The elegant properties of conformal mappings, when applied to two-dimensional lattices, find interesting applications in two-dimensional foams and other cellular or close-packed structures. In particular, the two-dimensional honeycomb (whose dual is the triangular lattice) may be transformed into various conformal patterns, which compare approximately to experimentally realizable two-dimensional foams. We review and extend the mathematical analysis of such transformations, with several illustrative examples. New results are adduced for the local curvature generated by the transformation.
|Number of pages||20|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 31 Dec 2009|
- conformal crystals