Hydrodynamically synchronized states in active colloidal arrays
  Colloidal particles moving in a fluid interact via the induced velocity field. The collective dynamic state for a class of actively forced colloids, driven by harmonic potentials via a rule that couples forces to configurations, to perform small oscillations around an average position, is shown by experiment, simulation and theoretical arguments to be determined by the eigenmode structure of the coupling matrix. It is remarkable that the dynamical state can therefore be predicted from the mean spatial configuration of the active colloids, or from an analysis of the fluctuations near equilibrium. This has the surprising consequence that while 2 particles, or polygonal arrays of 4 or more colloids, synchronize with the nearest neighbors in anti-phase, a system of 3 equally spaced colloids synchronizes in-phase. In the absence of thermal fluctuations, the stable dynamical state is predominantly formed by the eigenmode with longest relaxation time. 
Lo\"ic Damet and Giovanni M. Cicuta and Jurij Kotar and Marco   Cosentino Lagomarsino and Pietro Cicuta
cond-mat.soft physics.bio-ph