Active hydrodynamics of synchronization and ordering in moving oscillators

The nature of emergent collective behaviors of moving interacting physical agents is a long-standing open issue in physical and biological systems alike. This calls for studies on the control of synchronization and the degree of order in a collection of diffusively moving noisy oscillators. We address this by constructing a generic hydrodynamic theory for active phase fluctuations in a collection of a large number of nearly-phase-coherent moving oscillators in two dimensions. Our theory describes the general situation where phase fluctuations and oscillator mobility mutually affect each other. We show that the interplay between the active effects and the mobility of the oscillators leads to a variety of phenomena, ranging from synchronization with long-range, nearly-long-range, and quasi-long-range orders to instabilities and desynchronization with short-range order of the oscillator phases. We highlight the complex dependences of synchronization on the active effects. These should be testable in wide-ranging systems, e.g., oscillating chemical reactions in the presence of different reaction inhibitors and facilitators, live oriented cytoskeletal extracts, and vertebrate segmentation clocks.