Related papers: Conelike soap films spanning tetrahedra

Vertical soap films drain under the influence of gravity, as indicated by the downward motion of colorful horizontal interference fringes observed on their surfaces. In this study conducted with rectangular soap films, we experimentally…

We define a 2-normal surface to be one which intersects every 3-simplex of a triangulated 3-manifold in normal triangles and quadrilaterals, with one or two exceptions. The possible exceptions are a pair of octagons, a pair of unknotted…

Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the…

We have generated a novel form of shear banding in a 2D foam and measured the relative magnitude of drag forces on soap films at different lubrication layers. We injected air part way along a flowing bubble field in a narrow Hele-Shaw cell.…

In this paper, we show that small spherical soap bubbles in irreducible simply connected symmetric spaces of rank greater than one are constructed from the limits of a certain kind of modified mean curvature flows starting from small…

We study the local regularity of sliding almost minimal sets of dimension 2 in $R^n$ , bounded by a smooth curve $L$. These are a good way to model soap films bounded by a curve, and their definition is similar to Almgren's. We aim for a…

Millimeter-sized particles trapped at the surface of a liquid bath attract each other through the deformation of the liquid-air interface, a phenomenon known as "the Cheerios effect". We consider here a situation similar at first sight: the…

We investigate the motion through a wet tube of transverse soap films, or lamellae, of high surface dilatationnal modulus. Combining local thickness and velocity measurements in the wetting film, we reveal a zone of several centimeters in…

In two dimensional foams at equilibrium, triangular bubbles can be freely exchanged with 3-fold stars --three edges ending at a central vertex. This theorem is deduced here from Moukarzel's duality. Moreover, to probe the method, a few…

Cox & Jones recently devised and studied an interesting variant of the classical Plateau problem, a variant in which a helical soap film is confined to a cylindrical tube with circular cross-section. Through experiments, numerics, and some…

The solution to the Euler-Lagrange equation is an extremal functional.To understand that the functional is stationary at local extrema (maxima or minima), we propose a physics experiment that involves using soap film to form a catenoid. A…

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some…

The analogy between soap films thinning under border capillary suction and lamellar stacks of surfactant bilayers dehydrated by osmotic stress is explored, in particular in the highly dehydrated limit where the soap film becomes a Newton…

We investigate the motions of a bar structure consisting of two congruent tetrahedra, whose edges in their basic position form the face diagonals of a rectangular parallelepiped. The constraint of the motion is that the originally…

Motivated by the evaporation of soap films, which has a significant effect on their lifetime, we performed an experimental study on the evaporation of vertical surfaces with model systems based on hydrogels. From the analogy between heat…

In this paper we provide a large new family of embedded capillary surfaces inside polyhedral regions in the Euclidean space. The angle of contact of the examples we furnish is prescribed to be any value in $(\frac{\pi}{2}, \pi]$ and it is…

t has been shown that the flow of a simple liquid over a solid surface can violate the so-called no-slip boundary condition. We investigate the flow of polar liquids, water and glycerol, on a hydrophilic Pyrex surface and a hydrophobic…

Two tetrahedra are called orthologic if the lines through vertices of one and perpendicular to corresponding faces of the other are intersecting. This is equivalent to the orthogonality of non-corresponding edges. We prove that the…

In this paper, I consider a thin suspended liquid film, surrounded by a different fluid. Examples of such a system are soap films and liquid crystal films, surrounded by air. They are considered good models for two dimensional fluid…

We study a two-dimensional fluid of particles interacting through a spherically-symmetric and marginally soft two-body repulsion. This model can exist in three different crystal phases, one of them with square symmetry and the other two…