Free Access
Volume 21, Number 1, January-March 2015
Page(s) 190 - 216
Published online 09 December 2014
  1. F. Alouges, A. DeSimone and L. Heltai, Numerical strategies for stroke optimization of axisymmetric microswimmers. Math. Model. Meth. Appl. Sci. 21 (2011) 361–397. [Google Scholar]
  2. 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]
  3. F. Alouges, A. DeSimone and A. Lefebvre, Optimal strokes for axisymmetric microswimmers. Eur. Phys. J. E 28 (2009) 279–284. [CrossRef] [EDP Sciences] [Google Scholar]
  4. M. Arroyo, L. Heltai, D. Millán and A. DeSimone, Reverse engineering the euglenoid movement. Proc Natl. Acad. Sci. 109 (2012) 17874–17879. [Google Scholar]
  5. A. Bressan, Impulsive control of Lagrangian systems and locomotion in fluids. Discrete Contin. Dyn. Syst. 20 (2008) 1–35. [Google Scholar]
  6. G. Buttazzo, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations. Pitman Res. Notes Math. Longman, Harlow (1989). [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. S. Childress, Mechanics of Swimming and Flying. Vol. 2 of Cambridge Stud. Math. Biol. Cambridge University Press, Cambridge (1981). [Google Scholar]
  9. J.-M. Coron, Control and nonlinearity. Vol. 136 of Math. Surv. Monogr. AMS, Providence, RI, USA (2007). [Google Scholar]
  10. G. Dal Maso, A. DeSimone and M. Morandotti, An existence and uniqueness result for the motion of self-propelled micro-swimmers. SIAM J. Math. Anal. 43 1345–1368. [Google Scholar]
  11. A. DeSimone, L. Heltai, F. Alouges and A. Lefebvre-Lepot, Computing optimal strokes for low Reynolds number swimmers, in Natural locomotion in fluids and on surfaces: swimming, flying, and sliding, edited by S. Childress. IMA Vol. Math. Appl. Springer Verlag (2012). [Google Scholar]
  12. M.P. Do Carmo, Differential Geometry of Curves and Surfaces. Prentice Hall Inc., Upper Saddle River, New Jersey (1976). [Google Scholar]
  13. B.M. Friedrich, I.H. Riedel-Kruse, J. Howard and F. Jülicher, High precision tracking of sperm swimming fine structure provides strong test of resistive force theory. J. Exp. Biol. 213 (2010) 1226–1234. [CrossRef] [PubMed] [Google Scholar]
  14. G.P. Galdi, On the steady self-propelled motion of a body in a viscous incompressible fluid. Arch. Ration. Mech. Anal. 148 (1999) 53–88. [Google Scholar]
  15. G. Gray and G.J. Hancock, The propulsion of sea-urchin spermatozoa. J. Exp. Biol. 32 (1955) 802–814. [Google Scholar]
  16. J.K. Hale, Ordinary Differential Equations, 2nd edition. Robert E. Krieger Publishing Co., Huntington, NY (1980). [Google Scholar]
  17. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics with special applications to particulate media. Martinus Nijhoff Publishers, The Hague (1983). [Google Scholar]
  18. R. E. Johnson and C. J. Brokaw, Flagellar hydrodynamics. A comparison between Resistive-Force Theory and Slender-Body Theory. Biophys. J. 25 (1979) 113–127. [CrossRef] [PubMed] [Google Scholar]
  19. J. Koiller, K. Ehlers and R. Montgomery, Problems and progress in microswimming. J. Nonlinear Sci. 6 (1996) 507–541. [CrossRef] [MathSciNet] [Google Scholar]
  20. E. Lauga, T.R. Powers, The hydrodynamics of swimming microorganisms. Rep. Progr. Phys. 72 (2009) 9. [Google Scholar]
  21. M.J. Lighthill, On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Math. 5 (1952) 109–118. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Morandotti, Self-propelled micro-swimmers in a Brinkman fluid. J. Biol. Dyn. 6 Iss. sup1 (2012) 88–103. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  23. O. Pironneau and D. F. Katz, Optimal swimming of flagellated micro-organisms. J. Fluid Mech. 66 (1974) 391–415. [CrossRef] [Google Scholar]
  24. E.M. Purcell, Life at low Reynolds number. Amer. J. Phys. 45 (1977) 3–11. [Google Scholar]
  25. J. San Martín, T. Takahashi, M. Tucsnak, A control theoretic approach to the swimming of microscopic organisms. Quart. Appl. Math. 65 (2007) 405–424. [Google Scholar]
  26. G.I. Taylor, Analysis of the swimming of microscopic organisms. In vol. 209 of Proc. Roy. Soc. London, Ser. A (1951) 447–461. [Google Scholar]

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