Computer Science
Scientific paper
Oct 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000hscm.conf...32c&link_type=abstract
HAMILTONIAN SYSTEMS AND CELESTIAL MECHANICS (HAMSYS-98). Proceedings of the III International Symposium. Held 7-11 December 1998
Computer Science
2
Scientific paper
A geometrical approach for low Reynolds number swimming was introduced by Shapere and Wilczek1. Here we pursue some developments for the two dimensional theory. The outer membrane or the ciliary envelope of the planar organism is represented by the conformal image of the unit circle. Power expenditures and velocities can be computed using complex variable techniques. As an example, we present the calculations for a self deforming ellipse. The results compare well with observations for the nematode Turbatrix aceti. We also compute the most efficient swimming stroke, using the criterion efficiency = velocity/hydrodynamical power. A pattern noticed by SW for the circle and the sphere is confirmed: efficiency is optimized around certain high order geometric modes. For the case of a deforming membrane, these modes require great mechanical stress. However, such high order geometric modes are easily emulated by ciliary envelopes without extra (mechanical) power expenditure. Therefore, coordinated spatio-temporal ciliary movements, besides providing an inherent maneuverability, have the added advantage of saving energy.
Cherman Alexandre
Delgado Joaquín
Duda Fernando
Ehlers Kurt
Koiller Jair
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