Related papers: Conelike soap films spanning tetrahedra
The spontaneous spreading of non-volatile liquid droplets on solid substrates poses a classic problem in the context of wetting phenomena. It is well known that the spreading of a macroscopic droplet is in many cases accompanied by a thin…
The aim of this paper is to give a survey of the known results concerning centrally symmetric polytopes, spheres, and manifolds. We further enumerate nearly neighborly centrally symmetric spheres and centrally symmetric products of spheres…
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…
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…
The dynamics of thin films on a horizontal solid substrate is investigated in the case of non-Newtonian fluids exhibiting normal stress differences, the rheology of which is strongly non-linear. Two coupled equations of evolution for the…
In Part II of this study we consider two cases of three-phase coexistence. First, the capped capillary may allow for vapour, drop-like, and slab-like phases to coexist at the same values of temperature and chemical potential. Second, the…
Following Matveev, a k-normal surface in a triangulated 3-manifold is a generalization of both normal and (octagonal) almost normal surfaces. Using spines, complexity, and Turaev-Viro invariants of 3-manifolds, we prove the following…
We show that highly twisted minimal strips can undergo a non-singular transition, unlike the singular transitions seen in the M\"obius strip and the catenoid. If the strip is non-orientable this transition is topologically frustrated, and…
We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal…
We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all…
While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…
The elementary topological T1 process in a two-dimensional foam corresponds to the "flip" of one soap film with respect to the geometrical constraints. From a mechanical point of view, this T1 process is an elementary relaxation process…
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…
Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…
Thin liquid films on surfaces are part of our everyday life, they serve e.g. as coatings or lubricants. The stability of a thin layer is governed by interfacial forces, described by the effective interface potential, and has been subject of…
Even in simple geometries many complex fluids display non-trivial flow fields, with regions where shear is concentrated. The possibility for such shear banding has been known since several decades, but the recent years have seen an upsurge…
Three-dimensional topological crystalline insulators were recently predicted and observed in the SnTe class of IV-VI semiconductors, which host metallic surface states protected by crystal symmetries. In this work, we study thin films of…
All children enjoy blowing soap bubbles that also show up in our bath and when we wash dishes. We analyze the thinning and breaking of soap bubble neck when it is stretched. To contrast with the more widely studied film whose boundaries are…
The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. We…
In this article we prove a sufficient condition of quasi-normality in higher dimension for a family of meromorphic mappings in which each pair of functions of family shares some moving hypersurfaces. We also prove a normality criterion…