caa a22 4500 47703697X CHVBK 20180405111307.0 cr unu---uuuuu 170330e19961101xx s 000 0 eng 10.1007/BF02434055 doi (NATIONALLICENCE)springer-10.1007/BF02434055 Problems and progress in microswimming [Elektronische Daten] [J. Koiller, K. Ehlers, R. Montgomery] Summary: 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. Springer-Verlag New York Inc, 1996 Stokes' flows nationallicence geometric phases nationallicence nonholonomic control nationallicence 76D07 nationallicence 76Z10 nationallicence 93B29 nationallicence 93C10 nationallicence 51P05 nationallicence 53C05 nationallicence 47.15.Gf nationallicence 87.45.-k nationallicence 87.10.+e nationallicence 02.40.+m nationallicence 03.40.Gc nationallicence Koiller J. Laboratório Nacional de Computacão Científica, R. Lauro Muller 455, 22290-160, Rio de Janeiro, RJ, Brazil aut Ehlers K. Mathematics Department, University of California at Santa Cruz, Applied Sciences Building, 95064, Santa Cruz, CA, USA aut Montgomery R. Mathematics Department, University of California at Santa Cruz, Applied Sciences Building, 95064, Santa Cruz, CA, USA aut Journal of Nonlinear Science Springer-Verlag 6/6(1996-11-01), 507-541 0938-8974 6:6<507 1996 6 332 https://doi.org/10.1007/BF02434055 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02434055 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Koiller J. Laboratório Nacional de Computacão Científica, R. Lauro Muller 455, 22290-160, Rio de Janeiro, RJ, Brazil aut NATIONALLICENCE 700 1- Ehlers K. Mathematics Department, University of California at Santa Cruz, Applied Sciences Building, 95064, Santa Cruz, CA, USA aut NATIONALLICENCE 700 1- Montgomery R. Mathematics Department, University of California at Santa Cruz, Applied Sciences Building, 95064, Santa Cruz, CA, USA aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 6/6(1996-11-01), 507-541 0938-8974 6:6<507 1996 6 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer