Show simple item record Cox, S. J. Flikkema, E. 2010-04-27T17:23:56Z 2010-04-27T17:23:56Z 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.issn 1097-1440
dc.identifier.other PURE: 149342
dc.identifier.other PURE UUID: 1bbb7656-c10c-459a-bbe6-8940410eaaa0
dc.identifier.other dspace: 2160/4611
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.rights en
dc.title The minimal perimeter for N confined deformable bubbles of equal area en
dc.type /dk/atira/pure/researchoutput/researchoutputtypes/contributiontojournal/article en
dc.contributor.institution Mathematical Modelling of Structures, Solids and Fluids en
dc.contributor.institution Materials Research en
dc.contributor.institution Department of Physics en
dc.description.status Peer reviewed en

Files in this item

Aside from theses and in the absence of a specific licence document on an item page, all works in Cadair are accessible under the CC BY-NC-ND Licence. AU theses and dissertations held on Cadair are made available for the purposes of private study and non-commercial research and brief extracts may be reproduced under fair dealing for the purpose of criticism or review. If you have any queries in relation to the re-use of material on Cadair, contact

This item appears in the following Collection(s)

Show simple item record

Search Cadair

Advanced Search