scholarly journals Controllability of low Reynolds numbers swimmers of ciliate type

2020 ◽  
Vol 26 ◽  
pp. 31
Author(s):  
Jérôme Lohéac ◽  
Takéo Takahashi
Keyword(s):  
Rigid Body ◽  
Incompressible Fluid ◽  
Control Problem ◽  
Vector Fields ◽  
Viscous Incompressible Fluid ◽  
Exact Controllability ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Minimal Dimension ◽  
Stokes Fluid

We study the locomotion of a ciliated microorganism in a viscous incompressible fluid. We use the Blake ciliated model: the swimmer is a rigid body with tangential displacements at its boundary that allow it to propel in a Stokes fluid. This can be seen as a control problem: using periodical displacements, is it possible to reach a given position and a given orientation? We are interested in the minimal dimension d of the space of controls that allows the microorganism to swim. Our main result states the exact controllability with d = 3 generically with respect to the shape of the swimmer and with respect to the vector fields generating the tangential displacements. The proof is based on analyticity results and on the study of the particular case of a spheroidal swimmer.

scholarly journals The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation

2013 ◽  
Vol 23 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Alexander Khapalov
Keyword(s):  
Incompressible Fluid ◽  
Stokes Equation ◽  
Reynolds Numbers ◽  
The Self ◽  
Well Posedness ◽  
Propulsion Systems ◽  
Engineering Applications ◽  
Low Reynolds Numbers ◽  
Low Reynolds

We introduce and investigate the well-posedness of a model describing the self-propelled motion of a small abstract swimmer in the 3-D incompressible fluid governed by the nonstationary Stokes equation, typically associated with low Reynolds numbers. It is assumed that the swimmer’s body consists of finitely many subsequently connected parts, identified with the fluid they occupy, linked by rotational and elastic Hooke forces. Models like this are of interest in biological and engineering applications dealing with the study and design of propulsion systems in fluids.

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