Jonathan Selinger (Kent State U): Defects in Liquid Crystals: Topology, Geometry, and Mechanics

The concept of active matter describes systems of interacting objects that consume energy and transform it into movement. This concept was originally developed to describe biological systems, such as flocks of birds or schools of fish, in which the individual animals interact with each other and develop collective patterns of motion. Over the past 10-20 years, it has been applied to a wide range of systems, including swarms of bacteria, growth of epithelial tissue, and nonbiological systems such as self-propelled colloidal particles.

In many active systems, the interactions between particles lead to orientational order, analogous to a nematic liquid crystal. Unlike conventional nematic liquid crystals, active nematics do not relax to some equilibrium state that minimizes the free energy. Rather, they are continually in motion, with topological defects nucleating and annihilating.

In this talk, we present recent progress in understanding topological defects in liquid crystals, both conventional and active. We emphasize that topology is only one part of the theory of topological defects. Beyond topology, we need geometry to characterize the orientational properties of defects. We need energy and forces to understand the interactions between defects, and the conventional and active stimuli acting on them. Further, we need dynamics to understand the motion of defects under these forces, in the presence of dissipation. We discuss all these aspects of the theory of defects in both two and three dimensions.