講演者：Clément Moreau氏 (RIMS, 京都大学)
タイトル：Odd elasticity and Lie brackets: non-reciprocity for modelling and control of microscopic swimmer locomotion
The research on swimming micro-organisms and the design of swimming micro-robots is at the crossing between many fields, from theoretical fluid dynamics to biomechanics and medical applications. At the microscopic scale, locomotion through a fluid follows specific laws, due to the predominance of the viscous effects . One of the fundamental principles of locomotion in this regime, famously termed as the scallop theorem, states that non-reciprocal deformation is required to produce a net motion. I would like to elaborate on this simple concept of non-reciprocity and its many forms in microswimming studies, by presenting some of my works on modelling and control of microswimmers.
First, I will talk about our recent research on modelling the internal activity of living matter by non-reciprocal interactions. I will present the framework of ‘odd elasticity’ on which this analysis is based, and how it successfully applies to microscale locomotion, illustrating this on flagellar swimmer models.
Then, I will discuss controllability of microswimming models, which aims at determining whether a given swimmer may or may not reach a given target. To mathematically characterize controllability, one relies on Lie brackets, which are, in this context, a sort of measure of the non-reciprocity of a sequence of moves. Using these, we determined conditions to ensure controllability of magnetically-driven elastic swimmers.