Related papers: Solving the brachistochrone and other variational …
The paper is of scientific-methodical character. The classical soap film shape (minimal surface) problem is considered, the film being stretched between two parallel coaxial rings. An analytical approach based on relations to the…
After a short description of various classical solutions of Plateau's problem, we discuss other ways to model soap films, and some of the related questions that are left open. A little more attention is payed to a more specific model, with…
We study the equilibrium problem of a system consisting by several Kirchhoff rods linked in an arbitrary way and tied by a soap film, using techniques of the Calculus of Variations. We prove the existence of a solution with minimum energy,…
A review on the classical Plateau problem is presented. Then, the state of the art about the Kirchhoff-Plateau problem is illustrated as well as some possible future directions of research.
In this paper we first review the covering space method with constrained BV functions for solving the classical Plateau's problem. Next, we carefully analyze some interesting examples of soap films compatible with the covering space method:…
The Plateau's problem seeks to determine a surface of minimal area which spans a given boundary. It is widely studied for its varied mathematical formulations, applications and relevance to physical models such as soap films. We revisit the…
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…
The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical…
A soap film is actually a thin solid fluid bounded by two surfaces of opposite orientation. It is natural to model the film using one polyhedron for each side. Two problems are to get the polyhedra for both sides to be in the same place…
The present study aims to investigate the motion of buoyant rings in vertical soap films. Thickness differences and related bi-dimensional densities are considered as the motor leading to bi-dimensional buoyancy. We show how this effect can…
We study a variational model for soap films in which the films are represented by sets with fixed small volume rather than surfaces. In this problem, a minimizing sequence of completely "wet" films, or sets of finite perimeter spanning a…
In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in…
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…
A variational model is used to study the stability of a soap film spanning a flexible loop. The film is modeled as a fluid surface endowed with constant tension and the loop is modeled as an elastic rod resistant to both bending and twist.…
We analytically study a stationary free boundary problem describing a soap film bridge subjected to an electrostatic force. Starting from a cylinder that the soap film forms if its surface tension and the electrostatic force are perfectly…
We consider two models, a free boundary problem and a simplification thereof, which describe a soap film bridge subjected to an electrostatic force. For both models, we construct stationary solutions if the force is small, analyse their…
We propose here a fluid dynamics video relating the bursting of soap rigid films.
By employing the method of moving planes in a novel way we extend some classical symmetry and rigidity results for smooth minimal surfaces to surfaces that have singularities of the sort typically observed in soap films.
The Euler--Plateau problem, proposed by \cite{gm}, concerns a soap film spanning a flexible loop. The shapes of the film and the loop are determined by the interactions between the two components. In the present work, the Euler--Plateau…
A soap film, or a flexible membrane without bending and torsional stiffness, that is confined in a cylinder is shown to be susceptible to a surface-tension-driven instability when it is stretched or twisted. This leads to its breakdown and…