Discrete and periodic complex Ginzburg-Landau equation for a hydrodynamic active lattice.
Phys Rev E
; 103(6-1): 062215, 2021 Jun.
Article
in En
| MEDLINE
| ID: mdl-34271671
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.
Full text:
1
Collection:
01-internacional
Database:
MEDLINE
Language:
En
Journal:
Phys Rev E
Year:
2021
Document type:
Article
Affiliation country:
United States