Where are the Hedgehogs in Nematics?
Mark Hindmarsh

TL;DR
This paper explains why point defects, or 'hedgehogs', are rarely observed in nematic liquid crystals after rapid phase transitions, due to topological constraints reducing their expected density.
Contribution
It provides a topological analysis showing the extremely low expected density of hedgehog defects in nematics, clarifying experimental observations.
Findings
Point defect density is approximately 10^{-8} per initial domain.
Topological constraints explain the scarcity of hedgehogs.
No point defects are observed until the defect network coarsens significantly.
Abstract
In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (``hedgehogs''), but no point defects are observed until the defect network has coarsened appreciably. In this letter the expected density of point defects is shown to be extremely low, approximately per initially correlated domain, as result of the topology (specifically, the homology) of the order parameter space.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
