Capillary channels in a gravitational field

López, Rafael

doi:10.1088/0951-7715/20/7/003

Cited by 5 publications

(4 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A solution of this equation represents a plane curve z = g(y) whose curvature is proportional to its z-coordinate. These curves are well known in capillarity theory (see, for example, [1,10]).…”

Section: 6)mentioning

confidence: 99%

Separation of variables in equations of mean-curvature type

López¹

2016

Proceedings of the Royal Society of Edinburgh: Section A Mathem

Self Cite

View full text Add to dashboard Cite

show abstract

Section: 6)mentioning

confidence: 99%

Separation of variables in equations of mean-curvature type

López¹

2016

Proceedings of the Royal Society of Edinburgh: Section A Mathem

Self Cite

View full text Add to dashboard Cite

show abstract

“…Thus, the stability condition in Theorem 3.5 reduces to discern if ην n+1 is positive on each of the pieces of γ. A description of the generating curves of cylindrical stationary hypersurfaces appears in [23] for the case m = 1 and in [29] for arbitrary m.…”

Section: Discussionmentioning

confidence: 99%

A relation between critical points of Willmore-type energies, weighted areas and vertical potential energies

López¹,

Pámpano²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

This paper considers the energies of three different physical scenarios and obtains relations between them in a particular case. The first family of energies consists of the Willmore-type energies involving the integral of powers of the mean curvature which extends the Willmore and Helfrich energies. A second family of energies is the area functionals arising in weighted manifolds, following the theory developed by Gromov, when the density is a power of the height function. The third one is the free energies of a fluid deposited in a horizontal hyperplane when the potentials depend on the height with respect to this hyperplane. In this paper we find relations between each of them when the critical point is a hypersurface of cylindrical type. Cylindrical hypersurfaces are determined by their generating planar curves and for each of the families of energies, these curves satisfy suitable ordinary differential equations. For the Willmore-type energies, the equation is of fourth order, whereas it is of order two in the other two cases. We prove that the generating curves coincide for the Willmore-type energies without area constraint and for weighted areas, and the similar result holds for the generating curves of Willmore-type energies and of the vertical potential energies, after suitable choices of the physical parameters. In all the cases, generating curves are critical points for a family of energies extending the classical bending energy. In the final section of the paper, we analyze the stability of a liquid drop deposited on a horizontal hyperplane with vertical potential energies. It is proven that if the free interface of the fluid is a graph on this hyperplane, then the hypersurface is stable in the sense that it is a local minimizer of the energy. In fact, we prove that the hypersurface is a global minimizer in the class of all graphs with the same boundary.

show abstract

“…For the first one, we refer [18, pp. 1130-40], also [14]. A detailed description of the rotational capillary surfaces lies in [7].…”

Section: Cpd Capillary Surfacesmentioning

confidence: 99%