Problems and Progress in Microswimming

Journal of Nonlinear Science

Volumn 6, Issue 6, 1996, Pages 507-541

  Koiller, J ^a   Ehlers, K ^b   Montgomery, R ^b  

^a Labs Nac de Comp Cie   (Brazil)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Geometric phases; Nonholonomic control; Stokes' flows

Indexed keywords

EID: 0000095110     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02434055     Document Type: Article

References (84)

1. Abraham, R. and Marsden, J. E.: Foundations of Mechanics, Addison-Wesley, Reading, MA (1978).
2. Ambrose, W. and Singer, I. M.: A theorem on holonomy, Trans. AMS 75, 428-453 (1953).
3. Arnold, V., Kozlov, V. V., and Neishtadt, A. I.: Dynamical Systems III , Encyclopaedia of Mathematical Sciences, Springer-Verlag, New York (1988).
4. Berg, H.C.: Random Walks in Biology, expanded edition, Princeton University Press, Princeton, NJ (1993).
5. Berg, H. C. and Anderson, R. A.: Bacteria swim by rotating their flagellar filaments, Nature 245, 380-384 (1973).
6. Berg, H. C. and Purcell, E. M.: Physics of chemoreception. Biophys. J. 20, 193-219 (1977).
7. Berg, H. C.: Physics of bacterial chemotaxis, pp. 19-30 in Sensory Perception and Transduction in Aneural Organisms, eds. Colombetti, G., Lenci, F., and Song, P. S., Plenum, New York (1985).
8. Berg, H.C.: Studies of motile bacteria. In Physics News, ed. by Schewe, P. F., American Institute of Physics, New York (1991).
9. Berg, H. C.: Dynamic properties of bacterial flagellar motors. Nature 249, 77-79 (1974).
10. Berg, H. C. and Khan, S.: A model for the flagellar rotary motor. In Mobility and Recognition in Cell Biology, pp. 485-497, eds. Sund, H. and Veeger, C., deGruyter, Berlin (1983).
11. Berg, H. C., Manson, M. D., and Conley, M. P.: Dynamics and energetics of flagellar rotation in bacteria, Symp. Soc. Exp. Biol. 35, 1-31 (1982).
12. Berg, H. C.: Dynamics and energetics of the bacterial rotary motor. In Protein Dynamics and Energy Transduction, pp. 312-344, ed. Ishiwata, S.-I., Taniguchi Foundation (1980).
13. Berg, H.C.: Torque generation by the flagellar rotary motor, Biophys. J. 68, 163s-167s (1995).
14. Berg, H. C.: How to track bacteria, Rev. Sci. Instrum. 42, 868-871 (1971).
15. Blake, J. R.: Self propulsion due to oscillations on the surface of a cylinder at low Reynolds number. Bull. Austral. Math. Soc. 3, 255-264 (1971).
16. Blake, J. R.: A spherical envelope approach to ciliary propulsion, J. FluidMech. 46, 199-208 (1971).
17. Blake, J. R.: A model for the micro-structure in ciliated organisms, J. Fluid Mech. 55, 1-23 (1972).
18. Brennen, C.; An oscillating boundary layer theory for ciliary propulsion, J. Fluid Mech. 65, 799-824 (1974).
19. Brennen, C. and Winnet, H.: Fluid mechanics of propulsion by cilia and flagella, Ann. Rev. Fluid Mech. 9, 339-398 (1977).
20. Brockett, R. W. and Dai, L: Non-holonomic kinematics and the role of elliptic functions in constructive controllability, in Nonholonomic Motion Planning, eds. Li, Z., Canny, J. F., Kluwer, Dordrecht (1993).
21. Budrene, E. O. and Berg, H. C.: Complex patterns formed by motile cells of Escherichia coli, Nature 349, 630-633 (1991).
22. Budrene, E. O. and Berg, H. C.: Dynamics of formation of symmetrical patterns of chemotactic bacteria. Nature 376, 49-53 (6 July 1995).
23. Calleja, G. B.: Microbial Aggregation, CRC Press, Boca Raton, FL (1984).
24. Childress, S.: Mechanics of Swimming and Flying, Cambridge University Press (1981).
25. Chow, W. L.: Uber systeme van linearen partiellen differentialgleichungen ersten ordnung, Math. Ann. 117, 98-105 (1939).
26. Chwang, A. T. and Wu, T. Y.: A note on the helical movement of micro-organisms, Proc. Roy. Soc. Lond. B. 178, 327-346 (1971).
27. Curtis, H.: The Marvelous Animals: An Introduction to the Protozoa, The Natural History Press, New York (1968).
28. Ehlers, K. M.: The Geometry of Swimming and Pumping at Low Reynolds Number, Ph.D. Thesis, University of California, Santa Cruz (1995).
29. Ehlers, K. M, Berg, H. C., and Montgomery, R.: Do synechococcus swim using traveling surface waves?, Proc. Natl. Acad. Sci. USA 93, 8340-8344 (1996).
30. England, H.: Complex Variable Methods in Elasticity, Wiley-Interscience, New York (1971).
31. Fauci, L. J.: Computational modeling of the swimming of biflagellated algal cells, in Contemp. Math. 141, 91-102, ed. A. Y. Cheer, C. P. van Dam (1993).
32. Farina, M., Esquivel, D. M. S., and Lins de Barros, H. G. P.: Magnetic iron-sulphur crystals from a magnetotactic microorganism. Nature 343, 6255, 256-258 (1990).
33. Fearing, R. S.: Control of a micro-organism as a prototype micro-robot, Second Int. Symp. on Micromachines and Human Sciences, Nagoya, Japan, 1991.
34. Flam, F.: Swarms of mini-robots set to take on Mars terrain, Science 257, 1621, (18 Sept. 1992).
35. Greenbaum, A., Greengard, L., and Mayo, A.: On the numerical solution of the biharmonic equation on the plane, Physica D 60(1-4), 216-225 (1992).
36. Guell, D. C., Brenner, H., Frankel, R. B., and Hartman, H.: Hydrodynamic forces and band formation in swimming magnetotactic bacteria, J. Theor. Biol. 135, 525-542 (1988).
37. Guichardet, A.: On rotation and vibration motions of molecules, Ann. Inst. H. Poincaré, Phys. Theor. 40(3), 329-342 (1984).
38. Guillemin, V. and Sternberg, S.: Geometric Asymptotics, American Mathematical Society, Providence, RI (1977).
39. Hasimoto, H. and Sano, H.: Stokeslets and eddies in creeping flow, Ann. Rev. Fluid Mech. 12, 335-364 (1980).
40. Happel, J. and Brenner, H.: Low Reynolds Number Hydrodynamics, Kluwer Academic, Dordrecht (1991).
41. Higdon, J. J. L.: The generation of feeding currents by flagellar motions, J. Fluid Mech. 94(2), 305-330 (1979).
42. Hirsch, P.: Microcolony formation and consortia, in Microbial Adhesion and Aggregation, ed. K. C. Marshall, pp. 373-393, Springer-Verlag, New York (1984).
43. Ishihara, A., Segall, J. E., Block, S. M., and Berg, H. C.: Coordination of flagella on filamentous cells of Escherichia coli, J. Bacteriol. 155, 228-237 (1983).
44. Jahn, T. L., and Bovee, E. C.: Motile behavior of Protozoa, in Research in Protozoology, ed. Tze-Tuan Chen, vol. I, Pergamon, New York (1967).
45. Jones, R. D., Lemanski, C., and Jones, T. J.: Theory of attachment in Giardia. Biophys. J. 44, 185-190 (1983).
46. Jahn, T. L. and Votta, J. J.: Locomotion of protozoa, Ann. Rev. Fluid Mech. 4, 93-116 (1972).
47. Khan, S., Meister, M., and Berg, H. C.: Constraints on flagellar rotation, J. Mol. Biol. 184, 645-656 (1985).
48. Koehl, M. A. R.: Feeding at low Reynolds number by Copepods, Lect. Math. Life Sciences 14, 89-117 (1981).
49. Koehl, M. A. R.: Hairy little legs: feeding, smelling and swimming at low Reynolds numbers, in Contemp. Math. 141, 33-64, Fluid dynamics in biology, eds. Cheer, A. Y., van Dam, C. P. (1993).
50. Keller, S. T. and Wu, T. Y.: A porous prolate-spheroidal model for ciliated micro-organisms, J. Fluid Mech. 80(2), 259-278 (1977).
51. Lapidus, R. and Berg, H. C.: Gliding motility of Cytophaga sp.Strain U67, J. Bacteriology 151(1), 384-398 (1982).
52. Lins de Barros, H. G. P., Esquivel, D. M. S., and Farina, M.: Magnetotaxis, Sci. Progress Oxford 74, 347-359 (1990).
53. Li, Z. and Canny, J. F. (eds.): Nonholonomic Motion Planning, Kluwer, Dordrecht (1993).
54. Lighthill, J.: Biofluiddynamics: A survey, Contemp. Math. 141, 1-23 (1993), eds. Cheer, A. Y., van Dam, C. P.
55. Lighthill, L.: Mathematical Biofluidmechanics, SIAM (1975).
56. Lowe, G., Meister, M., and Berg, H. C.: Rapid rotation of flagellar bundles in swimming bacteria, Nature 325, 637-640 (1987).
57. Ludwig, W.: Zur theorie der flimmerbewegung (dynamik, nutzeffekt, energiebilanz), Z. vergl. Physiol. 13, 397-504 (1930).
58. Manson, M. D., Tedesco, P. M. and Berg, H. C.: Energetics of flagellar rotation in bacteria, J. Mol. Biol. 138, 541-561 (1980).
59. Marden, J. H. and Kramer, M. G.: Locomotor performance of insects with rudimentary wings, Nature 377, 332-334 (28 Sept. 1995).
60. Meister, M., Lowe, G., and Berg, H.C.: The proton flux through the bacterial flagellar motor, Cell 49, 643-650 (1987).
61. Meister, M. and Berg, H. C.: The stall torque of the bacterial flagellar motor, Biophys. J. 52, 413-419 (1987).
62. Montgomery, R.: Gauge theory of the falling cat, Fields Institute Communications 1, 193-218 (1993).
63. Montgomery, R.: Isoholonomic problems and some applications, Commun. Math. Phys. 128, 565-592 (1990).
64. Montgomery, R.: Nonholonomic control and gauge theory, in Nonholonomic Motion Planning, eds. Li, Z., Canny, J. F., Kluwer, Dordrecht (1993).
65. Murray, R. M. and Sastry, S. S.: Steering nonholonomic control systems using sinusoids, in Nonholonomic Motion Planning, ed. Li, Z., Canny, J. F., Kluwer, Dordrecht (1993).
66. Muskhelishvili, N. I.: Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff, Groningen, Holland (1953).
67. Nisbet, B.: Nutrition and Feeding Strategies in Protozoa, Croom Helm, London and Camberra (1984).
68. Nogueira, F. S. and Lins de Barros, H. G. P.: Study on the motion of magnetotactic bacteria, Eur. Biophys. J. 24, 13-21 (1995).
69. Peskin, C. S., McQueen, D. M.: Computational biofluid dynamics, in Contemp. Math. 141, 161-186, ed. Cheer, A. Y., van Dam, C. P. (1993).
70. Pedley, T. J. and Kessler, J. O.: Hydrodynamic phenomena in suspensions of swimming microorganisms, Ann. Rev. Fluid Mech. 24, 313-358 (1992).
71. Purcell, E.: Life at low Reynolds number, Am. J. Phys. 45, 3-11 (1977).
72. Ramia, M., Tullock, D. L., and Phan-Thien, N.: The role of hydrodynamic interaction in the locomotion of microorganisms, Biophys. J. 65, 755-778 (1993).
73. Ramia, M. and Swan, M. A.: The swimming of unipolar cells of spirillum volutans: Theory and observations, J. Exp. Biol. 187, 75-100 (1994).
74. Saier, M. H. and Jacobson, G. R.: The Molecular Basis of Sex and Differentiation, Springer-Verlag, New York (1984).
75. Shapere, A. and Wilczek, F.: Geometry of self-propulsion at low Reynolds number, J. Fluid Mech. 198, 557-585 (1989).
76. Shapere, A.: Gauge Theory of Deformable Bodies: A Theory of Something, Ph.D. thesis, Princeton University Physics Dept., Princeton, NJ (1989).
77. Sizemore, D. R., Branstrom, A., and Sadoff, J. C.: Attenuatd Shigella as a DNA delivery vehicle for DNA-mediated immunization. Science 270, 299-302 (13 October 1995).
78. Spormann, A. M.: Unusual swimming behavior of a magnetotactic bacterium, FEMS Microb. Ecol. 45, 37-45 (1987).
79. Taylor, G. I.: Analysis of the swimming of microscopic organisms, Proc. Roy. Soc. Lond. A 209, 447-461 (1951).
80. Taylor, G. I.: The action of waving cylindrical tails in propelling microscopic organisms, Proc. Roy. Soc. Lond. A 211, 225-239 (1952).
81. Yates, G.: How microorganisms move through water. Am. Sci. 74, 358-365 (1986).
82. Woodward, D. E., Tyson, R., Myerscough, M. R., Murray, J. D., Budrene, E. O., and Berg, H. C.: Spatio-temporal patterns generated by Salmonella typhimurium. Biophys. J. 68 2181-2189 (1995).
83. Weinbaum, S. and Ganatos, P.: Numerical multipole and boundary integral equation techniques in Stokes flow, Ann. Rev. Fluid Mech. 22, 275-316, 1990.
84. Wu, T. Y., Brennen, C., and Brokaw, C. (eds.): Swimming and Flying in Nature, vol. 1, Plenum, New York (1975).