We simulate a semi-flexible active filament that exhibits spontaneous oscillations on clamping and show self-propulsion when left free. The activity on the filament relies on the nano-dimers distributed at regular intervals along the chain. With an emphasis on the spontaneous beating of a clamped filament, we demonstrate that the two competing forces necessary for oscillation are the elastic forces due to polymer rigidity and the active forces due to chemical activity. In addition, we also study the synchronization of two extensile filaments and the role played by non-local hydrodynamic interactions. We observe a phase lock scenario between the filaments during their synchronous motion.
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