arXiv subjects

Gautier Lefebvre

Publications and source records attributed to Gautier Lefebvre.

7 recordsLinked to original sources

arXiv2023

Experimental observation of exceptional points in coupled pendulums

The concept of exceptional point (EP) is demonstrated experimentally in the case of a simple mechanical system consisting of two linearized coupled pendulums. Exceptional points correspond to specific values of the system parameters that yield defective eigenvalues. These spectral singularities which are typical of non-Hermitian system means that both the eigenvalues and their associated eigenvectors coalesce. The existence of an EP requires an adequate parameterization of the dynamical system. For this aim, the experimental device has been designed with two controllable parameters which are the length of one pendulum and a viscous-like damping which is produced via electromagnetic induction. Thanks to the observation of the free response of the coupled pendulums, most EP properties are experimentally investigated, showing good agreements with theoretical considerations. In contrast with many studies on EPs, mainly in the field of physics, the novelty of the present work is that controllable parameters are restricted to be real-valued, and this requires the use of adequate search algorithms. Furthermore, it offers the possibility of exploiting the existence of EPs in time-domain dynamic problems.

physics.comp-ph↗

arXiv2023

Subwavelength pulse focusing and perfect absorption in the Maxwell fisheye

Maxwell's fisheye is a paradigm for an absolute optical instrument with a refractive index deduced from the stereographic projection of a sphere on a plane. We investigate experimentally the dynamics of flexural waves in a thin plate with a thickness varying according to the Maxwell fisheye index profile and a clamped boundary. We demonstrate subwavelength focusing and temporal pulse compression at the image point. This is achieved by introducing a sink emitting a cancelling signal optimally shaped using a time-reversal procedure. Perfect absorption and outward going wave cancellation at the focus point are demonstrated. The time evolution of the kinetic energy stored inside the cavity reveals that the sink absorbs energy out of the plate ten times faster than the natural decay rate.

physics.class-ph↗

arXiv2017

Quantum revival for elastic waves in thin plate

Quantum revival is described as the time-periodic reconstruction of a wave packet initially localized in space and time. This effect is expected in finite-size systems which exhibits commensurable discrete spectrum such as the infinite quantum well. Here, we report on the experimental observation of full and fractional quantum revival for classical waves in a two dimensional cavity. We consider flexural waves propagating in thin plates, as their quadratic dispersion at low frequencies mimics the dispersion relation of quantum systems governed by Schrödinger equation. Time-dependent excitation and measurement are performed at ultrasonic frequencies and reveal a periodic reconstruction of the initial elastic wave packet.

quant-ph↗

arXiv2016

Unveiling Extreme Anisotropy in Elastic Structured Media

Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones and saddle points; identifying these, and the nature of the associated modes, from a direct reading of the dispersion surfaces is not straightforward, especially in three-dimensions or at high frequencies when several dispersion surfaces fold back in the Brillouin zone. A recently proposed asymptotic high frequency homogenisation theory is applied to a challenging time-domain experiment with elastic waves in a pinned metallic plate. The prediction of a narrow high-frequency spectral region where the effective medium tensor dramatically switches from positive definite to indefinite is confirmed experimentally; a small frequency shift of the pulse carrier results in two distinct types of highly anisotropic modes. The underlying effective equation mirrors this behaviour with a change in form from elliptic to hyperbolic exemplifying the high degree of wave control available and the importance of a simple and effective predictive model.

cond-mat.mtrl-sci↗

arXiv2016

One single static measurement predicts wave localization in complex structures

A recent theoretical breakthrough has brought a new tool, called \emph{localization landscape}, to predict the localization regions of vibration modes in complex or disordered systems. Here, we report on the first experiment which measures the localization landscape and demonstrates its predictive power. Holographic measurement of the static deformation under uniform load of a thin plate with complex geometry provides direct access to the landscape function. When put in vibration, this system shows modes precisely confined within the sub-regions delineated by the landscape function. Also the maxima of this function match the measured eigenfrequencies, while the minima of the valley network gives the frequencies at which modes become extended. This approach fully characterizes the low frequency spectrum of a complex structure from a single static measurement. It paves the way to the control and engineering of eigenmodes in any vibratory system, especially where a structural or microscopic description is not accessible.

cond-mat.dis-nn↗

arXiv2014

Erosion dynamics of a wet granular medium

Liquid may give strong cohesion properties to a granular medium, and confer a solid-like behavior. We study the erosion of a fixed circular aggregate of wet granular matter subjected to a flow of dry grains inside a half-filled rotating drum. During the rotation, the dry grains flow around the fixed obstacle. We show that its diameter decreases linearly with time for low liquid content, as wet grains are pulled-out of the aggregate. This erosion phenomenon is governed by the properties of the liquids. The erosion rate decreases exponentially with the surface tension while it depends on the viscosity to the power -1. We propose a model based on the force fluctuations arising inside the flow, explaining both dependencies: the capillary force acts as a threshold and the viscosity controls the erosion time scale. We also provide experiments using different flowing grains confirming our model.

cond-mat.soft↗

arXiv2014

Experiments on Maxwell's Fish-eye dynamics in elastic plates

We experimentally demonstrate that a Duraluminium thin plate with a thickness profile varying radially in a piecewise constant fashion as h(r)=h(0)(1+(r/Rmax)), with h(0)=0.5 mm, h(Rmax)=2 mm and Rmax=10 cm behaves in many ways as Maxwell's fish-eye lens in optics, since its imaging properties for a Gaussian pulse with central frequencies 30~kHz and 60~kHz are very similar to those predicted by ray trajectories (great circles) on a virtual sphere (rays emanating from the North pole meet at the South pole). However, refocusing time depends on the carrier frequency as a direct consequence of the dispersive nature of flexural waves in thin plates. Importantly, experimental results are in good agreement with Finite-Difference-Time-Domain simulations.

physics.class-ph↗