Active nematic multipoles: a threefold application of nematic harmonics

Dr Alexander Houston (University of York)

Thursday 2nd February, 2023 14:00-15:00 Maths 311B / Zoom (ID: 886 5500 9455)

Abstract

Many disparate biological systems can be modelled as active nematics. These possess the orientational ordering of nematic liquid crystals but are composed of self-driven constituents which break time-reversal symmetry on the local scale and induce striking non-equilibrium effects such as persistent currents. Two fundamental questions in the study of active nematics are how to extract useful work from their non-equilibrium dynamics and how to extend their topological defect-based description to three dimensions, in which the defects form geometrically-complex loops. I introduce a general description of localised distortions in active nematics using the novel framework of ‘active nematic multipoles’. This allows the identification of the dipolar and quadrupolar distortions that generate self-propulsion and self-rotation respectively and serves as a guide for the design of arbitrary flow responses. Applying this approach to the distortions originating from a defect loop reveals the part played by the loop’s geometry in its dynamics, in particular rotational effects due to non-planarity. Lastly, I use conformal mappings to solve analytically for the director in the presence of a colloid. This reveals how to generate those multipoles identified as relevant in active systems, but also shows how colloids can be designed which generate arbitrarily intricate nematic multipoles. These results aid the understanding of the basic responses of active nematics and open up pathways to novel nematic metamaterials as well as the design of bio-inspired micromachines.

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