Seminario di Equazioni Differenziali e Applicazioni: “Optimal strokes at low Reynolds number: the Copepod and Purcell swimmers”

Lunedì 19 Dicembre 2016, ore 12:30 - Aula 2BC30 - Nicola Bettiol


Lunedì 19 Dicembre 2016 alle ore 12:30 in Aula 2BC30, Nicola Bettiol (Université Bretagne Occidentale, Brest) terrà un seminario dal titolo “Optimal strokes at low Reynolds number: the Copepod and Purcell swimmers”.

Joint work with B. Bonnard and J. Rouot
We consider two different rigid links swimmer models at low Reynolds number: the Copepod swimmer (a symmetric swimmer recently introduced by [Takagi2015]) and the long-standing three-link Purcell swimmer [Purcell1977]. The design of strokes satisfying some performance criteria leads to investigate optimal control problems which can be analysed in the framework of sub-Riemannian geometry. In this context nilpotent approximations allow to compute strokes with small amplitudes, which in turn can be used numerically to obtain general strokes. A concept of ?geometric efficiency? (corresponding to the ratio between the displacement and the length of the stroke) is introduced to deduce global optimality properties, in particular for the Copepod case. For this model a detailed analysis of both abnormal and normal strokes is also described. First and second order optimality conditions, combined with numerical analysis, allow us to detect optimal strokes for both the Copepod and the Purcell swimmers. Direct and indirect numerical schemes are implemented in Bocop and Hampath software to perform numerical simulations, which are crucial to complete the theoretical study and evaluate the optimal solutions.

Rif. Int. M. Bardi, C. Marchi, C. Mariconda.

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