Abstract
Active nematics contain topological defects which under sufficient activity move, create and annihilate in a chaotic quasi-steady state, called active turbulence. However, understanding active defects under confinement is an open challenge, especially in three-dimensions. Here, we demonstrate the topology of three-dimensional active nematic turbulence under the spherical confinement, using numerical modelling. In such spherical droplets, we show the three-dimensional structure of the topological defects, which due to closed confinement emerge in the form of closed loops or surface-to-surface spanning line segments. In the turbulent regime, the defects are shown to be strongly spatially and time varying, with ongoing transformations between positive winding, negative winding and twisted profiles, and with defect loops of zero and non-zero topological charge. The timeline of the active turbulence is characterised by four types of bulk topology-linked events --- breakup, annihilation, coalescence and cross-over of the defects --- which we discuss could be used for the analysis of the active turbulence in different three-dimensional geometries. The turbulent regime is separated by a first order structural transition from a low activity regime of a steady-state vortex structure and an offset single point defect. We also demonstrate coupling of surface and bulk topological defect dynamics by changing from strong perpendicular to inplane surface alignment. More generally, this work is aimed to provide insight into three-dimensional active turbulence, distinctly from the perspective of the topology of the emergent three-dimensional topological defects.
Highlights
The ability of the material to employ externally or internally stored energy to spontaneously organize, flow, move, or change shape—i.e., be active—is found in a variety of materials [1]
The defect phenomena of the active nematic are explored in an elementary confinement of a droplet with fixed spherical shape by using mesoscopic numerical modeling of active nematodynamics [2,11,28,46], which was shown to give good agreement with experiments on dense active nematic systems [2,13,47]
The approach relies on the dynamic coupling between the material flow and the mesoscopic order parameter tensor Qij that covers the orientational ordering of active nematic
Summary
The ability of the material to employ externally or internally stored energy to spontaneously organize, flow, move, or change shape—i.e., be active—is found in a variety of materials [1]. A major class of active materials includes active nematics [2], which exhibit strong collective behavior and self-organization, emerging as local orientational order of material building blocks in material systems such as bacteria [3] and microtubule-kinesin mixtures [4,5]. A recurring behavior in active nematics is the formation of topological defects, i.e., regions of broken orientational order, which are subject to topological-invariant conservation [10].
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