Theory of synchronization and cooperative dynamics in active fluid systems

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In this project we constructed mathematical models of collective motion of cilia and flagella due to hydrodynamic interactions, and obtained the following results. We constructed a rigid-body rotor model of ciia and analyzed their dynamics in a pair and in one- and two-dimensional arrays. We showed that various synchronized states and traveling wave patterns arise depending on the pattern of the driving force, distance from the substrate, orbital shape and inclination, and flexibility of the cilia. We also numerically analyzed the collective transport phenomena due to many flagella in a bacterial carpet, and clarified the properties of collective synchronization transition due to a general class of long-range interactions by a field-theoretic method.