Abstract
In this paper we investigate different strategies to overcome the scallop theorem. We will show how to obtain a net motion exploiting the fluid’s type change during a periodic deformation. We are interested in two different models: in the first one that change is linked to the magnitude of the opening and closing velocity. Instead, in the second one it is related to the sign of the above velocity. An interesting feature of the latter model is the introduction of a delay-switching rule through a thermostat. We remark that the latter is fundamental in order to get both forward and backward motion.
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References
Alouges F, DeSimone A, Giraldi L, Zoppello M (2013) Self-propulsion of slender micro-swimmers by curvature control: N-link swimmers. Int J Non-Linear Mech 56:132–141
Alouges F, DeSimone A, Lefebvre A (2008) Optimal strokes for low Reynolds number swimmers: an example. J Nonlinear Sci 18:277
Becker LE, Koehler SA, Stone HA (2003) On self-propulsion of micro-machines at low Reynolds number: Purcell’s three-link swimmer. J Fluid Mech 490:15–35
Bessel F (1828) Investigations on the length of the seconds pendulum. Königlichen Akademie der Wissenschaften, Berlin
Bressan A (2008) Impulsive control of Lagrangian systems and locomotion in fluids. Discrete Contin Dyn Syst 20(1):1–35
Cheng JY, DeMont E (1996) Hydrodynamics of scallop locomotion: unsteady fluid forces on clapping shells. J Fluid Mech 317:73–90
Childress S (1981) Mechanics of swimming and flying. Cambridge University Press, Cambridge
Cicconofri G, DeSimone A (2016) Motion planning and motility maps for flagellar microswimmers. Eur Phys J E 39(7):72
Friedrich BM, Riedel-Kruse IH, Howard J, Jülicher F (2010) High-precision tracking of sperm swimming fine structure provides strong test of resistive force theory. J Exp Biol 213:1226–1234
Golestanian R, Ajdari A (2008) Analytic results for the three-sphere swimmer at low Reynolds number. Phys Rev E 77:036308
Gray J, Hancock J (1955) The propulsion of sea-urchin spermatozoa. J Exp Biol 32:802–814
Lighthill MJ (1975) Mathematical biofluiddynamics. Society of Industrial and Applied Mathematics, Philadelphia
Mason R, Burdick J (1999) Propulsion and control of deformable bodies in a Ideal fluid. In: Proceedings of the 1999 IEEE international conference on robotics and automation
Munnier A, Chambrion T (2010) Generalized scallop theorem for linear swimmers. arXivPreprint arXiv:1008.1098v1 [math-ph]
Munnier A, Chambrion T (2011) Locomotion and control of a self-propelled shape-changing body in a fluid. J Nonlinear Sci 21(3):325–385
Newman JN (1977) Marine hydrodynamics. MIT Press, Cambridge, p 402
Purcell EM (1977) Life at low Reynolds number. Am J Phys 45:3–11
Qiu T et al (2014) Swimming by reciprocal motion at low Reynolds number. Nat Commun 5:5119. doi:10.1038/ncomms6119
Visintin A (1994) Differential models of hysteresis. Springer, Heidelberg
Acknowledgements
The work has been developed within the OptHySYS project of the University of Trento that is gratefully acknowledged. Moreover we thank also Gruppo Nazionale Analisi Matematica Probabilitá e Applicazioni (GNAMPA) for partial financial support.
Funding
This study was funded by University of Trento and Gruppo Nazionale Analisi Matematica Probabilitá e Applicazioni (GNAMPA).
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Bagagiolo, F., Maggistro, R. & Zoppello, M. Swimming by switching. Meccanica 52, 3499–3511 (2017). https://doi.org/10.1007/s11012-017-0620-6
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DOI: https://doi.org/10.1007/s11012-017-0620-6