相关论文: When Soap Bubbles Collide

We consider nonlinear diffusion of some substance in a container (not necessarily bounded) with bounded boundary of class C^2. Suppose that, initially, the container is empty and, at all times, the substance at its boundary is kept at…

In this fluid dynamics video, we compare the deformation of two flexible particles as they propagate through a sudden constriction of a liquid filled channel under constant-flux flow: a gas bubble, and a capsule formed by encapsulating a…

Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvature and fixed or converging boundaries. In particular, we…

Consider the family of all perfect matchings of the complete graph $K_{2n}$ with $2n$ vertices. Given any collection $\mathcal M$ of perfect matchings of size $s$, there exists a maximum number $f(n,x)$ such that if $s\leq f(n,x)$, then…

Building on the recent theoretical work of Wray, Duffy and Wilson [J. Fluid Mech. 884, A45 (2020)] concerning the competitive diffusion-limited evaporation of multiple thin sessile droplets in proximity to each other, we obtain theoretical…

A fluid in the NVT ensemble at T less than the critical temperature T_c and rho = N/V somewhat in excess of rho_coex (density of the saturated gas in the gas-liquid transition) is considered. For V->infinity, a macroscopic liquid droplet…

In order to assess the physical mechanisms at stake when giant gas bubbles burst at the top of a magma conduit, laboratory experiments have been performed. An overpressurized gas cavity is initially closed by a thin liquid film, which…

We use ultra-high-speed video imaging to look at the initial contact of a drop impacting onto a liquid layer. We observe experimentally the vortex street and the bubble-ring entrapments predicted numerically, for high impact velocities, by…

We prove integral formulas for closed hypersurfaces in C^{n+1}, which furnish a relation between elementary symmetric functions in the eigenvalues of the complex Hessian matrix of the defining function and the Levi curvatures of the…

Let $\Sigma$ be a compact immersed stable capillary hypersurface in a wedge bounded by two hyperplanes in $\mathbb R^{n+1}$. Suppose that $\Sigma$ meets those two hyperplanes in constant contact angles and is disjoint from the edge of the…

We study a moving boundary problem modeling an injected fluid into another viscous fluid. The viscous fluid is withdrawn at infinity and governed by Darcy's law. We present solutions to the free boundary problem in terms of time-derivative…

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…

The void prediction in LCM processes sparks off interest within the composite material industry because it is a significant issue to keep the expected mechanical properties. The liquid properties, the preform geometry and the flow…

Considering a finite intersection of balls and a finite union of other balls in an Euclidean space, we propose an exact method to test whether the intersection is covered by the union. We reformulate this problem into quadratic programming…

We survey results on the problem of covering the space ${\mathbb R}^n$, or a convex body in it, by translates of a convex body. Our main goal is to present a diverse set of methods. A theorem of Rogers is a central result, according to…

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…

I briefly review the physics of cosmic bubble collisions in false-vacuum eternal inflation. My purpose is to provide an introduction to the subject for readers unfamiliar with it, focussing on recent work related to the prospects for…

We have developed a theory of air leakage at interfaces between two elastic solids with application to suction cups in contact with randomly rough surfaces. We present an equation for the airflow in narrow constrictions which interpolate…

We give a sketch of proof that any two (Lebesgue) measurable subsets of the unit sphere in $R^n$, for $n\ge 3$, with non-empty interiors and of the same measure are equidecomposable using pieces that are measurable.

The spontaneous formation of tiny bubbles in a liquid is at the root of the nucleation mechanism during the liquid-to-vapor transition of a metastable liquid. The smaller the bubbles the larger their probability to appear, and even for…