Séminaire d'Analyse

Modelling, control and analysis for micro-swimmers
Laetitia Giraldi
Thursday 17 April 2014 11:00 -  Tours -  Salle 1180 (Bât E2)

Résumé :
Swimming strategies at the microscopic scale involve different mechanisms to those at the human scale. At this scale, the flow is dominated by the viscosity effects of the water and becomes reversible. This feature, known as the scallop theorem needs to be circumvented in order to swim with strokes that produce a net motion of the swimmer. The talk proposes to give an overview of recent works on this topic by the author and collaborators [1-7]. In particular, we will show how these problems sit at the intersection between fluid mechanics, control theory, theory of PDE and geometry. References [1] F. Alouges, L. Giraldi. Enhanced controllability of low Reynolds number swimmers in the presence of a wall. Acta Applicandae Mathematicae, vol 28 issue 1 (2013), 153-179. [2] F. Alouges, A. DeSimone, L. Giraldi, M. Zoppello, Self-propulsion of slender micro- swimmers by curvature control: N-link swimmers. International Journal of Non-Linear Mechanics, Vol. 56, November 2013, 132-141. [3] L. Giraldi, P. Martinon, M. Zoppello, Controllability and Optimal Strokes for N-link Micro-swimmer. Proc. 52th Conf. on Dec. and Contr. (Florence, Italy), dec. 2013. [4] D. Grard-Varet, L. Giraldi Rough wall effect on micro-swimmers. Submitted. [5] T. Chambrion, L. Giraldi, A. Munnier Optimal strokes for driftless swimmers : A general geometric approach. Preprint [6] F. Alouges, A. DeSimone, L. Giraldi, M. Zoppello, Slender micro-swimmers controlled by a magnetic fields. in Preparation. [7] L. Giraldi Comment les spermatozoïdes nagent-ils ? http://mpt2013.fr/comment-les-spermatozoïdes-nagent-ils/

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