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

Adil Mughal, Demis Weaire

Research output: Contribution to journalArticle

8 Citations (SciVal)

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

Keywords

  • conformal crystals
  • foams
  • curvature

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