Related papers: Cartan's Magic Formula and Soap Film Structures
Bubbles and droplets are ubiquitous in many areas of engineering, including microfluidics where they can serve as microreactors for screening of chemical reactions. They are often formed out of a constriction (a microfluidic channel or a…
We give a geometric method for determining the cohomology groups of a polyhedral product under suitable freeness conditions or with coefficients taken in a field. This is done by considering first the special case for which the pairs of…
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…
Plateau's problem is to show the existence of an area minimizing surface with a given boundary, a problem posed by Lagrange in 1760. Experiments conducted by Plateau showed that an area minimizing surface can be obtained in the form of a…
At a certain infamous tea party, the Mad Hatter posed the following riddle: why is a raven like a writing-desk? We do not answer this question. Instead, we solve a related nonsense query: why is a soap bubble like a railway? The answer is…
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…
It is known for many years that the vorticity and the thickness fields in soap films are coupled and that the thickness wave propagates at the Marangoni wave speed. Based on the two observations, we propose a hypothesis that the vorticity…
Soap bubbles and foams have been extensively studied by scientists, engineers, and mathematicians as models for organisms and materials, with applications ranging from extinguishing fires to mining to baking bread. Here we provide some…
The perturbative stability of catenoidal soap films formed between parallel, equal radii, coaxial rings is studied using analytical and semi-analytical methods. Using a theorem on the nature of eigenvalues for a class of Sturm--Liouville…
If we pull out rapidly a metallic frame out of a surfactant solution, we arrive at a "young" soap film with relatively simple features, as noticed first by Lucassen. The weight of the film is equilibrated by a vertical gradient of surface…
Surface tension profiles in vertical soap films are experimentally investigated. Measurements are performed introducing deformable elastic objets in the films. The shape adopted by those objects set in the film can be related to the surface…
Regular polygons are characterized as area-constrained critical points of the perimeter functional with respect to particular families of perturbations in the class of polygons with a fixed number of sides. We also review recent results in…
Using mixtures of soap, water, and long chain polymers, free-floating soap bubbles can be formed with volumes approaching 100 m$^3$. Here we investigate how such thin films are created and maintained over time. We show how the extensional…
We investigate crystalline order on a two-dimensional paraboloid of revolution by assembling a single layer of millimeter-sized soap bubbles on the surface of a rotating liquid, thus extending the classic work of Bragg and Nye on planar…
Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume regions with boundaries of constant mean…
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 propose a physical mechanism to explain the crystal symmetries found in macromolecular and supramolecular micellar materials. We argue that the packing entropy of the hard micellar cores is frustrated by the entropic interaction of their…
Correlation in two-dimensional soap froth is analysed with an effective potential for the first time. Cells with equal number of sides repel (with linear correlation) while cells with different number of sides attract (with NON-bilinear)…
Thin cylindrical tethers are common lipid bilayer membrane structures, arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the Golgi apparatus. We study the shape and formation…
The Cartan formula relates the cup product and the action of the Steenrod algebra on mod~$p$ cohomology. For any pair of mod $p$ cocycles in a simplicial set, where $p$ is an odd prime, we effectively construct a natural coboundary…