The chimera state in colloidal phase oscillators with hydrodynamic interaction.

The chimera state is the incongruous situation where coherent and incoherent populations coexist in sets of identical oscillators. Using driven non-linear oscillators interacting purely through hydrodynamic forces at low Reynolds number, previously studied as a simple model of motile cilia supporting waves, we find concurrent incoherent and synchronised subsets in small arrays. The chimeras seen in simulation display a "breathing" aspect, reminiscent of uniformly interacting phase oscillators. In contrast to other systems where chimera has been observed, this system has a well-defined interaction metric, and we know that the emergent dynamics inherit the symmetry of the underlying Oseen tensor eigenmodes. The chimera state can thus be connected to a superposition of eigenstates, whilst considering the mean interaction strength within and across subsystems allows us to make a connection to more generic (and abstract) chimeras in populations of Kuramoto phase oscillators. From this work, we expect the chimera state to emerge in experimental observations of oscillators coupled through hydrodynamic forces.