流体动力学活动晶格的集体振动
Collective vibrations of a hydrodynamic active lattice
摘要：
最近的实验表明，准一维晶格的自推进液滴表现出集体不稳定性的形式，异相振荡和孤立波。这种流体动力学晶格是由一个垂直振动的流体浴，这调用一个在浴表面上的亚临界法拉第波场的外部强迫，介导的时空液滴coupling.By建模液滴晶格作为一个内存赋予系统与空间非本地耦合，我们在此合理化的形式和发病的不稳定性在这一类新的动态振荡器。我们确定的内存驱动的不稳定性的晶格作为一个功能的液滴的数量，并确定均匀的晶格配置排除几何约束。每个记忆驱动的不稳定性，然后被归类为一个超临界或亚临界Hopf分岔\emph{via}一个系统的弱非线性分析，合理化实验观察。我们进一步发现了一个以前未报道的破缺不稳定性，表现为晶格的旋转运动。数值模拟支持我们的研究结果，并提示进一步调查这个非线性动力系统。
英文摘要：
Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling.By modelling the droplet lattice as a memory-endowed system with spatially nonlocal coupling, we herein rationalise the form and onset of instability in this new class of dynamical oscillator. We identify the memory-driven instability of the lattice as a function of the number of droplets, and determine equispaced lattice configurations precluded by geometrical constraints. Each memory-driven instability is then classified as either a super- or sub-critical Hopf bifurcation \emph{via} a systematic weakly nonlinear analysis, rationalising experimental observations. We further discover a previously unreported symmetry-breaking instability, manifest as an oscillatory-rotary motion of the lattice. Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system.
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