Star-triangle equivalence in soap froths
arXiv:cond-mat/0303509 · doi:10.1080/09500830310001594291
Abstract
In two dimensional foams at equilibrium, triangular bubbles can be freely exchanged with 3-fold stars --three edges ending at a central vertex. This theorem is deduced here from Moukarzel's duality. Moreover, to probe the method, a few related properties are established: under slow gas diffusion, T2 processes are continuous for triangles but not for other types of bubbles. In general, the gas flow results in different configurations in the presence of a triangle than in the presence of a star.
7 pages, 4 figures (6 eps files)