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International audience; CFA 2018-Le Havre 371 Les personnes aveugles sont capables de localiser et de suivre une source sonore avec une efficacité remarquable. C'est une faculté qu'elles utilisent dans la vie de tous les jours par exemple pour suivre les pas de la personne qui les précèdent, afin de se déplacer dans la rue ou dans un bâtiment. Certaines personnes aveugles utilisent également cette faculté dans la pratique sportive, pour suivre un guide valide lors de la pratique de la course à pied ou du roller. Sur le même principe, il est possible de guider des personnes avec des sons spatialisés. Pour le montrer, nous avons développé un dispositif embarqué autonome capable de guider des personnes en utilisant des techniques de synthèse binaurale. Dans ce dispositif, nous utilisons à la fois, les informations fournies par un système de localisation temps réel (RTLS) précis et à faible latence, et les données d'orientation de la tête fournies par une centrale inertiels à bas cout (IMU). Ces données de positionnement sont utilisées pour produire des sons spatialisés par filtrage binaural afin de guider en temps réel une personne le long d'un parcours prédéfini. La personne déficiente visuelle va donc se déplacer vers le son, de la même façon qu'elle suivrait les pas d'un guide. Le système a été conçu afin de minimiser la latence globale, à la fois pour le système de localisation et le moteur de rendu audio binaural. Nous avons ainsi pu montrer qu'il était possible de guider des personnes en leur faisant suivre des sons spatialisés, de façon précise, naturelle et avec un entrainement minimum. Ce système permet déjà de guider des personnes aveugles pour pratiquer le roller dans un gymnase et ainsi leurs permettre de faire du sport de façon plus autonome.

A simple algorithm to calculate the maximum torsional load for a cylindrical shaft is presented. The algorithm is based on the notion of viscosity solutions to the eikonal equation, and is not restricted to simply-connected cross-sections. Applications to other, related problems, such as ferromagnetic thin films, and elastic buckling of thin film blisters are also discussed.

Abstract. The paper carries on our previous investigations on the complementary version of Purcell’s rotator (sPr3): a low-Reynolds-number swimmer composed of three balls of equal radii. In the asymptotic regime of very long arms, the Stokes-induced governing dynamics is derived, and then experimented in the context of energy-minimizing self-propulsion characterized in the first part of the paper. Graphical abstract

The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while removing the bother of the admissibility of test functions, it nevertheless simplifies the proof of all the standard compactness results which made classical two-scale convergence very worthy of interest: bounded sequences in $L^2_{\sharp}[Y,L^2(\Omega)]$ and $L^2_{\sharp}[Y,H^1(\Omega)]$ are proven to be relatively compact with respect to this new type of convergence. The strengths of the notion are highlighted on the classical homogenization problem of linear second-order elliptic equations for which first order boundary corrector-type results are also established. Eventually, possible weaknesses of the method are pointed out on a nonlinear problem: the weak two-scale compactness result for $\mathbb{S}^2$-valued stationary harmonic maps., Comment: 20 pages, 2 Figures

We present a phase field approach to wetting problems, related to the minimization of capillary energy. We discuss in detail both the Γ-convergence results on which our numerical algorithm are based, and numerical implementation. Two possible choices of boundary conditions, needed to recover Young's law for the contact angle, are presented. We also consider an extension of the classical theory of capillarity, in which the introduction of a dissipation mechanism can explain and predict the hysteresis of the contact angle. We illustrate the performance of the model by reproducing numerically a broad spectrum of experimental results: advancing and receding drops, drops on inclined planes and superhydrophobic surfaces.

We study local minimizers of the micromagnetic energy in small ferromagnetic 3d convex particles for which we justify the Stoner–Wohlfarth approximation: given a uniformly convex shape $$\Omega \subset \varvec{\mathbf {R}}^3$$ , there exist $$\delta _c$$ >0 and $$C > 0$$ such that for $$0 < \delta \le \delta _c$$ any local minimizer $$\mathbf {m}$$ of the micromagnetic energy in the particle $$\delta \Omega $$ satisfies $$\Vert \nabla \mathbf {m} \Vert _{L^2} \leqslant C \delta ^2$$ . In the case of ellipsoidal particles we strengthen this result by proving that, for $$\delta $$ small enough, local minimizers are exactly spatially uniform. This last result extends W.F. Brown’s fundamental theorem for fine 3d ferromagnetic particles Brown (J Appl Phys 39:463–488, 1968), Di Fratta et al. (Physica B 407(9):1368–1371, 2011) which states the same result but only for global minimizers. As a by-product of the method that we use, we establish a new Liouville type result for locally minimizing $$p$$ -harmonic maps with values into a closed subset of a Hilbert space. Namely, we establish that in a smooth uniformly convex domain of $$\mathbf {R}^d$$ any local minimizer of the $$p$$ -Dirichlet energy ( $$p > 1$$ , $$p \ne d$$ ) is constant.

Nowadays, nonhomogeneous and periodic ferromagnetic materials are the subject of a growing interest. Actually such periodic configurations often combine the attributes of the constituent materials, while sometimes, their properties can be strikingly different from the properties of the different constituents. These periodic configurations can be therefore used to achieve physical and chemical properties difficult to achieve with homogeneous materials. To predict the magnetic behavior of such composite materials is of prime importance for applications. The main objective of this paper is to perform, by means of Gamma-convergence and two-scale convergence, a rigorous derivation of the homogenized Gibbs-Landau free energy functional associated to a composite periodic ferromagnetic material, i.e. a ferromagnetic material in which the heterogeneities are periodically distributed inside the ferromagnetic media. We thus describe the Gamma-limit of the Gibbs-Landau free energy functional, as the period over which the heterogeneities are distributed inside the ferromagnetic body shrinks to zero., Comment: 21 pages, 1 figure. Keywords: Micromagnetics, Periodic Homogenization, Gamma Convergence, Two-scale Convergence, Demagnetizing Field

We formulate and solve the equations governing the dynamics of a microscopic artificial swimmer composed of a head and of a tail made of a thin film of permanent magnetic material. This is a variant of the model swimmer proposed by Dreyfus et al. in 2005, whose tail is a filament obtained from the assembly of super-paramagnetic beads. The swimmer is actuated by an oscillating magnetic field, and its geometry is inspired by that of sperm cells. Using values for the geometric and material parameters that are realistic for a magnetic multilayer, we show that the model swimmer can reach swimming speeds exceeding one body length per second, under reasonable values of the driving magnetic field. This provides a proof of principle for the viability of the concept. In addition, we discuss the possibility to steer the system along curved paths. Finally, we compare the propulsion mechanism (swimming `gait') of our swimmer with that of sperm cells. The main difference between the two is that, contrary to its biological template, our artificial system does not rely on the propagation of bending waves along the tail, at least for the range of material and geometric parameters explored in this article.

We discuss a reduced model to compute the motion of slender swimmers which propel themselves by propagating a bending wave along their body. Our approach is based on the use of resistive force theory for the evaluation of the viscous forces and torques exerted by the surrounding fluid, and on discretizing the kinematics of the swimmer by representing its body through an articulated chain of N rigid links capable of planar deformations. The resulting system of ODEs governing the motion of the swimmer is easy to assemble and to solve, making our reduced model a valuable tool in the design and optimization of bio-inspired engineered microdevices. We test the accuracy and robustness of our approach on three benchmark examples: Purcell's 3-link swimmer, Taylor's swimming sheet and some recent quantitative observations of circular motion of a sperm cell. An explicit formula for the displacement of Purcell's 3-link swimmer generated by a square stroke of small amplitude is also discussed. © 2013 Elsevier Ltd. All rights reserved.

We discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms., 34 pages, 15 figures. v2: Fixed a reference and eliminated journal style file. v3: Addressed referee's comments.

We present a theory for low-Reynolds-number axisymmetric swimmers and a general strategy for the computation of strokes of maximal efficiency. An explicit equation characterizing optimal strokes is derived, and numerical strategies to obtain solutions are discussed. The merits of this approach are demonstrated by applying it to two concrete examples: the three linked spheres of Najafi and Golestanian and the pushmepullyou of Avron, Kenneth, and Oakmin.

Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901–062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).

We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size.