Monday, april 7, 2:00pm, salle K1, bâtiment Kahn

Modelling, control and analysis for micro-swimmers
Laetitia Giraldi (ENS Lyon)

Swimming strategies at the microscopic scale involves different mechanisms than in the human scale. Indeed, the flow is dominated by the viscosity effects of the water and becomes reversible. This feature, known as the scallop theorem in that context needs to be circumvented when one wants to swim with strokes that produce a net motion of the swimmer.

The talk proposes to make a tour of recent works on this topic by the author and collaborators [1-7]. Particularly, we will show how these problems are 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 field. in Preparation.

[7] L. Giraldi Comment les spermatozoïdes nagent-ils ? mpt2013.fr