相关论文: On a calculus of variations problem

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 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…

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…

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,…

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…

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…

Branched flow can be observed when a laser beam is coupled into a soap film. This research theoretically explored the phenomenon through analogy between light wave and particles in form of Hamilton-Jacobian equation, further discussed the…

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.

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…

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 present paper extends the classical second-order variational problem of Herglotz type to the more general context of the Euclidean sphere S^n following variational and optimal control approaches. The relation between the Hamiltonian…

We consider the sloshing problem for an incompressible, inviscid, irrotational fluid in an open container, including effects due to surface tension on the free surface. We restrict ourselves to a constant contact angle and seek…

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…

The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…

The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…

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 prove existence and a.e. regularity of an area minimizing soap film with a bound on energy spanning a given Jordan curve in R^3. The energy of a film is defined to be the sum of its surface area and the length of its singular branched…

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…

A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and…

This article is devoted to the regular fractional Sturm--Liouville eigenvalue problem. Applying methods of fractional variational analysis we prove existence of countable set of orthogonal solutions and corresponding eigenvalues. Moreover,…