Abhrajit Laskar, Rajeev Singh, Somdeb Ghose, Gayathri Jayaraman, P. B. Sunil Kumar, R. Adhikari
Microscopic living organisms locomote in viscous fluids through spontaneous beating of filamentous structures anchored at one end, such as flagella and cilia. Prokaryotic flagella rotate rigidly like a corkscrew, while eukaryotic flagella are flexible and oscillate in a plane. We observe similar biomimetic beating behavior \emph{in silico} by clamping an active filament at one end and solving for hydrodynamics interactions. Highly active filaments become unstable to transverse perturbations and exhibit autonomous oscillations. This transition into a limit cycle occurs via a supercritical Hopf bifurcation. The time period and amplitude of beating increase with increasing filament length, but collapse to a master curve on appropriate scaling. An analytical calculation of the spectrum of the filament model in the free-draining approximation fails to capture oscillatory behavior, emphasizing the crucial role played by hydrodynamic interactions.
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http://arxiv.org/abs/1211.5368
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