Abstract

Swimming bacteria, growing cell tissues, molecular motors and microtubule systems confined to a substrate are examples of active matter films that exhibit long-range nematic (orientational) order. Intrinsic activity in these systems builds mechanical stresses that tend to destroy local nematic order through topological defects, which act as sources of persistent active flows. The overall evolution and functionality of biological matter is greatly influenced by these orientational defects. Yet, their formation and dynamics are driven by a complex interplay between topological singularities in the nematic order and active flow instabilities, and this is not completely understood.

In this talk, I will present a generic field theory of topological defects as zeros of the order parameter. The method is presented within the hydrodynamic model of active nematics; however, it also applies to superfluids, crystals and other ordered states with vanishing order parameter at the defect core. The dynamics of these kinds of defects is entirely determined by tracking the evolution of order parameter zeros. I will discuss how defect velocity is determined by flow and nematic distortions, and how the self-propulsion of the +1/2 defect depends on both friction and viscous dissipation. I will present analytical results on the active flows induced by isolated defects in infinite domains and discuss finite-size effects. The defect densities and density currents are easily derived with this formalism of tracking zeros; thus, it can be used as a theoretical framework for developing a hydrodynamic theory of defects.