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

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

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

Emergent three-dimensional dynamics of rapidly spinning, self-propelled particles in shear flow. Part II: Chiral objects

In the second part of this two-part study, we investigate the motion of three-dimensional, rigid, active particles in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. We consider the general class of objects with helicoidal symmetry, focusing on chiral objects without reflectional fore-aft symmetry, significantly broadening the class of objects studied in Part I. We perform an intricate multiple-scales asymptotic analysis to systematically derive emergent equations of motion for the angular and translational dynamics of the object that explicitly account for the significant effects of fast spinning. We show that the emergent dynamics due to rapid rotation can be described by generalized Jeffery's equations for the wide class of objects that exhibit helicoidal symmetry, significantly expanding the scope of Jeffery's seminal study. Furthermore, we use our analytic results to characterise and quantify the explicit effect of rotation on the effective hydrodynamic shape of the objects

Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals

When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals. Learning with these matrices requires using Riemanian geometry to account for their structure. In this paper, we propose a new method to deal with distributions of covariance matrices and demonstrate its computational efficiency on M/EEG multivariate time series. More specifically, we define a Sliced-Wasserstein distance between measures of symmetric positive definite matrices that comes with strong theoretical guarantees. Then, we take advantage of its properties and kernel methods to apply this distance to brain-age prediction from MEG data and compare it to state-of-the-art algorithms based on Riemannian geometry. Finally, we show that it is an efficient surrogate to the Wasserstein distance in domain adaptation for Brain Computer Interface applications

Première injection de lixiviat dans un digesteur anaérobique suivi par méthode géophysique.

3rd International Workshop on Geoelectrical MonitoringGELMON 2015, Vienna, AUT, 24-/11/2015 - 26/11/2015International audienceAnaerobic digestion (AD) has a high growing potential worldwide due to its combined environmental benefits such as reducing greenhouse gas, producing renewable energy, organic amendment and fertilizer. In France, 400 plants were recorded in 2015 which mainly handle agricultural residues using both liquid and solid state processes. The successful and efficient degradation of organic matter in AD needs balanced physical-chemical conditions for microbial development. Moisture content in the media, particularly, was found to be of great importance. Nevertheless, no information is available on the hydrodynamics of the circulation of the leachate through cattle manure or other agricultural residues. Moreover, agricultural residues and mixtures are particularly porous and heterogeneous and no data was found on the efficiency of those systems to humidify homogeneously such a substrate. The hydrodynamic flow characteristics and transfer time of the leachate are essential to design the optimal liquid injection system that will permit to reach uniform moisture content. Already applied in landfills for in-situ characterization of leachates flow through municipal solid waste (MSW), ERT was proven to give reliable results. The results led to the enhancement of the leachate injection system design and enriched the knowledge of MSW behavior. The non-intrusive, non-destructive and 3 dimensional response of the ERT method seems adapted to the study of the leachate infiltration through agricultural effluents in a SSAD plant. We present the first results of the use of 3D time-lapse electrical resistivity tomography performed during a leachate injection in a waste deposit cell in France (20 m3 of leachate was injected during 10 h). 72 electrodes and a Syscal PRO resistivity meter was used. For the inversion, the apparent resistivity have been interpreted taking into account (i) the boundary condition of the waste deposit cell (insulating boundary around the waste deposit cell) and (ii) the effects of temperature (indeed between the surface and the bottom of the waste deposit cell , we measured the variation of temperature in the range of +/-25 °C). The result highlighted the conductive character of this porous media with a resistivity included between 0.5 ohm.m and 10 ohm.m depending on the saturation state; we will show that the infiltration is clearly located by electrical resistivity tomography and that this media is very heterogeneous with complex infiltration shape. The first results suggest the interest of the 3D electrical resistivity tomography to study injection leachate injection in a SSAD plant