Problems and Progress in Microswimming

  • J. Koiller
  • K. Ehlers
  • R. Montgomery
Conference paper


Stokesian swimming is a geometric exercise, a collective game. In Part I, we review Shapere and Wilczek’s gauge-theoretical approach for a single organism. We estimate the speeds of organisms moving by propagating small amplitude waves, and we make a conjecture regarding a new inequality for the Stokes’ curvature. In Part II, we extend the gauge theory to collective motions. We advocate the influx of nonlinear control theory and subriemannian geometry. Computationally, parallel algorithms are natural, each microorganism representing a separate processor. In the final section, open questions motivated by biology are presented.

Key words

Stokes’ flows geometric phases nonholonomic control 


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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • J. Koiller
    • 1
  • K. Ehlers
    • 2
  • R. Montgomery
    • 2
  1. 1.Laboratόrio Nacional de Computacão CientíficaRio de JaneiroBrazil
  2. 2.Mathematics DepartmentUniversity of California at Santa CruzSanta CruzUSA

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