Principal Investigator

S T Hyde Applied Mathematics, RSPhysSE, ANU

Project Title

Medial Surface Analysis of Hyperbolic Structure

Brief Description for General Publications

Hyperbolic interfaces and bicontinuous labyrinth structures are ubiquitous in condensed matter science. Examples are the void space channel system in a sandstone, isopotential surfaces of crystalline structures, bilayer interfaces in mesophases of liquid crystal self-assembly, membranes of complex cells, etc. Traditionally the analysis of hyperbolic surfaces relies on curvature properties of the interface surface or on topological aspects of the underlying graph network. This project aims at analysing hyperbolic structure from a slightly different perspective - their capability of tiling space with parallel sets of the surface. This approach has interesting implications for the the notion of homogeneity of hyperbolic surfaces, and is important in understanding the physical origins of these complex structures. It is a numerical problem, since it relies on Voronoi diagram and medial axis methods, which are rarely accessible to analytic approaches.