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. 2015 Jul 6;12(108):20141358. doi: 10.1098/rsif.2014.1358

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© 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

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Figure 8. — Inhomogeneous driving forces and the appearance of defects. Rotor chains possess a Volvox-inspired intrinsic driving force , where ε_i = ε_i(σ) is a random number chosen from a normal distribution with mean of zero and standard deviation σ. The frequency bias along the chain is governed by the parameter C. (a–d) Kymographs showing the phase, sin(Φ_i), and phase difference, sin(Φ_i+1 − Φ_i), for various values of C, with σ = 0 (no polydispersity). An example phase defect is circled in white. (e) Kymographs for C = 0.02 with σ = 0.0279. (f) Intrinsic frequency distributions (black) for 60 different realizations with C = 0.02 and σ = 0.0279, along with their average (yellow). The magenta curve corresponds to the frequency profile used in (e) and the inset (g) shows power spectra of sin(Φ_i) for oscillators 1 (red), 8–9 (green) and 30 (blue) in this chain. (h) Extracted metachronal wavenumber k. Simulations without polydispersity (σ = 0, black, 19 simulations) and with polydispersity (σ = 0.0279, red, 210 simulations) are shown. Other parameters are given by a/d = 0.01, r₀/d = 0.5, l/d = 2 and Λ_i centred at Λ = 0.1.

Inline graphic — Inhomogeneous driving forces and the appearance of defects. Rotor chains possess a Volvox-inspired intrinsic driving force , where ε_i = ε_i(σ) is a random number chosen from a normal distribution with mean of zero and standard deviation σ. The frequency bias along the chain is governed by the parameter C. (a–d) Kymographs showing the phase, sin(Φ_i), and phase difference, sin(Φ_i+1 − Φ_i), for various values of C, with σ = 0 (no polydispersity). An example phase defect is circled in white. (e) Kymographs for C = 0.02 with σ = 0.0279. (f) Intrinsic frequency distributions (black) for 60 different realizations with C = 0.02 and σ = 0.0279, along with their average (yellow). The magenta curve corresponds to the frequency profile used in (e) and the inset (g) shows power spectra of sin(Φ_i) for oscillators 1 (red), 8–9 (green) and 30 (blue) in this chain. (h) Extracted metachronal wavenumber k. Simulations without polydispersity (σ = 0, black, 19 simulations) and with polydispersity (σ = 0.0279, red, 210 simulations) are shown. Other parameters are given by a/d = 0.01, r₀/d = 0.5, l/d = 2 and Λ_i centred at Λ = 0.1.