Experimental observation of topological transition in linear and nonlinear parametric oscillators.

Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is perturbed by a continuously parametrized defect. Initially in one of its stable states, the oscillator will be perturbed by the defect and finally reach another stable state, which can be its initial one or the other one. For some critical value of the defect parameter, the final state changes abruptly. We theoretically and experimentally investigate such transition both in the linear and nonlinear cases, and the effect of nonlinearities is discussed. A topological interpretation in terms of winding number is proposed, and we show that winding changes correspond to singularities in the temporal dynamics. An experimental observation of such transition is performed using parametric Faraday instability at the surface of a vibrated fluid.

Comprehensive refractive manipulation of water waves using electrostriction.

The control of wave propagation based on refraction principles offers unparalleled possibilities as shown by the striking example of optics. This approach is unfortunately limited for water waves as it relies mainly on variations of the liquid depth which, while controlling the wave velocity, also trigger nonlinearities and damping. In this article, we show experimentally that electrostriction allows to implement extensive refraction-based control of water waves in a precise and contactless manner. The setup consists of an electrode under high voltage placed above the grounded conductive water. The waves propagating under the electrode can be slowed down up to approximately half their speed compared to free propagation. We characterize the Snell-Descartes laws of refraction and the total internal reflection for the water waves. We implement emblematic refraction-based devices such as electrically tunable focusing lenses, waveguides without obstacles, and beam splitters based on frustrated internal reflection to perform interference experiments.

Experimental Implementation of Wave Propagation in Disordered Time-Varying Media.

Here, we study and implement the temporal analog in time disordered sytems. A spatially homogeneous medium is endowed with a time structure composed of randomly distributed temporal interfaces. This is achieved through electrostriction between water surface and an electrode. The wave field observed is the result of the interferences between reflected and refracted waves on the interfaces. Although no eigenmode can be associated with the wave field, several common features between space and time emerge. The waves grow exponentially depending on the disorder level in agreement with a 2D matrix evolution model such as in the spatial case. The relative position of the momentum gap appearing in the time modulated systems plays a central role in the wave field evolution. When tuning the excitation to compensate for the damping, transient waves, localized in time, appear on the liquid surface. They result from a particular history of the multiple interferences produced by a specific sequence of time boundaries.

Frequency Conversion Cascade by Crossing Multiple Space and Time Interfaces.

Time varying media recently emerged as promising candidates to fulfill the dream of controlling the wave frequency without nonlinear effects. However, frequency conversion remains limited by the dynamics of the variations of the propagation properties. Here we propose a new concept of space-time cascade to achieve arbitrary large frequency shifts by iterated elementary transformation steps. These steps use an intermediate medium in which wave packets enter and exit through noncommutative space and time interfaces. This concept avoids high frequency or subwavelength demanding metamaterials. Upward and downward frequency conversions are performed. The transmitted energy yield is given by the frequency ratio, regardless of impedence mismatch. We implement this concept with water waves controlled by electrostriction and achieve frequency conversion over 4 octaves.

Liquid walls and interfaces in arbitrary directions stabilized by vibrations.

Gravity shapes liquids and plays a crucial role in their internal balance. Creating new equilibrium configurations irrespective of the presence of a gravitational field is challenging with applications on Earth as well as in zero-gravity environments. Vibrations are known to alter the shape of liquid interfaces and also to change internal dynamics and stability in depth. Here, we show that vibrations can also create an "artificial gravity" in any direction. We demonstrate that a liquid can maintain an inclined interface when shaken in an arbitrary direction. A necessary condition for the equilibrium to occur is the existence of a velocity gradient determined by dynamical boundary conditions. However, the no-slip boundary condition and incompressibility can perturb the required velocity profile, leading to a destabilization of the equilibrium. We show that liquid layers provide a solution, and liquid walls of several centimeters in height can thus be stabilized. We show that the buoyancy equilibrium is not affected by the forcing.

Author Correction: Floating under a levitating liquid.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Floating under a levitating liquid.

When placed over a less dense medium, a liquid layer will typically collapse downwards if it exceeds a certain size, as gravity acting on the lower liquid interface triggers a destabilizing effect called a Rayleigh-Taylor instability1,2. Of the many methods that have been developed to prevent the liquid from falling3-6, vertical shaking has proved to be efficient and has therefore been studied in detail7-13. Stabilization is the result of the dynamical averaging effect of the oscillating effective gravity. Vibrations of liquids also induce other paradoxical phenomena such as the sinking of air bubbles14-19 or the stabilization of heavy objects in columns of fluid at unexpected heights20. Here we take advantage of the excitation resonance of the supporting air layer to perform experiments with large levitating liquid layers of up to half a litre in volume and up to 20 centimetres in width. Moreover, we predict theoretically and show experimentally that vertical shaking also creates stable buoyancy positions on the lower interface of the liquid, which behave as though the gravitational force were inverted. Bodies can thus float upside down on the lower interface of levitating liquid layers. We use our model to predict the minimum excitation needed to withstand falling of such an inverted floater, which depends on its mass. Experimental observations confirm the possibility of selective falling of heavy bodies. Our findings invite us to rethink all interfacial phenomena in this exotic and counter-intuitive stable configuration.