Addendum to "Local Controllability of the Two-Link Magneto-Elastic Micro-Swimmer"

In the above mentioned note (, , published in IEEE Trans. Autom. Cont., 2017), the first and fourth authors proved a local controllability result around the straight configuration for a class of magneto-elastic micro-swimmers.That result is weaker than the usual small-time local controllability (STLC), and the authors left the STLC question open. The present addendum closes it by showing that these systems cannot be STLC

Odd elastohydrodynamics: non-reciprocal living material in a viscous fluid

Motility is a fundamental feature of living matter, encompassing single cells and collective behavior. Such living systems are characterized by non-conservativity of energy and a large diversity of spatio-temporal patterns. Thus, fundamental physical principles to formulate their behavior are not yet fully understood. This study explores a violation of Newton's third law in motile active agents, by considering non-reciprocal mechanical interactions known as odd elasticity. By extending the description of odd elasticity to a nonlinear regime, we present a general framework for the swimming dynamics of active elastic materials in low-Reynolds-number fluids, such as wave-like patterns observed in eukaryotic cilia and flagella. We investigate the non-local interactions within a swimmer using generalized material elasticity and apply these concepts to biological flagellar motion. Through simple solvable models and the analysis of {\it Chlamydomonas} flagella waveforms and experimental data for human sperm, we demonstrate the wide applicability of a non-local and non-reciprocal description of internal interactions within living materials in viscous fluids, offering a unified framework for active and living matter physics.Comment: 18 pages, 9 figure

Local controllability of a magnetized Purcell's swimmer

International audienceThis paper focuses on the control theory aspects of the dynamics of a magnetized micro-swimmer robot model made of three rigid links. Under generic assumptions on the parameters, we show that the control system which describes the swimmer dynamics is locally controllable in small time around its equilibrium position (the straight line), but with bounded controls that do not go to zero as the target state gets closer to the initial state. This result is relevant for useful applications in the micro-swimming field, and provides better understanding of this type of two-control systems

Pierrelatte (26), Les Tomples - Du Néolithique sous la centrale

Pierrelatte (26), Les Tomples - Du Néolithique sous la central

The control of particles in the Stokes limit

There are numerous ways to control objects in the Stokes regime, with microscale examples ranging from the use of optical tweezers to the application of external magnetic fields. In contrast, there are relatively few explorations of theoretical controllability, which investigate whether or not refined and precise control is indeed possible in a given system. In this work, seeking to highlight the utility and broad applicability of such rigorous analysis, we recount and illustrate key concepts of geometric control theory in the context of multiple particles in Stokesian fluids interacting with each other, such that they may be readily and widely applied in this largely unexplored fluid-dynamical setting. Motivated both by experimental and abstract questions of control, we exemplify these techniques by explicit and detailed application to multiple problems concerning the control of two particles, such as the motion of tracers in flow and the guidance of one sphere by another. Further, we showcase how this analysis of controllability can directly lead to the construction of schemes for control, in addition to facilitating explorations of mechanical efficiency and contributing to our overall understanding of non-local hydrodynamic interactions in the Stokes limit

Hydrodynamics of elastic micro-filaments : model comparison and applications

International audienc

Un coteau bien orienté à Anse (Rhône). Sépultures de l’âge du Bronze ancien inédites dans la vallée de la Saône aval

National audienceUn coteau bien orienté à Anse (Rhône). Sépultures de l’âge du Bronze ancien inédites dans la vallée de la Saône ava

Generalised Jeffery's equations for rapidly spinning particles. Part 1: Spheroids

The observed behaviour of passive objects in simple flows can be surprisingly intricate, and is complicated further by object activity. Inspired by the motility of bacterial swimmers, in this two-part study we examine the three-dimensional motion of rigid active particles in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. Here, in Part 1, we develop a multiscale framework to investigate these emergent dynamics and apply it to simple spheroidal objects. In Part 2 (arXiv:2301.11032), we apply our framework to understand the emergent dynamics of more complex shapes; helicoidal objects with chirality. Via a multiple-scales asymptotic analysis for nonlinear systems, we systematically derive emergent equations of motion for long-term trajectories that explicitly account for the strong (leading-order) effects of fast spinning. Supported by numerical examples, we constructively link these effective dynamics to the well-known Jeffery's orbits for passive spheroids, deriving an explicit closed-form expression for the effective shape of the active particle, broadening the scope of Jeffery's seminal study to spinning spheroids