From: jms@symcom.math.uiuc.edu (John Sullivan)
Subject: Re: Foam
Date: 31 Mar 1999 03:35:33 GMT
Newsgroups: sci.math.research
In article <37008837.94C5AB7A@janpla.dk>, Jan wrote:
>What is a 'foam' toplogically and/or geometrically?
A bubble cluster is a collection of cells of fixed volumes which (locally)
minimizes total surface area. A foam is an infinite bubble cluster.
The easiest ones to study are triply periodic.
Due to results of Almgren, Taylor, Morgan, we know that minimizing
bubble clusters exist in any dimension. In the plane, they consist
of circular arcs meeting in 3s at equal angles. In 3d, they consist
of constant-mean-curvature surfaces, and combinatorially follow
the Plateau rules, making them combinatorially dual to triangulations.
For more information, see my article "The Geometry of Foams", available
on the web at http://www.math.uiuc.edu/~jms/Papers/
or in print in a new book Foams and Emulsions edited by
Rivier and Sadoc, and published by Kluwer.
--
John M. Sullivan
Asst Prof of Math
Univ. of Illinois
jms@math.uiuc.edu