Are large perimeter- minimizing two-dimensional clusters of equal-area bubbles hexagonal or circular?-Reference-Cited by-同舟云学术

Are large perimeter- minimizing two-dimensional clusters of equal-area bubbles hexagonal or circular?

Published:2013-01-08 Issue:2149 Volume:469 Page:20120392
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Cox S. J.¹,Morgan F.²,Graner F.³

Affiliation:

1. Institute of Mathematics and Physics, Aberystwyth University, Aberystwyth SY23 3BZ, UK

2. Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA

3. Matière et Systèmes Complexes, Université Paris Diderot, CNRS UMR 7057, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France

Abstract

A computer study of clusters of up to N =200 000 equal-area bubbles shows for the first time that partially rounding conjectured optimal hexagonal planar soap bubble clusters reduces perimeter. Different methods of creating optimal clusters are compared, and new candidate minimizers for several N are given.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2012.0392

Reference17 articles.

1. Morgan F. 2012 See http://sites.williams.edu/Morgan/2012/05/29/soap-bubbles-on-the-roof-of-the-met/.

2. The standard double soap bubble in R2uniquely minimizes perimeter

3. Proof of the planar triple bubble conjecture

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