Defect coarsening in three-dimensional active nematics

Coarsening of defect lines has a universal scaling in different physical systems; first described by Kibble for cosmic strings [1], predicted by Zurek in superfluid helium [2], and experimentally observed in nematic liquid crystals [3]. Here, we consider defect coarsening in three-dimensional active nematics [4,5], where following an initial quench the density of a defect line network decreases until a dynamic steady state is reached [6]. Activity-generated flows play an important part in the coarsening, which we demonstrate by constructing a phenomenological theory for defect density dynamics and validate it by a fully-resolved numerical simulation. First, we consider dynamics of a single loop, and then of a whole defect network following a quench or for a time-varying activity. Finally, our phenomenological equations are then compared to the time evolution of the defect line coarsening in other physical systems.

[1] T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A: Math. Gen. 9, 1387 (1976).

[2] W. H. Zurek, Cosmological experiments in superfluid helium?, Nature 317, 505 (1985).

[3] I. Chuang, R. Durrer, N. Turok and B. Yurke, Cosmology in the laboratory: Defect dynamics in liquid crystals, Science 251, 1336 (1991).

[4] G. Duclos et al, Topological structure and dynamics of three-dimensional active nematics, Science 367, 1120 (2020).

[5] Ž. Krajnik, Ž. Kos and M. Ravnik, Spectral energy analysis of bulk three-dimensional active nematic turbulence, Soft Matter 16, 9059 (2020).

[6] N. Kralj, M. Ravnik, Ž. Kos, to be submitted