Instabilities, defects, and defect ordering in an overdamped active nematic

Abstract

We consider a phenomenological continuum theory for an extensile, overdamped active nematic liquid crystal, applicable in the dense regime. Constructed from general principles, the theory is universal, with parameters independent of any particular microscopic realization. We show that it exhibits a bend instability similar to that seen in active suspensions, that leads to the proliferation of defects. We find three distinct nonequilibrium steady states: a defect-ordered nematic in which $+\frac{1}{2}$ disclinations develop polar ordering, an undulating nematic state with no defects, and a turbulent defective nematic. We characterize the phenomenology of these phases and identify the relationship of this theoretical description to experimental realizations and other theoretical models of active nematics.