Free Access
Volume 21, Number 3, July-September 2015
Page(s) 757 - 788
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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.