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1. 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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2. Geometry and external field positionally controlled nematic topological defects

   Kurioz, Pavlo; Kralj, Marko; Murray, Bryce S.; Rosenblatt, Charles; Kralj, Samo (January 2018, Beilstein journal of nanotechnology)

   Using a Landau–de Gennes approach, we study the impact of confinement topology, geometry and external fields on spatial positioning of nematic topological defects (TDs). In quasi two-dimensional systems we demonstrate that confinement enforced total topological charge m>>1 decays into elementary TDs bearing charge m=1/2. These assemble close to the bounding substrate to enable essentially bulk-like uniform nematic ordering in the central part of a system. This effect is reminiscent of the Faraday cavity phenomenon in electrostatics. We observe that in certain confinement geometries, varying the order parameter correlation length size could trigger global rotation of an assembly of TDs. Finally, we show that an external electric field could be used to drag the boojum finger tip towards a confinement cell interior. Assemblies of TDs could be exploited as traps for appropriate nanoparticles, opening several opportunities for development of functional nanodevices. 

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3. Structures, thermodynamics and dynamics of topological defects in Gay–Berne nematic liquid crystals

   https://doi.org/10.1039/D2SM01178F  

   Huang, Yulu; Wang, Weiqiang; Whitmer, Jonathan K.; Zhang, Rui (January 2023, Soft Matter)

   Topological defects are a ubiquitous phenomenon across different physical systems. A better understanding of defects can be helpful in elucidating the physical behaviors of many real materials systems. In nematic liquid crystals, defects exhibit unique optical signatures and can segregate impurities, showing their promise as molecular carriers and nano-reactors. Continuum theory and simulations have been successfully applied to link static and dynamical behaviors of topological defects to the material constants of the underlying nematic. However, further evidence and molecular details are still lacking. Here we perform molecular dynamics simulations of Gay–Berne particles, a model nematic, to examine the molecular structures and dynamics of +1/2 defects in a thin-film nematic. Specifically, we measure the bend-to-splay ratio K 3 / K 1 using two independent, indirect measurements, showing good agreement. Next, we study the annihilation event of a pair of ±1/2 defects, of which the trajectories are consistent with experiments and hydrodynamic simulations. We further examine the thermodynamics of defect annihilation in an NVE ensemble, leading us to correctly estimate the elastic modulus by using the energy conservation law. Finally, we explore effects of defect annihilation in regions of nonuniform temperature within these coarse-grained molecular models which cannot be analysed by existing continuum level simulations. We find that +1/2 defects tend to move toward hotter areas and their change of speed in a temperature gradient can be quantitatively understood through a term derived from the temperature dependence of the elastic modulus. As such, our work has provided molecular insights into structures and dynamics of topological defects, presented unique and accessible methods to measure elastic constants by inspecting defects, and proposed an alternative control parameter of defects using temperature gradient. 

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4. Co-revolving topological defects in a nematic liquid crystal

   Susser, Adam L.; Kralj, Samo; Rosenblatt, Charles (November 2021, Soft Matter)

   A patterned surface defect of strength m = +1 and its associated disclination lines can decompose into a pair of surface defects and disclination lines of strength m = +1/2. For a negative dielectric anisotropy liquid crystal subjected to an applied ac electric field E , these half-integer defects are observed to wobble azimuthally for E > than some threshold field and, for sufficiently large fields, to co-revolve antipodally around a central point approximately midway between the two defects. This behavior is elucidated experimentally as a function of applied field strength E and frequency ν , where the threshold field for full co-revolution scales as ν 1/2 . Concurrently, nematic electrohydrodynamic instabilities were investigated. A complete field vs. frequency “phase diagram” compellingly suggests that the induced fluctuations and eventual co-revolutions of the ordinarily static defects are coupled strongly to—and driven by—the presence of the hydrodynamic instability. The observed behaviour suggests a Lehmann-like mechanism that drives the co-revolution. 

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5. 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. N.; Langeslay, Blake; Aghvami, S. Ali; Fraden, Seth; Dogic, Zvonimir (February 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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