Discrete and periodic complex Ginzburg-Landau equation for a hydrodynamic active lattice

Thomson, S. J., Durey, M. and Rosales, R. R. (2021) Discrete and periodic complex Ginzburg-Landau equation for a hydrodynamic active lattice. Physical Review E, 103(6), 062215. (doi: 10.1103/PhysRevE.103.062215) (PMID:34271671)

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Abstract

A discrete and periodic complex Ginzburg-Landau equation, coupled to a mean equation, is systematically derived from a driven and dissipative lattice oscillator model, close to the onset of a supercritical Andronov-Hopf bifurcation. The oscillator model is inspired by recent experiments exploring active vibrations of quasi-one-dimensional lattices of self-propelled millimetric droplets bouncing on a vertically vibrating fluid bath. Our systematic derivation provides a direct link between the constitutive properties of the lattice system and the coefficients of the resultant amplitude equations, paving the way to compare the emergent nonlinear dynamics—namely, the onset and formation of discrete dark solitons, breathers, and traveling waves—against experiments. The framework presented herein is expected to be applicable to a wider class of oscillators characterized by the presence of a dynamic coupling potential between particles. More broadly, our results point to deeper connections between nonlinear oscillators and the physics of active and driven matter.

Item Type:Articles
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:Physical Review E
Publisher:American Physical Society
ISSN:1539-3755
ISSN (Online):1550-2376
Published Online:25 June 2021

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