arXiv subjects

Yves Pomeau

Publications and source records attributed to Yves Pomeau.

At least 37 records · Page 2Linked to original sources

arXiv2016

Equation for self-similar singularity of Euler 3D

The equations for a self-similar solution of an inviscid incompressible fluid are mapped into an integral equation which hopefully can be solved by iteration. It is argued that the exponent of the similarity are ruled by Kelvin's theorem of conservation of circulation. The end result is an iteration with a nonlinear term entering in a kernel given by a 3D integral (in general 3D flow) or 2D (for swirling flows), which seems to be within reach of present day computational power. Because of the slow decay of the similarity solution at large distances the total energy is diverging and recent mathematical results excluding a solution of the self-similar solution of Euler equation do not apply.

physics.flu-dyn↗

arXiv2016

Turbulence: does energy cascade exist?

To answer the question whether a cascade of energy exists or not in turbulence, we propose a set of correlation functions able to test if there is an irreversible transfert of energy, step by step, from large to small structures. These tests are applied to real Eulerian data of a turbulent velocity flow, taken in the wind grid tunnel of Modane, and also to a prototype model equation for wave turbulence. First we demonstrate the irreversible character of the flow by using multi-time correlation function at a given point of space. Moreover the unexpected behavior of the test function leads us to connect irreversibility and finite time singularities (intermittency). Secondly we show that turbulent cascade exists, and is a dynamical process, by using a test function depending on time and frequency. The cascade shows up only in the inertial domain where the kinetic energy is transferred more rapidly (on average) from the wavenumber $k_{1}$ to $k_{2}$ than from $k_{1}$ to $k'_{2}$ larger than $k_{2}$.

physics.flu-dyn↗

arXiv2016

Ultimate Statistical Physics: fluorescence of a single atom

We discuss the statistics of emission of photons by a single atom or ion illuminated by a laser beam at the frequency of quasi-resonance between two energy levels, a situation that corresponds to real experiments. We extend this to the case of two laser beams resonant with the energy differences between two excited levels and the ground state (three level atom in V-configuration). We use a novel approach of this type of problem by considering Kolmogorov equation for the probability distribution of the atomic state which takes into account first the deterministic evolution of this state under the effect of the incoming laser beam and the random emission of photons during the spontaneous decay of the excited state(s) to the ground state. This approach yields solvable equations in the two level atom case. For the three level atom case we set the problem and define clearly its frame. The results obtained are valid both in the opposite limits of rare and of frequent spontaneous decay, compared to the period of the optical Rabi oscillations due to the interaction between the resonant excitation and the atomic levels. Our theory gives access to various statistical properties of the fluorescence light, including one showing that its fluctuations in time are not invariants under time reversal. This result puts in evidence the fundamentally irreversible character of quantum measurements, represented here by the emission of photons of fluorescence.

physics.atom-ph↗

arXiv2016

A New Drop Fluidics Enabled by Magnetic Field Mediated Elasto-Capillary Transduction

This research introduces a new drop fluidics, which uses a deformable and stretchable elastomeric film as the platform, instead of the commonly used rigid supports. Such a soft film impregnated with magnetic particles can be modulated with an external electromagnetic field that produces a vast array of topographical landscapes with varying surface curvature, which, in conjunction with capillarity, can direct and control motion of water droplets efficiently and accurately. When a thin layer of oil is present on this film that is deformed locally, a centrosymmetric wedge is formed. A water droplet placed on this oil laden film becomes asymmetrically deformed thus producing a gradient of Laplace pressure within the droplet setting it to motion. A simple theory is presented that accounts for the droplet speed in terms of such geometric variables as the volume of the droplet and the thickness of the oil film covering the soft elastomeric film, as well as such material variables as the viscosity of the oil and interfacial tension of the oil-water interfaces. Following the verification of the theoretical result using well-controlled model systems, we demonstrate how the electromagnetically controlled elasto-capillary force can be used to manipulate the motion of single and/or multiple droplets on the surface of the elastomeric film and how such elementary operations as drop fusion and thermally addressed chemical transformation can be carried out in aqueous droplets. It is expected that the resulting drop fluidics would be suitable for digital control of drop motion by simply switching on and off the electromagnetic fields applied at different positions underneath the elastomeric film. We anticipate that this method of directing and manipulating water droplets is poised for its applications in various biochemical reaction engineering, an example of which is Polymerase Chain Reaction (PCR).

cond-mat.soft↗

arXiv2016

Elasto-buoyant heavy spheres: a unique way to test non-linear elasticity

Extra-large deformations in ultra-soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here we investigate this complex problem systematically with a simple experiment: by introducing a heavy bead of radius $a$ in an incompressible ultra-soft elastic medium. We find a scaling law for the penetration depth ($δ$) of the bead inside the softest gels as $δ\sim a^{3/2}$. While this result is inconsistent with an ideal neo-Hookean model of elastic deformation, according to which the displacement fields must diverge, it is vindicated by an original asymptotic analytic model developed in this article. This model demonstrates that the observed relationship is precisely at the demarcating boundary of what would be required for the field variables to either diverge or converge. This correspondence between a unique mathematical prediction and the experimental observation ushers in new insights into the behavior of the deformations of strongly non-linear materials.

cond-mat.mtrl-sci↗

arXiv2016

Coalescence of sessile drops

We present an experimental and theoretical description of the kinetics of coalescence of two water drops on a plane solid surface. The case of partial wetting is considered. The drops are in an atmosphere of nitrogen saturated with water where they grow by condensation and eventually touch each other and coalesce. A new convex composite drop is rapidly formed that then exponentially and slowly relaxes to an equilibrium hemispherical cap. The characteristic relaxation time is proportional to the drop radius R * at final equilibrium. This relaxation time appears to be nearly 10 7 times larger than the bulk capillary relaxation time t b = R * $η$/$σ$, where $σ$ is the gas--liquid surface tension and $η$ is the liquid shear viscosity. In order to explain this extremely large relaxation time, we consider a model that involves an Arrhenius kinetic factor resulting from a liquid--vapour phase change in the vicinity of the contact line. The model results in a large relaxation time of order t b exp(L/RT) where L is the molar latent heat of vaporization, R is the gas constant and T is the temperature. We model the late time relaxation for a near spherical cap and find an exponential relaxation whose typical time scale agrees reasonably well with the experiment. 1. Introduction Fusion or coalescence between drops is a key process in a wide range of phenomena: phase transition in fluids and liquid mixtures or polymers, stability of foams and emulsions, and sintering in metallurgy (Eggers 1998), which is why the problem of coalescence has already received considerable attention. Most of the studies of this process so far have been devoted to the coalescence of two spherical drops floating in a medium. The kinetics of the process before and after the drops have touched each other is governed by the hydrodynamics inside and outside the drops and by the van der Waals forces when the drops are within mesoscopic distance from each other (Yiantsios \& Davis 1991). The composite drop that results from the coalescence of two drops relaxes to a spherical shape within a time which is dominated by the relaxation of the flow inside and outside (Nikolayev, Beysens \& Guenoun 1996; Nikolayev \& Beysens 1997). There are no studies, to our knowledge, of the coalescence of two sessile drops after they touch each other. In this paper, we report a preliminary study of the dynamics and morphology of this process, in the case of hemispherical water droplets which grow slowly on a plane surface at the expense of the surrounding atmosphere, forming what is called 'dew' or 'breath figures' (Beysens et al. 1991; Beysens 1995). The drops eventually touch each other and coalesce to form an elongated composite

physics.flu-dyn↗

arXiv2015

The transition to turbulence in parallel flows: transition to turbulence or to regular structures

We propose a scenario for the formation of localized turbulent spots in transition flows, which is known as resulting from the subcritical character of the transition. We show that it is not necessary to add 'by hand" a term of random noise in the equations, in order to describe the existence of long wavelength fluctuations as soon as the bifurcated state is beyond the Benjamin-Feir instability threshold. We derive the instability threshold for generalized complex Ginzburg-Landau equation which displays subcriticality. Beyond and close to the Benjamin-Feir threshold we show that the dynamics is mainly driven by the phase of the complex amplitude which obeys Kuramoto-Sivashinsky equation while the fluctuations of the modulus are smaller and slaved to the phase (as already proved for the supercritical case). On the opposite, below the Benjamin-Feir instability threshold, the bifurcated state does loose the randomness associated to turbulence so that the transition becomes of the mean-field type as in noiseless reaction-diffusion systems and leads to pulse-like patterns.

nlin.CD↗

arXiv2014

Dynamics of self-gravitating systems : Variations on a theme by Michel Henon

In this contribution to the volume in memoriam of Michel Henon, we thought appropriate to look at his early scientific work devoted to the dynamics of large assemblies of interacting masses. He predicted in his PhD thesis that, in such a system, first a collapse of mass occurs at the center and that later binaries stars are formed there. Henceforth, the negative energy of binding of pairs becomes a source of positive energy for the rest of the cluster which evaporate because of that. We examine under what conditions such a singularity can occur, and what could happen afterwards. We hope to show that this fascinating problem of evolution of self-gravitating clusters keeps its interest after the many years passed since Henon thesis, and is still worth discussing now.

astro-ph.GA↗

arXiv2014

Gravity driven instability in elastic solids

We demonstrate the instability of the free surface of a soft elastic solid facing downwards. Experiments are carried out using a gel of constant density $ρ$, shear modulus $μ$, put in a rigid cylindrical dish of depth $h$. When turned upside down, the free surface of the gel undergoes a normal outgoing acceleration $g$. It remains perfectly flat for $ρg h/μ<α^* $ with $α^*\simeq 6$, whereas a steady pattern spontaneously appears in the opposite case. This phenomenon results from the interplay between the gravitational energy and the elastic energy of deformation, which reduces the Rayleigh waves celerity and vanishes it at the threshold.

cond-mat.soft↗

arXiv2014

Is vacuum dispersive?

The question we ask is: does the speed of light {\it{in vacuo}} depend on its frequency? While the answer is NO in the frame of classical physics, we point out that the opposite could be true if one takes into account the polarization of Dirac sea. We estimate the dependence of the index of refraction of vacuum + Dirac sea versus the wavelength of an incoming beam, and suggest a way to test this effect.

quant-ph↗

arXiv2014

Softening of edges of solids by surface tension

Surface tension tends to minimize the area of interfaces between pieces of matter in different thermodynamic phases, be they in the solid or the liquid state. This can be relevant for the macroscopic shape of very soft solids, and lead to a roughening of initially sharp edges. We calculate this effect for a neo-Hookean elastic solid, with assumptions corresponding to actual experiments, namely the case where an initially sharp edge is rounded by the effect of surface tension felt when the fluid surrounding the soft solid (and so surface tension) is changed at the solid/liquid boundary. We consider two opposite limits where the analysis can be carried to the end, the one of a shallow angle and the one of a very sharp angle. Both cases yield a discontinuity of curvature in the state with surface tension although the initial state had a discontinuous slope.

cond-mat.soft↗

arXiv2014

Study of a model for the distribution of wealth

An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of "money" has recently been proposed by one of us (RLR). This equation takes the form of an iterated nonlinear map of the distribution of wealth. The equilibrium distribution is known and takes a rather simple form. If this distribution is such that, at some time, the higher momenta of the distribution exist, one can find exactly their law of evolution. A seemingly simple extension of the laws of exchange yields also explicit iteration formulae for the higher momenta, but with a major difference with the original iteration because high order momenta grow indefinitely. This provides a quantitative model where the spreading of wealth, namely the difference between the rich and the poor, tends to increase with time.

nlin.AO↗

arXiv2014

Soft granular matter

We consider a dilute system of small hard beads or hard fibers immersed in a very soft gel able to withstand large elastic deformations. Because of its low to very low shear modulus, this system is very sensitive to small forces. We calculate the local deformation induced by a constant volume force, the inclusion weight. We explain how this deformation could be put in evidence by using techniques similar to the PIV method (particle image velocimetry) used to show complex velocity fields in transparent fluids.

cond-mat.soft↗

arXiv2013

Two dimensional Leidenfrost Droplets in a Hele Shaw Cell

We experimentally and theoretically investigate the behavior of Leidenfrost droplets inserted in a Hele-Shaw cell. As a result of the confinement from the two surfaces, the droplet has the shape of a flattened disc and is thermally isolated from the surface by the two evaporating vapor layers. An analysis of the evaporation rate using simple scaling arguments is in agreement with the experimental results. Using the lubrication approximation we numerically determine the shape of the droplets as a function of its radius. We furthermore find that the droplet width tends to zero at its center when the radius reaches a critical value. This prediction is corroborated experimentally by the direct observation of the sudden transition from a flattened disc into an expending torus. Below this critical size, the droplets are also displaying capillary azimuthal oscillating modes reminiscent of a hydrodynamic instability.

physics.flu-dyn↗

arXiv2013

Room temperature water Leidenfrost droplets

We experimentally investigate the Leidenfrost effect at pressures ranging from 1 to 0.05 atmospheric pressure. As a direct consequence of the Clausius-Clapeyron phase diagram of water, the droplet temperature can be at ambient temperature in a non-sophisticated lab environment. Furthermore, the lifetime of the Leidenfrost droplet is significantly increased in this low pressure environment. The temperature and pressure dependance of the evaporation rate are successfully tested against a recently proposed model. These results may pave a way to reach efficient Leidenfrost micro-fluidic and milli-fluidic applications.

cond-mat.soft↗

arXiv2013

Supernovae: an example of complexity in the physics of compressible fluids

The supernovae are typical complex phenomena in fluid mechanics with very different time scales. We describe them in the light of catastrophe theory, assuming that successive equilibria between pressure and gravity present a saddle-node bifurcation. In the early stage we show that the loss of equilibrium may be described by a generic equation of the Painlevé I form. In the final stage of the collapse, just before the divergence of the central density, we show that the existence of a self-similar collapsing solution compatible with the numerical observations imposes that the gravity forces are stronger than the pressure ones. This situation differs drastically in its principle from the one generally admitted where pressure and gravity forces are assumed to be of the same order. Our new self-similar solution (based on the hypothesis of dominant gravity forces) which matches the smooth solution of the outer core solution, agrees globally well with our numerical results. Whereas some differences with the earlier self-similar solutions are minor, others are very important. For example, we find that the velocity field becomes singular at the collapse time, diverging at the center, and decreasing slowly outside the core, whereas previous works described a finite velocity field in the core which tends to a supersonic constant value at large distances. This discrepancy should be important for explaining the emission of remnants in the post-collapse regime. Finally we describe the post-collapse dynamics, when mass begins to accumulate in the center, also within the hypothesis that gravity forces are dominant.

physics.flu-dyn↗

arXiv2013

Fluid motion induced by surface waves at low Reynolds number

We discuss the scaling laws for the flow generated in a viscous fluid by a wave propagating along a solid boundary. This has applications to the displacement of tiny objects on solids, under the effect of progressive surface waves and for the swimming of microanimals by undulation of ciliae along their body surface.

physics.flu-dyn↗

arXiv2012

Degenerate ground state and quantum tunneling in rotating condensates

Quantum tunneling introduces a fundamental difference between classical and quantum mechanics. Whenever the classical ground state is non-unique (degenerate), quantum mechanics restore uniqueness thanks to tunneling. A condensate in a rotating trap with a vortex can have such a degenerate classical ground state, a degeneracy that is excluded in the absence of rotation at least when the Gross-Pitaevskii equation applies. If the rotating trap has a center of symmetry, like a figure eight (a peanut), the vortex may be on either side with the same energy yielding a degenerate ground state, a degeneracy lifted by quantum tunneling. We explain how to compute the rate of tunneling in the WKB limit by estimating the action of the trajectory in the Euclidean version of the dynamics.

quant-ph↗