Figure 4. Variation of the scaled timeperiod ΓσT of filament beating with 
plotted for various values of κ and σ0 with L = 188, and (b, main panel) variation of the scaled amplitude L–1.46ρ with 
plotted for various lengths L with κ = 1.6.
In (a) we show the appearance of spontaneous oscillations in the filament at 
corresponding to rigid corkscrew rotation, followed by a transition at 
to flexible planar beating. In (b, inset) we show the increase in the unscaled amplitude with length.