Thomson, S. J., Durey, M. and Rosales, R. R. (2020) Collective vibrations of a hydrodynamic active lattice. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 476(2239), 20200155. (doi: 10.1098/rspa.2020.0155) (PMID:32831612) (PMCID:PMC7426053)
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Abstract
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.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Durey, Dr Matthew |
Authors: | Thomson, S. J., Durey, M., and Rosales, R. R. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences |
Publisher: | The Royal Society |
ISSN: | 1364-5021 |
ISSN (Online): | 1471-2946 |
Published Online: | 29 July 2020 |
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