The minimal perimeter for N confined deformable bubbles of equal area

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dc.contributor.author Cox, S. J.
dc.contributor.author Flikkema, E.
dc.date.accessioned 2010-04-27T17:23:56Z
dc.date.available 2010-04-27T17:23:56Z
dc.date.issued 2010-04-27
dc.identifier.citation Cox , S J & Flikkema , E 2010 , ' The minimal perimeter for N confined deformable bubbles of equal area ' Electronic Journal of Combinatorics , vol 17 , R45 . en
dc.identifier.other PURE: 149342
dc.identifier.other dspace: 2160/4611
dc.identifier.uri http://hdl.handle.net/2160/4611
dc.identifier.uri http://www.combinatorics.org/Volume_17/v17i1toc.html en
dc.identifier.uri http://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r45 en
dc.description Sponsorship: EPSRC Sponsorship: Edwin Flikkema holds a RCUK Fellowship. en
dc.description.abstract Candidates to the least perimeter partition of various polygonal shapes into N planar connected equal-area regions are calculated for N ≤ 42, compared to partitions of the disc, and discussed in the context of the energetic groundstate of a two-dimensional monodisperse foam. The total perimeter and the number of peripheral regions are presented, and the patterns classified according to the number and position of the topological defects, that is non-hexagonal regions (bubbles). The optimal partitions of an equilateral triangle are found to follow a pattern based on the position of no more than one defect pair, and this pattern is repeated for many of the candidate partitions of a hexagon. Partitions of a square and a pentagon show greater disorder. Candidates to the least perimeter partition of the surface of the sphere into N connected equal-area regions are also calculated. For small N these can be related to simple polyhedra and for N ≥ 14 they consist of 12 pentagons and N −12 hexagons. en
dc.language.iso eng
dc.relation.ispartof Electronic Journal of Combinatorics en
dc.title The minimal perimeter for N confined deformable bubbles of equal area en
dc.type Text en
dc.type.publicationtype Article (Journal) en
dc.contributor.institution Mathematical Modelling of Structures, Solids and Fluids en
dc.contributor.institution Materials Research en
dc.contributor.institution Institute of Mathematics & Physics (ADT) en
dc.description.status Peer reviewed en


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