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

水流过砂岩的方式取决于其孔隙的连通性，单个颗粒之间接触的筒仓中的力的平衡，以及车门中金属泡沫的抗冲击性对其单元格的排列。这些结构特性在数学上用拓扑学来描述。先进的三维X射线成像现在可以揭示微结构材料的内部细节。图像分析的最新发展意味着从这些图像中计算精确的拓扑信息是可能的。该项目旨在研究形状的基本措施如何影响复杂材料的物理特性，并阐明支撑这些关系的数学。

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. Recent developments in image analysis mean it is possible to compute accurate topological information from such images. This project aims to investigate how fundamental measures of shape influence the physical properties of complex materials and clarifies the mathematics that underpins these relationships.