Soap Froth: Some Universal Topological Properties
- Event time: 1:00pm
- Event date: 19th August 2002
- Speaker: Kwok Yip Szeto (University of Edinburgh)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB
Two-dimensional cellular structure constitutes a large class of patterns with important technological and scientific applications. Soap froth, poly-crystalline grain mosaics, and biological tissues are natural examples of random, space-filling cellular networks. Since cellular structures exist on scales ranging from microscopic to geological, much work has been devoted to the search for universal geometrical characteristics. Despite the enormous difference in length scales and different physical forces driving the evolution of the networks, there exist certain universal topological laws governing their similarity. These laws leave aside metrical properties (e.g., sizes of cells) and address the probability distribution of the number of edges of a given cell, or correlations between the numbers of edges of adjacent cells. One of the best-obeyed empirical laws is the Aboav-Weaire law. We have generalized this law and obtain some universal topological properties of two-dimensional trivalent cellular patterns from shell analysis of soap froth and computer generated Voronoi diagrams. Our work suggests new ways to look at clusters in patterns.
This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..