Collective vibrations of a hydrodynamic active lattice.
Proc Math Phys Eng Sci
; 476(2239): 20200155, 2020 Jul.
Article
in En
| MEDLINE
| ID: mdl-32831612
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.
Full text:
1
Collection:
01-internacional
Database:
MEDLINE
Type of study:
Prognostic_studies
Language:
En
Journal:
Proc Math Phys Eng Sci
Year:
2020
Document type:
Article
Affiliation country:
Estados Unidos