From optical to topological data analysis of colloidal and structured liquid crystals

Colloidal liquid crystals offer a route to change physical properties and create micro and nano structures. Optical methods only characterise relatively simple colloidal systems. More complex systems require powerful data analytic methods. We present a new approach using Topological Data Analysis to reveal the structural and morphological features in a nematic liquid crystal doped with gold nanoparticles confined in a thin capillary, including the changes occurring during phase transitions. Our topological framework allows us to identify distinct temperature-induced macroscopic states, obtain a geometric representation of the time-dependent topological states and identify several configurations with different degrees of symmetry and order.