31 research outputs found
Non-Hamiltonian features of a classical pilot-wave dynamics
A bouncing droplet on a vibrated bath can couple to the waves it generates,
so that it becomes a propagative walker. Its propulsion at constant velocity
means that a balance exists between the permanent input of energy provided by
the vibration and the dissipation. Here we seek a simple theoretical
description of the resulting non-Hamiltonian dynamics with a walker immersed in
a harmonic potential well. We demonstrate that the interaction with the
recently emitted waves can be modeled by a Rayleigh-type friction. The Rayleigh
oscillator has well defined attractors. The convergence toward them and their
stability is investigated through an energetic approach and a linear stability
analysis. These theoretical results provide a description of the dynamics in
excellent agreement with the experimental data. It is thus a basic framework
for further investigations of wave-particle interactions when memory effects
are included.Comment: 10 pages, 6 figure
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
Self-organization into quantized eigenstates of a classical wave driven particle
A growing number of dynamical situations involve the coupling of particles or
singularities with physical waves. In principle these situations are very far
from the wave-particle duality at quantum scale where the wave is probabilistic
by nature. Yet some dual characteristics were observed in a system where a
macroscopic droplet is guided by a pilot-wave it generates. Here we investigate
the behaviour of these entities when confined in a two-dimensional harmonic
potential well. A discrete set of stable orbits is observed, in the shape of
successive generalized Cassinian-like curves (circles, ovals, lemniscates,
trefoils...). Along these specific trajectories, the droplet motion is
characterized by a double quantization of the orbit spatial extent and of the
angular momentum. We show that these trajectories are intertwined with the
dynamical build-up of central wave-field modes. These dual self-organized modes
form a basis of eigenstates on which more complex motions are naturally
decomposed
Une mémoire ondulatoire : Etats propres, Chaos et Probabilités
A droplet bouncing on a vertically vibrated liquid bath can be self-propelled by the surface waves it generates. Theses Faraday waves are sustained by the vertical bath vibration for a memory time which can be tuned experimentally. The wave field thus contains in its interference pattern a memory of the past-trajectory. The resulting entity called a walker is characterized by the interaction between the drop and its surrounding waves through this path-memory.This thesis is devoted to an experimental and theoretical investigation of such a wave-mediated path-memory. For this purpose a bouncing drop is magnetically loaded with a droplet of ferrofluid and can then be trapped in an harmonic well. The drop is thus forced to interact with its own path. The confinement induces a self-organization process between the particle and its wave packet, leading to wave-type behavior for a particle. Notions such quantization or probability of measuring an eigenstate can thus be used for the walker dynamics description. These features originate from the temporal coherence of the walker’s dynamics. In that sense, the walker is an entity extended in time, we cannot reduce to a point-like approximation. It reminds us, in another context, the pilot wave theory developped by de Broglie at the beginning of the XXst century.Une goutte rebondissant sur un bain de liquide en vibration verticale peut se mettre spontanément en mouvement, sous l’action des ondes qu’elle a elle-même générées. Celles ci, appelées ondes de Faraday sont entretenues par la vibration du bain durant un temps de mémoire qui peut être contrôlé expérimentalement. Le champ d’ondes stationnaires généré par la goutte contient ainsi dans ses motifs d’interférence une mémoire de la trajectoire précédemment suivie. L’entité résultante appelée marcheur est caractérisée par cette interaction entre la goutte et les ondes qui l’entourent, via la mémoire de chemin.Cette thèse est consacrée à l’étude expérimentale et théorique de cette mémoire de chemin. Dans ce but, une goutte de liquide encapsulant un volume de ferrofluide est piégée dans un puits de potentiel harmonique d’origine magnétique. La goutte sera ainsi amenée à interagir avec les ondes qu’elle a précédemment générées. Ce confinement induit un processus d’auto-organisation entre la goutte et l’onde sous-jacente qui mène à des comportements de type ondulatoire pour une particule. Les notions de quantifications ou de probabilité de mesure d’un état propre peuvent ainsi être appliquées au cas d’un marcheur. Ces comportements révèlent que le marcheur est un exemple d’objet étendu en temps qui ne peut être réduit à une approximation ponctuelle rappelant, dans un tout autre contexte, la théorie de l’onde pilote développée par de Broglie au début du XXème siècle
Bubble deformation by a turbulent flow
We investigate the modes of deformation of an initially spherical bubble
immersed in a homogeneous and isotropic turbulent background flow. We perform
direct numerical simulations of the two-phase incompressible Navier-Stokes
equations, considering a low-density bubble in the high density turbulent flow
at various Weber number (the ratio of turbulent and surface tension forces)
using the air-water density ratio. We discuss a theoretical framework for the
bubble deformation in a turbulent flow using a spherical harmonic
decomposition. We propose, for each mode of bubble deformation, a forcing term
given by the statistics of velocity and pressure fluctuations, evaluated on a
sphere of the same radius. This approach formally relates the bubble
deformation and the background turbulent velocity fluctuations, in the limit of
small deformations. The growth of the total surface deformation and of each
individual mode is computed from the direct numerical simulations using an
appropriate Voronoi decomposition of the bubble surface. We show that two
successive temporal regimes occur: the first regime corresponds to deformations
driven only by inertial forces, with the interface deformation growing linearly
in time, in agreement with the model predictions, whereas the second regime
results from a balance between inertial forces and surface tension. The
transition time between the two regimes is given by the period of the first
Rayleigh mode of bubble oscillation. We discuss how our approach can be used to
relate the bubble lifetime to the turbulence statistics and eventually show
that at high Weber number, bubble lifetime can be deduced from the statistics
of turbulent fluctuations at the bubble scale
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
Build-up of macroscopic eigenstates in a memory-based constrained system
International audienceA bouncing drop and its associated accompanying wave forms a walker. Based on previous works, we show in this article that it is possible to formulate a simple theoretical framework for the walker dynamics. It relies on a time scale decomposition corresponding to the effects successively generated when the memory effects increase. While the short time scale effect is simply responsible for the walkerʼs propulsion, the intermediate scale generates spontaneously pivotal structures endowed with angular momentum. At an even larger memory scale, if the walker is spatially confined, the pivots become the building blocks of a self-organization into a global structure. This new theoretical framework is applied in the presence of an external harmonic potential, and reveals the underlying mechanisms leading to the emergence of the macroscopic spatial organization reported by Perrard et al (2014 Nature Commun. 5 3219)
Experimental study of internal wave generation by convection in water
We experimentally investigate the dynamics of water cooled from below at 0^oC
and heated from above. Taking advantage of the unusual property that water's
density maximum is at about 4^oC, this set-up allows us to simulate in the
laboratory a turbulent convective layer adjacent to a stably stratified layer,
which is representative of atmospheric and stellar conditions. High precision
temperature and velocity measurements are described, with a special focus on
the convectively excited internal waves propagating in the stratified zone.
Most of the convective energy is at low frequency, and corresponding waves are
localized to the vicinity of the interface. However, we show that some energy
radiates far from the interface, carried by shorter horizontal wavelength,
higher frequency waves. Our data suggest that the internal wave field is
passively excited by the convective fluctuations, and the wave propagation is
correctly described by the dissipative linear wave theory
Génération d'ondes gravito-inertielles par la turbulence
Dans de nombreuses situations géophysiques et astrophysiques, une couche de fluide turbulent se situe au dessus ou en-dessous d'une zone stratifiée stable. C'est par exemple le cas des zones convective et radiative des étoiles. Alors que cette zone stratifiée a longtemps été assimilée à une zone immobile, il s'avère qu'elle est en fait le siège de mouvements oscillatoires (ondes gravito- inertielles) excités par la turbulence voisine. Ces ondes sont susceptibles de transporter de la quantité de mouvement et de l'énergie, donc d'influer significativement sur la dynamique du système considéré. Il est donc primordial de comprendre leur génération et leurs caractéristiques