N-link swimmers swimming alone or in pairs

Abstract: This talk presents two models of swimmers immersed in a low Reynolds number fluid, both of them involving the so-called N -link swimmer. The first one studies the 3-dimensional N-link swimmer swimming alone [1], the second focuses on two planar 2-link swimmers swimming together [2]. Both models rely on Resistive Force Theory, which is a good approximation of hydrodynamic forces at low Reynolds number for slender swimmers and allows us to cast the equations of motion as ODEs. These equations can be seen as control systems where the controls are the velocity of deformation of the swimmers. We prove that the 3 dimensional N -link swimmer is fully controllable and we show the existence of optimal controls for some cost functionals. Regarding the coupled swimmers, even if, taken singularly, they are non-controllable units (because of Purcell’s celebrated Scallop Theorem), we prove that taking into account the hydrodynamic interaction they can achieve a net motion after a periodic sequence of shape changes. Moreover, under suitable approximations, we are able to optimize the displacement.

[1] R. Marchello, M, Morandotti, H. Shum, M. Zoppello. The N -link swimmer in three dimensions: controllability and optimality results. Accepted for publication in Acta Applicandae Mathematicae (2022)

[2] M. Zoppello, M. Morandotti, H. Gadˆelha. Controlling non-controllable scallops. Submitted.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).