Self-propulsion of N-hinged 'Animats' at low Reynolds number

Qualitative Theory of Dynamical Systems

Volumn 4, Issue 2, 2003, Pages 139-167

  de Araújo, Gerusa Alexsandra ^a   Koiller, Jair ^b  

^a LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

^b FUNDAÇÃO GETÚLIO VARGAS   (Brazil)

Author keywords

Connections and curvature; Nonholonomic constraints; Stokes flows

Indexed keywords

EID: 84896804655     PISSN: 15755460     EISSN: 16623592     Source Type: Journal    
DOI: 10.1007/BF02970856     Document Type: Article

References (50)

1. V.I. Arnold, V.V. Kozlov, and A.I. Neishtadt, Dynamical Systems III/, (Encyclopaedia of Mathematical Sciences, vol. 3, Springer, New York 1988).
2. L.E. Becker, S.A. Koehler and H.A. Stone, On self-propulsion of micromachines al low Reynolds number: Purcell's three-link swimmer, submitted to J. Fluid. Mech.
3. J. R. Blake, A spherical envelope approach to ciliary propulsion, J.Fluid Mech. 46, 199-208 (1971).
4. J.R. Blake, Self propulsion due to oscillations on the surface of a cylinder at low Reynolds number, Bull.Austral.Math.Soc.3, 255-264 (1971).
5. J.R. Blake, Infinite models for ciliary propulsion, J.Fluid Mech. 49, 209-222 (1971).
6. J.R. Blake, A model for the micro-structure in ciliated organisms, J.Fluid Mech. 55, 1-23 (1972).
7. C. Brennen, An oscillating boundary layer theory for ciliary propulsion, J.Fluid Mech. 65, 799-824 (1974).
8. C. Brennen, H. Winnet, Fluid Mechanics of propulsion by cilia and flagella, Ann.Rev.Fluid Mech. 9, 339-398 (1977).
9. C. Brokaw, Descriptive and mechanistic models of flagellar motility, p. 128-139, in W. Alt, G. Hoffmann, eds., Biological Motion (Springer Verlag Lecture Notes in Biomathematics, 89, 1990).
10. C. Brokaw, Control of flagellar bending: a new agenda based on dyneyn diversity, Cell Motil. Cytosk. 28, 199-204 (1994).
11. R.G. Brown, http://www.phy.duke.edu/ rgb/Class/phy41/node11.html
12. K. Ehlers, The Geometry of Swimming and Pumping at Low Reynolds number (Ph.D. Thesis, Univ. of Calif., Santa Cruz, 1995).
13. K. Ehlers, A. Samuel, H. Berg, R. Montgomery, Do cyanobacteria swim using traveling surface waves?, Proc. Nat. Acad. Sci, 93 8340-8343 (1996).
14. L.J. Fauci, S. Gueron (Editors), Computational Modeling in Biological Fluid Dynamics (Springer Verlag IMA Volumes in Mathematics and Its Applications, 124, 2001).
15. S.F. Goldstein, Morphology of developing bends in sperm flagella, p. 127-132., in T.Y. Wu, C. Brennen, C. Brokaw, eds. Swimming and Flying in Nature, (Plenum Press, New York, 1975), vol.1.
16. J. Happel, H. Brenner, Low Reynolds number Hydrodynamics (Kluwer Acad. Pub., 1991).
17. H. Hertz, The principles of mechanics, presented in a new form. Pref. by H. von Helmholtz, (Dover Publications, New York, 1956).
18. J.J.L. Higdon, The generation of feeding currents by flagellar motions, J.Fluid Mech. 94:2, 305-330 (1979).
19. S.T. Keller, T.Y. Wu, A porous prolate-spheroidal model for ciliated microorganisms, J.Fluid Mech. 80:2, 259-278 (1977).
20. J. Koiller, R. Montgomery and K. Ehlers, Problems and progress in Microswimming, J.Nonlinear Science 6, 507-541 (1996).
21. J. Koiller, M. A. Raupp, J. Delgado, K. Ehlers and R. Montgomery, Spectral methods for Stokes flows, Computational and Applied Mathematics, 17:3, 343-371 (1998).
22. J. Koiller, J. Delgado, On efficiency calculations for nonholonomic locomotion problems: an application to microswimming, Rep. Math. Phys.42, no. 1-2, 165-183 (1998).
23. J. Koiller, K. Ehlers, A. Cherman, J. Delgado, R. Montgomery and F. Duda, Low Reynolds Number Swimming in Two Dimensions, Proceedings of the III International Symposium of Hamiltonian Systems and Celestial Mechanics (MAMSYS98), (World Scientific Monograph Series in Mathematics - Vol. 6, ed. by J. Delgado, E. A. Lacomba, E. Prez-Chavela, World Scientific, Singapore, 2000).
24. J. Koiller, et al., The E. Coli collective, Momentum Maps and Geometric Phases, in H. Cabral and F. Diacu eds., Classical and Celestial Mechanics (Princeton U. Press, New Jersey, 2002).
25. J. Lighthill, On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds number, Commun. Pure Appl. Math. 5, 109-118 (1952).
26. J. Lighthill, Mathematical Biofluidmechanics (SIAM, Philadelphia, PA, 1975).
27. J. Lighthill, Flagellar hydrodynamics, SIAM Review 18, 161-230 (1976).
28. J. Lighthill, Biofluiddynamics: a survey, in Contemp. Math, 141, 1-23, ed. By A.Y.Cheer, C.P.van Dam (1993).
29. J. Lighthill, Reinterpreting the basic theorem of flagellar hydrodynamics, J. Eng. Math. 30, 25-34 (1996).
30. N. Liron, The LDL theorem - historical perspective and critique, p. 1533-1540, in Biofluidynamics: in memory of Sir James Lighthill (J. Wiley Math. Methods Appl. Sci. 24, 17-18, 2001).
31. J.E. Marsden, T. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems (Springer Texts in Applied Mathematics 17, 1999).
32. R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications, (American Mathematical Society Mathematical Surveys and Monographs 91, 2002).
33. R. Montgomery, Nonholonomic control and gauge theory, in Nonholonomic Motion Planning, ed. by Li,Z., Canny, J.F., Kluwer (1993).
34. G. Oster, Darwin's Motors, Nature 417, 25 (2002).
35. O. Pironneau, D.F. Katz, Optimal swimming motions of flagella, in Swimming and Flying in Nature, (Plenum Press, New York, 1975), vol.1, ed. by T.Y. Wu, C. Brennen, C. Brokaw, p. 161-170.
36. O. Pironneau, D.F. Katz, Optimal swimmimg of flagellated micro-organisms, J. Fluid Mechanics 66, part 2, 391-425 (1974).
37. M. Porter, W. Sale, The 9+2 axoneme anchors multiple inner arm dyneins and a network of kinases and phosphatases that control motility, J. Cell. Biol. 151:5, F37-F42 (2000).
38. C. Pozrikids, Boundary Integral and Singularity Methods for Linearized Viscous flow (Cambridge Texts in Applied Mathematics, 1992).
39. E. Purcell, Life at low Reynolds number, Amer.J. Phys. 45, 3-11 (1977).
40. E. Purcell,The efficiency of propulsion by a rotating flagellum, Proc. Natl. Acad. Sci. USA 94, 11307-11311 (1997).
41. P. Satir, The cilium as a biological nanomachine, FASEB J. 13, S235-S237 (1999).
42. P. Satir, Control molecules in Protozoan Ciliary Motility, Jpn. J. Protozool 36:2, 87-96 (2003).
43. A. Shapere, Gauge Theory of Deformable Bodies: A Theory of Something, (Ph.D. thesis, Princeton University Physics Department, 1989).
44. A. Shapere and F. Wilczek, F., Geometry of self-propulsion at low Reynolds number, J.Fluid Mech. 198, 557-585 (1989).
45. A. Shapere and F. Wilczek, Efficiencies of self-propulsion at low Reynolds number, J.Fluid Mech. 198, 587-599 (1989).
46. M. Schliwa, Molecular Motors (J. Wiley, 2003).
47. P. Sugrue, J. Avolio, P. Satir and M.E. Holwill, Computer modelling of Tetrahymena axonemes at macromolecular resolution. Interpretation of electron micrographs, Journal of Cell Science, Vol 98, Issue 1, 5-16 (1991).
48. G.I. Taylor, Analysis of the swimming of microscopic organisms, Proc.R.Soc.Lond.A 209, 447-461 (1951).
49. H.C. Taylor, P. Satir, M. Holwill, Assessment of inner dynein arm structure and possible function in ciliary and flagellar axonemes, Cell Motil. Cytoskel. 43, 167-177 (1999). See also http://www.wadsworth.org/albcon97/abstract/holwill.htm,http://www.wadsworth.org/albcon97/abstract/guevara.htm.
50. T.Y. Wu, C. Brennen, C. Brokaw, eds. Swimming and Flying in Nature, (Plenum Press, New York, 1975), vol.1.