The hydraulic bump: The surface signature of a plunging jet

When a falling jet of fluid strikes a horizontal fluid layer, a hydraulic jump arises downstream of the point of impact provided a critical flow rate is exceeded. We here examine a phenomenon that arises below this jump threshold, a circular deflection of relatively small amplitude on the free surface, that we call the hydraulic bump. The form of the circular bump can be simply understood in terms of the underlying vortex structure and its height simply deduced with Bernoulli arguments. As the incoming flux increases, a breaking of axial symmetry leads to polygonal hydraulic bumps. The relation between this polygonal instability and that arising in the hydraulic jump is discussed. The coexistence of hydraulic jumps and bumps can give rise to striking nested structures with polygonal jumps bound within polygonal bumps. The absence of a pronounced surface signature on the hydraulic bump indicates the dominant influence of the subsurface vorticity on its instability

Tunable bimodal explorations of space from memory-driven deterministic dynamics

We present a wave-memory-driven system that exhibits intermittent switching between two propulsion modes in free space. The model is based on a pointlike particle emitting periodically cylindrical standing waves. Submitted to a force related to the local wave-field gradient, the particle is propelled, while the wave field stores positional information on the particle trajectory. For long memory, the linear motion is unstable and we observe erratic switches between two propulsive modes: linear motion and diffusive motion. We show that the bimodal propulsion and the stochastic aspect of the dynamics at long time are generated by a Shil'nikov chaos. The memory of the system controls the fraction of time spent in each phase. The resulting bimodal dynamics shows analogies with intermittent search strategies usually observed in living systems of much higher complexity. © 2019 American Physical Society

Light-mediated cascaded locking of Multiple nano-optomechanical oscillators

Collective phenomena emerging from nonlinear interactions between multiple oscillators, such as synchronization and frequency locking, find applications in a wide variety of fields. Optomechanical resonators, which are intrinsically nonlinear, combine the scientific assets of mechanical devices with the possibility of long distance controlled interactions enabled by traveling light. Here we demonstrate light-mediated frequency locking of three distant nano-optomechanical oscillators positioned in a cascaded configuration. The oscillators, integrated on a chip along a common coupling waveguide, are optically driven with a single laser and oscillate at gigahertz frequency. Despite an initial mechanical frequency disorder of hundreds of kilohertz, the guided light locks them all with a clear transition in the optical output. The experimental results are described by Langevin equations, paving the way to scalable cascaded optomechanical configurations

Transition to chaos in wave memory dynamics in a harmonic well : deterministic and noise-driven behaviour

International audienceA walker is the association of a sub-millimetric bouncing drop moving along with a co-evolving Faraday wave. When confined in a harmonic potential, its stable trajectories are periodic and quan-tised both in extension and mean angular momentum. In this article we present the rest of the story, specifically the chaotic paths. They are chaotic and show intermittent behaviours between unstable quantised set of attractors. First we present the two possible situations we find experimentally. Then we emphasise theoretically two mechanisms that lead to unstable situations. It corresponds either to noise-driven chaos or low-dimensional deterministic chaos. Finally we characterise experimentally each of these distinct situations. This article aims at presenting a comprehensive investigation of the unstable paths in order to complete the picture of walkers in a two dimensional harmonic potential

Multistable Free States of an Active Particle from a Coherent Memory Dynamics

International audienceWe investigate the dynamics of a deterministic self-propelled particle endowed with coherent memory. We evidence experimentally and numerically that it exhibits several stable free states. The system is composed of a self-propelled drop bouncing on a vibrated liquid driven by the waves it emits at each bounce. This object possesses a propulsion memory resulting from the coherent interference of the waves accumulated along its path. We investigate here the transitory regime of the buildup of the dynamics which leads to velocity modulations. Experiments and numerical simulations enable us to explore unchartered areas of the phase space and reveal the existence of a self-sustained oscillatory regime. Finally, we show the coexistence of several free states. This feature emerges both from the spatiotemporal nonlocality of this path memory dynamics as well as the wave nature of the driving mechanis