Related papers: Covers, soap films and BV functions
V. Arnold's problem 1987-14 asks whether there exist smooth hypersurfaces in $R^N$ (other than the conics in odd-dimensional spaces) for which the volume of the segment cut by any hyperplane from the body bounded by such a hypersurface is…
The capillary levelling of cylindrical holes in viscous polystyrene films was studied using atomic force microscopy as well as quantitative analytical scaling arguments based on thin film theory and self-similarity. The relaxation of the…
We consider a carpet of self-propelled particles at the liquid-gas interface of a liquid film on a solid substrate. The particles excert an excess pressure on the interface and also move along the interface while the swimming direction…
Video segmentation is a popular task, but applying image segmentation models frame-by-frame to videos does not preserve temporal consistency. In this paper, we propose a method to extend a query-based image segmentation model to video using…
Carpets under consideration here, in the context of pressure acoustic waves propagating in a compressible fluid, do not touch the ground: they levitate in mid-air (or float in mid-water), which leads to approximate cloaking for an object…
Shallow flow or thin liquid film models are used for a wide range of physical and engineering problems. Shallow flow models allow capturing the free surface of the fluid with little effort and reducing the three-dimensional problem to a…
We study a free boundary problem describing a tubular soap film bridge driven by an electrostatic force. To realize the electrostatic force, the soap film bridge is placed inside an outer metal cylinder and a voltage difference between this…
Wrinkling is commonly observed as mechanical instability when a stiff thin film bound on a compliant thick substrate undergoes in-plane compression exceeding a threshold. Despite significant efforts to create a broad range of surface…
The model problem of scattering of a sound wave by an infinite plane structure formed by a semi-infinite acoustically hard screen and a semi-infinite sandwich panel perforated from one side and covered by a membrane from the other is…
Following on from ``Hyperbolic Plateau problems'' (by the same author), we provide a complete geometric description of solutions to the Plateau problem $(S,\phi)$ when $S$ is a compact Riemann surface with a finite number of points removed.
Video frame interpolation aims at synthesizing intermediate frames from nearby source frames while maintaining spatial and temporal consistencies. The existing deep-learning-based video frame interpolation methods can be roughly divided…
We consider the slow flow of a viscous incompressible liquid in a channel of constant but arbitrary cross section shape, driven by non-uniform suction or injection through the porous channel walls. A similarity transformation reduces the…
Wetting of sessile bubbles on solid and liquid surfaces has been studied. A model is presented for the contact angle of a sessile bubble based on a modified Young equation - the experimental results agree with the model. A hydrophilic…
The aim of this paper is to obtain new fine properties of entropy solutions of nonlinear scalar conservation laws. For this purpose, we study some "fractional $BV$ spaces" denoted $BV^s$, for $0 < s \leq 1$, introduced by Love and Young in…
Thin-film flows of viscoelastic fluids are encountered in various industrial and biological settings. The understanding of thin viscous film flows in Newtonian fluids is very well developed, which for a large part is due to the so-called…
We consider the lifetime of rectangular vertical soap films and we explore the influence of relative humidity and both dimensions on the stability of large soap films, reaching heights of up to 1.2 m. Using an automated rupture detection…
The merging of two soap bubbles is a fundamental fluid mechanical process in foam formation. In the present experimental study the liquid films from two soap bubbles are brought together. Once the liquid layers initially separated by a gas…
Video Frame Interpolation synthesizes non-existent images between adjacent frames, with the aim of providing a smooth and consistent visual experience. Two approaches for solving this challenging task are optical flow based and kernel-based…
Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.
We use the functional integral technique of Edwards and Lenard to solve the statistical mechanics of a one dimensional Coulomb gas with boundary interactions leading to surface charging. The theory examined is a one dimensional model for a…