The minimal perimeter for \(N\) confined deformable bubbles of equal area
type: Item
instance of: scholarly article
title: The minimal perimeter for \(N\) confined deformable bubbles of equal area
zbMATH Open document ID: 1225.05074
author: B. E. Eshmatov
published in: The Electronic Journal of Combinatorics
publication date: 2010-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/231779
full work available at URL: v17i1r45.html
review text: Summary: Candidates to the least perimeter partition of various polygonal shapes into \(N\) planar connected equal-area regions are calculated for \(N \leqslant 42\), 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.
Mathematics Subject Classification ID: 05B40
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 74G65
zbMATH DE Number: 5721439
zbMATH Keywords: energetic groundstate of a two-dimensional monodisperse foam
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5721439