Monique Chyba (University of Hawaii) Sub-Riemannian geometry, Hamiltonian dynamics, Micro-swimmers, Copepod nauplii and Copepod robot Sponsored by the Meyer Fund

Tue, Mar. 17 12:10pm (MATH …

Kempner

Uri Shapira (Israel Institute of Technology) TBA

Tue, Mar. 17 3pm (MATH 350)

Algebraic Geometry

Klaus Hulek (Institute for Algebraic Geometry, Leibniz University Hannover) TBA Sponsored by the Meyer Fund

X

The copepod model is a simplification of the 3-link Purcell swimmer and is relevant to analyze more complex micro-swimmers. The mathematical model is validated by observations performed by a team from Hawaii, showing the agreement between the predicted and observed motions. Sub-Riemannian geometry will be introduced, assuming that displacements are minimizing the expanded mechanical energy of the micro-swimmer. The objective is to maximize the efficiency of a stroke (the ratio between the displacement produced by a stroke and its length). Using the Maximum Principle in the framework of Sub-Riemannian geometry, this leads to analyze family of periodic controls producing strokes to determine the most efficient one. Finally a robotic copepod is presented whose aim is to validate the computations and very preliminary results are given.