Capillary instability in a two-component Bose-Einstein condensate

Capillary instability and the resulting dynamics in an immiscible two-component Bose-Einstein condensate are investigated using the mean-field and Bogoliubov analyses. A long, cylindrical condensate surrounded by the other component is dynamically unstable against breakup into droplets due to the interfacial tension arising from the quantum pressure and interactions. A heteronuclear system confined in a cigar-shaped trap is proposed for realizing this phenomenon experimentally.Comment: 7 pages, 6 figure

Stability of viscous long liquid filaments

We study the collapse of an axisymmetric liquid filament both analytically and by means of a numerical model. The liquid filament, also known as ligament, may either collapse stably into a single droplet or break up into multiple droplets. The dynamics of the filament are governed by the viscosity and the aspect ratio, and the initial perturbations of its surface. We find that the instability of long viscous filaments can be completely explained by the Rayleigh-Plateau instability, whereas a low viscous filament can also break up due to end pinching. We analytically derive the transition between stable collapse and breakup in the Ohnesorge number versus aspect ratio phase space. Our result is confirmed by numerical simulations based on the slender jet approximation and explains recent experimental findings by Castrejon-Pita et al., PRL 108, 074506 (2012).Comment: 7 page

Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates

Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of the short-range polar contribution to the disjoining pressure. The case of a periodic array of hydrophobic stripes transverse to the slope is studied in detail using a combination of direct numerical simulation and branch-following techniques. Under appropriate conditions the ridges may either depin and slide downslope as the slope is increased, or first breakup into drops via a transverse instability, prior to depinning. The different transition scenarios are examined together with the stability properties of the different possible states of the system.Comment: Physics synopsis link: http://physics.aps.org/synopsis-for/10.1103/PhysRevE.83.01630

Solving the brachistochrone and other variational problems with soap films

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction, has been submitted to the American Journal of Physic

An exact algorithm for the constraint satisfaction problem : application to dependance computing in automatic parallelization

Projet CHLOEThe constraint satisfaction problem - denoted by CSP - consists in proving the emptiness of a domain defined by a set of constraints or the existence of a solution. Numerous applications arise in the computer science field (artificial intelligence, vectorization, verification of programs,...). In the case of the study of dependence computing in automatic parallelization, classical methods in literature may break down for some instances of CSP, even with small sizes. By constrast the new method - denoted by FAS3T (Fast Algorithm for the Small Size constraints Satisfaction problem Type) - we propose allows an efficient solution of the CSP concrete instances generated by the VATIL vectorizer. Comparative computational results are reported

Quantum Suppression of the Rayleigh Instability in Nanowires

A linear stability analysis of metallic nanowires is performed in the free-electron model using quantum chaos techniques. It is found that the classical instability of a long wire under surface tension can be completely suppressed by electronic shell effects, leading to stable cylindrical configurations whose electrical conductance is a magic number 1, 3, 5, 6,... times the quantum of conductance. Our results are quantitatively consistent with recent experiments with alkali metal nanowires.Comment: 10 pages, 5 eps figures, updated and expanded, accepted for publication in "Nonlinearity

Bubbling in a co-flow at high Reynolds numbers

The physical mechanisms underlying bubble formation from a needle in a co-flowing liquid environment at high Reynolds numbers are studied in detail with the aid of experiments and boundary-integral numerical simulations. To determine the effect of gas inertia the experiments were carried out with air and helium. The influence of the injection system is elucidated by performing experiments using two different facilities, one where the constancy of the gas flow-rate entering the bubble is ensured, and another one where the gas is injected through a needle directly connected to a pressurized chamber. In the case of constant flow-rate injection conditions, the bubbling frequency has been shown to hardly depend on the gas density, with a bubble size given by db / ro  ? 6U? K * U + k2 /? U- 1? 1/3 for U? 2, where U is the gas-to-liquid ratio of the mean velocities, ro is the radius of the gas injection needle, and k * = 5,84 and k2 = 4,29, whit db / ro3,3U1 / 3 for U1.. Nevertheless, in this case the effect of gas density is relevant to describe the final instants of bubble breakup, which take place at a time scale much smaller than the bubbling time, tb. This effect is evidenced by the liquid jets penetrating the gas bubbles upon their pinch-off. Our measurements indicate that the velocity of the penetrating jets is considerably larger in air bubbles than in helium bubbles due to the distinct gas inertia of both situations. However, in the case of constant pressure supply conditions, the bubble size strongly depends on the density of the gas through the pressure loss along the gas injection needle. Furthermore, under the operating conditions reported here, the equivalent diameters of the bubbles are between 10% and 20% larger than their constant flow-rate counterparts. In addition, the experiments and the numerical results show that, under constant pressure supply, helium bubbles are approximately 10% larger than air bubbles due to the gas density effect on the bubbling process

Wetting and Minimal Surfaces

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple diagrammatic rules to calculate the non-linear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.Comment: 22 page

Minimal surfaces bounded by elastic lines

In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution to the Plateau problem. But what happens if a soap film spans a loop of inextensible but flexible wire? We consider this simple query that couples Plateau's problem to Euler's Elastica: a special class of twist-free curves of given length that minimize their total squared curvature energy. The natural marriage of two of the oldest geometrical problems linking physics and mathematics leads to a quest for the shape of a minimal surface bounded by an elastic line: the Euler-Plateau problem. We use a combination of simple physical experiments with soap films that span soft filaments, scaling concepts, exact and asymptotic analysis combined with numerical simulations to explore some of the richness of the shapes that result. Our study raises questions of intrinsic interest in geometry and its natural links to a range of disciplines including materials science, polymer physics, architecture and even art.Comment: 14 pages, 4 figures. Supplementary on-line material: http://www.seas.harvard.edu/softmat/Euler-Plateau-problem