Dynamics of Topological Defects in Active Nematics
Topological defects - singular tears of the order parameter field that cannot be removed by smooth deformations - are often formed in quenches from the disordered state or when order is frustrated by curvature, external fields or boundary conditions. In equilibrium two-dimensional systems, such as thin films of superfluids, crystals, liquid crystals and magnets, order-disorder transitions are controlled by defect unbinding described via the Berezinskii-Kosterlitz-Thouless mapping of the statistical physics of defects onto a Coulomb gas. In active liquid crystals, topological defects become motile particles and proliferate spontaneously in the state of self-sustained turbulent-like motion ubiquitously observed in these systems.
In this talk I will outline a framework for formulating the statistical physics of defects in active nematics as quasiparticles and show that by viewing the active nematic as a collection of swarming and interacting active defects, the onset of active turbulence can be described as an activity-driven defect unbinding transition. A hydrodynamic theory of the gas of unbound defects additonally captures states of hierarchically organized active matter and the role of activity gradients for confining defects and harnessing active flows.
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