A lower bound for the area of Plateau foams
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
A lower bound for the area of Plateau foamsDate
2020-04-07Publisher
SpringerBibliographic citation
Gimeno, V., Markvorsen, S. & Sotoca, J.M. A lower bound for the area of Plateau foams. J Inequal Appl 2020, 96 (2020). https://doi.org/10.1186/s13660-020-02362-4Type
info:eu-repo/semantics/articlePublisher version
https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s ...Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
Real foams can be viewed as geometrically well-organized dispersions of more or less spherical bubbles in a liquid. When the foam is so drained that the liquid content significantly decreases, the bubbles become ... [+]
Real foams can be viewed as geometrically well-organized dispersions of more or less spherical bubbles in a liquid. When the foam is so drained that the liquid content significantly decreases, the bubbles become polyhedral-like and the foam can be viewed now as a network of thin liquid films intersecting each other at the Plateau borders according to the celebrated Plateau’s laws.
In this paper we estimate from below the surface area of a spherically bounded piece of a foam. Our main tool is a new version of the divergence theorem which is adapted to the specific geometry of a foam with special attention to its classical Plateau singularities.
As a benchmark application of our results, we obtain lower bounds for the fundamental cell of a Kelvin foam, lower bounds for the so-called cost function, and for the difference of the pressures appearing in minimal periodic foams. Moreover, we provide an algorithm whose input is a set of isolated points in space and whose output is the best lower bound estimate for the area of a foam that contains the given set as its vertex set. [-]
Investigation project
Spanish Government Ministerio de Economía y Competitividad (MINECO-FEDER), grant MTM2017-84851-C2-2-P, Ministerio de Ciencia, Innovación y Universidades (grant RTI2018-098651-B-C54) ; Universitat Jaume I (grant UJI-B2018-35 and grant UJI-B2018-44).Rights
© The Author(s) 2020.
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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