Topological Charges in Biaxial Nematic Liquid Crystal

Biaxial nematic liquid crystals use ellipsoid-like molecules that have principal axes of three different lengths. Such systems can exhibit the formation of topological point defects, known as hedgehog configurations. As a consequence of the hairy ball theorem, such hedgehogs additionally need vortex-like singularities resembling spins.
This Demonstration shows three types of topological charge configurations on a sphere: , , . The analogy of these three hedgehogs with three leptons (electron, muon, tau) has been pointed out [1].
Use the "evolving phase" slider to twist the longest axis and modify the topological charge (number of rotations) with the "latitude" and "longitude" sliders.
You can also modify the ellipsoid shape with the three "axes lengths" sliders. Use the "number of ellipsoids" slider to set the number of ellipsoids in the figure.

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References
[1] J. Duda, "Framework for Liquid Crystal Based Particle Models." arxiv.org/abs/2108.07896.
[2] Wikipedia. "Biaxial Nematic." (Oct 20, 2021) en.wikipedia.org/wiki/Biaxial_nematic.
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