Curvature in conformal mappings of two-dimensional lattices and foam structure

Authors Organisations
Type Article
Original languageEnglish
Pages (from-to)219-238
Number of pages20
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume465
Issue number2101
DOI
Publication statusPublished - 31 Dec 2009
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Abstract

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.

Keywords

  • conformal crystals, foams, curvature