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A lower bound for the area of Plateau foams
dc.contributor.author | Gimeno, Vicent | |
dc.contributor.author | Markvorsen, Steen | |
dc.contributor.author | Martínez Sotoca, José | |
dc.date.accessioned | 2020-05-14T10:58:49Z | |
dc.date.available | 2020-05-14T10:58:49Z | |
dc.date.issued | 2020-04-07 | |
dc.identifier.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/s13660-020-02362-4 | ca_CA |
dc.identifier.uri | http://hdl.handle.net/10234/187985 | |
dc.description.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 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. | ca_CA |
dc.format.extent | 23 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Springer | ca_CA |
dc.rights | © The Author(s) 2020. | ca_CA |
dc.rights | Atribución 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-sa/4.0/ | * |
dc.subject | foams | ca_CA |
dc.subject | bubbles | ca_CA |
dc.subject | density | ca_CA |
dc.subject | pressure | ca_CA |
dc.subject | comparison geometry | ca_CA |
dc.title | A lower bound for the area of Plateau foams | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1186/s13660-020-02362-4 | |
dc.relation.projectID | 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). | ca_CA |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-020-02362-4 | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
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