Patterns of synchronization in the hydrodynamic coupling of active colloids

TL;DR

This paper investigates how active colloidal particles coupled hydrodynamically synchronize in different patterns, providing analytical solutions for their collective oscillation states based on the number of particles.

Contribution

It introduces a piece-wise linear model for active colloids with hydrodynamic coupling and analytically characterizes their synchronization patterns.

Findings

Synchronization depends on particle number

Particles synchronize in in-phase, anti-phase, or phase-locked states

Analytical solutions describe the dynamical behavior

Abstract

A system of active colloidal particles driven by harmonic potentials to oscillate about the vertices of a regular polygon, with hydrodynamic coupling between all particles, is described by a piece-wise linear model which exhibits various patterns of synchronization. Analytical solutions are obtained for this class of dynamical systems. Depending only on the number of particles, the synchronization occurs into states in which nearest neighbors oscillate either in-phase, or anti-phase, or in phase-locked (time-shifted) trajectories.