arXiv subjects

Martine Le Berre

Publications and source records attributed to Martine Le Berre.

At least 19 recordsLinked to original sources

arXiv2025

Novel Electrical Characterization Method for Antiferroelectrics using a Positive Up Negative Down Approach

This study demonstrates the effectiveness of AFE-PUND, a revisited Positive Up Negative Down (PUND) protocol for characterizing antiferroelectric (AFE) materials, in analyzing $ZrO_2$ films across different thicknesses, revealing key trends. The proposed AFE-PUND method enables the isolation of switching currents from non-switching contributions, allowing precise extraction of remanent polarization and coercive field from hysteresis loops. The remanent polarization increases with film thickness, reflecting enhanced domain stability, while endurance cycles highlight the wake-up effect and its eventual degradation due to fatigue in thicker films. Similarly, coercive fields decrease with thickness, indicating reduced switching barriers and a clearer transition between tetragonal and orthorhombic phases. The method provides valuable insights into micro-structural influences, such as defect accumulation, grain size, and domain wall pinning, which critically affect device performance. AFE-PUND thus establishes itself as an essential tool for advancing the understanding and optimization of antiferroelectric materials.

cond-mat.mtrl-sci↗

arXiv2025

A mixing length model for arbitrary geometry: the case of parallel flows

We present a phenomenological model for the mixing length used in turbulence models. It has the advantage of naturally accounting for the object's geometry while satisfying the standard symmetries of the Navier-Stokes equations. We employ the model to study channel flow and pipe flow. We calibrate the three model parameters to recover the damping in the viscous sub-layer, the log-law of the wall, and the outer region behaviors. Our model compares favorably to friction factor measurements in the pipe flow at high Reynolds numbers and gives analytical predictions of the mixing length for several canonical flows.

physics.flu-dyn↗

arXiv2024

Comparative Performance of Fluorite-Structured Materials for Nanosupercapacitor Applications

Over the last fifteen years, ferroelectric and antiferroelectric ultra thin films based on fluorite-structured materials have drawn significant attention for a wide variety of applications requiring high integration density. Antiferroelectric $ZrO_2$, in particular, holds significant promise for nanosupercapacitors, owing to its potential for high energy storage density (ESD) and high efficiency ($η$). This work assesses the potential of high-performance $Hf_{1-x}Zr_{x}O_2$ thin films encapsulated by TiN electrodes that show linear dielectric (LD), ferroelectric (FE), and antiferroelectric (AFE) behavior. Oxides on silicon are grown by magnetron sputtering and plasma-enhanced atomic layer deposition. ESD and $η$ are compared for FE, AFE, and LD samples at the same electrical field (3.5 MV/cm). As expected, ESD is higher for the FE sample ($95 J/cm^3$), but $η$ is ridiculously small ($\approx$ 55%), because of the opening of the FE hysteresis curve inducing high loss. Conversely, LD samples exhibit the highest efficiency (nearly 100%), at the expense of a lower ESD. AFE $ZrO_2$ thin film strikes a balance between FE and LD behavior, showing reduced losses compared to the FE sample but an ESD as high as $52 J/cm^3$ at 3.5 MV/cm. This value can be further increased up to $84 J/cm^3$ at a higher electrical field (4.0 MV/cm), with an $η$ of 75%, among the highest values reported for fluorite-structured materials, offering promising perspectives for future optimization.

physics.app-ph↗

arXiv2021

Turbulent plane Poiseuille flow

The ultimate goal of a sound theory of turbulence in fluids is to close in a rational way the Reynolds equations, namely to express the time averaged turbulent stress tensor as a function of the time averaged velocity field. This closure problem is a deep and unsolved problem of statistical physics whose solution requires to go beyond the assumption of a homogeneous and isotropic state, as fluctuations in turbulent flows are strongly related to the geometry of this flow. This links the dissipation to the space dependence of the average velocity field. Based on the idea that dissipation in fully developed turbulence is by singular events resulting from an evolution described by the Euler equations, it has been recently observed that the closure problem is strongly restricted, and that it implies that the turbulent stress is a non local function (in space) of the average velocity field, an extension of classical Boussinesq theory of turbulent viscosity. The resulting equations for the turbulent stress are derived here in one of the simplest possible physical situation, the turbulent Poiseuille flow between two parallel plates. In this case the integral kernel giving the turbulent stress, as function of the averaged velocity field, takes a simple form leading to a full analysis of the averaged turbulent flow in the limit of a very large Reynolds number. In this limit one has to match a viscous boundary layer, near the walls bounding the flow, and an outer solution in the bulk of the flow. This asymptotic analysis is non trivial because one has to match solution with logarithms. A non trivial and somewhat unexpected feature of this solution is that, besides the boundary layers close to the walls, there is another "inner" boundary layer near the center plane of the flow.

physics.flu-dyn↗

arXiv2020

Turbulence in a wedge: the case of the mixing layerTurbulence in a wedge: the case of the mixing layer

The ultimate goal of a sound theory of turbulence in fluids is to close in a rational way the Reynolds equations, namely to express the tensor of turbulent stress as a function of the time average of the velocity field. Based on the idea that dissipation in fully developed turbulence is by singular events resulting from an evolution described by the Euler equations, it has been recently observed that the closure problem is strongly restricted, and that it implies that the turbulent stress is a non local function in space of the average velocity field, a kind of extension of classical Boussinesq theory of turbulent viscosity. This leads to rather complex nonlinear integral equation(s) for the time averaged velocity field. This one satisfies some symmetries of the Euler equations. Such symmetries were used by Prandtl and Landau to make various predictions about the shape of the turbulent domain in simple geometries. We explore specifically the case of mixing layer for which the average velocity field only depends on the angle in the wedge behind the splitter plate. This solution yields a pressure difference between the two sides of the splitter which contributes to the lift felt by the plate. Moreover, because of the structure of the equations for the turbulent stress, one can satisfy the Cauchy-Schwarz inequalities, also called the realizability conditions, for this turbulent stress. Such realizability conditions cannot be satisfied with a simple turbulent viscosity.

physics.flu-dyn↗

arXiv2020

Theory of ice-skating

Almost frictionless skating on ice relies on a thin layer of melted water insulating mechanically the blade of the skate from ice. Using the basic equations of fluid mechanics and Stefan law, we derive a set of two coupled equations for the thickness of the film and the length of contact, a length scale which cannot be taken as its value at rest. The analytical study of these equations allows to define a small a-dimensional parameter depending on the longitudinal coordinate which can be neglected everywhere except close to the contact points at the front and the end of the blade, where a boundary layer solution is given. This solution provides without any calculation the order of magnitude of the film thickness, and its dependence with respect to external parameters like the velocity and mass of the skater and the radius of profile and bite angle of the blade, in good agreement with the numerical study. Moreover this solution also shows that a lubricating water layer of macroscopic thickness always exists for standard values of ice skating data, contrary to what happens in the case of cavitation of droplets due to thermal heating (Leidenfrost effect).

physics.flu-dyn↗

arXiv2019

Scaling laws in turbulence

Following the idea that dissipation in turbulence at high Reynolds number is by events singular in space-time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows scaling laws should depend only on quantities appearing in the Euler equations. This excludes viscosity or a turbulent length as scaling parameters and constrains drastically possible analytical pictures of this limit. We focus on the law of drag by Newton for a projectile moving quickly in a fluid at rest. Inspired by the Newton's drag force law (proportional to the square of the speed of the moving object in the limit of large Reynolds numbers), which is well verified in experiments when the location of the detachment of the boundary layer is defined, we propose an explicit relationship between Reynolds's stress in the turbulent wake and quantities depending on the velocity field (averaged in time but depending on space), in the form of an integro-differential equation for the velocity which is solved for a Poiseuille flow in a circular pipe.

physics.flu-dyn↗

arXiv2019

Supernova implosion-explosion in the light of catastrophe theory

The present understanding of supernova explosion of massive stars as a two-step process, with an initial gravitational collapse toward the center of the star followed by an expansion of matter after a bouncing on the core, meets several difficulties. We show that it is not the only possible one: a simple model based on fluid mechanics, catastrophe theory, and stability properties of the equilibrium state shows that one can have also a simultaneous inward/outward motion in the early stage of the instability of the supernova described by a dynamical saddle-center bifurcation. The existence of this simultaneous inward/outward motion is sensitive to the model in such systems with long-range interactions. If a constant temperature is assumed (canonical ensemble), an overall inward motion occurs, but if one imposes with the same equation of state the constraint of energy conservation (microcanonical ensemble) there is an inward velocity field near the center of the star together with an outward velocity field in the rest of the star. We discuss the expansion stage of the remnants away from the collapsed core, and propose a new explanation for the formation of shock waves in the ejecta which differs from the usual Sedov-Taylor self-similar description.

astro-ph.SR↗

arXiv2019

Implosion-explosion in supernovae

Supernovae explosions of massive stars are nowadays believed to result from a two-step process, with an initial gravitational core collapse followed by an expansion of matter after a bouncing on the core. This scenario meets several difficulties. We show that it is not the only possible one: a simple model based on fluid mechanics and stability properties of the equilibrium state shows that one can have also a simultaneous inward/outward motion in the early stage of the instability of the supernova. This shows up in the slow sweeping across a saddle-center bifurcation found when considering equilibrium states associated to the constraint of energy conservation. We first discuss the weakly nonlinear regime in terms of a Painlevé I equation. We then show that the strongly nonlinear regime displays a self-similar behavior of the core collapse. Finally, the expansion of the remnants is revisited as an isentropic process leading to shocks formation.

astro-ph.SR↗

arXiv2019

Leray turbulence: what can we learn from acceleration compared to velocity

In a recent paper we presented evidence for the occurence of Leray-like singularities with positive Sedov-Taylor exponent $α$ in turbulent flows recorded in Modane's wind tunnel, by looking at simultaneous acceleration and velocity records. Here we use another tool which allows to get other informations on the dynamics of turbulent bursts. We compare the structure functions for velocity and acceleration in the same turbulent flows. This shows the possible contribution of other types of self-similar solutions because this new study shows that statistics is seemingly dominated by singularities with small positive or even negative values of the exponent $α$, that corresponds to "weakly singular" solutions with singular acceleration, and regular velocity. We present several reasons explaining that the exponent $α$ derived from the structure functions curves, may look to be negative.

physics.flu-dyn↗

arXiv2019

Conservation of the circulation for the Euler and Euler-Leray equations

It is well-known that the circulation of the velocity field of a fluid along a closed material curve is conserved for any solution of the Euler equation. We offer a slightly more explicit proof of that fact than that generally found in the literature. We then rewrite that property in terms of the rescaled variables and functions leading to the Euler-Leray equations and appropriate for studying self-similar solutions. We finally discuss the implications of the conservation of circulation on the existence of such solutions.

physics.flu-dyn↗

arXiv2019

A case of strong non linearity: intermittency in highly turbulent flows

It has long been suspected that flows of incompressible fluids at large or infinite Reynolds number (namely at small or zero viscosity) may present finite time singularities. We review briefly the theoretical situation on this point. We discuss the effect of a small viscosity on the self-similar solution of the Euler equations for inviscid fluids. Then we show that single point records of velocity fluctuations in the Modane wind tunnel display correlations between large velocities and large accelerations in full agreement with scaling laws derived from Leray's equations (1934) for self-similar singular solutions of the fluid equations. Conversely those experimental velocity-acceleration correlations are contradictory to the Kolmogorov scaling laws.

physics.flu-dyn↗

arXiv2019

Blowing-up solutions of the axisymmetric Euler equations for an incompressible fluid

A 1934 paper by Leray posed the question of the regularity of solutions of the dynamical equations for incompressible inviscid fluids with smooth initial data. Since there has been many attempts to answer this question. Leray examined the possibility of self-similar solutions becoming singular in finite time at a definite space-time location. We reexamine this question in the light of a thorough analysis of the equations for the self-similar solution in axisymmetric geometries with a dependence on a logarithm of time besides the one due to the transformation to self-similar variables.

physics.flu-dyn↗

arXiv2018

Quantum mechanics as a statistical theory: a short history and a worked example

A major question in our understanding of the fabric of the world is where the randomness of some quantum phenomena comes from and how to represent it in a rational theory. The statistical interpretation of quantum mechanics made its way progressively since the early days of the theory. We summarize the main historical steps and then we outline how the randomness gains to be depicted by using tools adapted to Markov processes. We consider a model system corresponding to experimental situations, namely a single two-level atom submitted to a monochromatic light triggering transitions from the ground to the excited state. After a short summary of present quantum approaches, we explain how a general "kinetic-like" Kolmogorov equation yields the statistical properties of the fluorescent light radiated by the atom which makes at once Rabi oscillations between the two states, and random quantum jumps with photo-emission. As an exemple we give the probability distribution of the time intervals between two successive emitted photons by using the Kolmogorov equation.

quant-ph↗

arXiv2018

Recording of Leray-type singular events in a high speed wind tunnel

It has long been suspected that flows of incompressible fluids at very large or infinite Reynolds may present finite time singularities. We review briefly the theoretical situation on this point. Then we show that single point records of velocity fluctuations in the Modane wind tunnel show correlations between large velocities and large accelerations that are in agreement with the scaling laws for such singularities as derived by Leray in 1934. Conversely the experimental correlations between velocity and acceleration are not explainable by Kolmogorov scalings. This implies in particular that the singularities cannot be seen as the end of a cascade in the sense of Kolmogorov, but are best described as singular events in the sense of Leray.

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↗

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↗