Hydrodynamic Instabilities, Pattern Formation and Topology in Active

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Active liquid crystals have come to represent an archetype for active matter, offering a framework for organising ideas about biological processes and biologically inspired materials, ranging from bacterial swarms and growing colonies to the cell cytoskeleton. Certain generic traits for active materials, such as spontaneous flows, hydrodynamic instabilities and active turbulence, have been identified using the phenomenology of liquid crystals. This area continues to provide fundamental questions in non-equilibrium physics, with potentially widespread applications across biology. For the most part, existing work has focused on nematic or polar phases, and also largely on a two-dimensional characterisation. Chirality is ubiquitous in nature, appearing both in biological structures and in suspen- sions of the filaments and biopolymers that they are made from. For instance, DNA forms chiral liquid crystalline phases in solution. However, the effects of active stresses on chiral materials and structures have so far not been studied.This project will develop the characterisation and understanding of chiral active materials using the framework and phenomenology of cholesteric liquid crystals. We will extend and continue initial work in my group on the fundamental hydrodynamic instabilities in active cholesterics, in particular to a full three-dimensional analysis, to account for the influence of boundary conditions, or confinement, and to study the stability of different passive cholesteric textures. For instance, it would be natural to determine the morphology of thin films on substrates, or of active cholesteric droplets