Collective vibrations of a hydrodynamic active lattice
Name
2003.02220.pdf
Description
Submitted version
Size
6.57 MB
Format
Adobe PDF
Checksum (MD5)
059a99de043d3a5100d24df07fb2cf78
Author(s)
Thomson, SJ
Durey, M
Rosales, RR
Date Issued
2020
Journal
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher
The Royal Society
Version
Original manuscript
Abstract
© 2020 The Author(s). 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1098/RSPA.2020.0155
