DYNAMICS OF A COMPLETE WETTING LIQUID UNDER EVAPORATION

International audienceWetting phenomena are extensively studied from a experimental to a theoretical point of view (see Refs. [1, 2] for reviews) and much attention has been drawn recently to the case of the dynamics of liquid droplet under evaporation [3-9]. In this paper, we propose a model of a contact line under evaporation and total wetting conditions taking into account van der Waals interactions and the divergent nature of evaporation near the border of the liquid evidenced by Deegan et al. [3]. We apply this result to study the dynamics of an evaporating droplet in complete wetting situation

Scaling of the elastic contribution to the surface free energy of a nematic on a sawtoothed substrate

We characterize the elastic contribution to the surface free energy of a nematic in presence of a sawtooth substrate. Our findings are based on numerical minimization of the Landau-de Gennes model and analytical calculations on the Frank-Oseen theory. The nucleation of disclination lines (characterized by non-half-integer winding numbers) in the wedges and apexes of the substrate induces a leading order proportional to qlnq to the elastic contribution to the surface free energy density, q being the wavenumber associated with the substrate periodicity.Comment: 7 pages, 6 figures, accepted for publication in Physical Review

Boundary layers and emitted excitations in nonlinear Schrodinger superflow past a disk

The stability and dynamics of nonlinear Schrodinger superflows past a two-dimensional disk are investigated using a specially adapted pseudo-spectral method based on mapped Chebychev polynomials. This efficient numerical method allows the imposition of both Dirichlet and Neumann boundary conditions at the disk border. Small coherence length boundary-layer approximations to stationary solutions are obtained analytically. Newton branch-following is used to compute the complete bifurcation diagram of stationary solutions. The dependence of the critical Mach number on the coherence length is characterized. Above the critical Mach number, at coherence length larger than fifteen times the diameter of the disk, rarefaction pulses are dynamically nucleated, replacing the vortices that are nucleated at small coherence length

Safety and efficacy of fluoxetine on functional outcome after acute stroke (AFFINITY): a randomised, double-blind, placebo-controlled trial

Background Trials of fluoxetine for recovery after stroke report conflicting results. The Assessment oF FluoxetINe In sTroke recoverY (AFFINITY) trial aimed to show if daily oral fluoxetine for 6 months after stroke improves functional outcome in an ethnically diverse population. Methods AFFINITY was a randomised, parallel-group, double-blind, placebo-controlled trial done in 43 hospital stroke units in Australia (n=29), New Zealand (four), and Vietnam (ten). Eligible patients were adults (aged ≥18 years) with a clinical diagnosis of acute stroke in the previous 2–15 days, brain imaging consistent with ischaemic or haemorrhagic stroke, and a persisting neurological deficit that produced a modified Rankin Scale (mRS) score of 1 or more. Patients were randomly assigned 1:1 via a web-based system using a minimisation algorithm to once daily, oral fluoxetine 20 mg capsules or matching placebo for 6 months. Patients, carers, investigators, and outcome assessors were masked to the treatment allocation. The primary outcome was functional status, measured by the mRS, at 6 months. The primary analysis was an ordinal logistic regression of the mRS at 6 months, adjusted for minimisation variables. Primary and safety analyses were done according to the patient's treatment allocation. The trial is registered with the Australian New Zealand Clinical Trials Registry, ACTRN12611000774921. Findings Between Jan 11, 2013, and June 30, 2019, 1280 patients were recruited in Australia (n=532), New Zealand (n=42), and Vietnam (n=706), of whom 642 were randomly assigned to fluoxetine and 638 were randomly assigned to placebo. Mean duration of trial treatment was 167 days (SD 48·1). At 6 months, mRS data were available in 624 (97%) patients in the fluoxetine group and 632 (99%) in the placebo group. The distribution of mRS categories was similar in the fluoxetine and placebo groups (adjusted common odds ratio 0·94, 95% CI 0·76–1·15; p=0·53). Compared with patients in the placebo group, patients in the fluoxetine group had more falls (20 [3%] vs seven [1%]; p=0·018), bone fractures (19 [3%] vs six [1%]; p=0·014), and epileptic seizures (ten [2%] vs two [<1%]; p=0·038) at 6 months. Interpretation Oral fluoxetine 20 mg daily for 6 months after acute stroke did not improve functional outcome and increased the risk of falls, bone fractures, and epileptic seizures. These results do not support the use of fluoxetine to improve functional outcome after stroke

Ondes de surface le long de gouttes

The memoir presents a research topic a research that has been occupying me for eight years now. It is devoted to the study of surface waves propagating at the surface of drops which have either an elongated rectilinear geometry (typically around 50 cm in length and a centimetre in width), or a toroidal geometry. They are either placed on a super-hydrophobic substrate at room temperature, or levitating above a heated substrate. Because of the shape of the substrate supporting them, they are not subject to the Plateau-Rayleigh instability, provided their volume is sufficient. Moreover, in the case of the torus, they don't close their hole.The propagation of surface waves along these drops can be studied by analyzing the deformations of the free interface along their borders. Various modes of propagation have been identified: varicose modes, the dispersion relation of which we have characterized that takes the form of a capillary-gravity dispersion relation with effective values for gravity, surface tension and depth; sinuous modes and sloshing modes, characterized by well-defined cutoff frequencies. These systems are quasi-one-dimensional, non-dissipative, dispersive and nonlinear. The propagation of Korteweg--de Vries solitons in depression has been observed along rectilinear drops.Both our drop geometries are original systems carrying out studies related to wave turbulence phenomena. Moreover, in the case of the torus, a doubly discrete family of excitations can interact with each other. Finally, the vertical forcing of a toroidal drop leads to the emergence of modes and, beyond a certain threshold, Faraday waves develop along the free surface, initially curved in all directions.Ce mémoire présente une thématique de recherche qui m'occupe depuis maintenant huit ans. Elle est consacrée à l'étude des ondes de surface se propageant à la surface de gouttes qui ont, ou bien une géométrie rectiligne très allongée (typiquement d'une cinquantaine de centimètres en longueur et de l'ordre du centimètre en largeur), ou bien une géométrie torique. Elles sont soit posées sur un substrat super-hydrophobe à température ambiante, soit en lévitation au-dessus d'un substrat chauffé. À cause de la forme du substrat qui les supporte, elles ne sont pas le siège de l'instabilité de Plateau--Rayleigh pourvu que leur volume soit suffisant. De plus, dans le cas du tore, elles ne referment pas leur trou.La propagation d'ondes de surface le long de ces gouttes peut être étudiée en analysant les déformations de l'interface libre le long de leurs bords. Différents modes de propagation ont été mis en évidence : des modes variqueux dont nous avons caractérisé la relation de dispersion, qui prend la forme d'une relation de dispersion gravito-capillaire avec des valeurs effectives de gravité, de tension de surface et de profondeur ; des modes sinueux et des modes de ballottement, caractérisés par des pulsations de coupure bien définies. Ces systèmes sont des systèmes quasi-1D, peu dissipatifs, dispersifs et non linéaires et la propagation de solitons de Korteweg--de Vries en dépression a été observée le long des gouttes rectilignes.Nos deux géométries de gouttes sont ainsi des systèmes originaux pour réaliser des études liées aux phénomènes de turbulence d'ondes. En outre, dans le cas du tore, nous sommes spécifiquement en présence d'une famille doublement discrète d'excitations qui peuvent interagir entre elles. Enfin, le forçage vertical d'une goutte torique conduit à l'émergence de modes et, passé un certain seuil, des ondes de Faraday se développent le long de la surface libre, initialement courbée dans toutes les directions

Stabilité et dynamique d'écoulements de fluides parfaits barotropes autour d'un obstacle en présence de dispersion

Pierre COULLET, rapporteur Laurent LIMAT, examinateur Caroline NORE, examinateur Dominique SALIN, président Laurette TUCKERMAN, rapporteurThis thesis presents a series of works all dealing with extended nonlinear Hamiltonian systems including a saddle-node bifurcation. In the first part of this manuscript, we study the transition to dissipation of one-dimensional systems subjected to a local forcing and described by sine-Gordon or nonlinear Schrödinger equations (NLSE). We analytically compute the stationary states of these equations and characterize the dynamical behavior near these stationary solutions close to the bifurcation. When a gap in the dispersion relation exists, the dynamics is that of Hamiltonian systems. Conversely, when there is no gap in the dispersion relation, the dynamics of the system is coupled with the emission of sound waves that stands for an effective damping. The behavior is then typical of dissipative systems; we also show that the temporal eigenmodes undergo a spatial delocalization. The second part of this thesis is devoted to the study of two types of two-dimensional flow past an obstacle of perfect barotropic fluids: a superflow described by the NLSE and a free surface flow in the shallow water limit, with dispersive effects due to capillary forces. When the dispersive effects tend to zero, both flows have the limit of an Eulerian compressible flow with a boundary layer close to the obstacle that can be computed analytically. Using branch following methods based on pseudo-spectral methods, we calculate the bifurcation diagram of both flows. At supercritical regime, we show that in the case of the NLSE, the system starts emitting excitations, the nature of which depends on the ratio of the coherence length on the obstacle size. In the case of the shallow water flow, this emission is replaced by a finite time singularity at which dewetting occurs.Cette thèse regroupe une série de travaux ayant tous trait à des systèmes hamiltoniens non linéaires spatialement étendus présentant une bifurcation nœud-col. Elle est constituée de deux parties. Nous étudions dans une première partie la transition à la dissipation de systèmes unidimensionnels soumis à un forçage local et régis par des équations de type sine-Gordon ou Schrödinger non linéaire (ESNL). Nous en calculons analytiquement les solutions stationnaires et caractérisons le comportement dynamique au voisinage de celles-ci près de la bifurcation. Lorsque la relation de dispersion des systèmes possède une fréquence de coupure, le comportement dynamique est caractéristique de systèmes hamiltoniens. A contrario, lorsque la relation de dispersion ne possède pas de fréquence de coupure, la dynamique du système se couple avec l'émission d'ondes sonores qui joue le rôle d'un amortissement effectif. Elle devient alors typique de systèmes dissipatifs. En outre, les modes propres temporels du système subissent une délocalisation spatiale. La seconde partie de la thèse concerne l'étude de deux types d'écoulements bidimensionnels de fluides parfaits barotropes autour d'un obstacle : un écoulement décrit par l'ESNL et un écoulement à surface libre dans l'approximation eau peu profonde, où sont pris en compte les effets dispersifs dus aux effets de tension de surface. Lorsque la longueur caractérisant la dispersion des ondes sonores tend vers zéro, ces deux écoulements se réduisent à l'écoulement autour d'un disque d'un fluide eulérien compressible, auquel se superpose une couche limite que nous calculons analytiquement. Par des méthodes de suivi de branches fondés sur des développements pseudo-spectraux, nous calculons le diagramme de bifurcation complet des deux écoulements. En étudiant la dynamique des deux systèmes au-delà de la bifurcation, nous mettons en évidence une émission d'excitations (dans le cas de l'ESNL) dont la nature dépend du rapport de la longueur de cohérence sur la taille de l'obstacle. Dans le cadre de l'écoulement en eau peu profonde, cette émission est remplacée par une singularité à temps fini de démouillage

Stabilité et dynamique d'écoulements de fluides parfaits barotropes autour d'un obstacle en présence de dispersion

PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF

Experimental observation of periodic Korteweg-de Vries solitons along a torus of fluid

For Supplementary Material, see http://www.msc.univ-paris-diderot.fr/~falcon/EPL22/EPL22.htmlInternational audienceWe report on the experimental observation of solitons propagating along a torus of fluid. We show that such a periodic system leads to significant differences compared to the classical plane geometry. In particular, we highlight the observation of subsonic elevation solitons, and a nonlinear dependence of the soliton velocity on its amplitude. The soliton profile, velocity, collision, and dissipation are characterized using high resolution space-time measurements. By imposing {\em periodic boundary conditions} onto Korteweg-de Vries (KdV) equation, we recover these observations. A nonlinear spectral analysis of solitons (periodic inverse scattering transform) is also implemented and experimentally validated in this periodic geometry. Our work thus reveals the importance of periodicity for studying solitons and could be applied to other fields involving periodic systems governed by a KdV equation

A numerical direct scattering method for the periodic sine-Gordon equation

International audienceWe propose a procedure for computing the direct scattering transform of the periodic sine-Gordon equation. This procedure, previously used within the periodic Korteweg-de Vries equation framework, is implemented for the case of the sine-Gordon equation and is validated numerically. In particular, we show that this algorithm works well with signals involving topological solitons, such as kink or anti-kink solitons, but also for non-topological solitons, such as breathers. It also has the ability to distinguish between these different solutions of the sine-Gordon equation within the complex plane of the eigenvalue spectrum of the scattering problem. The complex trace of the scattering matrix is made numerically accessible, and the influence of breathers on the latter is highlighted. Finally, periodic solutions of the sine-Gordon equation and their spectral signatures are explored in both the large-amplitude (cnoidal-like waves) and low-amplitude (radiative modes) limits