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We calculate the hydrodynamic flow field generated far from a cilium which is attached to a surface and beats periodically. In the case of two beating cilia, hydrodynamic interactions can lead to synchronization of the cilia, which are nonlinear oscillators. We present a state diagram where synchronized states occur as a function of distance of cilia and the relative orientation of their beat. Synchronized states occur with different relative phases. In addition, asynchronous solutions exist. Our work could be relevant for the synchronized motion of cilia generating hydrodynamic flows on the surface of cells.
Cilia and flagella are hair-like extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consi
Carpets of actively bending cilia can exhibit self-organized metachronal coordination. Past research proposed synchronization by hydrodynamic coupling, but if such coupling is strong enough to overcome active phase noise had been addressed only for p
In embryonic development, programmed cell shape changes are essential for building functional organs, but in many cases the mechanisms that precisely regulate these changes remain unknown. We propose that fluid-like drag forces generated by the motio
Synchronization among arrays of beating cilia is one of the emergent phenomena in biological processes at meso-scopic scales. Strong inter-ciliary couplings modify the natural beating frequencies, $omega$, of individual cilia to produce a collective
Sperm swimming at low Reynolds number have strong hydrodynamic interactions when their concentration is high in vivo or near substrates in vitro. The beating tails not only propel the sperm through a fluid, but also create flow fields through which s