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Mathematical methods for analysis swimming at low Reynolds number

Abstract : This thesis is devoted to the mathematical study of the swimming at low Reynolds number. The controllability and the optimal problems associated with the displacement of micro- swimmers are the main points developed in this work. In the first part, we study the controllability and the optimal control problem in time associated with a reduced model of swimmers, called the"N-link swimmer". In the second part, we study the boundary effect on the controllability of particular micro-swimmers made by several balls linked each others by thin jacks. Firstly, we analyze the effect of a plane wall on the mobility of these swimmers. Then, we generalize these results where the wall is rough. We demonstrate that a controllable swimmer remains controllable in a half space delimited by a wall (plane or rough) whereas the reachable set of a non controllable one is increased by the presence of a wall. The last part is devoted to provide a general framework to study optimal controllability of driftless swimmers. We focus on the study of optimal strokes i.e. periodic shape changes. More precisely, we are interested in the existence of optimal strokes, minimizing or maximizing various cost functionals, qualitative properties of the optimal strokes, regularity and monotony of the value functions.
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Submitted on : Tuesday, October 15, 2013 - 2:20:26 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:31 PM
Long-term archiving on: : Friday, April 7, 2017 - 11:11:47 AM


  • HAL Id : pastel-00873294, version 1



Laetitia Giraldi. Mathematical methods for analysis swimming at low Reynolds number. Optimization and Control [math.OC]. Ecole Polytechnique X, 2013. English. ⟨NNT : 2013EPXX0047⟩. ⟨pastel-00873294⟩



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