Related papers: Disks that are double spiral staircases
Consider a convex domain B of space. We prove that there exist complete minimal surfaces which are properly immersed in B. We also demonstrate that if D and D' are convex domains with D bounded and the closure of D contained in D' then any…
Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well…
Trapped substances between a 2D crystal, such as graphene, and an atomically flat substrate, for example, hexagonal boron nitride, give rise to the formation of bubbles. We show that the size, shape and internal pressure inside these…
It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes…
Together with the Moebius strip, the Klein bottle is one of the intriguing objects in the universe of geometry, sometimes appearing in non-mathematical contexts too. Until now, several parametrizations of it as a surface immersed in…
The flow of thin liquid films on inclined or vertical surfaces is one of immense importance, with applications spanning many types of process industries, due to the increased mass and heat transfer brought about by the presence of waves on…
This paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most 4\pi must be smoothly embedded. Related results are proved for varifolds and for soap film surfaces.
Two kinds of configurations involving steps on surfaces are reviewed. The first one results from an initially planar vicinal surface, i.e. slightly deviating from a high-symmetry (001) or (111) orientation. In some cases, these surfaces…
We describe the extension of a "viscous froth" model to the dynamics of a wet foam in a Hele-Shaw cell. The two-dimensional model includes the friction experienced by the soap films as they are dragged along the cell walls, while retaining…
For centuries, bubbles have fascinated artists, engineers, and scientists alike. In spite of century-long research on them, new and often surprising bubble phenomena, features, and applications keep popping up. In this paper I sketch my…
Cleaning surfaces with bubbles has been a topic of discussion in recent years due to the growing interest in sustainable methods for cleaning. Specifically, a method of using air bubbles to sanitize agricultural produce has been proposed as…
We consider the deposition of a film of viscous liquid on a flat plate being withdrawn from a bath, experimentally and theoretically. For any plate speed $U$, there is a range of ``thick'' film solutions whose thickness scales like…
We consider a porous solid covered with a water film (or with a drop) in situations where the liquid is pumped in, either spontaneously (if the porous medium is hydrophilic) or mechanically (by an external pump). The dynamics of dewetting…
E. Calabi and J. Cao showed that a closed geodesic of least length in a two-sphere with nonnegative curvature is always simple. Using min-max theory, we prove that for some higher dimensions, this result holds without assumptions on the…
Let $M$ be an $n$-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-\kappa^2$. Using the cone total curvature $TC(\Gamma)$ of a graph $\Gamma$ which was introduced…
Much of a protoplanetary disk is thermally controlled by irradiation from the central star. Such a disk, long thought to have a smoothly flaring shape, is unstable to the so-called 'irradiation instability'. But what's the outcome of such…
We study circle packings with the combinatorics of a triangulated disk in the plane and parametrize deformations of circle packings in terms of vertex rotation and cross ratios. We show that there is a Weierstrass representation formula…
Recent high-resolution interferometric observations of protoplanetary disks at (sub-)millimeter wavelengths reveal omnipresent substructures, such as rings, spirals, and asymmetries. A detailed investigation of eight rings detected in five…
This paper has two main parts. The first one presents a direct path from microscopic dynamics to Debye screening, Landau damping and collisional transport. It shows there is more simplicity in microscopic plasma physics than previously…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…