Collective vibrations of a hydrodynamic active lattice
Collective vibrations of a hydrodynamic active lattice
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DOI：
10.1098/rspa.2020.0155
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发表时间：
2020-03
期刊：
影响因子：
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通讯作者：
Stuart J. Thomson;Matthew Durey;R. Rosales
中科院分区：
文献类型：
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作者：
Stuart J. Thomson;Matthew Durey;R. Rosales
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。该流体动力学晶格由垂直振动流体浴的外部强迫驱动，其在浴表面上引起亚临界法拉第波场，介导时空液滴耦合。通过将液滴晶格建模为具有空间非局部耦合的记忆赋予系统，我们在此合理化了这类新的动态振荡器中的不稳定性的形式和发作。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，然后归类为一个超或亚临界Hopf分叉通过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。
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 non-local coupling, we herein rationalize 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 subcritical Hopf bifurcation via a systematic weakly nonlinear analysis, rationalizing 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.