Synchronization in A Carpet of Hydrodynamically Coupled Rotors with Random Intrinsic Frequency

TL;DR

This study explores how hydrodynamic interactions induce synchronization among a 2D array of rotors with random natural frequencies, revealing a gradual transition to collective motion influenced by frequency heterogeneity.

Contribution

It introduces a model of non-locally coupled rotors mimicking bacterial carpets, analyzing synchronization transition and the impact of intrinsic heterogeneity.

Findings

Narrow frequency distributions are necessary for collective motion.

The transition from coherence to incoherence is gradual.

Critical behavior differs from globally coupled oscillator models.

Abstract

We investigate synchronization caused by long-range hydrodynamic interaction in a two-dimensional, substrated array of rotors with random intrinsic frequencies. The rotor mimics a flagellated bacterium that is attached to the substrate ("bacterial carpet") and exerts an active force on the fluid. Transition from coherent to incoherent regimes is studied numerically, and the results are compared to a mean-field theory. We show that quite a narrow distribution of the intrinsic frequency is required to achieve collective motion in realistic cases. The transition is gradual, and the critical behavior is qualitatively different from that of the conventional globally coupled oscillators. The model not only serves as a novel example of non-locally coupled oscillators, but also provides insights into the role of intrinsic heterogeneities in living and artificial microfluidic actuators.