Related papers: Covers, soap films and BV functions
The paper focuses on a model describing the spreading of an insoluble surfactant on a thin viscous film with capillary effects taken into account. The governing equation for the film height is degenerate parabolic of fourth order and…
Video inpainting, which aims at filling in missing regions of a video, remains challenging due to the difficulty of preserving the precise spatial and temporal coherence of video contents. In this work we propose a novel flow-guided video…
The displacement of a suspension of particles by an immiscible fluid in a capillary tube or in a porous media is a canonical configuration that finds application in a large number of natural and industrial applications, including water…
This note concerns the so-called pyjama problem, whether it is possible to cover the plane by finitely many rotations of vertical strips of half-width $\varepsilon$. We first prove that there exist no periodic coverings for…
We present a systematic study of capillary filling for a binary fluid by using a mesoscopic lattice Boltzmann model for immiscible fluids describing a diffusive interface moving at a given contact angle with respect to the walls. The…
The structure of liquid foams follows simple geometric rules formulated by Plateau 150 years ago. By placing such foam on a microtextured hydrophilic surface, we show that the bubble footprint exhibits a morphological transition. This…
It is known for many years that the vorticity and the thickness fields in soap films are coupled and that the thickness wave propagates at the Marangoni wave speed. Based on the two observations, we propose a hypothesis that the vorticity…
The present paper is concerned with new Besov-type space of variable smoothness. Nonlinear spline-approximation approach is used to give atomic decomposition of such space. Characterization of the trace space on hyperplane is also obtained.
We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…
Lattice structures, distinguished by their customizable geometries at the microscale and outstanding mechanical performance, have found widespread application across various industries. One fundamental process in their design and…
We review a certain problem on covering triangles in the plane. Equivalently, it can be viewed as a family of 'isobilliard' inequalities in convex shapes, and as a special case of Viterbo's conjecture in symplectic geometry. We give an…
We describe the structure of the singular sets of constant curvature, convex hypersurfaces in hyperbolic space for general convex curvature functions. We apply this result to the study of the ideal Plateau problem in hyperbolic space for…
In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results…
In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Our study provides interface Hamiltonians for…
We find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface tension. We consider the evolution from both periodic and…
Surface tension-driven flow techniques have recently emerged as an efficient means of shedding light into the rheology of thin polymer films. Motivated by experimental and theoretical approaches in films bearing a varying surface…
We experimentally investigate the impact of a liquid jet on a soap film. We observe that the jet never breaks the film and that two qualitatively different steady regimes may occur. The first one is a refraction-like behavior obtained at…
A solid withdrawn from a liquid bath entrains a film. In this review, after recalling the predictions and results for pure Newtonian liquids coated on simple solids, we analyze the deviations to this ideal case exploring successively three…
Current state-of-the-art methods for video inpainting typically rely on optical flow or attention-based approaches to inpaint masked regions by propagating visual information across frames. While such approaches have led to significant…
We study the behavior of an elastic loop embedded in a flowing soap film. This deformable loop is wetted into the film and is held fixed at a single point against the oncoming flow. We interpret this system as a two-dimensional flexible…