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Hydrodynamic Synchronization of Spontaneously Beating Filaments

“…However, far from the bifurcation, nonlinearities give rise to a reversal in the direction of propagation [34], with sperm-like waveforms shown in Fig. 1(b) that resemble experiments [37] and have beating frequencies f ∼ 10 − 15 Hz. In the following discussion, we focus on this anterograde propagation regime as it is biologically most relevant.…”

“…Model formulation.-The flagellar axoneme is a 3D structure with circular cross-section composed of 9+2 pairs of microtubules arranged in a cyclic fashion [35]. Following past models [26,30,34,[36][37][38][39], we idealize this structure as a planar projection with diameter a and length L, where microtubules are represented by two polar filaments x ± clamped at the base [ Fig. 1(a)].…”