Related papers: Solving the brachistochrone and other variational …
For a given boundary set consisting of arcs and vertices, with two or more arcs meeting at each vertex, we treat the problem of estimating the area density of a soap film-like surface spanning the boundary.
A field theory to describe electrostatic interactions in soap films, described by electric multi-layers with a generalized thermodynamic surface-charging mechanism, is studied. In the limit where the electrostatic interactions are weak this…
What are the possible shapes of various things and why? For instance, when a closed wire or a frame is dipped into a soap solution and is raised up from the solution, the surface spanning the wire is a soap film. What are the possible…
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…
We classify cylindrical surfaces in the Euclidean space whose mean curvature is a $n$th-power of the distance to a reference plane. The generating curves of these surfaces, called $n$-elastic curves, have a variational characterization as…
Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For…
We solve the brachistochrone problem for a particle travelling through a spherical mass distribution of uniform density. We examine the connection between this problem and the popular "gravity elevator" result. The solution is compared to…
We consider different generalizations of the Brachistochrone Problem in the context of fundamental concepts of classical mechanics. The correct statement for the Brachistochrone problem for nonholonomic systems is proposed. It is shown that…
A variational model for epitaxially strained films accounting for the presence of dislocations is considered. Existence, regularity and some qualitative properties of solutions are addressed.
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 free boundary problem describing a tubular soap film bridge driven by an electrostatic force. To realize the electrostatic force, the soap film bridge is placed inside an outer metal cylinder and a voltage difference between this…
Dynamic buckling may occur when a load is rapidly applied to, or removed from, an elastic object at rest. In contrast to its static counterpart, dynamic buckling offers a wide range of accessible patterns depending on the parameters of the…
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…
If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by…
Wrinkling is commonly observed as mechanical instability when a stiff thin film bound on a compliant thick substrate undergoes in-plane compression exceeding a threshold. Despite significant efforts to create a broad range of surface…
We follow the diffusive motion of colloidal particles of diameter $d$ in soap films of varying thickness $h$ with fluorescence microscopy. Diffusion constants are obtained both from one- and two-particle microrheological measurements of…
We study the Plateau problem with a lower dimensional obstacle in $\mathbb{R}^n$. Intuitively, in $\mathbb{R}^3$ this corresponds to a soap film (spanning a given contour) that is pushed from below by a "vertical" 2D half-space (or some…
Influence diagrams are a decision-theoretic extension of probabilistic graphical models. In this paper we show how they can be used to solve the Brachistochrone problem. We present results of numerical experiments on this problem, compare…
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 present a quasi-two dimensional model of flowing soap films that bears striking similarity to the compressible Navier-Stokes equations. The variation in soap film thickness that is commonly used for flow visualization in experiments is…