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Soft matter systems have some common features, typically showing high susceptibility to deformation under small mechanical or thermal stress, and the significant complexity of their components (liquid crystals, polymers, biological tissues, etc). These characteristics make the mathematical modelling of soft materials challenging and, in most cases, powerful analytic methods are required for accurate and quantitative characterisation of their dynamics.

Topological data analysis is a relatively new tool that uses the shape of the data to obtain meaningful information. Several topological data analytic tools have been successfully applied in the analysis of time-independent data of soft matter systems. These analyses have allowed characterising the morphology of soft materials, the atomic configurations of complex organic molecules and ion aggregation systems.

In this project, funded by the Leverhulme Trust, partially ordered, composite nanomaterials, with complex structural and physical behaviour are investigated. Our analytic framework, based on topological data analysis, provides both a qualitative and quantitative characterisation of the dynamical behaviour of a wide range of semi-ordered soft matter, captures the degree of organisation at a mesoscopic level, tracking their time-evolution and ultimately detecting the order-disorder transition at the microscopic scale.