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1. Annihilation of Highly-Charged Topological Defects

   https://doi.org/10.3390/cryst10080673  

   Klemenčič, Eva; Kurioz, Pavlo; Ambrožič, Milan; Rosenblatt, Charles; Kralj, Samo (August 2020, Crystals)

   We studied numerically external stimuli enforced annihilation of a pair of daughter nematic topological defect (TD) assemblies bearing a relatively strong topological charge |m|=3/2. A Landau- de Gennes phenomenological approach in terms of tensor nematic order parameter was used in an effectively two-dimensional Cartesian coordinate system, where spatial variations along the z-axis were neglected. A pair of {m=3/2,m=−3/2} was enforced by an appropriate surface anchoring field, mimicking an experimental sample realization using the atomic force microscope (AFM) scribing method. Furthermore, defects were confined within a rectangular boundary that imposes strong tangential anchoring. This setup enabled complex and counter-intuitive annihilation processes on varying relevant parameters. We present two qualitatively different annihilation paths, where we either gradually reduced the relative surface anchoring field importance or increased an external in-plane spatially homogeneous electric field E. The creation and depinning of additional defect pairs {12,−12} mediated the annihilation in such a geometry. Furthermore, we illustrate the absorption of TDs by sharp edges of the confining boundary, accompanied by m=±1/4↔∓1/4 winding reversal of edge singularities, and also E-driven zero-dimensional to one-dimensional defect core transformation. 

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2. Electric field driven reconfigurable multistable topological defect patterns

   https://doi.org/https://doi.org/10.1103/PhysRevResearch.2.013176  

   Harkai, S.; Murray, B.S.; Rosenblatt, C.; Kralj, S. (January 2020, Physical review research)

   Topological defects appear in symmetry breaking phase transitions and are ubiquitous throughout Nature. As an ideal testbed for their study, defect configurations in nematic liquid crystals (NLCs) could be exploited in a rich variety of technological applications. Here we report on robust theoretical and experimental investigations in which an external electric field is used to switch between predetermined stable chargeless disclination patterns in a nematic cell, where the cell is sufficiently thick that the disclinations start and terminate at the same surface. The different defect configurations are stabilized by a master substrate that enforces a lattice of surface defects exhibiting zero total topological charge value. Theoretically, we model disclination configurations using a Landau-de Gennes phenomenological model. Experimentally, we enable diverse defect patterns by implementing an in-house-developed atomic force measurement scribing method, where NLC configurations are monitored via polarized optical microscopy. We show numerically and experimentally that an “alphabet” of up to 18 unique line defect configurations can be stabilized in a 4 × 4 lattice of alternating s = ±1 surface defects, which can be “rewired” multistably using appropriate field manipulation. Our proof-of-concept mechanism may lead to a variety of applications, such as multistable optical displays and rewirable nanowires. Our studies also are of interest from a fundamental perspective. We demonstrate that a chargeless line could simultaneously exhibit defect-antidefect properties. Consequently, a pair of such antiparallel disclinations exhibits an attractive interaction. For a sufficiently closely spaced pair of substrate-pinned defects, this interaction could trigger rewiring, or annihilation if defects are depinned. 

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3. Self-organized dynamics and the transition to turbulence of confined active nematics

   https://doi.org/10.1073/pnas.1816733116  

   Opathalage, Achini; Norton, Michael M.; Juniper, Michael P.; Langeslay, Blake; Aghvami, S. Ali; Fraden, Seth; Dogic, Zvonimir (March 2019, Proceedings of the National Academy of Sciences)

   We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements in disks, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates toward the confinement core over multiple rotation cycles, while the associated nematic director field evolves from a distinct double spiral toward a nearly circularly symmetric configuration. The collapse of the defect orbits is punctuated by another boundary-localized nucleation event, that sets up long-term doubly periodic dynamics. Comparing experimental data to a theoretical model of an active nematic reveals that theory captures the fast procession of a pair of + 1 / 2 defects, but not the slow spiral transformation nor the periodic nucleation of defect pairs. Theory also fails to predict the emergence of circular flows in the weak confinement regime. The developed confinement methods are generalized to more complex geometries, providing a robust microfluidic platform for rationally engineering 2D autonomous flows. 

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4. Dynamics of Active Defects on the Anisotropic Surface of an Ellipsoidal Droplet

   https://doi.org/10.1103/PhysRevX.14.031049  

   Clairand, Martina; Mozaffari, Ali; Hardoüin, Jerôme; Zhang, Rui; Doré, Claire; Ignés-Mullol, Jordi; Sagués, Francesc; de_Pablo, Juan J; Lopez-Leon, Teresa (September 2024, Physical Review X)

   We investigate the steady state of an ellipsoidal active nematic shell using experiments and numerical simulations. We create the shells by coating microsized ellipsoidal droplets with a protein-based active cytoskeletal gel, thus obtaining ellipsoidal core-shell structures. This system provides the appropriate conditions of confinement and geometry to investigate the impact of nonuniform curvature on an orderly active nematic fluid that features the minimum number of defects required by topology. We identify new time-dependent states where topological defects periodically oscillate between translational and rotational regimes, resulting in the spontaneous emergence of chirality. Our simulations of active nematohydrodynamics demonstrate that, beyond topology and activity, the dynamics of the active material are profoundly influenced by the local curvature and viscous anisotropy of the underlying droplet, as well as by external hydrodynamic forces stemming from the self-sustained rotational motion of defects. These results illustrate how the incorporation of curvature gradients into active nematic shells orchestrates remarkable spatiotemporal patterns, offering new insights into biological processes and providing compelling prospects for designing bioinspired micromachines. Published by the American Physical Society2024 

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5. Decomposition of strongly charged topological defects

   Kralj, S.; Murray, B.; Rosenblatt, C. (April 2017, Physical review. E, Statistical, nonlinear and soft matter physics)

   We study decomposition of geometrically enforced nematic topological defects bearing relatively large defect strengths m in effectively two-dimensional planar systems. Theoretically, defect cores are analyzed within the mesoscopic Landau - De Gennes approach in terms of the tensor nematic order parameter. We demonstrate a robust tendency of defect decomposition into elementary units where two qualitatively different scenarios imposing total defect strengths to a nematic region are employed. Some theoretical predictions are verified experimentally, where arrays of defects bearing charges m = ±1, and even m = ±2, are enforced within a plane-parallel nematic cell using an AFM scribing method. 

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