Topological data analysis for enhanced modelling of the physical properties of complex micro-structured materials.

Skeletonization and partitioning using topological methods. The initial data is a 2D slice from an micro-CT image of Mt Gambier Limestone. Image credit: Olaf Delgado-Friedrichs

Project description for ARC Future Fellowship FT 140100604

The way water flows through sandstone depends on the connectivity of its pores, the balance of forces in a grain silo on the contacts between individual grains, and the impact resistance of metal foam in a car door on the arrangement of its cells. These structural properties are described mathematically by topology. Advanced three-dimensional x-ray imaging can now reveal the internal detail of micro-structured materials and recent developments in image analysis mean it is possible to compute accurate topological information from such images. This project investigates how fundamental measures of shape influence the physical properties of complex materials and clarifies the mathematics that underpins these relationships.

The project will develop new quantitative relationships between measures of shape derived from x-ray images of micro-structured materials and their physical properties. This will enhance both scientific understanding of natural materials and engineering design of advanced manufactured materials.

EPINET: Euclidean Patterns from Non-Euclidean Tilings

This is a long-term project with Stephen Hyde and Stuart Ramsden to construct three-dimensional crystalline structures via two-dimensional hyperbolic geometry.   Our investigations of theoretical structures have led to new models for materials including  metal-organic frameworks, light-weight rigid isotropic microstructures, and insights into the way keratin filaments are arranged in mammalian skin.

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