)$ isometry (e.g. surfaces of revolution). Our work suggests some simple rules to engineer topological modes on surfaces in passive and active soft matter systems.
