Free Access
Issue
ESAIM: COCV
Volume 21, Number 3, July-September 2015
Page(s) 757 - 788
DOI https://doi.org/10.1051/cocv/2014046
Published online 13 May 2015
  1. F. Alouges, A. DeSimone and A. Lefebvre, Optimal strokes for low Reynolds number swimmers : an example. J. Nonlinear Sci. 18 (2008) 277–302. [Google Scholar]
  2. F. Alouges and L. Giraldi, Enhanced controllability of low Reynolds number swimmers in the presence of a wall. Acta Applicandae Mathematicae 128 (2013) 153–179. [Google Scholar]
  3. F. Alouges, A. DeSimone, L. Giraldi and M. Zoppello, Self-propulsion of slender micro-swimmers by curvature control: N-link swimmers. J. Non-Linear Mech. 56 (2013) 132–141. [Google Scholar]
  4. F. Alouges, A. DeSimone, L. Heltai, A. Lefebvre and B. Merlet, Optimally swimming Stokesian robots. Discrete Contin. Dyn. Syst. Ser. B 18 (2013). [Google Scholar]
  5. A.P. Berke, L. Turner, H.C. Berg and E. Lauga, Hydrodynamic attraction of swimming microorganisms by surfaces. Phys. Rev. Lett. 101 (2008). [Google Scholar]
  6. J.R. Blake, A note on the image system for a Stokeslet in a no-slip boundary. Math. Proc. Cambridge Philos. Soc. 70 (1971) 303. [Google Scholar]
  7. T. Chambrion and A. Munnier, Locomotion and control of a self-propelled shape-changing body in a fluid. J. Nonlinear Sci. 21 (2011) 325–385. [Google Scholar]
  8. J.M. Coron, Control and Nonlinearity. American Mathematical Society (2007). [Google Scholar]
  9. G.P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stockes Equations. Springer (2011). [Google Scholar]
  10. D. Gérard Varet and M. Hillairet, Computation of the drag force on a rough sphere close to a wall. ESAIM: M2AN 46 (2012) 1201–1224. [CrossRef] [EDP Sciences] [Google Scholar]
  11. L. Giraldi, P. Martinon and M. Zoppello, Controllability and optimal strokes for N-link micro-swimmer. Proc. of 52th Conf. on Decision and Control (Florence, Italy) (2013). [Google Scholar]
  12. R. Golestanian and A. Ajdari, Analytic results for the three-sphere swimmer at low Reynolds. Phys. Rev. E 77 (2008) 036308. [CrossRef] [Google Scholar]
  13. A. Henrot and M. Pierre, Variation et optimisation de formes. Une analyse géométrique. [A geometric analysis]. Vol. 48 of Math. Appl. Springer, Berlin, 2001. [Google Scholar]
  14. V. Jurdjevic, Geometric control theory. Cambridge University Press (1997). [Google Scholar]
  15. E. Lauga and T. Powers, The hydrodynamics of swimming micro-organisms. Rep. Prog. Phys. 72 (2009) 09660. [Google Scholar]
  16. R. Ledesma-Aguilar and J.M. Yeomans, Enhanced motility of a microswimmer in rigid and elastic confinement. Phys. Rev. Lett. 111 (2013) 138101. [CrossRef] [PubMed] [Google Scholar]
  17. J. Lighthill, Mathematical biofluiddynamic. Soc. Ind. Appl. Math. Philadelphia, Pa. (1975) [Google Scholar]
  18. J. Lohéac and A. Munnier, Controllability of 3D low Reynolds swimmers. ESAIM: COCV 20 (2014) 236–268. [CrossRef] [EDP Sciences] [Google Scholar]
  19. J. Lohéac, J.F. Scheid and M. Tucsnak, Controllability and time optimal control for low Reynolds numbers swimmers. Acta Appl. Math. 123 (2013) 175–200. [CrossRef] [Google Scholar]
  20. R. Montgomery, A tour of subriemannian geometries, theirs geodesics and applications. American Mathematical Society (2002). [Google Scholar]
  21. A. Najafi and R. Golestanian, Simple swimmer at low Reynolds number: Three linked spheres. Phys. Rev. E 69 (2004) 062901. [CrossRef] [Google Scholar]
  22. Y. Or and M. Murray, Dynamics and stability of a class of low Reynolds number swimmers near a wall. Phys. Rev. E 79 (2009) 045302. [CrossRef] [Google Scholar]
  23. E.M. Purcell, Life at low Reynolds number. Am. J. Phys. 45 (1977) 3–11. [CrossRef] [Google Scholar]
  24. S.H. Rad and A. Najafi, Hydrodynamic interactions of spherical particles in a fluid confined by a rough no-slip wall. Phys. Rev. E 82 (2010) 036305. [CrossRef] [Google Scholar]
  25. L. Rothschild, Non-random distribution of bull spermatozoa in a drop of sperm suspension. Nature (1963). [Google Scholar]
  26. D.J. Smith and J.R. Blake, Surface accumulation of spermatozoa: a fluid dynamic phenomenon. Math. Sci. 34 (2009) 74–87. [MathSciNet] [Google Scholar]
  27. D.J. Smith, E.A. Gaffney, J.R. Blake and J.C. Kirkman-Brown, Human sperm accumulation near surfaces: a simulation study. J. Fluid Mech. 621 (2009) 289–320. [CrossRef] [Google Scholar]
  28. G. Taylor, Analysis of the swimming of microscopic organisms. Proc. R. Soc. London A 209 (1951) 447–461. [Google Scholar]
  29. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis. AMS, Chelsea (2005). [Google Scholar]
  30. E.F. Whittlesey, Analytic functions in Banach spaces. Proc. Amer. Math. Soc. 16 (1965) 1077–1083. [Google Scholar]
  31. H. Winet, G.S. Bernstein and J. Head, Observation on the response of human spermatozoa to gravity, boundaries and fluid shear. Reproduction 70 (1984). [Google Scholar]
  32. H. Winet, G.S. Bernstein and J. Head, Spermatozoon tendency to accumulate at walls is strongest mechanical response. J. Androl. (1984). [Google Scholar]
  33. C. Ybert, C. Barentin, C. Cottin-Bizonne, P. Joseph and L. Bocquet, Achieving large slip with superhydrophobic surfaces: scaling laws for generic geometries. Phys. Fluids 19 (2007). [Google Scholar]

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