Curvature in conformal mappings of 2D lattices and foam structure

Details Curvature in conformal mappings of 2D lattices and foam structure Curvature in conformal mappings of 2D lattices and foam structure

2008-01-16

arxiv.org/abs/0801.2474v2

Proc. R. Soc. A, 465, 219-238, 2009

Physics

Condensed Matter

Soft Condensed Matter

19 pages, to be submitted for a special issue of Philosophical Magazine in memory of M A Fortes

Scientific paper

10.1098/rspa.2008.0260

The elegant properties of conformal mappings, when applied to two dimensional (2D) lattices, find interesting applications in 2D foams and other cellular or close packed structures. In particular the 2D honeycomb (whose dual is the triangular lattice) may be transformed into various conformal patterns, which compare approximately to experimentally realisable 2D foams. We review and extend the mathematical analysis of such transformations, with several illustrative examples, and an account is given of the related work in energy minimisation problems. New results are adduced for the local curvature generated by the transformation.

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