Self-propulsion and crossing statistics under random initial conditions

We investigate the crossing of an energy barrier by a self-propelled particle described by a Rayleigh friction term. We reveal the existence of a sharp transition in the external force field whereby the amplitude dramatically increases. This corresponds to a saddle point transition in the velocity flow phase space, as would be expected for any type of repulsive force field. We use this approach to rationalize the results obtained by Eddi \emph{et al.} [\emph{Phys. Rev. Lett.} \textbf{102}, 240401 (2009)] who studied the interaction between a drop propelled by its accompanying wave field and a submarine obstacle. This wave particle entity can overcome potential barrier, suggesting the existence of a "macroscopic tunneling effect". We show that the effect of self-propulsion is sufficiently strong to generate crossing of the high energy barrier. By assuming a random distribution of initial angles, we define a probability distribution to cross the potential barrier that matches with the data of Eddi \emph{et al.}. This probability is similar to the one encountered in statistical physics for Hamiltonian systems \textit{i.e.} a Boltzmann exponential law.Comment: 7 pages, 4 figure

Magnetocapillary self-assemblies: locomotion and micromanipulation along a liquid interface

This paper presents an overview and discussion of magnetocapillary self-assemblies. New results are presented, in particular concerning the possible development of future applications. These self-organizing structures possess the notable ability to move along an interface when powered by an oscillatory, uniform magnetic field. The system is constructed as follows. Soft magnetic particles are placed on a liquid interface, and submitted to a magnetic induction field. An attractive force due to the curvature of the interface around the particles competes with an interaction between magnetic dipoles. Ordered structures can spontaneously emerge from these conditions. Furthermore, time-dependent magnetic fields can produce a wide range of dynamic behaviours, including non-time-reversible deformation sequences that produce translational motion at low Reynolds number. In other words, due to a spontaneous breaking of time-reversal symmetry, the assembly can turn into a surface microswimmer. Trajectories have been shown to be precisely controllable. As a consequence, this system offers a way to produce microrobots able to perform different tasks. This is illustrated in this paper by the capture, transport and release of a floating cargo, and the controlled mixing of fluids at low Reynolds number.Comment: 10 pages, 8 figures review pape

Waveguides for walking droplets

When gently placing a droplet onto a vertically vibrated bath, a drop can bounce without coalescing. Upon increasing the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well defined speed. We investigate the confinement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that 1d confinement is optimal for narrow channels of width of $D \simeq 1.5 \lambda_F$. We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels.Comment: 8 pages, 6 figure

Statics and dynamics of magnetocapillary bonds

When ferromagnetic particles are suspended at an interface under magnetic fields, dipole-dipole interactions compete with capillary attraction. This combination of forces has recently given promising results towards controllable self-assemblies, as well as low Reynolds swimming systems. The elementary unit of these assemblies is a pair of particles. Although equilibrium properties of this interaction are well described, dynamics remain unclear. In this letter, the properties of magnetocapillary bonds are determined by probing them with magnetic perturbations. Two deformation modes are evidenced and discussed. These modes exhibit resonances whose frequencies can be detuned to generate non-reciprocal motion. A model is proposed which can become the basis for elaborate collective behaviours

Remote control of self-assembled microswimmers

Physics governing the locomotion of microorganisms and other microsystems is dominated by viscous damping. An effective swimming strategy involves the non-reciprocal and periodic deformations of the considered body. Here, we show that a magnetocapillary-driven self-assembly, composed of three soft ferromagnetic beads, is able to swim along a liquid-air interface when powered by an external magnetic field. More importantly, we demonstrate that trajectories can be fully controlled, opening ways to explore low Reynolds number swimming. This magnetocapillary system spontaneously forms by self-assembly, allowing miniaturization and other possible applications such as cargo transport or solvent flows.Comment: 5 pages, 5 figures articl

Scattering theory of walking droplets in the presence of obstacles

We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a pilot wave for the droplet. This leads to so called walking droplets or walkers. Since the seminal experiment by {\it Couder et al} [Phys. Rev. Lett. {\bf 97}, 154101 (2006)] there have been many attempts to accurately reproduce the experimental results. We propose to describe the trajectories of a walker using a Green function approach. The Green function is related to the Helmholtz equation with Neumann boundary conditions on the obstacle(s) and outgoing boundary conditions at infinity. For a single-slit geometry our model is exactly solvable and reproduces some general features observed experimentally. It stands for a promising candidate to account for the presence of arbitrary boundaries in the walker's dynamics.Comment: 17 pages, 5 figure

Critères de conception en service des bétons renforcés de fibres basés sur la perméabilité à l'eau

RÉSUMÉ Dans un contexte nord-américain où les structures sont exposées à des conditions environnementales très sévères, les cas de détérioration précoce des structures en béton armé se font de plus en plus fréquents. De fait, la durabilité des structures est directement influencée par la fissuration en condition de service. La présence de fissure offre un chemin préférentiel à l'eau et aux agents agressifs dans le béton qui viennent accélérer la dégradation du béton armé. Il va sans dire que ces problèmes de durabilité conduisent à d'importants coûts socio-économiques et impacts environnementaux. L'inclusion de fibres métalliques au béton s'avère une solution à la dégradation précoce des infrastructures. Les fibres amènent un meilleur contrôle de la fissuration en service. En d'autres mots, les fibres pontent les ouvertures de fissures conduisant à un plus grand nombre de fissures d'ouverture plus fines. Ce contrôle accru de la fissuration par les fibres gêne davantage la pénétration d'eau et d'agents agressifs dans le béton en comparaison au béton armé couramment utilisé. Le potentiel de durabilité du béton renforcé de fibres (BRF) a été démontré dans plusieurs études. Cependant, très peu d'entre-elles se sont intéressées à l'identification de critères de conception en service adaptés au BRF. Ce faisant, la pleine exploitation des BRF s'avère limitée et peut constituer un frein à leur utilisation. Ainsi, l'objectif général de ce projet de recherche était de proposer des critères de conception en service offrant une durabilité adéquate pour les bétons fibrés à haute et ultra-haute performance (BFHP et BFUP) de sorte qu'ils puissent prolonger la durée de vie utile des infrastructures.----------ABSTRACT In a North American context where structures are exposed to severe environmental conditions, cases of reinforced concrete structures showing premature deterioration are becoming increasingly frequent. In fact, the durability of structures is directly influenced by cracking in serviceability. Cracks provide a preferential path for water and aggressive agents penetration into the concrete, which accelerates concrete and steel reinforcement degradation. Needless to say, these durability problems lead to significant socio-economic costs and environmental impacts. The inclusion of steel fibers in concrete offers a solution to premature degradation of infrastructures. The addition of fibers improves the crack control of concrete in serviceability. In other words, the crack bridging effect of fibers leads to the creation of a higher number of narrower cracks. This crack control enhancement given by the fibers greatly reduces the penetration of water and aggressive agents into the concrete in comparison with commonly used reinforced concrete. The sustainability potentiel of fiber reinforced concrete (FRC) has been demonstrated in several studies. Yet very few of them showed interest in the identification of design criteria adapted to FRC in serviceability. Therefore, the full exploitation of FRC proves to be limited and may constitute a barrier to their use. Thus, the general objective of this research project was to propose design criteria at serviceability limit state providing convenient durability for high performance fiber reinforced concrete (HPFRC) and ultra high performance fiber reinforced concrete (UHPFRC) so that they can extend the service life of structures

Bouncing dynamics of a spring

peer reviewe

Overload wave-memory induces amnesia of a self-propelled particle

Information storage, for short "memory", is a key element of autonomous, out-of-equilibrium dynamics, in particular in biological entities. In synthetic active matter, however, the implementation of internal memory in agents is often limited or even absent. As a consequence, most of the investigations in the field of active matter had no choice but to ignore the influence of memory on the dynamics of these systems. We take here the opportunity to explore this question by leveraging one of the very few experimental physical system in which memory can be described in terms of a single and most importantly tunable scalar quantity. Here we consider a particle propelled at a fluid interface by self-generated stationary waves. The amount of souvenirs stored in the wave-memory field can be tuned, allowing for a throughout investigation of the properties of this memory-driven dynamics. We show numerically and experimentally that the accumulation of information in the wave field induces the loss of long-range time correlations. The dynamics can then be described by a memory-less process. We rationalize the resulting statistical behavior by defining an effective temperature for the particle dynamics and by evidencing a minimization principle for the wave field