Rowers Coupled Hydrodynamically. Modeling Possible Mechanisms for the Cooperation of Cilia

We introduce a model system of stochastic entities, called rowers which include some essentials of the behavior of real cilia. We introduce and discuss the problem of symmetry breaking for these objects and its connection with the onset of macroscopic, directed flow in the fluid. We perform a mean field-like calculation showing that hydrodynamic interaction may provide for the symmetry breaking mechanism and the onset of fluid flow. Finally, we discuss the problem of the metachronal wave in a stochastic context through an analytical calculation based on a path integral representation of our model equation. FOM Institute for Atomic and Molecular Physics (AMOLF), Kruislaan 407, 1098 SJ Amsterdam, The Netherlands; Tel. +31 (0)20 6081234 ; fax +31 (0)20 6684106 ; e-mail address [email protected] Università degli Studi di Milano, Dip. Fisica, Via Celoria 16, 20100 Milano, Italy; Tel. +39 (0)2 58357477 ; fax +39 (0)2 58357480 ; e-mail address [email protected] Politecnico di Milano, Dip. Fisica, Pza Leonardo Da Vinci 32, 20100 Milano, Italy; Tel. +39 (0)2 23996133 ; fax +39 (0)2 23996126 ; e-mail address [email protected]