Related papers: On Plateau's Problem for Soap Films with a Bound o…
We consider area minimizing $m$-dimensional currents $\mathrm{mod}(p)$ in complete $C^2$ Riemannian manifolds $\Sigma$ of dimension $m+1$. For odd moduli we prove that, away from a closed rectifiable set of codimension $2$, the current in…
We investigate the equilibrium properties of a single area-minimising bubble trapped between two narrowly-separated parallel curved plates. We begin with the simple case of a a bubble trapped between concentric spherical plates. We develop…
We consider the wetting transition on a planar surface in contact with a semi-infinite fluid. In the classical approach, the surface is assumed to be solid, and when interaction between solid and fluid is sufficiently short-range, the…
In an incompressible velocity field, the surface area of a volume varies with time, but volume remains unchanged. If incidentally the surface becomes spherical along time, the area reaches a local minimum, since sphere has the least area…
Diffusion of a penetrating liquid in a polymeric material does not often satisfy the classical diffusion equations and requires taking relaxational (viscoelastic) properties of the polymer into account. We investigate a boundary value…
"The Life of a Free Soap Film" is a fluid dynamics video for the Gallery of Fluid Motion intended to showcase the novel experimental techniques that we have developed in our laboratory to study the retraction of planar liquid films of…
On a finite-volume hyperbolic $3$-manifold, we establish an upper bound on the area of closed embedded surfaces with constant mean curvature at least one, depending on the mean curvature and the genus bounds. This area bound implies…
The difficulty in exploring potential energy surfaces, which are nonconvex, stems from the presence of many local minima, typically separated by high barriers and often disconnected in configurational space. We obtain the global minimum on…
A novel surface correction method is proposed for bond based peridynamics which ensures energy consistency with a classical reference body for general affine deformations. This method is validated for simple geometries and then applied to a…
A Jordan curve on the Riemann sphere can be encoded by its conformal welding, a circle homeomorphism. The Loewner energy measures how far a Jordan curve is away from being a circle, or equivalently, how far its welding homeomorphism is away…
The random deposition model must be enriched to reflect the variety of surface roughness due to some material characteristics of the film growing by vacuum deposition or sputtering. The essence of the computer simulation in this case is to…
We consider the parabolic $p$-Laplace equation with $p>2$ in a moving thin domain under a Neumann type boundary condition corresponding to the total mass conservation. When the moving thin domain shrinks to a given closed moving…
In continuing the study of harmonic mapping from 2-dimensional Riemannian simplicial complexes in order to construct minimal surfaces with singularity, we obtain an a-priori regularity result concerning the real analyticity of the free…
We investigate the sliding dynamics of a millimeter-sized particle trapped in a horizontal soap film. Once released, the particle moves toward the center of the film in damped oscillations. We study experimentally and model the forces…
We combine experiments and theoretical derivations to study the evolution of a stretched soap bubble and compare it with an open film to highlight the effect of volume conservation. We identify a critical length for both surfaces, beyond…
We study a boundary value problem associated with a system of two second order differential equations with cubic nonlinearity which model a film of superconductor material subjected to a tangential magnetic field. We show that for an…
The structural properties of polymers adsorbed onto a surface have been widely investigated using self-consistent mean-field theories. Recently, analytical mean-field theories have been applied to study polymer adsorption on curved surfaces…
The surface tension of flowing soap films is measured with respect to the film thickness and the concentration of soap solution. We perform this measurement by measuring the curvature of the nylon wires that bound the soap film channel and…
We prove local boundedness of generalized solutions to a large class of variational problems of linear growth including boundary value problems of minimal surface type and models from image analysis related to the procedure of…
Solving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of 'surface', 'area' and 'boundary'. The…