Active defects in flat and curved spaces

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Nambisan, Jyothishraj
Fernandez-Nieves, Alberto
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The interaction and dynamics of topological defects have inspired numerous studies across physics over centuries. They manifest as salient features in liquid crystalline materials, as regions where the underlying director field is undefined. Liquid crystals can be intrinsically driven out of equilibrium via an energy input at the level of the constituent particles, thus forming a unique class of non-equilibrium systems, known as active liquid crystals. In this thesis, we explore the rich phenomenology of topological defects observed in the microtubule-kinesin active nematic system, confined to surfaces of different topology and varying curvature. In 2D flat space, we observe short-range ferromagnetic alignment of +1/2 defects, mediated by -1/2 defects in between. This is primarily driven by passive elastic mechanisms, as confirmed via hydrodynamic simulations of active and passive liquid crystals. However, the system does not develop any long-range or quasi-long-range order over time. The qualitative features of defect-defect correlations are found to be independent of defect density. In curved space experiments, we observe a clear preference for the orientation of defects and persistent long-range order detected on highly curved regions of toroidal drops. This is a remarkable confirmation that curvature, and gradients of it, have a major role in intrinsically biasing the alignment of defects. This is in stark contrast to random, isotropic defect orientations found in locally flat regions. We then propose an idealized mechanism of defect alignment subject to curvature gradients, which is currently being inspected via agent-based simulations of an active multi-defect system. The observation of surface curvature as an aligning field is much more fundamental than recent works in similar systems, where patterned substrates and external fields have been used to align defects and create order. We also present the first experimental confirmation of hyperuniformity in an active system of topological defects. Originally conceived from the mathematical study of point patterns, hyperuniform systems are characterized by the suppression of large-scale fluctuations in the number (or density) of particles like a perfect crystal, while being isotropic like a liquid that has no long-range spatial or orientational order. Our discovery is unique, as it is the entire system that is hyperuniform, and not any specific snapshot or microstate of it. We quantify the degree of hyperuniformity using existing tests in literature and contrast the results with randomly distributed and manually dragged point patterns. The origins of hyperuniformity is found to be connected to the intrinsic creation-annihilation mechanisms of the defects and the constant average number of defects, even in the active turbulent state. The confirmation of hyperuniformity in our system also contrasts with giant number fluctuations, that are generally seen as a hallmark of active matter. Overall, our work explores the rich interplay of activity, topology and curvature in a liquid crystalline system and how topological defects interact to develop correlations and orientational order subject to the governing factors. More generally, our work provides an exciting test bed with associated techniques to study active matter in a controlled experimental setting.
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