# Controllability properties of a class of systems modeling swimming microscopic organisms

Mario Sigalotti; Jean-Claude Vivalda

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 16, Issue: 4, page 1053-1076
- ISSN: 1292-8119

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topSigalotti, Mario, and Vivalda, Jean-Claude. "Controllability properties of a class of systems modeling swimming microscopic organisms." ESAIM: Control, Optimisation and Calculus of Variations 16.4 (2010): 1053-1076. <http://eudml.org/doc/250744>.

@article{Sigalotti2010,

abstract = {
We consider a finite-dimensional model for the motion of
microscopic organisms whose propulsion
exploits
the action of a layer of cilia covering its surface.
The model couples
Newton's laws driving the organism,
considered as
a rigid body, with
Stokes equations governing the surrounding fluid.
The action of the
cilia is described by a set of controlled
velocity fields on the surface of the organism.
The first contribution of the paper is the proof
that such a system
is generically controllable
when the space of controlled velocity fields is at least three-dimensional. We also provide
a complete characterization of controllable systems
in the case in which
the organism has a spherical shape. Finally, we
offer a complete picture of controllable and non-controllable systems under the additional hypothesis
that
the organism and the fluid have
densities of the same order of magnitude.
},

author = {Sigalotti, Mario, Vivalda, Jean-Claude},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Swimming micro-organisms; ciliata; high viscosity; nonlinear systems; controllability; models of swimming micro-organisms},

language = {eng},

month = {10},

number = {4},

pages = {1053-1076},

publisher = {EDP Sciences},

title = {Controllability properties of a class of systems modeling swimming microscopic organisms},

url = {http://eudml.org/doc/250744},

volume = {16},

year = {2010},

}

TY - JOUR

AU - Sigalotti, Mario

AU - Vivalda, Jean-Claude

TI - Controllability properties of a class of systems modeling swimming microscopic organisms

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/10//

PB - EDP Sciences

VL - 16

IS - 4

SP - 1053

EP - 1076

AB -
We consider a finite-dimensional model for the motion of
microscopic organisms whose propulsion
exploits
the action of a layer of cilia covering its surface.
The model couples
Newton's laws driving the organism,
considered as
a rigid body, with
Stokes equations governing the surrounding fluid.
The action of the
cilia is described by a set of controlled
velocity fields on the surface of the organism.
The first contribution of the paper is the proof
that such a system
is generically controllable
when the space of controlled velocity fields is at least three-dimensional. We also provide
a complete characterization of controllable systems
in the case in which
the organism has a spherical shape. Finally, we
offer a complete picture of controllable and non-controllable systems under the additional hypothesis
that
the organism and the fluid have
densities of the same order of magnitude.

LA - eng

KW - Swimming micro-organisms; ciliata; high viscosity; nonlinear systems; controllability; models of swimming micro-organisms

UR - http://eudml.org/doc/250744

ER -

## References

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